Kelly M. Gilkey, Michael P. McRae, Elise A. Griffi n, Aditya S. Kalluri, and Jerry G. Myers

Glenn Research Center, Cleveland, Ohio

Bayesian Analysis for Risk Assessment of Selected 

Medical Events in Support of the Integrated 

Medical Model Effort

NASA/TP—2012-217120

July 2012
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Kelly M. Gilkey, Michael P. McRae, Elise A. Griffi n, Aditya S. Kalluri, and Jerry G. Myers

Glenn Research Center, Cleveland, Ohio

Bayesian Analysis for Risk Assessment of Selected 

Medical Events in Support of the Integrated 

Medical Model Effort

NASA/TP—2012-217120

July 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors would like to express their thanks to Marlei Walton, Ph.D., and Dr. Eric Kerstman, both of Wyle Integrated 

Science and Engineering at the NASA Johnson Space Center, for their thoughtful review and discussions of the 

data presented in this document. The authors would also like to acknowledge support from the 

Exploration Medical Capability Element of NASA’s Human Research Program.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

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5301 Shawnee Road

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Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by expert reviewer(s). 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TP—2012-217120 iii

Contents

Summary........................................................................................................................................................................ 1

1.0 Introduction......................................................................................................................................................... 1

1.1 Bayesian Analysis.................................................................................................................................... 1

1.2 Methods................................................................................................................................................... 2

2.0 Medical Events ................................................................................................................................................... 3

2.1 Angina Pectoris........................................................................................................................................ 3

2.1.1 Data and Methods...................................................................................................................... 3

2.1.2 Bayesian Updates To Improve Estimates of Angina Incidence Rates, and Analysis 

Results........................................................................................................................................ 4

2.1.3 Discussion.................................................................................................................................. 4

2.2 Appendicitis............................................................................................................................................. 5

2.2.1 Data and Methods...................................................................................................................... 5

2.2.2 Bayesian Updates To Improve Estimates of Appendicitis Incidence Rates, and 

Analysis Results......................................................................................................................... 5

2.2.3 Discussion.................................................................................................................................. 6

2.3 Atrial Fibrillation ..................................................................................................................................... 6

2.3.1 Data and Methods...................................................................................................................... 7

2.3.2 Bayesian Updates To Improve Estimates of Atrial Fibrillation Incidence Rates, and 

Analysis Results......................................................................................................................... 7

2.3.3 Discussion.................................................................................................................................. 8

2.4 Atrial Flutter ............................................................................................................................................ 8

2.4.1 Data and Methods...................................................................................................................... 8

2.4.2 Bayesian Updates To Improve Estimates of Atrial Flutter Incidence, and Analysis 

Results........................................................................................................................................ 8

2.4.3 Discussion.................................................................................................................................. 9

2.5 Dental Abscess......................................................................................................................................... 9

2.5.1 Data and Methods...................................................................................................................... 9

2.5.2 Bayesian Updates To Improve Estimates of Dental Abscess Incidence Rates, and 

Analysis Results.......................................................................................................................10

2.5.3 Discussion................................................................................................................................10

2.6 Dental Caries .........................................................................................................................................11

2.6.1 Data and Methods....................................................................................................................11

2.6.2 Bayesian Updates To Improve Estimates of Dental Caries Incidence Rates, and 

Analysis Results.......................................................................................................................11

2.6.3 Discussion................................................................................................................................12

2.7 Dental Periodontal Disease ....................................................................................................................12

2.7.1 Data and Methods....................................................................................................................12

2.7.2 Bayesian Updates To Improve Estimates of Periodontal Disease Incidence Rates, 

and Analysis Results...............................................................................................................13

2.7.3 Discussion................................................................................................................................13

2.8 Gallstone Disease...................................................................................................................................14

2.8.1 Data and Methods....................................................................................................................14

2.8.2 Bayesian Updates To Improve Estimates of Gallstone Incidence Rates, and Analysis 

Results......................................................................................................................................15

2.8.3 Discussion................................................................................................................................15

2.9 Herpes Zoster.........................................................................................................................................16

2.9.1 Data and Methods....................................................................................................................16

2.9.2 Bayesian Updates To Improve Estimates of Herpes Zoster Incidence Rates, and 

Analysis Results.......................................................................................................................16

2.9.3 Discussion................................................................................................................................17

2.10 Renal Stones ..........................................................................................................................................17

2.10.1 Data and Methods....................................................................................................................17
NASA/TP—2012-217120 iv

2.10.2 Bayesian Updates To Improve Estimates of Renal Stone Incidence Rates, and 

Analysis Results.......................................................................................................................18

2.10.3 Discussion................................................................................................................................18

2.11 Seizure ...................................................................................................................................................18

2.11.1 Data and Methods....................................................................................................................19

2.11.2 Bayesian Updates To Improve Estimates of Seizure Incidence Rates, and Analysis 

Results......................................................................................................................................19

2.11.3 Discussion................................................................................................................................20

2.12 Stroke .....................................................................................................................................................20

2.12.1 Data and Methods....................................................................................................................20

2.12.2 Bayesian Updates To Improve Estimates of Stroke Incidence Rates, and Analysis 

Results......................................................................................................................................21

2.12.3 Discussion................................................................................................................................21

3.0 Discussion.........................................................................................................................................................21

Appendix A .—Data from Lifetime Surveillance of Astronaut Health (LSAH) .........................................................23

Appendix B .—Calculating Error Factor From 95-Percent Confidence Intervals.......................................................25

B.1 Angina Pectoris......................................................................................................................................25

B.2 Atrial Fibrillation ...................................................................................................................................25

B.3 Atrial Flutter ..........................................................................................................................................25

B.4 Dental Events (Abscess, Caries, and Periodontal Disease)....................................................................26

B.5 Gallstone Disease...................................................................................................................................26

B.6 Herpes Zoster.........................................................................................................................................26

B.7 Seizure ...................................................................................................................................................27

Appendix C .—Bayesian Inference Using Gibbs Sampling (WinBUGS) Procedure and Code................................. 29

C.1 WinBUGS Procedure.............................................................................................................................29

C.2 WinBUGS Code ....................................................................................................................................29

C.2.1 Angina......................................................................................................................................29

C.2.2 Appendicitis.............................................................................................................................29

C.2.3 Atrial Fibrillation .....................................................................................................................30

C.2.4 Atrial Flutter ............................................................................................................................30

C.2.5 Dental Abscess.........................................................................................................................31

C.2.6 Dental Caries............................................................................................................................31

C.2.7 Dental Periodontal Disease ......................................................................................................31

C.2.8 Gallstone Disease.....................................................................................................................31

C.2.9 Herpes Zoster...........................................................................................................................32

C.2.10 Renal Stones ............................................................................................................................32

C.2.11 Seizure .....................................................................................................................................33

C.2.12 Stroke.......................................................................................................................................33

Appendix D .—Statistical Combination of Independent Distributions........................................................................35

References ...................................................................................................................................................................37
NASA/TP—2012-217120 1 

Bayesian Analysis for Risk Assessment of Selected Medical Events in 

Support of the Integrated Medical Model Effort

Kelly M. Gilkey, Michael P. McRae, Elise A. Griffin, Aditya S. Kalluri, and Jerry G. Myers

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

The Exploration Medical Capability project is creating a 

catalog of risk assessments using the Integrated Medical 

Model (IMM). The IMM is a software-based system intended 

to assist mission planners in preparing for spaceflight missions 

by helping them to make informed decisions about medical 

preparations and supplies for combating and treating various 

medical events. IMM uses Probabilistic Risk Assessment, 

which deals with low-probability, high-consequence events of 

complex physiological processes, although high-probability, 

low-consequence events are also of interest. The objective is 

to use statistical analyses to inform the IMM decision tool 

with estimated probabilities of medical events occurring during an exploration mission. Because data regarding astronaut 

health are limited, Bayesian statistical analysis is used. 

Bayesian inference combines prior knowledge, such as data 

from the general U.S. population, the U.S. Submarine Force, 

or the analog astronaut population located at the NASA 

Johnson Space Center, with observed data for the medical 

condition of interest. The posterior results reflect the best 

evidence for specific medical events occurring in flight. 

Bayes’ theorem provides a formal mechanism for combining 

available observed data with data from similar studies to 

support the quantification process. This is especially relevant 

when dealing with physiological data from the astronaut corps, 

where data are relatively sparse (zero in some cases). Bayes’ 

theorem depends on the consideration of all uncertainties 

(both known and unknown) that are fundamental to the 

assessment of risk. All Bayesian updates were performed 

using the open-source numerical update code called the 

Bayesian inference Using Gibbs Sampling (WinBUGS). 

WinBUGS is a computer software program that uses Markovchain Monte Carlo methods to perform Bayesian analysis of 

complex statistical models.

The IMM team performed Bayesian updates on the following medical events: angina, appendicitis, atrial fibrillation, 

atrial flutter, dental abscess, dental caries, dental periodontal 

disease, gallstone disease, herpes zoster, renal stones, seizure, 

and stroke. 

1.0 Introduction

The Integrated Medical Model (IMM) is a software-based 

system that will quantify health risks, identify medical needs, 

develop potential mitigation procedures, and assist in the 

preparation of spaceflight missions. Because data regarding 

astronaut health are limited, the IMM team used Bayesian 

statistical analysis. Bayesian inference combines prior knowledge, such as data from a similar study, with observed data for 

the event of interest. The outcome is a posterior result that 

reflects the best evidence for specific medical events occurring 

in flight. The IMM team performed Bayesian updates on the 

following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, gallstone disease, herpes zoster, renal stones, 

seizure, and stroke. 

1.1 Bayesian Analysis 

Because classical statistical techniques are not suitable for 

assessing the risk of low-probability, high-consequence 

events, an alternative risk-modeling framework, Probabilistic 

Risk Assessment (PRA), was developed that works within a 

scenario-based concept of risk that best informs decision

making (Ref. 1). PRA integrates a collection of models and 

quantifies integral risk metrics and their uncertainties (e.g., the 

probability of the loss of crew and the associated uncertainty). 

This modeling framework is supported by the application of 

Bayes’ theorem of probability. The theorem provides a formal 

mechanism for combining all available information, such as 

engineering and qualification test data, field experience, expert 

judgment, and data from similar systems to support the 

quantification process. This is especially relevant when 

dealing with astronaut medical event data, which are relatively 

sparse (zero in some cases). Bayes’ theorem depends on an 

honest treatment of the uncertainties that are fundamental to 

risk assessment and is based on a subjective interpretation of 

probability (Ref. 1). 

Within PRA aleatory models, most of the parameters are 

uncertain. This layer of imprecision is defined as epistemic 

uncertainty, which represents how accurate the developer’s 

state of knowledge is about the model, regardless of the model 

type. If an aleatory model is used (e.g., binomial) or a deterministic model is used (e.g., a fault tree), and if any parameter 

of these models is uncertain, then the model has epistemic 

uncertainty. Bayesian quantification methods are utilized to 

determine the nature of the epistemic uncertainty. In the 

Bayesian approach, probability quantifies the degree of belief 

and is used to describe the plausibility of an event. Frequentist 

inference generally relies on a mathematically consistent way 

to incorporate nonempirical data, which allows for the 

propagation of uncertainties throughout the logic model 
NASA/TP—2012-217120 2 

(Ref. 1). Often this approach is not available for astronaut 

medical event data. A solution is to incorporate Bayesian 

analysis, allowing for an alternative interpretation of probability. Information about the parameter, beyond what is in the 

data, is included in the estimate, and Monte Carlo sampling is 

used to propagate uncertainties through the logic analysis. 

Some of the typical uncertainties associated with PRA 

assumptions include disagreement or lack of accuracy when 

the probabilities of physical processes are estimated, limited 

knowledge of the parameters in phenomenological equations, 

unknown parameter values, inaccurate parameter values, and 

the inherent variability of stochastic processes. The Bayesian 

approach provides a formal mechanism for combining all 

available information, such as engineering and qualification 

test data, field experience, expert judgment, and data from 

similar systems. The types of information available for 

parameter values might include prior data—general engineering knowledge and historical information from similar 

events—and observed data for the event of interest in the 

system under study.

1.2 Methods

For the medical events investigated in this study, the 

astronaut population and the occurrences are very low. 

Consequently, Bayesian methods were deemed to be necessary to produce better estimates of the probable incidence 

rates. The Bayesian process allows researchers to make 

inferences to determine the probability that a hypothesis is 

true, conditional on all available evidence. In these Bayesian 

updates, preflight and in-flight astronaut data (obtained from 

the Lifetime Surveillance of Astronaut Health (LSAH), see 

Appendix A) became the experimental data, and prior data 

were found through a variety of sources, including the general 

U.S. population, the U.S. Submarine Force, and the analog 

astronaut population at the NASA Johnson Space Center. The 

analog population is a group of people with similar physiological characteristics such as age, height, weight, health 

conditions, and lifestyles—including activity levels and health 

habits—as members of the astronaut corps. Preflight and 

in-flight calculations varied slightly for different medical 

events, based on when specific medical events started being 

tracked by LSAH and what data were available at the time of 

the specific request (Ref. 2). The renal stone data request was 

the first request made to LSAH, and in-flight astronaut data 

for this medical event includes shuttle transport system missions (STS–1 to STS–114), International Space Station 

missions (Expeditions 1 to 8 and 10 to 13), and Mir missions 

(seven astronauts total). The subsequent requests (in chronological order of request) were stroke, appendicitis, dental 

problems (abscess, caries, and periodontal disease), herpes 

zoster, atrial fibrillation, and atrial flutter (requests made 

in June 2010), and angina, seizure, and gallstone disease 

(requests made in December 2010). 

All prior data used to define the incidence rate were 

assumed to be lognormal. The Poisson distribution was chosen 

to be the governing probability distribution (i.e., likelihood) 

for incidence values because it includes time (person-years) as 

an element in the probability equation. Time is an essential 

variable because it allows the probabilities to increase as the 

time of a space mission increases. Because Poisson distributions were used, an average rate for the incidences of these 

medical events had to be assumed. Consequently, the 

Bayesian update approach was used to calculate the distribution (mean and uncertainty) of the incidence rate associated 

with the Poisson distribution, and this approach is described 

for each of the medical events addressed in the report. 

When Bayesian analyses are performed, certain data must 

be present for the calculations. For the prior data, the mean 

incidence rate and the error factor (EF) were required to 

adequately parameterize the assumed lognormal distribution. 

The EF represents the variance in the model, which is defined 

as the square root of the ratio of the 95th and 5th percentiles. 

This definition for the EF can be leveraged to relate percentiles of the standard normal distribution to define the percentiles of the lognormal distribution as illustrated by Bedford 

and Cooke (Ref. 3). In this case,

ln(EF) = Φ(0.95) × σ = 1.645 × σ 

where σ is the standard deviation, Φ is the cumulative distribution function, 0.95 is the standard deviation at the 95th 

percentile of the distribution, and 1.645 is a constant representing the value of Φ at 0.95. For additional discussion on 

how the EF can be calculated from the confidence interval 

(CI) (see Appendix B).

The numerical update code called Bayesian inference 

Using Gibbs Sampling (WinBUGS) was used to perform all 

Bayesian updates. WinBUGS is a computer software program that performs Bayesian analysis of complex statistical 

models using Markov-chain Monte Carlo methods. It grew 

from a statistical research project at the Medical Research 

Council Biostatistics Unit, but it is now being developed 

jointly with the Imperial College School of Medicine at 

St. Mary’s, London. This open-source software is available 

on the Web.

In most cases, the Bayesian process followed a standardized 

approach that combined the prior data with observed astronaut 

incidence data. Depending on the medical event, two or more 

Bayesian updates had to be performed with WinBUGS to 

adequately capture all the available data relating to the 

condition being examined. Appendix C provides the procedures that were used to construct and implement multiple 

Bayesian analyses of each medical event. An outline of the 

general procedure for completing a Bayesian update follows 

(Ref. 1):

(1) Begin with a probabilistic model for the process of 

interest and encode the aleatory uncertainty. For these 

analyses, this involves identifying the conditions that 

most affect the event, the type of data (incidence rates), 

and how the conditions and data are represented.
NASA/TP—2012-217120 3 

(2) Specify a prior distribution for the parameter(s) in this 

update, quantifying epistemic uncertainty (quantifying 

the degree of belief about the possible parameter 

values). For the IMM Bayesian analysis, this involved 

reviewing data identified in the Clinical Findings Form 

and reviewing the literature to capture appropriate 

(multistep) prior data. 

