bluuebunny/crossref_metadata_2025 huggingface dataset:
Use of backcalculation for estimation of the probability of progression from hiv infection to aids
Authors: Marion Stephen A. , Schechter Martin T.
Published: April 2007

Backcalculation has been used to estimate the rate of past HIV infection and to predict future AIDS incidence. In this study we examine another use: estimating the probability of progression from HIV infection to AIDS as a function of time from infection. Given observed AIDS incidence data, the technique of backcalculation estimates the most likely number of persons infected with HIV in the past. Assumptions about probability of progression from HIV infection to AIDS are necessary. By varying these assumptions and examining the resulting goodness of fit to the AIDS incidence data, we can theoretically estimate parameters of progression. We report on implementation of this method and examine its practical utility in deciding among four competing progression models specified on a priori grounds. The four specific models comprise three Weibull distributions with medians of 8, 10, and 12 years, respectively, and one model that beings as a Weibull with 8 year median but where the hazard is level after 3.5 years. To employ asymptotic maximum likelihood methods, we define a two parameter family of progression models that includes all four a priori models. One parameter sets the scale for an initial Weibull progression (the shape parameter being fixed for all models), and the other specifies a levelling point after which the hazard remains constant.

AIDS incidence data from Canada's national surveillance system provided the empiric data for this evaluation. First we corrected these data for reporting delay by Poisson modelling of the delay distribution. We used three parametric families of infection curves: step‐function, log‐logistic, and logistic.

The results support the hypothesis of an early levelling of the hazard function. When we fixed the scale parameter to that of the Weibull curve with 8 year median, the maximum likelihood estimate of the levelling point was 2.7 years, and a clearly superior fit was produced compared to a pure Weibull progression with the same scale parameter (likelihood ratio chi‐square of 10.6 on 1 degree of freedom, p = 0.001). The maximum was indistinguishable in fit from the levelling point of 3.5 years hypothesized in advance (chi‐square = 0.30, d.f. = 1, p = 0.58). Backcalculation, however, could not determine the Weibull scale parameter itself because the likelihood was quite flat as a function of this parameter. We conclude that one must determine the parameters governing the initial shape of the hazard function from other kinds of data.

We interpret the model with levelling of the hazard as an empirical description of progression in a real population rather than as natural history in a homogeneous population. We make comparisons with other recently proposed models of progression.
Using orthogonal polynomial scores in summarizing and evaluating longitudinal data collected in phase I and II clinical pharmacology studies
Authors: Bradstreet Thomas E.
Published: April 2007

Orthogonal polynomial scores (OPS) is a simple, biologically meaningful approach to characterize longitudinal data in phase I and II clinical pharmacology trials. It describes average, linear, quadratic and higher order polynomial characteristics of each subject's response over time with use of composite scores computed from linear combinations of the observed data. The statistical evaluation of the composite scores is univariate. For studies with a small number of experimental units and with many repeated measures, OPS may offer advantages over the use of summary measures such as the maximum response (MAX), the time at which MAX occurred (TMAX), or the area under the response curve (AUC), and other popular approaches such as time‐point‐by‐time‐point, split‐plot, and multivariate analyses.
Two‐stage tests for studying monotherapy and combination therapy in two‐by‐two factorial trials
Authors: Hung H. M. James
Published: April 2007

Two‐stage testing involves a preliminary test of a nuisance parameter prior to testing main hypothesis. In a two‐by‐two factorial trial, the treatment interaction is the nuisance to the inference about the efficacy of one of the treatments given alone. In comparing a combination therapy to both of its component therapies, the nuisance parameter is the difference in the component effects. When the preliminary test is an integral part of inference about the main parameter, the actual level of significance for the two‐stage test procedure can be much higher than the desired nominal level. If one places no restriction on the value of the nuisance parameter, then any two‐stage test with its significance level properly controlled has undesirable properties. This applies to comparative studies of combination agents relative to the component agents. When the interaction with an ineffective treatment is null, two‐stage testing may have some power advantage for assessing monotherapy efficacy.
Markov chain modelling of bioassay toxicity procedures
Authors: Hadjinicola George , Goldstein Larry
Published: April 2007

Many bioassay procedures to test a new substance for toxicity, like some phase I clinical trials, can be modelled as first‐order Markov chains with absorbing states. We provide a general framework for such procedures. We show how one may calculate under any dose response curve assumption final absorption probabilities, and a number of total average costs such as time required until trial completion, number of subjects treated, number of subjects exhibiting unaceptable levels of toxicity, and amount of medication administered. One may use the above information associated with the trial for an a priori comparison between competing designs under consideration. We provide an example of such a comparison.
Confidence limits based on the first occurrence of an event
Authors: George Varghese T. , Elston Robert C.
Published: April 2007

Confidence limits for population prevalence based on the first occurrence of an item in a medical database, or for incidence based on time to first occurrence, should be based on the geometric or exponential distributions, respectively. These intervals are presented and compared with the corresponding intervals based on the binomial and Poisson distributions. The lower confidence limits are shown to be the same, but the upper limits are smaller, hence leading to shorter intervals. Applications of these intervals are also presented.
Sample size and power for prospective analysis of relative risk
Authors: Blackwelder William C.
Published: April 2007