(3) Obtain the observed data for the population of interest. 

Here data from the LSAH were heavily leveraged to 

support the reserved data requirements. In the case of 

no known incidents, only the total observation times in 

the appropriate segregated time span (in-flight and preflight) were required.

(4) Obtain the posterior (i.e., updated) distribution for the 

parameter(s) of interest. Here one or more WinBUGS 

scripts were created to perform the Markov-chain integration of the Bayesian analysis. 

(5) Check the validity of the output. Output validity has 

several meanings, including convergence of the Markov 

chain, indicating that an appropriate representation of 

the data has been numerically determined, as well as the 

adequacy of the integrated calculations to represent the 

true understanding of the incidence rate and the 

associated uncertainty.

For this analysis, 75 000 Monte Carlo samplings were used 

for all medical events because this was a relatively safe 

indication that the Markov chain had reached its steady state. 

As rule of thumb for convergence, the WinBUGS manual 

suggests running until the Monte Carlo error is <5 percent of 

the sample mean or until the Brooks-Gelman-Rubin statistic is 

<1.2. These conditions were achieved with 75 000 samples in 

all cases. Analysis validity was confirmed through review with 

IMM team subject matter experts with regard to both the 

process and the analysis findings. 

2.0 Medical Events

The following medical events were analyzed: angina, 

appendicitis, atrial fibrillation, atrial flutter, dental abscess, 

dental caries, dental periodontal disease, gallstone disease, 

herpes zoster, renal stones, seizure, and stroke.

2.1 Angina Pectoris

Angina pectoris is chest pain that occurs when part of the 

heart muscle does not get enough oxygenated blood. It is not 

a disease, but is typically a symptom of coronary heart 

disease—the most common type of heart disease in adults 

and occurs when plaque builds up on the inner walls of the

coronary arteries, which can lead to a heart attack (Ref. 4).

There are several different types of angina: stable, unstable, 

variant (Prinzmetal’s angina), and microvascular. The most 

common type of angina is stable angina, which has a regular 

pattern and occurs when the heart is working harder than usual 

(Ref. 4). Stable angina is not a heart attack, but it can suggest 

that a heart attack is more likely in the future. There are many

different risk factors for angina pectoris, including high

cholesterol, high blood pressure, smoking, diabetes or insulin 

resistance, being overweight or obese, inactivity, unhealthy 

diet, metabolic syndrome, familial history, and age—angina 

risk increases for males over the age of 45 and females over 

the age of 55 (Ref. 4). 

Because of the potential severe medical problems associated 

with angina pectoris, understanding the probability of angina 

pectoris occurring in flight was deemed to be necessary. 

Incidence rates from the general population (Ref. 5), the 

analog astronaut population, and the active astronaut corps 

(Ref. 6, personal communication) were used to find this 

probability. A Bayesian update was used to combine these 

data to yield a probability distribution for the average incidence of angina pectoris during exploration missions. 

2.1.1 Data and Methods

The data describing the average rate of angina incidence in 

the general population came from an article in the British 

Heart Journal (Ref. 5). The article follows 110 patients 

(70 males and 40 females) who were 70 years of age or less 

with no history of coronary heart disease when they presented 

for the first time with typical angina. All data were supplied as 

incidences per 1000 person-years and were reported for males 

and females between the ages of 41 and 50. Table 1 reports the 

average rates of angina for males and females, the corresponding 95-percent CIs, and the EFs (which were calculated as 

described in Appendix B, Section B.1). Total CI data (for 

males and females) between the ages of 41 and 50 were not 

presented in this article and were, therefore, not calculated in 

this analysis.

Incidences of angina in the analog astronaut population per 

person-years were obtained from LSAH (see Table 2 and 

Ref. 6, personal communication) because of the high number 

of risk factors for angina pectoris. 

Incidences of angina in the astronaut corps and the number 

of person-years for preflight and in-flight astronauts were 

obtained from LSAH (see Table 3 and Ref. 6, personal 

communication). There were no cases of angina during any 

point in the study.

TABLE 1.—INCIDENCE OF ANGINA PECTORIS IN ADULTS 

IN THE UNITED KINGDOM 

Statistic Males Females

Angina incidence in adults 41 to 

50 years of age per 1000 person-years 0.63 0.47

95-percent confidence interval (CI) for 

angina incidence in adults per 1000 

person-years 0.24 to 1.02 0.12 to 0.82

Angina incidence in adults 41 to 

50 years of age per person-year

Error factor (EF) for angina incidence 

in adults 41 to 50 years of age

6.3×10-4

1.77

4.7×10-4

2.08
NASA/TP—2012-217120 4 

TABLE 2.—INCIDENCE OF ANGINA PECTORIS IN 

THE ANALOG ASTRONAUT POPULATION

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females

Total person-years 2213.0 2808.6

Angina cases 6 0

Angina incidence rate, events per person-year 2.71×10–4 0

TABLE 3.—INCIDENCE OF ANGINA PECTORIS IN 

PREFLIGHT AND IN-FLIGHT MISSION-READY, 

ACTIVE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females

Preflight astronauts

Total person-years 1970.4 264.8

Angina cases 0 0

Angina incidence rate, events per person-year 0 0

In-flight astronauts

Total person-years 32.0 6.5

Angina cases 0 0

Angina incidence rate, events per person-year 0 0

2.1.2 Bayesian Updates To Improve Estimates of 

Angina Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the angina incidence rate in the astronaut corps 

and to find an approximation suitable for the IMM effort. 

Three steps and Bayesian updates were performed. The first 

step used the general population data (Ref. 5) as priors to 

update the analog astronaut population data (Ref. 6, personal 

communication). This step was performed two times, once 

each for males and females. The posterior results from this 

step describe the angina incidence rates for the analog astronaut population. In the second step, the data from these 

posterior results, namely the mean and the 5th and 95th 

percentiles, were used as the priors to update the preflight 

astronaut data for males and females. In the third step, the data 

from the preflight posterior results were used as the priors to 

update the in-flight astronaut data for males and females. 

Ultimately, four probability distributions were found to 

describe the incidence rate for angina in preflight and in-flight

male and female astronauts. Appendix C provides the code 

used in WinBUGS, and an outline of the input data for each 

step follows.

Step 1: The general United Kingdom population incidence 

rates per person-year for females and males, and the associated EFs from Table 1, were used for the priors in 

WinBUGS. The updated analog astronaut population data 

from LSAH included the number of person-years and the 

number of angina cases for males and females (Table 2). The 

posterior results from this Bayesian update were Poisson 

probability distributions for males and females in the analog 

astronaut population. Table 4 shows the means, 5th and 95th 

percentiles, and standard deviations.

TABLE 4.—RESULTS OF BAYESIAN ANALYSIS 

FOR ANGINA PECTORIS IN THE ANALOG 

ASTRONAUT POPULATION

Angina incidence rate, λanalog, events per person-year

Statistic Males Females

Mean 4.15×10–4 3.72×10–4

Standard deviation 9.99×10–5 1.55×10–4

5 percent 2.69×10–4 1.77×10–4

95 percent 5.93×10–4 6.63×10–4

TABLE 5.—RESULTS OF BAYESIAN ANALYSIS FOR 

ANGINA PECTORIS IN PREFLIGHT MISSION-READY, 

ACTIVE MALE AND FEMALE ASTRONAUTS

Angina incidence rate, λastronaut, events per person-year

Statistic Males Females

Mean 3.96×10–4 3.65×10–4

Standard deviation 9.38×10–5 1.53×10–4

5 percent 2.62×10–4 1.74×10–4

95 percent 5.56×10–4 6.53×10–4

TABLE 6.—RESULTS OF BAYESIAN ANALYSIS 

FOR ANGINA PECTORIS IN IN-FLIGHT 

MALE AND FEMALE ASTRONAUTS

Angina incidence rate, λastronaut, events per person-year

Statistic Males Females

Mean 3.95×10–4 3.64×10–4

Standard deviation 9.21×10–5 1.53×10–4

5 percent 2.64×10–4 1.74×10–4

95 percent 5.61×10–4 6.53×10–4

Step 2: The posterior results from Step 1—the means and 

the 5th and 95th percentiles from Table 4—along with the 

LSAH preflight data in Table 3 were used in WinBUGS to 

update the preflight astronaut data. The posterior results from 

this Bayesian update were Poisson probability distributions for 

angina incidence in preflight male and female astronauts. 

Table 5 shows the means, 5th and 95th percentiles, and 

standard deviations.

Step 3: The posterior results from Step 2—the means and 

the 5th and 95th percentiles from Table 5, along with the 

LSAH in-flight data in Table 3 were used in WinBUGS to 

update the in-flight astronaut data. The posterior results from 

this Bayesian update were Poisson probability distributions for 

angina incidence in in-flight male and female astronauts. 

Table 6 shows the means, 5th and 95th percentiles, and 

standard deviations.

2.1.3 Discussion

This analysis should be considered rather limited because it 

assumes an average incidence rate of angina pectoris, with no 

specific data for important factors such as overall health, diet, 

activity levels, metabolic syndrome, and familial history. The 

general population data from Gandhi et al. (Ref. 5) include a 

large proportion of smokers and ex-smokers (34 and
NASA/TP—2012-217120 5 

43 percent, respectively) and a large proportion of individuals 

classified as overweight and obese (50 and 27 percent, 

respectively). An individual was classified as overweight if he 

or she had a body mass index of 25 to 29 kg/m2

, and an 

individual was classified as obese if he or she had a body mass 

index greater than or equal to 30 kg/m2

. In addition, there may 

be minor differences between the diets and lifestyles of the 

United Kingdom population used in Gandhi et al. and the U.S. 

astronaut population. However, both populations are from 

well-developed, industrial countries in similar temperate 

regions. Accordingly, the present analysis assumes that their 

diets are similar to a high degree. The use of the analog 

astronaut population data may help to counteract some of the 

inaccuracies from these differences. The analog astronaut 

population may more closely reflect the actual risk factors that 

might influence an astronaut’s propensity to develop angina 

pectoris. In spite of the limitations, the assumptions, and the 

data available, this analysis is probably a reasonable approximation of the incidence of angina pectoris during exploration 

missions. The current results can serve as a baseline for future 

studies that include more data and risk parameters. 

2.2 Appendicitis

Because appendicitis may greatly affect the performance, 

health, and morale of crewmembers, evaluating the probability 

that an astronaut may encounter appendicitis during an 

exploration mission was deemed to be necessary. Appendicitis, the inflammation of the appendix, could be life-threatening 

for a crewmember lacking immediate medical care. The 

probability of an astronaut encountering appendicitis was 

estimated using data from the general U.S. population (Refs. 7 

and 8) as well as from astronaut data from LSAH (Ref. 9, 

personal communication). A Bayesian update was used to 

combine the incidence rates from these sources to estimate the

probability distribution for the rate of appendicitis during 

exploration missions. 

2.2.1 Data and Methods

General population data regarding the incidence rate of 

appendicitis was extracted using a longitudinal, nationally 

representative, population-based study that was conducted on 

the incidence of appendicitis in the general U.S. population by 

the National Ambulatory Medical Care Survey and National 

Hospital Ambulatory Medical Care Survey (3-year average, 

2003 to 2005) (Ref. 8). Because this source does not differentiate gender and ethnicity data by age, incidence rates differentiating between males and females and between whites and 

blacks were not been included in this calculation. Only the 

data for the hospital discharges (all-listed diagnoses) were

included, because these data are presumably more reliable 

than data from ambulatory care visits. The incidence is 

98/100 000 in females and 118/100 000 in males, for a ratio 

TABLE 7.—INCIDENCE OF APPENDICITIS IN U.S. 

ADULTS 45 TO 64 YEARS OF AGE

Appendicitis incidence in adults 45 to 64 years 

of age per 100 000 persons per yeara

 ................................... 93

Appendicitis incidence rate in adults 45 to

64 years of age, events per person-year.................... 9.30×10–4

a

All-listed diagnoses for hospital discharges.

TABLE 8.—INCIDENCE OF APPENDICITIS IN PREFLIGHT 

AND IN-FLIGHT MISSION-READY, ACTIVE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females Total

Preflight astronauts

Total person-years 1400 244 1644

Appendicitis cases 2 0 2

Appendicitis incidence rate, 

events per person-year 1.43×10–3 0 1.22×10–3

In-flight astronauts

Total person-years 31.9 6.4 38.3

Appendicitis cases 0 0 0

Appendicitis incidence rate, 

events per person-year 0 0 0

of 1:1.20. Table 7 shows the incidence rate of appendicitis in 

U.S. adults 45 to 64 years of age (Ref. 8). The rate for adults 

45 to 64 years of age was used because it more accurately

reflects the age of active astronauts and because the incidence rate is lower than that for people 15 to 24 years of age

(which have the highest incidence rate, Ref. 8). Data from 

Addiss et al. (Ref. 7), which included data for males and 

females that was differentiated by age groups, was used to 

estimate the EF as 1.2. 

Incidences of appendicitis in the analog astronaut population were obtained from the LSAH (Ref. 9, personal communication) and are summarized in Table 8. There were no 

occurrences of appendicitis in in-flight astronauts, and there 

were no occurrences in female astronauts. The highest 

incidence rate was in preflight male astronauts. Because there 

were no age-differentiated data for males and females available for the general population, the data for male and female 

astronauts were combined.

2.2.2 Bayesian Updates To Improve Estimates of 

Appendicitis Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the incidence rate of appendicitis in the 

astronaut corps and provide a first-order approximation 

suitable for the IMM effort. General population data (Ref. 8) 

were used to determine an informed lognormal conjugate for 

the incidence rate of appendicitis in the general U.S. population (λgeneral). This was used as a prior to update LSAH 

preflight data in Step 1 of the Bayesian implementation, 
NASA/TP—2012-217120 6 

yielding an updated appendicitis incidence rate. In Step 2, the 

posterior result of Step 1 was used as the prior and was

updated with LSAH in-flight data in WinBUGS. The result 

was an estimation of the appendicitis incidence rate in astronauts during an exploration mission. Appendix C provides the 

code used in WinBUGS as well as the sampling procedure. 

Step 1: First, WinBUGS was informed with the mean incidence rate of the general population from Table 7 and the EF

(1.2).

Step 2: The input parameters of Step 1 were used to perform 

a Bayesian update with 75 000 Monte Carlo samples on the 

number of events and time (person-years) from the LSAH 

preflight data (Table 8). 

Step 3: The posterior result of Step 2—the mean incidence 

rate—was dissected and used as the prior for the second 

update. The 5th and 95th percentiles from the lognormal 

Poisson distribution in Step 2 were used to calculate the EF. 

Table 9 shows the results for preflight astronauts.

Step 4: The input parameters of Step 1 were used to perform 

a second Bayesian update with 75 000 Monte Carlo samples 

on the number of in-flight events and person-years from the 

LSAH in-flight data (Table 8). Appendix C provides details.

This process returned an estimate of the rate of appendicitis 

in in-flight astronauts with respect to the general population 

(Table 10). This rate can be used as the input rate to a Poisson 

distribution to estimate the probability of appendicitis occurring in flight. 

TABLE 9.—RESULTS OF BAYESIAN ANALYSIS FOR 

APPENDICITIS IN TOTAL PREFLIGHT MISSIONREADY, ACTIVE ASTRONAUTS

Appendicitis incidence rate, λastronaut, events per person-year

Mean 9.35×10–4

Standard deviation 1.04×10–4

5 percent 7.75×10–4

Median 9.29×10–4

95 percent 1.11×10–3

TABLE 10.—RESULTS OF BAYESIAN ANALYSIS 

FOR APPENDICITIS IN TOTAL IN-FLIGHT 

ASTRONAUTS

Appendicitis incidence rate, λastronaut, events per person-year

Mean 9.34×10–4

Standard deviation 1.03×10–4

5 percent 7.76×10–4

Median 9.28×10–4

95 percent 1.11×10–3

2.2.3 Discussion

This approximation is limited in that it assumes an average 

incidence rate of appendicitis irrespective of environmental 

conditions and the cause of appendicitis. There also were 

limitations in the data for the general population in that the 

incidence rate data for males and females and for blacks and 

whites were not age-differentiated. Everhart reports that the 

rate in whites was twice that of blacks and that the rate for 

males was 20 percent greater than for females (Ref. 8, these 

statements, however, do not take into account the ages being 

reported). According to another source for general population 

data, the highest incidence rates of appendicitis are found in 

15 to 24 year olds, with 74 percent of all appendicitis cases 

found in 5 to 34 year olds (Ref. 10). In the mission-ready 

astronaut corps, the mean age for females is 43.8 years and the 

mean age for males is 45.3 years. Another assumption was 

made to use only hospital discharge data, not ambulatory care 

data, because patients being discharged from the hospital 

presumably carry a more definitive diagnosis of appendicitis 

because of the availability of better imaging technology and 

the increased likelihood that exploratory surgery was 

conducted (Ref. 8). However, these Bayesian updates yield a 

reasonable representation of the appendicitis incidence rate 

given the occurrence data available and the assumptions made 

during construction of the estimate. 

Future estimates may be more accurate if data for males, 

females, and different ethnicities are available for various age 

ranges. More accurate estimates also could be made with 

further analysis of appendicitis occurrence in post-flight 

astronauts as well as greater understanding of the physiological pathways that lead to the obstruction, inflammation, and 

infection of the appendix. The current data will serve as the 

baseline for future estimates that utilize additional physiological parameters. 

2.3 Atrial Fibrillation

One of the most common forms of heart arrhythmias is 

atrial fibrillation (AF). It is characterized by rapid, haphazard 

atrial contractions. Although AF is known to increase the 

likelihood of stroke and can be an underlying factor for death, 

it generally is not immediately threatening. AF is accompanied 

by debilitating symptoms, such as dizziness, shortness of 

breath, heart palpitations, and fatigue. Although these symptoms may not pose great difficulties for the general population, an AF episode could be detrimental to an astronaut crew 

on a space mission. Because of this high risk, determining the 

probability of AF was deemed to be necessary to help keep 

astronauts safe. Incidence rates from the astronaut corps

(Ref. 11, personal communication) and the general population

(Ref. 12) were used to determine this probability. A Bayesian 

update was used to combine these data to yield a probability 

distribution for AF incidence.
NASA/TP—2012-217120 7 

2.3.1 Data and Methods

The average rate of AF incidence in the general population 

used in this probability estimate came from an article in the 

journal Circulation (Ref. 12). These data were gathered from a 

cohort of patients at the Mayo Clinic in Olmsted County, 

Minnesota, from 1980 to 2000. An AF event was included if it 

was the first event for a particular patient and was verified by 

an electrocardiogram. These data were separated by age and 

year. In an attempt to closely approximate the current astronaut population, the most recent data from 1995 to 2000 for 

males and females under 55 were used. Data included the 

95-percent CI for males, females, and the total from 1995 to 

2000. However, these data were not specific to age, but were for 

all ages from 1995 to 2000. It was assumed that the 95-percent 

CI for all ages could be used as the 95-percent CI for those 

under 55. Appendix B, Section B.2, provides the steps for 

calculating the EF. All data were supplied as incidences per 

1000 person-years. Table 11 gives the average AF incidence per 

person-year for men, women, and total, along with the EFs.

Incidences of AF in the astronaut corps and the number of 

person-years for preflight and in-flight astronauts were 

obtained from LSAH (see Table 12). There were no cases of 

AF in females during any point in the study.

2.3.2 Bayesian Updates To Improve Estimates of Atrial 

Fibrillation Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the AF incidence rate in the astronaut corps to 

find an approximation suitable for the IMM effort. Two steps 

and Bayesian updates were performed. The first step used 

the general population data (Ref. 12) as priors to update the 

LSAH preflight data (Ref. 11, personal communication). 

This step was performed three times, once each for males, 

females, and the total. The posterior results from this step 

describe the AF incidence rate for preflight astronauts. In the 

second step, the data from these posterior results, namely the 

means and the 5th and 95th percentiles, were then used as 

the priors to update the in-flight astronaut data for males, 

females, and the total. Ultimately, six probability distributions were found describing the AF incidence rate for 

preflight and in-flight male, female, and total astronauts. 

Appendix C shows the code used in WinBUGS, and an 

outline of the input data for each step follows. 

Step 1: For females, males, and the total, the AF incidence 

per person-year in the general U.S. population (Table 11) and 

the EF were used for the priors in WinBUGS to update the 

number of AF cases for male and female astronauts from 

LSAH data (Table 12). Table 13 gives the posterior data from 

this step.

Step 2: The posterior results from Step 1—the means and 

the 5th and the 95th percentiles (Table 13) were used as the 

priors in WinBUGS to update the in-flight astronaut data 

from LSAH (Table 12). Table 14 shows the posterior results 

of this Bayesian update: a Poisson probability distribution 

for the means, 5th and 95th percentiles, and standard deviations of the AF incidence rate of in-flight astronauts. 

TABLE 11.—INCIDENCE OF ATRIAL FIBRILLATION (AF) IN U.S. ADULTS

Statistic Males Females Total

AF incidence in adults under 55 years of age 

per 1000 person-years 0.64 0.21 0.425

95-percent confidence interval (CI) for AF 

incidence in adults per 1000 person-years 0.32 to 0.96 0.01 to 0.41 0.24 to 0.60

AF incidence rate in adults under 55 years of 

age, events per person-year 6.40×10–4 2.10×10–4 4.25×10–4

Error factor (EF) for AF incidence in adults 

under 55 years of age 1.56 2.97 1.45

TABLE 12.—INCIDENCE OF ATRIAL FIBRILLATION (AF) IN PREFLIGHT 

AND IN-FLIGHT MISSION-READY, ACTIVE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females Total

Preflight astronauts

Total person-years 6502.7 336.8 6839.5

AF cases 4 0 4

AF incidence rate, events per person-year 6.15×10–4 0 5.85×10–4

In-flight astronauts

Total person-years 31.8 6.5 38.3

AF cases 0 0 0

AF incidence rate, events per person-year 0 0 0
NASA/TP—2012-217120 8 

TABLE 13.—RESULTS OF BAYESIAN ANALYSIS 

FOR ATRIAL FIBRILLATION (AF) IN PREFLIGHT 

MISSION-READY, ACTIVE MALE, FEMALE, 

AND TOTAL ASTRONAUTS

AF incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 6.29×10–4 2.02×10–4 4.43×10–4

Standard deviation 1.51×10–4 1.46×10–4 9.39×10–5

5 percent 4.12×10–4 5.60×10–5 3.06×10–4

95 percent 9.02×10–4 4.76×10–4 6.11×10–4

TABLE 14.—RESULTS OF BAYESIAN ANALYSIS FOR 

ATRIAL FIBRILLATION (AF) IN IN-FLIGHT MALE, 

FEMALE, AND TOTAL ASTRONAUTS

AF incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 6.28×10–4 2.02×10–4 4.42×10–4

Standard deviation 1.52×10–4 9.99×10–6 9.36×10–5

5 percent 4.12×10–4 1.86×10–4 3.06×10–4

95 percent 9.05×10–4 2.19×10–4 6.09×10–4

2.3.3 Discussion

These results are limited because they assume an average 

AF incidence rate and do not include specific data for ethnicity, previous cardiac diseases, or health. Also, assumptions 

were made when non-age-specific 95-percent CI were used for 

age-specific data. Understanding these limitations is necessary 

in applying these results. In spite of this limitation, the 

assumptions, and the data available, Table 13 and Table 14

present a reasonable approximation of AF incidence. These 

results can serve as a baseline for future studies that include

further investigations into the causes of AF and more data and 

risk parameters for AF.

2.4 Atrial Flutter

Although atrial flutter (AFL) is less prevalent than AF, both 

are characterized by rapid atrial contractions. In contrast to 

AF, the quick AFL contractions are conducted in a regular 

pattern relative to ventricular contractions. Like AF, AFL is 

not immediately life threatening, though it can raise the 

chance of stroke. In addition, both atrial arrhythmias have 

similar debilitating symptoms, and both conditions could

threaten the success of an astronaut if they were to occur in 

space. So that the proper amount of medications can be on 

hand for future in-flight AFL cases, the probability of AFL

must be determined. A Bayesian update was used to combine 

experimental data from AFL incidence rates from the astronaut corps (Ref. 11, personal communication) and prior AFL 

incidence data from the general population (Ref. 13) to find 

this probability. 

2.4.1 Data and Methods

The general population data describing the rate of AFL used 

in this probabilistic calculation came from Granada et al. 

(Ref. 13). This study examined the rate of AFL from the 

Marshfield Epidemiologic Study Area in Wisconsin from 

1991 to 1995. AFL cases were confirmed with electrocardiograms, using the International Classification of Disease code 

ICD 427.32 to define AFL. To approximate the age of the 

astronaut corps, the data recorded for men, women, and the 

total under the age of 50 were used. Included with these data 

were the 95-percent CI for men, women, and the total. These 

95-percent CI were not specific to age, however, so they were 

too wide to be applied directly to the data for adults less than 

50 years of age. Ratios between the number of AFL cases and 

95-percent CI width of all ages versus the incidence rates and 

95-percent CI width for those under 50 were used to find a 

new 95-percent CI width for adults under 50 years of age. 

Appendix B, Section B.3, gives the steps for this calculation as 

well as for the calculation of the 95-percent CI into the EF.

These data gave the number of incidences and the number of 

person-years for males, females, and the total. Table 15 gives 

the calculated incidence rates and the corresponding EFs.

AFL incidence data for the astronaut corps were supplied 

by LSAH (Ref. 11, personal communication). The number of 

AFL cases and person-years were included for in-flight and 

preflight male, female, and total astronauts, as shown in 

Table 16.

2.4.2 Bayesian Updates To Improve Estimates of Atrial 

Flutter Incidence, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the AFL incidence rate in the astronaut corps

and provide an approximation suitable for the IMM effort. 

This process took two steps. The first step was to update in 

WinBUGS the AFL incidence rate data for preflight astronauts

performed three times, once each for males, females, and the 

total. The posterior results from the first step, including the 

means and the 5th and 95th percentiles, were used as the 

priors for another Bayesian update to the in-flight astronaut 

data. This was performed three times (once each for males, 

females, and the total) and yielded the Poisson probability 

distribution curves for the likelihood of an AFL occurrence in 

space. After these two steps, six Bayesian updates were 

performed with WinBUGS: for preflight and in-flight male, 

female, and total astronauts. Appendix C provides the 

WinBUGS code that was used, and an outline of each step, 

including the data used, follows.

Step 1: The general population incidence rates and EFs for 

males, females, and the total (Table 15) were used as the 

priors for a Bayesian update with WinBUGS on the number of 

cases and person-years for preflight astronauts from LSAH 

(Table 16). Table 17 shows the posterior results from 

this step.
NASA/TP—2012-217120 9 

TABLE 15.—INCIDENCE OF ATRIAL FLUTTER (AFL) 

IN U.S. ADULTS FROM 1991 TO 1995

Statistic Males Females Total

AFL cases in adults under 

50 years of age 6 2 8

Number of person-years in 

the study 84 915 82 250 167 165

95-percent confidence interval 

(CI) for AFL in adults per 

100 000 person-years ±0.24 ±0.14 ±0.13

AFL incidence rate for adults 

under 50 years of age per 

person-year 7.07×10–5 2.43×10–5 4.79×10–5

Recalculated 95-percent CI for 

AFL incidence in adults per 

100 000 person-years ±0.013 ±0.004 ±0.006

Error factor (EF) for AFL 

incidence in adults under 

55 years of age 1.17 1.18 1.11

TABLE 16.—INCIDENCE OF ATRIAL FLUTTER (AFL) IN 

PREFLIGHT AND IN-FLIGHT MISSION-READY, 

ACTIVE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females Total

Preflight astronauts

Total person-years 6502.7 336.8 6839.4

AFL cases 0 0 0

AFL incidence rate, events per 

person-year 0 0 0

In-flight astronauts

Total person-years 31.8 6.5 38.3

AFL cases 0 0 0

AFL incidence rate , events per 

person-year 0 0 0

TABLE 17.—RESULTS OF BAYESIAN ANALYSIS FOR 

ATRIAL FLUTTER (AFL) IN PREFLIGHT MISSION-READY, 

ACTIVE MALE, FEMALE, AND TOTAL ASTRONAUTS

AFL incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 7.05×10–5 2.43×10–5 4.77×10–5

Standard deviation 6.71×10–6 2.45×10–6 3.04×10–6

5 percent 6.00×10–5 2.05×10–5 4.29×10–5

95 percent 8.21×10–5 2.85×10–5 5.29×10–5

TABLE 18.—RESULTS OF BAYESIAN ANALYSIS FOR 

ATRIAL FLUTTER (AFL) IN IN-FLIGHT MALE, 

FEMALE, AND TOTAL ASTRONAUTS

AFL incidence rate, λastronaut ̧ events per person-year

Statistic Males Females Total

Mean 7.05×10–5 2.43×10–5 4.77×10–5

Standard deviation 6.74×10–6 2.42×10–6 3.04×10–6

5 percent 6.00×10–5 2.05×10–5 4.29×10–5

95 percent 8.21×10–5 2.84×10–5 5.29×10–5

Step 2: This step used WinBUGS to combine the posterior 

results from Step 1—the means and the 5th and 95th percentiles (Table 17)—with the in-flight astronaut data from Table 16. 

The result of this Bayesian update was the Poisson probability 

distribution for the AFL incidence rate in in-flight male, 

female, and total astronauts. Table 18 shows the means, the 

5th and 95th percentiles, and the standard deviations.

2.4.3 Discussion

Like the AF analysis, this analysis is also limited because it 

assumes an average incidence rate of AFL. There are no 

specific data for important risk factors such as ethnicity or 

previous cardiac diseases and health. Also assumptions were 

made when non-age-specific 95-percent CI were used for agespecific data. These limitations should be kept in mind when 

this analysis is used. Despite the limitations, however, this 

analysis is a reasonable approximation of AFL incidence and 

can serve as a baseline until further investigations into the risk 

parameters and causes of AFL are made. 

2.5 Dental Abscess

Because a dental abscess may greatly affect crewmember 

performance, health, and morale, evaluating the probability 

that an astronaut may encounter a dental abscess during an 

exploration mission was deemed to be necessary. An abscess 

results from the infection of pulp material in the tooth caused 

by complications such as decayed, cracked, or broken teeth

(Ref. 14). U.S. Submarine Force (Ref. 15) and astronaut data 

from LSAH (Ref. 16, personal communication) were used to 

estimate the probability of an astronaut encountering dental 

abscess. The submarine crew data analysis defined periapical 

abscesses as 2010 ICD–9–CM code 522 (pulp and periapical), 

and the astronaut data from LSAH defined dental abscess as 

“abscess diagnosis,” with no reference to ICD–9 coding. A 

Bayesian update was used to combine information from these 

sources to estimate the average incidence rate of abscess. 

2.5.1 Data and Methods

Submarine force data were used because of the physiological similarity of the U.S. Submarine Force to astronauts.

Deutsch (Ref. 15) conducted studies from 1997 to 2000 on the 

incidence of various dental emergencies in U.S. Submarine 

Force personnel. The medical history of submarine missions 

was useful for this statistical analysis because of their similarities to exploration-class missions. For example, both occur in 

confined, remotely located environments where professional 

medical care is not immediately available. Also, a medical 

event of low probability and high consequence could cause a 

mission to cease (Refs. 17 and 18). Although there are 

similarities between a submarine mission and a space exploration mission, it is important to note that smoking was 
NASA/TP—2012-217120 10

TABLE 19.—INCIDENCE OF DENTAL ABSCESS IN 

240 PATROLS OF THE U.S. SUBMARINE FORCE

Total person-years................................................................ 5946.9

Total visits due to abscess........................................................... 21

Abscess incidence rate, events per person-year................3.53×10–3

95-percent confidence interval (CI) ............................. 0.69 to 3.80

Error factor (EF) ...................................................................... 1.48

TABLE 20.—INCIDENCE OF DENTAL ABSCESS IN 

PREFLIGHT AND IN-FLIGHT MISSION-READY, 

ACTIVE MALE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Preflight astronauts

Total person-years...................................................................475.2

Number of crewmembers.............................................................77

Abscess cases ..............................................................................19

Abscess incidence rate, events per person-year .................4.0×10–2

In-flight astronauts

Total person-years.....................................................................31.9

Abscess cases................................................................................ 0

Abscess incidence rate, events per person-year ............................ 0

TABLE 21.—RESULTS OF BAYESIAN ANALYSIS 

FOR DENTAL ABSCESS IN PREFLIGHT MISSIONREADY, ACTIVE MALE ASTRONAUTS

Abscess incidence rate, λastronaut, events per person-year

Mean 8.26×10–3

Standard deviation 1.80×10–3

5 percent 5.64×10–3

Median 8.09×10–3

95 percent 1.15×10–2

TABLE 22.—RESULTS OF BAYESIAN ANALYSIS 

FOR DENTAL ABSCESS IN IN-FLIGHT 

MALE ASTRONAUTS

Abscess incidence rate, λastronaut, events per person-year

Mean 8.16×10–3

Standard deviation 1.80×10–3

5 percent 5.58×10–3

Median 7.98×10–3

95 percent 1.14×10–2

significantly associated with the occurrence of a periodontalrelated emergency and also with the occurrence of any dental 

emergency. There is probably a greater percentage of smokers 

among the U.S. Submarine Force than among astronauts. In 

addition, the submarine study is limited in that it applies only to 

adult men and that the overwhelming majority (88.5 percent) of 

the sailors followed in this study were Caucasian. In addition, 

submarine crew members are generally more senior than the 

average sailor (70.5 percent were 25 years old or older).

Table 19 shows the submarine crew data. The EF was determined from the 95-percent CI as outlined in Appendix B, 

Section B.4. 

Table 20 shows the LSAH dental abscess data for the astronaut corps from LSAH (Ref. 16, personal communication). 

For this analysis, data for the mission-ready, active female 

astronaut population was not used because the U.S. Submarine 

Force data used in the Bayesian update was for males only. 

2.5.2 Bayesian Updates To Improve Estimates of Dental 

Abscess Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the incidence rate of dental abscess in the 

astronaut corps and provide a first-order approximation 

suitable for the IMM effort. One Bayesian update was performed using data for the U.S. Submarine Force and for 

mission-ready, active male astronauts. The submarine crew 

data were used to form an informed lognormal conjugate prior 

for the incidence rate of dental abscess in the U.S. Submarine 

Force and data on preflight incidences in male astronauts, 

yielding an updated incidence rate of abscess. In Step 3, the 

posterior result of Step 1 was used as the prior and was 

updated in WinBUGS with LSAH in-flight data. The result 

was an estimate of the incidence rate of abscess in astronauts 

during an exploration mission. Appendix C provides the code 

used in WinBUGS as well as the sampling procedure. 

Step 1: WinBUGS was informed with the mean abscess 

incidence rate for the U.S. Submarine Force and the EF from 

Table 19. 

Step 2: A Bayesian update was performed with 75 000 Monte 

Carlo samplings on the number of events and person-years for 

preflight male astronauts from LSAH data (Table 20). 

Step 3: The mean incidence rate for preflight astronauts 

from Step 1 (Table 21) was used as the prior for the second 

update, and the EF was calculated as 1.43 from the 95th and 

5th percentiles from Step 1.

Step 4: A second Bayesian update was performed with 

75 000 Monte Carlo samples on the input parameters of 

Step 3: the number of events and person-years for in-flight 

male astronauts (Table 20). Appendix C provides details.

This process returned an estimate of the incidence rate of 

dental abscess in the astronaut corps (λastronaut) with respect to 

the U.S. Submarine Force. This can be used as the input rate to 

a Poisson distribution to estimate the probability of abscess 

occurring during flight. Table 22 illustrates the results of the 

implementation.

2.5.3 Discussion

The number of events per person-years for the submarine

population (Table 19) is 3.53×10–3 versus 8.16×10–3 for male 

astronauts (Table 22). In both submarine and astronaut data, 

there may be cases of underreporting. Astronaut health is 

typically tracked through annual physicals, where questions 

related to dental health may or may not be asked. There may 

be demographic differences between the submarine and 

astronaut data, including rates of smoking, age differences, 

and racial differences. The age difference may be important 

to note because recommended preventative dental practices 
NASA/TP—2012-217120 11

tend to evolve over time. Current recommended dental 

practices include daily flossing, brushing teeth twice a day for 

at least 2 minutes, seeing a dentist twice a year, and drinking 

fluoridated water (the number of communities in the United 

States with fluoridated water grows each year) (Refs. 19 

to 22). The differences between population demographics and 

access to fluoridated water may lead to discrepancies in 

incidence rates. Also, because women do not serve as submarine crewmembers, female astronaut data were not used in 

this Bayesian calculation. Future analyses should include data 

for women.

2.6 Dental Caries

Because dental caries may greatly affect crewmember 

performance, health, and morale, evaluating the probability 

that an astronaut may encounter dental caries during an 

exploration mission was deemed to be necessary. Caries are 

caused by certain bacteria in the oral flora that release acid as 

a byproduct of carbohydrate metabolism. The acid dissolves

the calcium phosphate of the enamel and dentin (Refs. 20

and 21). U.S. Submarine Force data (Ref. 15) and astronaut 

data from LSAH (Ref. 16, personal communication) were

used to estimate the probability of an astronaut encountering 

dental caries. The submarine crew data defined dental caries 

as 2010 ICD–9–CM code 521 (hard tissues and caries), and 

the astronaut data from LSAH defined dental caries as 

“primary caries, secondary caries, or order unknown,” with 

no reference to ICD–9 coding. For this analysis, the sum of 

all three caries categories was used for astronauts. A Bayesian 

update was used to combine the information from these 

sources to estimate the average rate of caries. 

2.6.1 Data and Methods

The medical history of submarine missions was useful 

because they are similar to exploration-class missions. For 

example, both occur in confined, remotely located environments where professional medical care is not immediately

available. Also, a medical event of low probability and high 

consequence could cause a mission to cease (Refs. 17 and 

18). It is important to note that smoking was significantly 

associated with the occurrence of a periodontal-related 

emergency and also with the occurrence of any dental 

emergency. It is likely that there is a greater percentage of 

smokers among sailors than among the astronaut corps. This 

study is limited in that it included only adult men and that 

the overwhelming majority (88.5 percent) of these men were

Caucasian. In addition, submarine crew members are 

generally more senior than the average sailor (70.5 percent

were 25 years old or older). Table 23 shows the submarine 

crew data. The EF was determined from the 95-percent CI as 

outlined in Appendix B, Section B.4. 

TABLE 23.—INCIDENCE OF DENTAL CARIES IN 

240 PATROLS OF THE U.S. SUBMARINE FORCE

Total person-years......................................................... 5946.9

Total visits due to caries....................................................... 29

Caries incidence rate, events per person-year........... 4.88×10–3

95-percent confidence interval (CI)......................... 0.3 to 1.53

Error factor (EF)................................................................ 1.11

TABLE 24.—INCIDENCE OF DENTAL CARIES IN 

PREFLIGHT AND IN-FLIGHT MISSION-READY, 

ACTIVE MALE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Preflight astronauts

Total person-years........................................................... 475.2

Number of crewmembers ..................................................... 77

Caries cases........................................................................ 168

Caries incidence rate, events per person-year........... 3.54×10–1

In-flight astronauts

Total person-years............................................................. 31.9

Caries cases............................................................................ 0 

Caries incidence rate, events per person-year......................... 0

Table 24 shows the data from LSAH (Ref. 16, personal 

communication). For this analysis, data for the mission-ready, 

active female astronaut population was not used because the 

U.S. Submarine Force data only included males. 

2.6.2 Bayesian Updates To Improve Estimates of Dental 

Caries Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the incidence rate of dental caries in the 

astronaut corps and provide a first-order approximation 

suitable for the IMM effort. One Bayesian update was done 

using data for the U.S. Submarine Force and for missionready, active male astronauts. The submarine crew data were

used to form an informed lognormal conjugate prior for the 

incidence rate of dental caries in U.S. Submarine Force 

personnel as well as for preflight incidences in male astronauts, yielding a posterior result for the updated incidence rate 

of caries. In Step 3, the posterior result of Step 1 was used as 

the prior, and updated LSAH in-flight data were used in 

WinBUGS. The result was an estimate for the incidence rate 

of abscess in astronauts during an exploration mission 

(Table 24). Appendix C shows the code used in WinBUGS as 

well as the sampling procedure.

Step 1: WinBUGS was informed with the U.S. Submarine 

Force mean incidence rate and the EF from Table 23. 

Step 2: A Bayesian update was performed with 75 000 

Monte Carlo samplings on the number of events and personyears for preflight male astronauts from LSAH data 

(Table 24). Table 25 shows the results. 
NASA/TP—2012-217120 12

TABLE 25.—RESULTS OF BAYESIAN ANALYSIS 

FOR DENTAL CARIES IN PREFLIGHT MISSIONREADY, ACTIVE MALE ASTRONAUTS

Caries incidence rate, λastronaut, events per person-year

Mean 9.42×10–3

Standard deviation 5.94×10–4

5 percent 8.48×10–3

Median 9.40×10–3

95 percent 1.04×10–2

TABLE 26.—RESULTS OF BAYESIAN ANALYSIS 

FOR DENTAL CARIES IN IN-FLIGHT MISSIONREADY, ACTIVE MALE ASTRONAUTS

Caries incidence rate, λastronaut, events per person-year

Mean 9.41×10–3

Standard deviation 5.95×10–4

5 percent 8.46×10–3

Median 9.39×10–3

95 percent 1.04×10–2

Step 3: The mean incidence rate from Step 1 (Table 25) was 

used as the prior for the second update, and the EF was calculated as 1.11 from the 95th and 5th percentiles from Step 1.

Step 4: A second Bayesian update was performed with 

75 000 Monte Carlo samples on the input parameters of Step 3: 

the number of in-flight events and person-years for in-flight 

male astronauts from LSAH data (Table 24). Appendix B, 

Section B.4, provides details.

This process returned an estimate of the incidence rate of 

dental caries in the astronaut corps (λastronaut) with respect to 

the U.S. Submarine Force. This incidence rate was used as 

input to a Poisson distribution to estimate the probability of 

caries occurring during flight. Table 26 shows the results.

2.6.3 Discussion

The number of dental caries events per person-year was 

4.88×10–3 in the U.S. Submarine Force versus 9.41×10–3 for 

male astronauts. In both the submarine crew and astronaut 

data, there may be cases of underreporting. Astronaut health is 

typically tracked through annual physicals, where questions 

related to dental health may or may not be asked. There may 

be demographic differences between the submarine crew and 

astronaut data, including rates of smoking, age differences, 

and racial differences. The age difference may be important to 

note because recommended preventative dental practices tend 

to evolve over time, as described in Section 2.5.3 and in 

References 17 to 21. The differences between population 

demographics and access to fluoridated water may have 

produced discrepancies in incidence rates. Also, because

women do not serve as submarine crewmembers, female 

astronaut data were not used in this Bayesian calculation.

Future analyses should include data for women.

2.7 Dental Periodontal Disease 

Because periodontal disease may greatly affect crewmember

performance, health, and morale, evaluating the probability 

that an astronaut may develop periodontal disease during an 

exploration mission was deemed to be necessary. Periodontal 

disease involves inflammation and infection that destroy the 

tissues that support the teeth, including the gums, the 

periodontal ligaments, and the tooth sockets (alveolar bone)

(Ref. 22). Gingivitis is a form of periodontal disease due to the 

long-term effects of plaque deposits. U.S. Submarine Force

data (Ref. 15) and astronaut data from LSAH (Ref. 16, 

personal communication) were used to estimate the probability 

of an astronaut encountering periodontal disease. The submarine crew data defined periodontal disease as 2010 ICD–9–

CM code 523 (gingival and periodontal disease), and LSAH 

defined periodontal disease as “periodontal disease diagnosis,”

with no reference to ICD–9 coding. A Bayesian update was 

used to combine information from these sources to estimate 

the average rate of periodontal disease. 

2.7.1 Data and Methods

The medical history of submarine missions was useful for 

this statistical analysis because these missions are similar to 

exploration-class missions: both occur in confined, remotely 

located environments where professional medical care is not 

immediately available. Also, a medical event of low probability and high consequence could cause a mission to fail 

(Refs. 17 and 18). Data from Deutsch (Ref. 15) regarding the 

incidence of periodontal disease and gingivitis in the U.S. 

Submarine Force were used because of these similarities (see

Table 27). However, it is important to note that smoking was 

significantly associated with the occurrence of a periodontalrelated emergency as it was with the occurrence of any dental 

emergency. The percentage of smokers among sailors is 

probably greater than among the astronaut corps. The U.S. 

Submarine Force study is limited in that it applies only to 

adult men, and the overwhelming majority (88.5 percent) of 

these men were Caucasian. In addition, submarine crew 

members are generally more senior than the average sailor 

(70.5 percent were 25 years old or older). Table 27 shows the 

results, where the EF was determined from the 95-percent CI 

as outlined in Appendix B, Section B.4. 

The IMM team obtained data regarding the incidence of 

periodontal disease in the astronaut corps from LSAH (Ref. 16, 

personal communication) (see Table 28). Because the U.S. 

Submarine Force data used in this Bayesian update was for 

males only, data for the mission-ready, active female astronaut 

population were not used.
NASA/TP—2012-217120 13

TABLE 27.—INCIDENCE OF GINGIVAL AND 

PERIODONTAL DISEASE IN 240 PATROLS 

OF THE U.S. SUBMARINE FORCE

Total person-years ............................................... 5946.9

Total visits due to periodontal disease ........................10

Periodontal disease incidence rate, 

events per person-year.................................. 1.68×10–3

95-percent confidence interval (CI)............. 0.33 to 4.19

Error factor (EF) ...................................................... 6.24

TABLE 28.—INCIDENCE OF PERIODONTAL DISEASE 

IN PREFLIGHT AND IN-FLIGHT MISSION-READY, 

ACTIVE MALE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Preflight astronauts

Total person-years......................................................................... 475.2

Number of crewmembers................................................................... 77

Periodontal disease cases ................................................................... 56

Periodontal disease incidence rate, events per person-year.... 1.18×10–1

In-flight astronauts

Total person-years........................................................................... 31.9

Periodontal disease cases ..................................................................... 0 

Periodontal disease incidence rate, events per person-year.................. 0 

2.7.2 Bayesian Updates To Improve Estimates of 

Periodontal Disease Incidence Rates, and 

Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the incidence rate of periodontal disease in the 

astronaut corps and provide a first-order approximation 

suitable for the IMM effort. One Bayesian update was performed using U.S. Submarine Force data and data for missionready, active male astronauts. The submarine crew data were

used to form an informed lognormal conjugate prior for the 

incidence rate of periodontal disease in U.S. Submarine Force 

personnel and male astronauts, yielding a posterior result of

the updated incidence rate of periodontal disease. In Step 3, 

the posterior result of Step 1 was used as the prior and was

updated with LSAH in-flight data in WinBUGS. The result 

was an estimation of the incidence rate of periodontal disease 

in astronauts during an exploration mission. Appendix C

provides the code used in WinBUGS as well as the sampling 

procedure.

Step 1: WinBUGS was informed with the U.S. Submarine 

Force mean incidence rate and the EF from Table 27. 

Step 2: A Bayesian update was performed with 75 000 Monte 

Carlo samplings on the number of events and person-years for 

preflight male astronauts from LSAH data (Table 28). 

Step 3: The mean incidence rate for preflight astronauts

from Step 1 (Table 29) was used as the prior for the second 

update, and the 95th and 5th percentiles from Step 1 were used 

to calculate the EF. 

TABLE 29.—RESULTS OF BAYESIAN ANALYSIS FOR 

PERIODONTAL DISEASE IN TOTAL PREFLIGHT 

MISSION-READY, ACTIVE MALE ASTRONAUTS

Periodontal disease incidence rate, λastronaut, events per person-year

Mean 1.10×10–1

Standard deviation 1.52×10–2

5 percent 8.62×10–2

Median 1.09×10–1

95 percent 1.36×10–1

TABLE 30.—RESULTS OF BAYESIAN ANALYSIS 

FOR PERIODONTAL DISEASE IN IN-FLIGHT 

MALE ASTRONAUTS

Periodontal disease incidence rate, λastronaut, events per person-year

Mean 1.03×10–1

Standard deviation 1.41×10–2

5 percent 8.16×10–2

Median 1.02×10–1

95 percent 1.28×10–1

Step 4: A second Bayesian update was performed with 

75 000 Monte Carlo samples on the input parameters of 

Step 3: the number of events and person-years for in-flight 

male astronauts from LSAH data (Table 28). Appendix C 

provides details.

This process returned an estimate of the incidence rate of 

periodontal disease in the astronaut corps (λastronaut) with 

respect to the U.S. Submarine Force (Table 30). This rate can 

be used as the input rate to a Poisson distribution to estimate 

the probability of periodontal disease occurring during 

flight. 

2.7.3 Discussion

The number of periodontal disease events per person-year in 

the submarine population is 2 orders of magnitude less than that 

of the male astronauts. In both the submarine and astronaut data, 

there may be cases of underreporting. Astronaut health is 

typically tracked through annual physicals, where questions 

related to dental health may or may not be asked. In addition,

there may be demographic differences between the submarine 

crew and astronaut data, including rates of smoking, age, and 

race. The age difference may be important to note because

recommended preventative dental practices tend to evolve over 

time, as described in Section 2.5.3 and References 19 to 22. 

These differences and differences in access to fluoridated water 

may lead to discrepancies in incidence rates. Also, because

women do not serve as submarine crewmembers, female astronaut data were not used in this Bayesian calculation. Future 

analyses should include data for women.
NASA/TP—2012-217120 14

2.8 Gallstone Disease 

The presence of cholesterol stones or bile pigment-based 

stones in the gallbladder is a relatively common condition that

can lead to a variety of serious complications. Risk factors for 

gallstone disease include age, obesity, diabetes mellitus, 

pregnancy, and alcohol use. In addition, during the reproductive years, the condition is about 4 times more likely in 

women than in men. This gender discrepancy diminishes with 

age. Although gallstones may be asymptomatic, the complications of symptomatic gallstone, or biliary disease may have a 

negative impact on crewmember health, morale, and performance. The current standard treatment for most complications 

of biliary disease is cholecystectomy, or surgical removal of 

the gallbladder (Ref. 23). Three of the severe complications of 

gallstone disease are acute cholecystitis, acute biliary pancreatitis, and acute cholangitis. Acute cholecystitis, or inflammation of the gallbladder, can lead to progressive pain, fever, and 

possible necrosis of the gallbladder. Treatment requires 

antibiotics and early surgical intervention (Ref. 23). Biliary 

pancreatitis occurs when a gallstone passes into and through 

the common bile duct, leading to abdominal pain and potential 

inflammation. Treatment for this condition includes endoscopic removal of the stone and cholecystectomy (Ref. 23). 

Cholangitis is the infection of an obstructed bile duct, causing 

pain and fever (Ref. 24). Owing to the debilitating symptoms 

of these conditions and the difficulties that surgical treatment 

requirements pose for space exploration missions, calculating 

the incidence rate of severe gallstone disease in astronauts was 

deemed to be necessary. A Bayesian update was used to 

combine the incidence rates of acute cholecystitis, biliary 

pancreatitis, and cholangitis from a general population study 

with data on the incidence of severe gallstone disease in the 

astronaut corps from LSAH to yield a probability distribution 

describing the incidence rate of severe gallstone disease in 

astronauts (Ref. 6, personal communication).

2.8.1 Data and Methods

So that a first-order estimate of the incidence rate of severe 

gallstone disease in the astronaut and general populations

could be obtained, the assumption was first made that gallstone disease occurs at some characteristic constant rate 

(λgallstone) over the period of interest. This allowed the number 

of gallstone events to be represented as a Poisson process with 

characteristic rate λgallstone. 

The probability distribution describing this rate in the general population was determined from a study published in the 

Canadian Medical Association Journal that used data from the 

Canadian Institute for Health Information, the Ontario Health 

Insurance Plan physicians claims database, and the Registered 

Persons Database to determine the annual incidence rates of 

acute cholecystitis, acute biliary pancreatitis, and acute 

cholangitis per 100 000 people from 1988 to 2000. The study 

determined incidence rates for the three events separately. In 

addition, incidence rates were stratified by males and females

and by age (Ref. 6, personal communication). 

Independence of occurrence was assumed for the different 

age groups and different diseases when these incidence rates 

were combined for the Bayesian analysis (as described in 

Appendix D) to make sure that the estimate of severe gallstone 

disease incidence in the total general population would be as 

similar as possible to that in the astronaut corps. Incidences 

provided in the study for ages 18 to 44 and 45 to 64 were 

combined to estimate the incidence of severe gallstone disease 

for a general population aged 18 to 64. It was assumed that the 

distributions describing the two groups were independent. The 

incidence rates for the three separate diseases determined in 

this fashion were summed to provide an estimate of the total 

severe gallstone disease incidence, again with the assumption 

that the distributions were independent. This procedure was 

repeated for men, women, and the total. 

Appendix D provides the method used to combine incidence 

rates with the assumption of statistical independence of the age 

groups and conditions. Table 31 summarizes the incidence rates 

in the general population that were determined via this procedure. The study provided 95-percent CIs for each incidence rate

that were combined in a fashion consistent with independent 

distributions and were used to determine estimates for the 

standard error of the general population incidence rates. These 

standard error estimates were used to construct 90-percent CIs

for the incidence rates, which were used, in turn, to calculate the 

EFs. Table 31 provides the calculated incidence rates for men, 

women, and the total, along with the EFs. Appendix B, 

Section B.5, summarizes the technique used to determine the EF 

from the 95-percent CI provided in Reference 25. 

Data concerning the incidence of severe gallstone disease in 

the astronaut corps were obtained from the LSAH (Ref. 6, 

personal communication), as summarized in Table 32. There 

were no occurrences of severe gallstone disease in in-flight 

astronauts, and there were no occurrences at any stage in 

female astronauts. The three preflight occurrences of gallstone 

TABLE 31.—CALCULATED INCIDENCE OF GALLSTONE DISEASE IN ONTARIO FROM 1988 TO 2000

Statistic Males Females Total

Gallstone cases in adults 18 to 64 years of age per 100 000 person-years (derived) 76.9 126.6 101.7

90-percent confidence interval (CI) for gallstone disease occurrences (derived) 76.1 to 77.6 125.6 to 127.5 101.2 to 102.3

Gallstone incidence in adults 18 to 64 years of age, events/person-year 7.69×10–4 1.27×10–3 1.02×10–3

Error factor (EF) for gallstone incidence in adults 18 to 64 years of age 1.01 1.01 1.01
NASA/TP—2012-217120 15

TABLE 32.—INCIDENCE OF GALLSTONE DISEASE IN 

PREFLIGHT AND IN-FLIGHT MISSION-READY, 

ACTIVE MALE AND FEMALE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females Total

Preflight astronauts

Total person-years 1970.4 264.8 2235.2

Gallstone cases 3 0 3

Gallstone incidence rate, λastronaut, 

events per person-year 1.52×10–3 0 1.34×10–3

In-flight astronauts

Total person-years 32.0 6.5 38.5

Gallstone cases 0 0 0

Gallstone incidence rate, λastronaut, 

events per person-year 0 0 0

disease in men were all 3 to 6 years preflight. Table 32 shows 

the preflight and in-flight incidence rates.

2.8.2 Bayesian Updates To Improve Estimates of 

Gallstone Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to obtain a 

first-order estimate of the incident rate of gallstone disease in 

the astronaut corps. The analysis combined information from 

the Canadian general population with available information on 

gallstone incidence in astronauts. Informed lognormal priors 

for the incidence rate of gallstone disease in the general 

population was determined from information in Urbach et al.

(Ref. 25), as described in Appendix D. Step 1 of the Bayesian 

analysis used this prior to update the LSAH preflight data on 

gallstone disease incidence in astronauts. This resulted in 

posterior results describing the incidence rate in preflight 

astronauts. The posterior results were used as priors for the

second step, which updated the LSAH data for gallstone 

disease incidence in in-flight astronauts. The result was a firstorder estimate of the incidence rate of severe gallstone disease 

in astronauts on a long-duration exploration-class mission.

This procedure was performed three times, once each for 

male, female, and total astronauts. In each Bayesian update, 

75 000 update steps were used. Appendix C provides the code 

used in WinBUGS, and an outline of the input data used in 

each step follows.

Step 1: For males, females, and the total, the general population incidence rates and EFs were used to inform the 

lognormal priors in WinBUGS. The LSAH preflight data that 

were updated included the number of gallstone disease cases 

and the recorded number of person-years for each population.

Table 33 shows the gallstone incidence rates for preflight 

astronauts and provides the posterior results from this step: the 

incidence of gallstone disease in male, female, and total 

preflight astronauts. 

Step 2: The posterior results from Step 1—the means and the 

5th and the 95th percentiles (Table 33)—were used as priors in 

WinBUGS to update the LSAH data for in-flight astronauts 

TABLE 33.—RESULTS OF BAYESIAN ANALYSIS 

FOR GALLSTONE DISEASE IN PREFLIGHT 

MISSION-READY, ACTIVE ASTRONAUTS

Gallstone incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 7.69×10–4 1.27×10–3 1.02×10–3

Standard deviation 4.65×10–6 7.64×10–6 6.12×10–6

5 percent 7.62×10–4 1.25×10–3 1.01×10–3

95 percent 7.77×10–4 1.28×10–3 1.03×10–3

TABLE 34.—RESULTS OF BAYESIAN ANALYSIS FOR 

GALLSTONE DISEASE IN IN-FLIGHT ASTRONAUTS

Gallstone incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 7.69×10–4 1.27×10–3 1.02×10–3

Standard deviation 4.65×10–6 7.68×10–6 6.18×10–6

5 percent 7.62×10–4 1.25×10–3 1.01×10–3

95 percent 7.77×10–4 1.28×10–3 1.03×10–3

(Table 32). This Bayesian update resulted in probability 

distributions for the incidence of gallstone disease in male, 

female, and total astronauts during spaceflight (Table 34).

2.8.3 Discussion

Like the other analyses presented in this study, this analysis is 

limited because it assumes a constant incidence rate for gallstone disease without accounting for physiological and environmental risk factors. Future analyses should consider 

important risk factors, including age, obesity, and diet. In 

addition, assumptions of independence were made to compute a 

general gallstone disease incidence rate from the diseasespecific rates obtained from the literature, but the incidence

rates for different conditions and age groups might not be 

wholly independent. Furthermore, this analysis uses the 

combined incidence rates of three severe complications of 

gallstone disease as an estimate of the incidence rate for total

gallstone disease, but these three conditions alone may not 

provide a sufficiently broad consideration of the complications 

of gallstone disease. This is evident in the fact that the incidence 

rate of gallstone disease in the in-flight male astronauts 

(1.52×10–3 events/person-year) is almost twice that of the 

general male population (7.69×10–4 events/person-year in 

Ref. 25)—a counterintuitive result. In addition, minor differences may exist between the diets and lifestyles of the Ontario 

population used and the U.S. astronaut population (Ref. 25). 

However, both populations are from well-developed, industrial 

countries in similar North American temperate regions. 

Accordingly, for the present analysis it was assumed that the

diets are similar to a high degree. Incorporation of additional 

possible complications or related conditions might improve this 

estimate. Any use of these results must account for these limitations, but this analysis is “a reasonable estimate” of the 

incidence rate of gallstone-related diseases in astronauts.
NASA/TP—2012-217120 16

The accuracy of this analysis could be improved if more 

data relating to the risk factors for and the physiology of 

gallstone formation and related complications were incorporated. The current results can serve as a baseline for future 

gallstone disease predictions.

2.9 Herpes Zoster

The first infection of the varicella-zoster virus results in 

chicken pox. Reactivation of this virus in the cranial nerve or 

the dorsal root ganglia results in a painful rash known as 

herpes zoster (HZ) (Ref. 26)—a skin disease more commonly 

known as shingles. The cause for reactivation is unknown, but 

higher incidence rates are found for the elderly, and reactivation is generally associated with a weakened immune system (Ref. 26). Because the virus lives in the nerve, HZ is 

extremely painful. The probability of HZ incidences must be 

calculated to ensure that enough medications are supplied for 

any and all shingles outbreaks during a space mission. The

general population data used in this calculation must roughly 

match the age of active astronauts because HZ reactivation 

rates increase exponentially with age. The general population 

data used came from a 2005 article in the Journal of General

Internal Medicine (Ref. 26). A Bayesian update was use to 

combine these data with HZ incidence data from the astronaut 

corps to yield a probability distribution describing the average 

HZ incidence rate in astronauts.

2.9.1 Data and Methods

For the general population data, Reference 26 pulled HZ

incidence rates from the Medstat MarketScan database, which 

2001. Incidences of HZ were defined by the 9th revision of the 

ICD. Data included the number of HZ cases per the number of 

person-years for males, females, and the total who were 40 to 

49 years of age. These data were simplified to incidences per 

person-year for males, females, and the total. The 95-percent 

CI per 1000 person-years also is given for males, females, and 

the total for ages 40 to 49. These intervals were converted into 

the EFs for males, females, and the total. Appendix B, Section B.6, shows the steps for these conversions, and Table 35 

shows the average HZ incidence per person-year for males, 

females, and the total, along with the corresponding EFs.

The LSAH supplied data that describe the incidence of HZ 

and the number of person-years for preflight and in-flight 

male, female, and total astronauts (Table 36 and Refs. 27 

and 28, personal communications).

2.9.2 Bayesian Updates To Improve Estimates of Herpes

Zoster Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the incidence rate of HZ in astronauts and 

provide an approximation suitable for the IMM effort. The 

first step was to perform a Bayesian update on the preflight

astronaut data for HZ incidence with the general population 

data from Reference 26. An update was performed for males, 

females, and the total. The posterior results from this step 

describe the incidence rate of HZ in preflight astronauts. 

The means and the 5th and 95th percentiles from this first 

step then served as the priors for the second step and were 

used to perform a Bayesian update on the in-flight astronaut

data. The update yielded the incidence rates of HZ in in-flight 

TABLE 35.—INCIDENCE OF HERPES ZOSTER (HZ) IN U.S. ADULTS FROM 2000 TO 2001

Statistic Males Females Total

HZ cases in adults 40 to 49 years of age 473 740 1213

Number of person-years in the study 190 653 228 677 419 330

95-percent confidence interval (CI) for HZ incidence in 

adults 40 to 49 years of age per 1000 person-years 2.3 to 2.8 3.0 to 3.5 2.7 to 3.0

HZ incidence rate in adults 40 to 49 years of age per person-year 2.5×10–3 3.2×10–3 2.9×10–3

Error factor (EF) for HZ incidence in adults 40 to 49 years of age 1.09 1.07 1.04

TABLE 36.—INCIDENCE OF HERPES ZOSTER (HZ) IN PREFLIGHT AND 

IN-FLIGHT MISSION-READY, ACTIVE ASTRONAUTS 

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females Total

Preflight astronauts

Total person-years 1985.9 273.1 2259.0

HZ cases 8 0 8

HZ incidence rate, events per person-year 4.0×10–3 0 3.5×10–3

In-flight astronauts

Total person-years 32.5 6.5 39.0

HZ cases 1 0 1

HZ incidence rate, events per person-year 3.08×10–3 0 2.56×10–3
NASA/TP—2012-217120 17

TABLE 37.—RESULTS OF BAYESIAN ANALYSIS FOR 

HERPES ZOSTER (HZ) IN PREFLIGHT MISSION-READY, 

ACTIVE MALE, FEMALE, AND TOTAL ASTRONAUTS

HZ incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 2.50×10–3 3.23×10–3 2.90×10–3

Standard deviation 1.31×10–4 1.33×10–4 6.91×10–5

5 percent 2.29×10–3 3.02×10–3 2.78×10–3

95 percent 2.72×10–3 3.45×10–3 3.01×10–3

TABLE 38.—RESULTS OF BAYESIAN ANALYSIS 

FOR HERPES ZOSTER IN IN-FLIGHT MALE, 

FEMALE, AND TOTAL ASTRONAUTS

Herpes incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 2.51×10–3 3.23×10–3 2.90×10–3

Standard deviation 1.31×10–4 1.30×10–4 7.04×10–5

5 percent 2.30×10–3 3.02×10–3 2.79×10–3

95 percent 2.73×10–3 3.45×10–3 3.02×10–3

astronauts. Appendix C provides the WinBUGS code used, 

and an outline of the data for these steps follows.

Step 1: The general population HZ incidence per personyear for males, females, and the total and the corresponding 

EFs used as the priors in this step came from Reference 26. 

The LSAH data updated in this step included the number of 

preflight person-years and HZ incidences for males, females, 

and the total. Table 35 shows the incidence rates and the 

corresponding EFs for the general population, and Table 36 

shows the incidences for preflight astronauts. Table 37 shows 

the posterior results: Poisson probability distributions for 

males, females, and the total.

Step 2: The means and the 5th and 95th percentiles from the 

posterior results of Step 1 (Table 37) were used as the priors 

for this step. Table 36 shows the LSAH data for in-flight 

astronauts, and Table 38 shows the posterior results from 

Step 2: the incidence of HZ in in-flight astronauts.

2.9.3 Discussion

Understanding the limitation of assuming an average rate 

for HZ incidence is necessary for the appropriate use of these 

data. HZ incidence rate increases exponentially with age (the 

rate for 50 to 59 year olds is double the rate for 40 to 49 year 

olds). Therefore, capturing the ages closest to the astronaut 

corps is imperative (Ref. 26). In spite of these limitations, this 

analysis is a reasonable approximation of HZ incidence. These 

data could also be used as a baseline for any future studies 

relating to HZ. 

2.10 Renal Stones 

Data from LSAH (Ref. 29, personal communication) and 

the National Institutes of Health (NIH) (Ref. 30) were used to 

estimate the probability of an astronaut developing a renal 

stone during or after space flight. A Bayesian update was used 

to combine information from these sources to estimate the 

average rate of renal stone formation. This analysis uses only 

data pertaining to renal stone occurrence, not data related to 

blood or urine chemistry.

2.10.1 Data and Methods

The LSAH temporal distribution of renal stone formation 

provided to the IMM team indicates that the assumptions that 

(1) the rates (λ) of renal stone incidences are constant over the 

period of interest and (2) the probability of occurrence follows 

a Poisson distribution are probably erroneous. However, the 

authors believe that these assumptions are currently the “best 

approximation” on the basis of nonattributable data from 

short-duration-mission (<20 days) participants. Only one data 

point is available for renal stone incidence during longduration missions (~180 days) at this time.

Table 39 shows the general population incidence rate of 

renal stones from the NIH as of 2004 (Ref. 30). The incidence

of renal stones differed for males and females, but for this 

analysis, the differences between males and females were not 

considered, and the average incidence rate of renal stones of

1.8×10–3 was used. An EF of 2.236 was found by taking the 

square root of the ratio 3 to 0.6. 

The LSAH data for the astronaut population at Johnson 

were of interest because renal stone incidence is geographically dependent because of dietary habits, lifestyle, and other 

factors. The LSAH data were used to capture discrepancies 

due to geography. Table 40 shows the renal stone incidence 

data for this ground-based comparison population from 

Pietrzyk et al. (Ref. 31). 

There have been no incidences of renal stones in in-flight 

astronauts (Table 41 and Ref. 31). In Table 41, the total 

number of person-years reported includes the timeframe for 

in-flight data.

TABLE 39.—INCIDENCE OF RENAL STONES IN 

THE U.S. GENERAL POPULATION AS OF 2004

Statistic Males Females

Renal stone cases, events per 1000 person-years 1 to 3 0.6 to 1

Mean number of events per 1000 person-years............................ 1.8

Renal stone incidence rate, events per person-year ............. 1.8×10–3
NASA/TP—2012-217120 18

TABLE 40.—INCIDENCE OF RENAL STONES IN THE 

ANALOG ASTRONAUT POPULATION 

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Number of participants ............................................................. 927

Renal stone cases........................................................................ 74

Number of person-years .................................................... 17 740.8

Renal stone incidence rate, events per person-year............ 4.2×10–3

TABLE 41.—INCIDENCE OF RENAL STONES 

IN IN-FLIGHT ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Renal stone cases.......................................................................... 0

Number of person-years ........................................................... 25.1

Renal stone incidence rate, events per person-year....................... 0

2.10.2 Bayesian Updates To Improve Estimates of Renal 

Stone Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the renal stone incidence rate for astronauts 

and provide a first-order approximation suitable for the IMM 

effort. One Bayesian update was performed without distinguishing between data for males and females. The data from 

the NIH (Ref. 30) were used to form an informed lognormal 

conjugate prior for the incidence rate of renal stones in the 

general U.S. population (λgeneral). This prior was used to update 

the LSAH astronaut data in Step 1 of the Bayesian implementation, yielding a posterior result for the updated incidence rate 

of renal stones. In Step 2, the posterior result of Step 1 was

used as the prior to update the LSAH in-flight astronaut data 

in WinBUGS. The result was an estimation of the incidence 

rate of renal stone formation in astronauts during an exploration mission. Appendix C provides the code used in 

WinBUGS as well as the sampling procedure. 

Step 1: WinBUGS was informed with the mean incidence 

rate λgeneral from Table 39 and the EF (2.236).

Step 2: A Bayesian update was performed with 75 000 

Monte Carlo samples on the input parameters of Step 1: the 

number of events and person-years for preflight astronauts

from Table 40. 

Step 3: The posterior result of Step 2—the mean incidence 

rate (Table 42) was dissected and used as the prior for the 

second update. The 5th and 95th percentiles from the lognormal Poisson distribution in Step 2 (Table 43) were used to 

calculate the EF. 

Step 4: A second Bayesian update was performed with 

75 000 Monte Carlo samples on the input parameters of 

Step 1: the number of events and person-years for in-flight 

astronauts (Table 41). 

This process returned an estimate of the incidence rate of 

renal stone formation in in-flight astronauts with respect to the 

general population and the LSAH analog population (Table 43). 

This can be used as the input rate to a Poisson distribution to 

estimate the probability of a renal stone occurrence. 

TABLE 42.—RESULTS OF BAYESIAN ANALYSIS 

FOR RENAL STONES IN THE ANALOG 

ASTRONAUT POPULATION

Renal stone incidence rate, λanalog, events per person-year

Mean 3.97×10–3

Standard deviation 4.58×10–4

5 percent 3.24×10–3

95 percent 4.74×10–3

TABLE 43.—RESULTS OF BAYESIAN ANALYSIS 

FOR RENAL STONES IN IN-FLIGHT 

ASTRONAUTS (ESTIMATE)

Renal stone incidence rate, λastronaut, events per person-year

Mean 3.96×10–3

Standard deviation 4.60×10–4

5 percent 3.25×10–3

95 percent 4.76×10–3

2.10.3 Discussion

This analysis should be considered limited in that it assumes 

an average incidence rate of renal stones, irrespective of the 

renal stone type or environmental conditions. The results are a

reasonable representation of the renal stone incidence rate 

given the data available and the assumptions made during 

construction of the estimate.

More accurate estimates could be made with further analysis of differences between males and females and the urinary

and serum chemistry values that pertain to renal stone formation. The current data will serve as the baseline for future 

estimates that utilize biochemical renal stone forming and 

inhibiting parameters. 

2.11 Seizure

Because a seizure may greatly affect crewmember performance, health, and morale, evaluating the probability that an 

astronaut may experience a seizure during an exploration 

mission was deemed to be necessary. A seizure is a major 

disruption of electrical signaling between neurons in the brain, 

and epilepsy is a disorder characterized by the recurrence of 

seizures. In normal brain function, neurons communicate with 

other neurons, glands, and muscles via electrochemical 

impulses. These neuronal impulses propagate along the axon, 

initiating the release of neurotransmitters that flow across the 

synaptic cleft to the dendrites of an adjacent cell. A balance 

between excitatory and inhibitory neurotransmitters controls 

the firing of electrical impulses. When excitatory neurotransmitters exceed the threshold, an action potential results. A 

seizure is an episode of continual and uncontrolled neuronal 

firing causing convulsions, muscle contractions, and unconsciousness. Seizures may be triggered by head trauma, physical

 
NASA/TP—2012-217120 19

and emotional stress, fatigue, and external stimuli. However, 

most cases of seizure are idiopathic (Ref. 32). Data from the 

general population (Ref. 33) and astronaut data from the 

LSAH (Ref. 6, personal communication) were used to estimate the probability of an astronaut experiencing a seizure. A 

Bayesian update was used to combine the incidence rates of 

seizure from these sources to yield an appropriate incidence 

rate of seizure. The rate was assumed to be constant, and a 

Poisson probability distribution was assumed to govern the 

probability of seizure.

2.11.1 Data and Methods

General population data for the incidence rate of a first 

unprovoked (idiopathic) seizure were obtained from a 

Rochester, Minnesota, epidemiologic project (Ref. 33). A 

seizure was defined as an abnormal and excessive discharge of 

a set of neurons in the brain. In this study, incidence rates of 

epilepsy and of all unprovoked seizures were considered. An 

idiopathic seizure is one that occurs without an identified 

cause. Of all seizures, 61 to 66 percent are idiopathic and 23 to 

35 percent are generalized tonic-clonic (Refs. 33 and 34). The

incidence per 100 000 person-years of a first unprovoked 

seizure in adults 40 to 54 years of age was slightly higher in 

males (29) than in females (25). For this estimate, the incidence rate of seizures in males and females was averaged as 

shown in Table 44. Because there is not a significant variation 

in the incidence of seizure between males and females, the 

average incidence rate was considered appropriate. The incidence of seizure is related to age—incidence rates were high

for infants younger than 1 year and highest for persons older 

than 75 years of age. CI information was not available for a 

first unprovoked seizure. Therefore, the EF was estimated 

from the 90th-percentile CI constructed from total population 

data for epilepsy. A person experiencing a single unprovoked 

seizure was not diagnosed with epilepsy and thus was not 

included in the CI data. The incidence rate of a first unprovoked seizure was 33 percent higher than the incidence rate of 

epilepsy, primarily because individuals who experienced only 

one unprovoked seizure were added. Data for this estimate 

were averaged from three age ranges: 40 to 44, 45 to 49, and 

50 to 54, yielding an average age of 47 years. The EF was 

estimated to be 1.19 from a 90th-percentile CI constructed 

from male and female data from a population aged 40 to 

54 years (see Appendix B, Section B.7).

Data for the incidence of seizure in the astronaut corps were 

obtained from the LSAH (Ref. 6, personal communication), 

and are summarized in Table 45. There were no occurrences 

of seizure in in-flight astronauts.

TABLE 44.—INCIDENCE OF TOTAL SEIZURES IN THE 

GENERAL POPULATION AGED 40 TO 54 YEARS IN 

ROCHESTER, MINNESOTA, FROM 1935 TO 1984

Average incidence per 100 000 person-years......................... 27

Seizure incidence rate, events per person-year..............2.7×10-4

TABLE 45.—INCIDENCE OF SEIZURES IN PREFLIGHT 

AND IN-FLIGHT MISSION-READY, ACTIVE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females Total

Preflight astronauts

Total person-years 1970.4 264.8 2235.2

Seizure cases 0 0 0

Seizure incidence rate, events 

per person-year 0 0 0

In-flight astronauts

Total person-years 32.0 6.6 38.6

Seizure cases 0 0 0

Seizure incidence rate, events 

per person-year 0 0 0

TABLE 46.—RESULTS OF BAYESIAN ANALYSIS 

FOR SEIZURES IN TOTAL PREFLIGHT MISSIONREADY, ACTIVE ASTRONAUTS 

Seizure incidence rate, λastronaut, events per person-year

Mean 2.68×10-4

Standard deviation 2.84×10-5

5 percent 2.24×10-4

Median 2.67×10-4

95 percent 3.17×10-4

2.11.2 Bayesian Updates To Improve Estimates of 

Seizure Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the incidence rate of seizure in the astronaut 

corps and provide a first-order approximation suitable for the 

IMM effort. The general population data (Ref. 33) were used 

to determine an informed lognormal conjugate prior for the 

incidence rate of seizure in the general U.S. population 

(λgeneral). This prior was used to update LSAH preflight data in 

Step 1 of the Bayesian implementation, yielding a posterior 

result of the updated incidence rate of seizure. In Step 2, the 

posterior result of Step 1 was used as the prior and was

updated with LSAH in-flight data in WinBUGS. The result 

was an estimation of the incidence rate of seizure in astronauts 

during an exploration mission. Appendix C contains the code 

used in WinBUGS as well as the sampling procedure. 

Step 1: WinBUGS was informed with the mean incidence 

rate of the general population from Table 44 and the EF.

Step 2: A Bayesian update was performed with 75 000 

Monte Carlo samples on the input parameters of Step 1: the 

number of events and person-years for preflight astronauts 

from LSAH (Table 45). 

Step 3: The posterior result of Step 2—the mean incidence 

rate (Table 46) was dissected and used as the prior for the second 

update, and the 5th and 95th percentiles from the lognormal 

Poisson distribution in Step 2 were used to calculate the EF.

Step 4: A second Bayesian update was performed with 

75 000 Monte Carlo samples on the input parameters of 

Step 1: the number of events and person-years for in-flight 

astronauts (Table 45). Appendix C provides details.
NASA/TP—2012-217120 20

TABLE 47.—RESULTS OF BAYESIAN ANALYSIS 

FOR SEIZURES IN TOTAL IN-FLIGHT 

ASTRONAUTS

Seizure incidence rate, λastronaut, events per person-year

Mean 2.70×10-4

Standard deviation 2.88×10-5

5 percent 2.25×10-4

Median 2.68×10-4

95 percent 3.19×10-4

Table 47 shows the results: an estimate of the incidence rate 

of seizure in in-flight astronauts with respect to the general 

population. This rate can be used as the input rate to a Poisson 

distribution probability to estimate the probability of seizure 

occurring in flight. 

2.11.3 Discussion

This analysis is limited in that it assumes an average incidence rate of seizure irrespective of the environmental 

conditions and the cause of seizure. In addition, the EF was 

calculated with epilepsy data, not unprovoked seizure data, 

because Reference 33 did not have CI data on the first unprovoked seizure. Also, data regarding repeated occurrences of 

seizures could influence the predicted rate of incidence 

because it is known that having a single seizure greatly 

increases the likelihood of subsequent seizures. The results 

should be used with an understanding of these limitations. 

However, these results probably give a reasonable representation of the incidence rate of seizures given the data available 

and the assumptions made when the estimate was constructed. 

More accurate estimates could be made with further analysis of seizure occurrence in post-flight astronauts and greater 

understanding of the cause of seizures. The current analysis 

data will serve as the baseline for future estimates of the 

incidence of seizures in astronauts.

2.12 Stroke

Because a stroke may greatly affect crewmember performance and health, evaluating the probability that an astronaut 

may experience a stroke during an exploration mission was 

deemed to be necessary. The most common type of stroke is 

ischemic stroke (also referred to as a cerebral infarction)

(Ref. 35), where blood flow to the brain is blocked by blood 

clots and/or by fatty deposits called plaque in the blood vessel 

linings. According to the Centers for Disease Control (CDC), 

about 85 percent of all strokes are ischemic (Ref. 35). This 

analysis only used data pertaining to stroke incidence for ages 

similar to those of mission-ready astronauts, not data related to 

blood pressure or other physiological conditions. A Bayesian 

update was used to combine the incidence rates of stroke from 

the LSAH (Ref. 36, personal communication) and the general 

U.S. population (Ref. 37) to estimate the average rate of stroke. 

2.12.1 Data and Methods

As of 2010, the American Heart Association (Ref. 37) gave 

the incidence rate of ischemic stroke in U.S. residents 45 to 

54 years of age as 1.1 to 2.7 per 1000 person-years for males 

and 0.7 to 2.2 per 1000 person–years for females.

Reference 37 considers the higher incidence rates for black 

men and women (2.7 and 2.2, respectively) to be unreliable, 

although a rationale for this view is not specified. The lower 

incidence rate data are for white men and women (1.1 and 0.7, 

respectively). This Bayesian calculation only includes the data 

for whites (see Table 48), although data for black men and 

women were used in calculating the EFs: males, 1.567; 

females, 1.773; and total, 1.254. Data from this publication 

indicate that the prevalence of stroke among Hispanics and 

Latinos is higher than among whites but smaller than among 

blacks (Ref. 37).

As of 2007 there were 101 astronauts that were mission 

ready (20 females and 81 males). The LSAH data were given 

for males and females, so data for white males, females, and 

the total were used for the general population calculation. For 

this analysis, gender, age, ethnicity, and type of stroke—

ischemic—were simplified and assumed to be lognormal, as 

shown in Table 48.

Data received from LSAH (Ref. 36, personal communication) are given in Table 49. Of the two incidents of preflight 

stroke, one occurred 0 to 3 years prior to flight and one 

occurred 3 to 6 years prior to flight. The fact that there were 

no strokes recorded for female astronauts may negate the 

assumption of an average incidence rate for the entire period 

of interest.

TABLE 48.—INCIDENCE OF STROKE IN U.S. ADULTS 

45 TO 54 YEARS OF AGE

Statistic Males Females Total

Stroke incidence in white 

adults aged 45 to 54 years 

per 1000 person-years 1.1 0.7 0.9

Mean stroke incidence rate in 

adults aged 45 to 54 years, 

events per person-year 1.10×10–3 7.00×10–4 9.00×10–4

TABLE 49.—INCIDENCE OF STROKE IN PREFLIGHT AND 

IN-FLIGHT MISSION-READY, ACTIVE ASTRONAUTS

[From Lifetime Surveillance of Astronaut Health (LSAH).]

Statistic Males Females Total

Preflight astronauts

Total person-years 3478.6 336.8 3815.4

Stroke cases 2 0 2

Stroke incidence rate, events 

per person-year 5.75×10–4 0 5.24×10–4

In-flight astronauts

Total person-years 31.8 6.5 38.3

Stroke cases 0 0 0

Stroke incidence rate, events 

per person-year 0 0 0
NASA/TP—2012-217120 21

2.12.2 Bayesian Updates To Improve Estimates of Stroke 

Incidence Rates, and Analysis Results

The following steps were taken with WinBUGS to improve 

the estimate of the incidence of stroke in astronauts and provide a first-order approximation suitable for the IMM effort. 

Two steps and Bayesian updates were performed. The first step 

used the general population data (Ref. 37) as a prior to update 

the LSAH preflight data (Ref. 36, personal communication).

This step was performed three times, once each for males, 

females, and the total. The posterior results from this step 

describe the stroke incidence rates for preflight astronauts. In 

the second step, the data from these posterior results, namely 

the means and the 5th and 95th percentiles, were used as the 

priors to update the in-flight astronaut data for females, males, 

and the total. Ultimately, six probability distributions were 

found describing the stroke incidence rate for preflight and 

in-flight male, female, and total astronauts. Appendix C

provides the code used in WinBUGS, and an outline of the 

input data for each step follows.

Step 1: The stroke incidence per person-year for the general 

U.S. population for females, males, and the total and the EFs 

were used as the priors in WinBUGS to update the LSAH data 

(Table 49) for the number of stroke cases and person-years for 

males, females, and the total. Table 50 provides the posterior 

results from this step.

Step 2: A Bayesian update was performed with the posterior 

results from Step 1—the means and the 5th and 95th percentiles (Table 50) to update the LSAH in-flight astronaut data 

(Table 49). The result was a probability distribution for the 

stroke incidence rate in in-flight astronauts (Table 51).

TABLE 50.—RESULTS OF BAYESIAN ANALYSIS FOR 

STROKE IN PREFLIGHT MISSION-READY, ACTIVE 

MALE, FEMALE, AND TOTAL ASTRONAUTS

Stroke incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 9.81×10–4 6.80×10–4 8.78×10–4

Standard deviation 2.42×10–4 2.41×10–4 1.17×10–4

5 percent 6.37×10–4 3.64×10–4 6.99×10–4

Median 9.54×10–4 6.42×10–4 8.70×10–4

95 percent 1.4×10–3 1.1×10–3 1.1×10–3

TABLE 51.—RESULTS OF BAYESIAN ANALYSIS FOR 

STROKE IN IN-FLIGHT MALE, FEMALE, 

AND TOTAL ASTRONAUTS

Stroke incidence rate, λastronaut, events per person-year

Statistic Males Females Total

Mean 9.80×10–4 6.80×10–4 8.77×10–4

Standard deviation 2.38×10–4 2.36×10–4 1.22×10–4

5 percent 6.41×10–4 3.71×10–4 6.93×10–4

Median 9.52×10–4 6.42×10–4 8.69×10–4

95 percent 1.4×10–3 1.1×10–3 1.1×10–3

2.12.3 Discussion

This analysis is limited in that it assumes an average incidence rate of stroke, with little data regarding stroke type or

environmental conditions. Also, because the data for blacks in

the general population were considered to be unreliable, this 

analysis only considered data from white males and females 

from the general population. These results should be used with

a full understanding of these limitations. However, they are

reasonable representations of the incidence rate of stroke 

given the data available and the assumptions made when the 

estimate was constructed. 

More accurate estimates could be made with further analysis of stroke incidence in post-flight astronauts and the 

physiological data that pertain to stroke occurrence. If more 

reliable data for the general U.S. population (specifically for 

different ethnicities) becomes available in the future, this 

analysis should be updated with that data. The current data 

will serve as the baseline for future estimates. 

3.0 Discussion

Tables 52 and 53 summarize the results of the Bayesian 

analyses for all medical events in preflight and in-flight 

astronauts. 

A review of the data for various medical events demonstrates limitations that are common to all events. The analysis 

of each medical condition assumes an average incidence rate 

despite environmental effects and contributing physiological 

factors. There are certainly discrepancies between the general 

U.S. population, the U.S. Submarine Force, the analog 

astronaut population at the NASA Johnson Space Center, and 

the astronaut corps. The data reported in the literature for the 

various medical events has inherent uncertainty and reliability 

problems depending on the manner in which the study or 

survey was conducted.

There are a host of factors that could improve the IMM 

team’s ability to make more accurate estimates of the incidence rates, including incorporating biomedical parameters 

into the model and having access to more precise data (in the 

astronaut corps and in the general U.S. and submarine populations) related to age, ethnicity, gender, previous medical 

conditions, existing lifestyle choices, and so on. Having age-, 

ethnicity-, and gender-specific CI would greatly improve the 

calculation of the total incidence rates. However, given that 

these Bayesian analyses were performed to support the IMM 

by providing input source data, the intrinsic nature of this 

probabilistic model and its associated sensitivity analyses of 

output data will also guide the need for future updates. As 

components of IMM source input data, the incidence rate data 

described herein will be subject to periodic review to ensure 

that they are current and relevant as described in the IMM 

Configuration Management Plan (Ref. 38).
NASA/TP—2012-217120 22

TABLE 52.—RESULTS OF BAYESIAN ANALYSIS FOR ALL 

MEDICAL EVENTS IN PREFLIGHT MISSION-READY, 

ACTIVE MALE, FEMALE, AND TOTAL ASTRONAUTS

Medical event incidence rate, λastronaut, events per year

Statistic Males Females Total

Angina pectoris

Mean 3.96×10–4 3.65×10–4 N/A

Standard deviation 9.38×10–5 1.53×10–4 N/A

Appendicitis

Mean N/A N/A 9.35×10–4

Standard deviation N/A N/A 1.04×10–4

Atrial fibrillation (AF)

Mean 6.29×10–4 2.02×10–4 4.43×10–4

Standard deviation 1.51×10–4 1.46×10–4 9.39×10–5

Atrial flutter (AFL)

Mean 7.05×10–5 2.43×10–5 4.77×10–5

Standard deviation 6.71×10–6 2.45×10–6 3.04×10–6

Dental abscess

Mean 8.26×10–3 N/A N/A

Standard deviation 1.80×10–3 N/A N/A

Dental caries

Mean 9.42×10–3 N/A N/A

Standard deviation 5.94×10–4 N/A N/A

Dental periodontal disease

Mean 1.10×10–1 N/A N/A

Standard deviation 1.52×10–2 N/A N/A

Gallstone disease

Mean 7.69×10–4 1.27×10–3 1.02×10–3

Standard deviation 4.65×10–6 7.64×10–6 6.12×10–6

Herpes zoster (HZ)

Mean 2.50×10–3 3.23×10–3 2.90×10–3

Standard deviation 1.31×10–4 1.33×10–4 6.91×10–5

Renal stones

Mean N/A N/A 3.97×10–3

Standard deviation N/A N/A 4.58×10–4

Seizure

Mean N/A N/A 2.68×10-4

Standard deviation N/A N/A 2.84×10-5

Stroke

Mean 9.81×10–4 6.80×10–4 8.78×10–4

Standard deviation 2.42×10–4 2.41×10–4 1.17×10–4

Glenn Research Center

National Aeronautics and Space Administration

Cleveland, Ohio, June 18, 2012

TABLE 53.—RESULTS OF BAYESIAN ANALYSIS FOR ALL 

MEDICAL EVENTS IN IN-FLIGHT MALE, FEMALE, 

AND TOTAL ASTRONAUTS

Medical event incidence rate, λastronaut, events per year

Statistic Males Females Total

Angina pectoris

Mean 3.95×10–4 3.64×10–4 N/A

Standard deviation 9.21×10–5 1.53×10–4 N/A

Appendicitis

Mean N/A N/A 9.34×10–4

Standard deviation N/A N/A 1.03×10–4

Atrial fibrillation (AF)

Mean 6.28×10–4 2.02×10–4 4.42×10–4

Standard deviation 1.52×10–4 9.99×10–6 9.36×10–5

Atrial flutter (AFL)

Mean 7.05×10–5 2.43×10–5 4.77×10–5

Standard deviation 6.74×10–6 2.42×10–6 3.04×10–6

Dental abscess

Mean 8.16×10–3 N/A N/A

Standard deviation 1.80×10–3 N/A N/A

Dental caries

Mean 9.41×10–3 N/A N/A

Standard deviation 5.95×10–4 N/A N/A

Dental periodontal disease

Mean 1.03×10–1 N/A N/A

Standard deviation 1.41×10–2 N/A N/A

Gallstone disease

Mean 7.69×10–4 1.27×10–3 1.02×10–3

Standard deviation 4.65×10–6 7.68×10–6 6.18×10–6

Herpes zoster (HZ)

Mean 2.51×10–3 3.23×10–3 2.90×10–3

Standard deviation 1.31×10–4 1.30×10–4 7.04×10–5

Renal stones

Mean N/A N/A 3.96×10–3

Standard deviation N/A N/A 4.60×10–4

Seizure

Mean N/A N/A 2.70×10-4

Standard deviation N/A N/A 2.88×10-5

Stroke

Mean 9.80×10–4 6.80×10–4 8.77×10–4

Standard deviation 2.38×10–4 2.36×10–4 1.22×10–4
NASA/TP—2012-217120 23

Appendix A.—Data from Lifetime Surveillance of Astronaut Health (LSAH)

Table 54 shows the data that were supplied by LSAH.

TABLE 54.—LIFETIME SURVEILLANCE OF ASTRONAUT HEALTH (LSAH) DATA

Preflight astronauts In-flight astronauts

Statistic Males Females Statistic Males Females

Angina pectoris

Total person-days 719 196 96 669 Total person-days 11 680 2372.5

Total person-years 1970.4 264.8 Total person-years 32.0 6.5

Angina cases 0 0 Angina cases 0 0 

Appendicitis

Total person-days 510 875 89 019 Total person-days 11 643.5 2336

Total person-years 1399.7 243.9 Total person-years 31.9 6.4

Appendicitis cases 2 0 Appendicitis cases 0 0 

Atrial fibrillation (AF)

Total person-days 2 373 481 122 915 Total person-days 11 607 2372.5

Total person-years 6502.7 336.8 Total person-years 31.8 6.5

AF cases 4 0 AF cases 0 0 

Atrial flutter (AFL)

Total person-days 2 373 481 122 915 Total person-days 11 607 2372.5

Total person-years 6502.7 336.8 Total person-years 31.8 6.5

AFL cases 0 0 AFL cases 0 0 

All dental problems studied

Total person-days 173 450.6 43 855.2 Total person-days 11 643.5 2336

Total person-years 475.2 120.2 Total person-years 31.9 6.4

Caries cases 168 24 Caries cases 0 0 

Abscess cases 19 1 Abscess cases 0 0 

Periodontal disease cases 56 9 Periodontal disease cases 0 0 

Gallstone disease

Total person-days 719 196 96 669 Total person-days 11 680 2372.5

Total person-years 1970.4 264.8 Total person-years 32.0 6.5

Gallstone cases 3 0 Gallstone cases 0 0 

Herpes zoster (HZ)

Total person-days 724 861 99 684 Total person-days 11 862.5 2372.5

Total person-years 1985.9 273.1 Total person-years 32.5 6.5

HZ cases 8 0 HZ cases 1 0 

Renal stonesa

Total person-days N/A N/A Total person-days 9161.5

Total person-years N/A N/A Total person-years 25.1

Renal stone cases N/A N/A Renal stone cases 0 

Seizure

Total person-days 719 196 96 669 Total person-days 11 680 2372.5

Total person-years 1970.4 264.8 Total person-years 32.0 6.5

Seizure cases 0 0 Seizure cases 0 0 

Stroke

Total person-days 1 269 681 12 2915 Total person-days 11 607 2372.5

Total person-years 3478.6 336.8 Total person-years 31.8 6.5

Stroke cases 2 0 Stroke cases 0 0 a

Totals only—no breakdown by males and females.

NASA/TP—2012-217120 25

Appendix B.—Calculating Error Factor From 95-Percent Confidence Intervals

For general population data to be applicable to these 

Bayesian updates, the error factor (EF) for each data set had to

be found. Although no data in this study gave the EF, some 

data gave the standard deviation, leading to an easy conversion to the EF. However, many times the standard deviation 

was not given, so the EF had to be calculated using the 

95-percent confidence interval (CI). The general steps involved converting the 95-percent CI into a 90-percent CI. 

From the 90-percent CI, the 95th and 5th percentiles were

found and then used in a simple equation to calculate the EF. 

The specific calculation steps for each medical event varied. 

These steps are shown in Sections B.1 to B.7. 

B.1 Angina Pectoris

The following steps were used to obtain the EF for the 

angina data: 

(1) The 95-percent CI width was used to find the standard 

deviation σ from Equation (B1) from Lapin’s book 

(Ref. 39):

( ) 95%

2

n width

zα

σ =

(B1)

where zα/2 is 1.96 for the 95-percent CI, n is the number 

of participants, and width95% is 1.2 for males and 0.55 

for females.

(2) Next, Equation (B1) and σ were used to find the 

90-percent CI width:

2 z n α

σ ×

= width90% (B2)

where zα/2 = 1.64 for the 90-percent CI. The 90-percent 

CI width was calculated as 1.00 for males and 0.46 for 

females.

(3) Then, the 95th percentile was found by adding the 

90-percent CI width to the mean, and the 5th percentile 

was found by subtracting the 90-percent CI width from 

the mean.

The 95th percentile was calculated as 5.80 for males 

and 1.56 for females. The 5th percentile was calculated 

as 3.80 for males and 0.64 for females.

(4) Finally Equation (B3) was used to find EF: 

95th

5th

EF =

(B3)

EF was calculated as 1.24 for males and 1.56 for 

females.

B.2 Atrial Fibrillation

The following steps were used to obtain the EF for atrial 

fibrillation (AF) data:

(1) The 95-percent CI width was used to find σ from 

Equation (B1), where zα/2 is 1.96 and width95% is 0.32 

for males, 0.2 for females, and 0.18 for the total.

Next Equation (B1) and σ were used to find the 

90-percent CI width—resulting in Equation (B2),

where zα/2 = 1.64 for the 90-percent CI. 

(2) Then, the 95th percentile was found by adding the 

90-percent CI width to the mean, and the 5th percentile 

was found by subtracting the 90-percent CI width from 

the mean.

(3) Finally, Equation (B3) was used to find EF.

B.3 Atrial Flutter

With the atrial flutter (AFL) data, additional steps had to be 

taken prior to converting the 95-percent CI into the 90-percent

CI. The CIs were too wide to be applied directly to the rates of 

AFL for adults under 50 years of age because doing so would 

have created negative values for the 5th and 2.5th percentile. 

A proportion was set up to counter this problem. The proportion was between the number of cases for adults under

50 years of age and the number of cases for all ages. It was set 

equal to the proportion of the unknown 95-percent CI width x

for adults under 50 years of age and the known 95-percent CI 

width for all ages. An example of the calculation for the 

95-percent CI for men under 50 years of age follows:

AFL cases in men under 50 years

AFL cases in all men

95% CI width for men under 50 years

95% CI width for all men =

6 AFL cases

112 AFL cases 0.24

x =

(B4)

x = ±0.011

This assumption of proportional 95-percent CI was applied to 

the women and total adults under 50 years of age as well. The

three calculated 95-percent CIs for adults under 50 years of 

age follow: 

Men: ±0.013-percent cases per 100 000 person-years

Women: ±0.004-percent cases per 100 000 person-years

Total: ±0.006-percent cases per 100 000 person-years
NASA/TP—2012-217120 26

Because the journal article used (Ref. 13) did not include 

the number of participants for each age group and gender, 

Equation (B1), which was used to find the 90-percent CI for 

the AF data, could not be used directly to find the 90-percent

CI for the AFL data. However, because σ and n remain 

constant for the 90- and 95-percent CIs, they can be canceled 

out, leaving Equation (B5): 

( ) 1.64 90% CI 95% CI

1.96 =

(B5)

The 95th and 5th percentiles and the EF for AF were found 

with following the steps. More specifically, Steps 3 and 4 for 

determining the EF from the AF section were used. 

B.4 Dental Events (Abscess, Caries, and 

Periodontal Disease) 

The following steps were used to obtain the EF for the 

dental data:

(1) The 95-percent CI width was used to find σ from 

Equation (B1), where zα/2 is 1.96 for the 95-percent CI 

and width95% is 1.6 for abscess, 0.615 for caries, and 

1.93 for periodontal disease. 

(2) Next, Equation (B1) and σ were used to find the 

90-percent CI width—resulting in Equation (B2),

where zα/2 = 1.64 for the 90-percent CI. 

The 90-percent CI width was calculated as 1.3 for 

abscess, 0.51 for caries, and 1.61 for periodontal disease. 

(3) Then, the 95th percentile was found by adding the 

90-percent CI width to the mean, and the 5th percentile 

was found by subtracting the 90-percent CI width from 

the mean.

The 95th percentile was calculated as 4.80 for abscess, 

5.41 for caries, and 3.31 for periodontal disease. The 

5th percentile was calculated as 2.20 for abscess, 4.39 

for caries, and 0.09 for periodontal disease.

(4) Finally, Equation (B3) was used to find EF. 

EF was calculated as 1.48 for abscess, 1.11 for caries, 

and 6.24 for periodontal disease.

B.5 Gallstone Disease 

The following steps were used to obtain the EF for the 

gallstone data:

(1) The 95-percent CI was used to determine the standard 

error SE from a modified form of Lapin’s equation 

(Ref. 39): 

95%

2

width SE zα

= (B6)

where SE n = σ and zα/2 =1.96 for the 95-percent 

CI.

(2) The standard error was used to compute the 95th and 

5th percentiles according to the following definition: 

95th percentile = mean + zα/2 (SE) 

5th percentile = mean + zα/2 (SE)

where zα/2 = 1.64 for the 90-percent CI.

(3) Then, the EF was computed with Equation (B3).

B.6 Herpes Zoster

The following steps were used to obtain the EF for the 

herpes data:

(1) The 95-percent CI was converted to the 90-percent CI 

using Equation (B7) from Lapin (Ref. 39, p. 311): 

z 2 width n α

σ × =

(B7)

where zα/2 is 1.96 for the 95-percent CI and 1.64 for the 

90-percent CI. 

(2) Next, the 5th and 95th percentiles were found from the 

90-percent CI. The 95th percentile was found by adding 

the 90-percent CI width to the mean, and the 5th percentile was found by subtracting the 90-percent CI from 

the mean.

(3) Finally, the EF was found from Equation (B3). 

Because Reference 26 did not include the number of participants or the standard deviation for each age group and gender, 

Equation (B7) could not be used directly. Entering the 

variables for the 95- and 90-percent CIs into the formula 

resulted in Equation (B8): 

95% 90%CI 95% : width 1.96 90% : width

1.64

CI CI

n

n

  σ =    

σ =

(B8)

Because σ and n were constant for both CIs, they could be 

canceled out and substitution could be performed to yield

Equation (B9):

( ) 1.64 90% 95%

1.96

CI = CI

(B9)
NASA/TP—2012-217120 27

B.7 Seizure

The following steps were used with the data from Hauser, 

Annegers, and Kurland (Ref. 33 and Table 55) to obtain the 

EF for the seizure data.

TABLE 55.—SEIZURE INCIDENCE OVER 10-YEAR PERIODS 

PER 100 000 PERSON-YEARS IN THE GENERAL POPULATION 

OF ROCHESTER, MINNESOTA, AGED 40 TO 54 YEARS 

Age Years that data were collected

1935 to 

1944

1945 to 

1954

1955 to 

1964

1965 to 

1974

1975 to 

1984

40 to 44 12 32 42 19 26

45 to 49 7 35 29 20 23

50 to 54 26 31 49 18 32

The mean seizure incidence (total) per 100 000 people was 

26.73, and the standard deviation was 10.95.

A 90-percent CI was constructed as follows: 

0.90 = P (–z ≤ Z ≤ z) (B10) 

x z

n

− μ =   σ     (B11) 

( ) 1 1 1 0.95 1.645

2 z − −   α =Φ − =Φ =     (B12) 

where P is probability, z is the normal deviate of the stated 

percentile, μ is the true mean, and Φ is the cumulative density 

function. For significance level α = 0.10, sample mean x = 

26.73, standard deviation σ = 10.95, and number of samples n

= 15,

0.90 = P (22.08 ≤ μ ≤ 31.38) (B13) 

Thus, the EF was found by 

95% 31.38 1.19

5% 22.08

EF = = =

(B14) 

NASA/TP—2012-217120 29

Appendix C.—Bayesian Inference Using Gibbs 

Sampling (WinBUGS) Procedure and Code

C.1 WinBUGS Procedure

To estimate of the probability of a certain medical event, 

open WinBUGS and create a new document. Type the 

WinBUGS script for the medical event of interest (see 

Section C.2). Next, open the Specification Tool under the 

Model tab. Highlight “model” in the code and click “check 

model” in the Specification Tool. WinBUGS will respond 

with “model is syntactically correct” in the status bar. If the 

model is not syntactically correct, follow the prompts given 

by WinBUGS in the status bar to modify the code. After the 

model is checked, load the data by highlighting “list” in the 

code and click “load data.” WinBUGS will respond “data 

loaded.” Click “compile,” and WinBUGS will respond 

“model compiled.” Click “gen inits,” and WinBUGS will 

respond “initial values generated, model initialized.” Now 

open the Sample Monitor Tool under the Inference tab. Type 

“lambda” into the drop-down box labeled “node,” click 

“set,” and then select. Type “1001” into the box labeled 

“beg” and highlight “5,” “median,” and “95” under “percentiles.” Now open the Update Tool under the Model tab. In 

the “updates” box, type “75000” and click “update.” When 

the model has completed its iterations, the results of the 

update may be viewed by returning to the Sample Monitor 

Tool, selecting “lambda” under node, and clicking the “stats” 

button. The lognormal Poisson distribution that was constructed may be viewed by clicking the “density" button on 

the Sample Monitor Tool. 

C.2 WinBUGS Code

C.2.1 Angina

Males

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.00063, EF= 1.77, events= 6, time= 22137.0) 

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.000415, EF=1.48, events= 0, time= 1970.4) 

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.000396, EF=1.46, events= 0, time= 32.0) 

Females

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.00047, EF= 2.08, events= 0, time= 2808.6) 

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.000372, EF=1.94, events= 0, time= 264.8) 

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.000365, EF=1.94, events= 0, time= 6.5) 

C.2.2 Appendicitis

Total

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.000930, EF= 1.2, events= 2, time= 1644)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.000935, EF=1.198, events= 0, time= 38.3)
NASA/TP—2012-217120 30

C.2.3 Atrial Fibrillation

Males

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=4, time=6502.7, mean=0.000640, EF=1.56)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=0, time=31.8, mean=0.000629, super=0.000902, 

sub=0.000412)

Females

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=336.8, mean=0.000210, EF=2.97)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=0, time=6.5, mean=0.000202, super=0.000476, 

sub=0.000560)

Total

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=4, time=6839.4, mean=0.000425, EF=1.45)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=0, time=38.3, mean=0.000443, super=0.000611, 

sub=0.000306)

C.2.4 Atrial Flutter

Males

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=6502.7, mean=0.0000707, EF=1.17)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=0, time=31.8, mean=0.0000705, super=0.0000821, 

sub=0.0000600)

Females

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=336.8, mean=0.0000243, EF=1.18)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=0, time=6.5, mean=0.0000243, super=0.0000285, 

sub=0.0000205)
NASA/TP—2012-217120 31

Total

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=6839.4, mean=0.0000479, EF=1.11)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=0, time=38.3, mean=0.0000477, super=0.0000529, 

sub=0.0000429)

C.2.5 Dental Abscess

model { events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=19, time=475.2, mean=0.00353, EF=1.48)

model { events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=31.9, mean=0.00826, EF=1.43)

C.2.6 Dental Caries

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=168, time=475.2, mean=0.00488, EF=1.11)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=31.9, mean=0.00942, EF=1.11)

C.2.7 Dental Periodontal Disease

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=56, time=475.2, mean=0.00168, EF=6.24)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=31.9, mean=0.110, EF=1.26)

C.2.8 Gallstone Disease

Males

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=3, time=1970.4, mean=0.000769, EF=1.01)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=32.0, mean=0.0007691, EF=1.01)

Females

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=264.8, mean=0.001266, EF=1.01)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=6.5, mean=0.001266, EF=1.01)
NASA/TP—2012-217120 32

Total

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

time <- menpreflight + womenpreflight}

list(events=3, menpreflight=1970.4, womenpreflight = 264.8, 

mean=0.001017, EF=1.01)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

time <- meninflight + womeninflight}

list(events=0, meninflight=32.0, womeninflight = 6.5, 

mean=0.001017, EF=1.01) 

C.2.9 Herpes Zoster

Males

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=8, time=1985.9, mean=0.0025, EF=1.09)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=1, time=32.5, mean=0.00250, super=0.00272, 

sub=0.00229)

Females

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=273.1, mean=0.0032, EF=1.07)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=0, time=6.5, mean=0.00323, super=0.00345, 

sub=0.00302) 

Total

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=8, time=2259.0, mean=0.0029, EF=1.04)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2)

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2

EF <- pow(div, 1/2)

div <- super/sub}

list(events=1, time=39.0, mean=0.00290, super=0.00301, 

sub=0.00278)

C.2.10 Renal Stones

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=74, time=17740.8, mean=0.0018, EF=2.236)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

EF <- pow(x,1/2)

x <- p95/p5

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.00397, p95= 0.00474, p5= 0.00324, events= 0, 

time= 25.1)
NASA/TP—2012-217120 33

C.2.11 Seizure

Total

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.00027, EF= 1.19, events= 0, time= 2235.2)

model {events ~ dpois(mean.poisson)

mean.poisson <- lambda*time

lambda ~ dlnorm(mu, tau)

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(mean= 0.00027, EF=1.19, events= 0, time= 38.6)

C.2.12 Stroke

Males

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time 

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=2, time=3478.6, mean=0.00110, EF=1.567)

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time 

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=31.8, mean=0.000981, EF=1.482)

Females

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time 

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=336.8, mean=0.000700, EF=1.773)

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time 

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=6.5, mean=0.000680, EF=1.739)

Total

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time 

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=2, time=3815.3, mean=0.000900, EF=1.254)

model {events ~ dpois(mean.poisson) 

mean.poisson <- lambda*time 

lambda ~ dlnorm(mu, tau) 

tau <- 1/pow(sigma, 2) 

sigma <- log(EF)/1.645

mu <- log(mean) - pow(sigma, 2)/2}

list(events=0, time=38.3, mean=0.000878, EF=1.254)

NASA/TP—2012-217120 35

Appendix D.—Statistical Combination of Independent Distributions

Although the objective of the current study is to obtain 

estimates of incidence rate for various medical events in 

astronauts, these rates are not always available for the events 

under investigation. Instead, rates may be available for more 

specific complications or diseases, which must then be 

combined in a statistically correct fashion to provide an 

estimate of the total incidence of the disease category under 

study. In the current study, the analysis of gallstone disease 

serves as a primary example. Urbach et al. (Ref. 25) provided 

incidence data stratified by age and gender for three different 

gallstone-related conditions: namely, acute cholecystitis, acute 

biliary pancreatitis, and acute cholangitis. For an estimate of 

total gallstone disease incidence in the general population to 

be obtained, these incidence rates—and their associated 

uncertainties—needed to be combined in a statistically 

accurate fashion. The method in which this was accomplished 

is presented in this appendix. 

Combination of individual disease incidence rates depends 

on an assumption of independence. This assumption allows 

the uncertainties of the incidences to be combined in a fashion 

dictated by the rules of probability. As noted in the following 

discussion, the variance of the scaled sum of two independent 

distributions is simply the sum of their variances, multiplied 

by the square of the scaling factor: 

Let X and Y be two independent random variables, and let 

Z = a(X + Y):

( ) 2 22 2

z xy σ = σ +σ a (D1)

Accordingly, the following relationship holds for the 

standard deviation of the combined distribution:

2 2

z xy σ = σ +σ a

(D2)

This relation was applied to the data available for the various gallstone conditions in order to determine the combined 

incidence of general gallstone disease. The raw data presented 

in Reference 25 provided separate incidence rates for three 

different gallstone conditions and for three discrete age 

groups: 18 to 44, 45 to 64, and ≥65. Because the present study 

required an estimate of total gallstone disease incidence in the 

astronaut-like age range, 18 to 64, six separate distributions 

had to be combined in this manner for males and females in 

the three ranges. 

Assumptions were made in the interpretation of the incidence rates presented in Reference 25 to leverage Equation 

(D2) in combining the uncertainties of independent distributions. (1) The incidence of a given condition in a particular 

age group was assumed to be independent of the incidence of 

the same condition in other age groups. (2) The incidence of a 

particular condition was assumed to be independent of the 

incidence of the other two conditions. (3) The incidence in 

males was assumed to be independent of the incidence in 

females.

Reference 25 provided the annual incidence per 100 000 

persons for each category, as well as a 95-percent CI for this 

value. The standard error of each incidence rate was determined as follows: 

95% CI – (mean – 1.96 • SE, mean + 1.96 • SE) 

95% upper limit 95% lower limit

3.92

CI CI SE − ∴ = (D3)

The standard error of the mean SE is the standard deviation 

of the sample mean of a population distribution. Therefore, the 

standard error can be used in the same fashion as the standard 

deviation σ is used in Equation (D2) to properly account for 

uncertainty when independent incidence rates are combined. 

It was assumed that age groups were independent from each 

other, so an incidence rate λ for ages 18 to 64 was found for 

each specific condition by averaging the λ provided for ages

18 to 44 and 45 to 64. The standard error for the new combined distribution was determined from Equations (D2) and 

(D3): 

18 to 64 18 to 44 45 to 64 ( ) 1

2 λ = λ +λ

(D4) 

2 2

18 to 64 18 to 44 45 to 64

1

2 ∴= + SE SE SE

This process was used for all three gallbladder conditions 

for data for both males and females to determine an incidence 

rate for each condition. These three conditions were then 

combined in a simple additive fashion, again with the assumption of the independence of incidence and applying the 

formula for determining combined standard error:

λ = λ +λ +λ total 1 2 3 ( )

(D5)

222

total 1 2 3 ∴ = ++ SE SE SE SE

This process was applied to incidence data for both males 

and females, yielding values of the total gallstone disease 

incidence. The total incidence rate was determined by averaging the incidence rates for males and females, again combining the standard errors with the same procedure used to 

average the age-specific incidence rates. 

NASA/TP—2012-217120 37

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Bayesian Analysis for Risk Assessment of Selected Medical Events in Support of the 

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14. ABSTRACT

The Exploration Medical Capability project is creating a catalog of risk assessments using the Integrated Medical Model (IMM). The IMM 

is a software-based system intended to assist mission planners in preparing for spaceflight missions by helping them to make informed 

decisions about medical preparations and supplies needed for combating and treating various medical events using Probabilistic Risk 

Assessment. The objective is to use statistical analyses to inform the IMM decision tool with estimated probabilities of medical events 

occurring during an exploration mission. Because data regarding astronaut health are limited, Bayesian statistical analysis is used. Bayesian 

inference combines prior knowledge, such as data from the general U.S. population, the U.S. Submarine Force, or the analog astronaut 

population located at the NASA Johnson Space Center, with observed data for the medical condition of interest. The posterior results reflect 

the best evidence for specific medical events occurring in flight. Bayes’ theorem provides a formal mechanism for combining available 

observed data with data from similar studies to support the quantification process. The IMM team performed Bayesian updates on the 

following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, 

gallstone disease, herpes zoster, renal stones, seizure, and stroke.

15. SUBJECT TERMS

Risk; Probability theory; Mission planning; Life sciences; Bayes theorem; Astronaut health; Space flight; Diseases 

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