In a placebo‐controlled vaccine efficacy trial of a trial of equivalence of vaccines, one may wish to show that relative risk of disease is less than a specified value R0, not equal to one. This paper compares three methods for estimating relative risk in the binomial setting, based on a logarithmic transformation, likelihood scores, and a Poisson approximation. Exact power and size of test are calculated by enumeration of possible binomial outcomes, and power is approximated from asymptotic formulations. Although the score method is generally preferable, for most studies of practical interest the log and score methods are comparable, and the Poisson method is also appropriate for small risks, up to about 0.05. When true and null relative risks are less than one, unequal allocation of study individuals can increase power, and the asymptotic formula for the log method may substantially understimate power; in such a study the power approximation for the score method is more reliable, even if the log method is used in analysis. Exact power calculations are helpful in planning studies. The log and Poisson methods, but not the score method, apply readily in the case of unequal follow‐up.
Methods for epidemiologic analyses of multiple exposures: A review and comparative study of maximum‐likelihood, preliminary‐testing, and empirical‐bayes regression
Authors: Greenland Sander
Published: April 2007

Many epidemiologic investigations are designed to study the effects of multiple exposures. Most of these studies are analysed either by fitting a risk‐regression model with all exposures forced in the model, or by using a preliminary‐testing algorithm, such as stepwise regression, to produce a smaller model. Research indicates that hierarchical modelling methods can outperform these conventional approaches. I here review these methods and compare two hierarchical methods, empirical‐Bayes regression and a variant I call ‘semi‐Bayes’ regression, to full‐model maximum likelihood and to model reduction by preliminary testing. I then present a simulation study of logistic‐regression analysis of weak exposure effects to illustrate the type of accuracy gains one may expect from hierarchical methods. Finally, I compare the performance of the methods in a problem of predicting neonatal mortality rates. Based on the literature to date, I suggest that hierarchical methods should become part of the standard approaches to multiple‐exposure studies.
Kaplan—meier, marginal or conditional probability curves in summarizing competing risks failure time data?
Authors: Pepe Margaret Sullivan , Mori Motomi
Published: April 2007

In the context of competing risks the Kaplan—Meier estimator is often unsuitable for summarizing failure time data. We discuss some alternative descriptive methods including marginal probability and conditional probability estimators. Two‐sample test statistics are also presented.
Sequential monitoring of clinical trials: The role of information and brownian motion
Authors: Lan K. K. Gordon , Zucker David M.
Published: April 2007

Sequential monitoring has been a topic of major interest in clinical trials methodology over the past two decades. This paper presents a unified conceptual framework for sequential monitoring that covers a wide variety of monitoring procedures in a wide variety of clinical trial settings. The central elements of this framework consist of a suitable concept of statistical information and a scheme for using this concept as a basis for summarizing the accumulating results of a trial in a standardized form, through a stochastic process that can be shown to approximate classical Brownian motion. The ideas are developed in a simple step‐by‐step fashion and illustrated by several practical examples.
Conditioned life tables from registries with unidentified random losses
Authors: Tallis G. M. , Leppard P. , O'neill T. J.
Published: April 2007

We identify two types of random loss that may afflict registries which use ‘passive follow‐up’. The effects of these errors on estimates related to survival are examined mathematically and numerically. A procedure for correcting the attendant biases is suggested, and its strengths and limitations are explored.
Power of testing proportions in small two‐sample studies when sample sizes are equal
Authors: Davis Alan B.
Published: April 2007

In planning experiments having two groups of equal but small size, investigators face the uncertainty of power calculations that rely on asymptotic methods. This paper presents a method for determining power for two‐sided tests. I compare two randomization tests, Fisher's exact test (FET), and the mid‐P (MID), with the uncorrected chi‐square test (CHI). Results show power as a function of relative risk for these methods, and assesses their relative power and type I error rates. MID is shown to have intermediate power between CHI, which is the most powerful, and FET, the least powerful. Situations are shown in which CHI and MID occasionally exceed the nominal level of α.
The application of developments in theoretical biostatistics to epidemiologic research
Authors: Obrams G. Iris , Hjortland Marthana
Published: April 2007

Report of a workshop held on 18 July 1991 at the National Institutes of Health in Bethesda, MD. Workshop participants were: William J. Blot, National Cancer Institute, Bethesda, MD; Ronald S. Brookmeyer, Johns Hopkins University, Baltimore, MD; Theodore Colton, Boston University, Boston, MA; Genrose D. Copley, National Cancer Institute, Rockville, MD; Mitchell Gail, National Cancer Institute, Rockville, MD; Nancy L. Geller, National Heart, Lung and Blood Institute, Bethesda, MD; Frank E. Harrell, Jr., Duke University, Durham, NC; Marthana Hjortland, National Cancer Institute, Rockville, MD; Elizabeth Holly, Northern California Cancer Center, Belmont, CA; Michel Ibrahim, University of North Carolina, Chapel Hill, NC; Stephen W. Lagakos, Dana‐Farber Cancer Institute, Boston, MA (written report only); G. Iris Obrams, National Cancer Institute, Rockville, MD; Wasema Rida, National Institute of Allergy and Infectious Diseases, Rockville, MD; Jonathan Samet, New Mexico Tumor Registry, Albuquerque, NM; Robert F. Woolson, University of Iowa, Iowa City, IA; and Mimi C. Yu, University of Southern California, Los Angeles, CA (Chair).
Confidence intervals for a binomial proportion
Authors: Vollset Stein Emil
Published: April 2007

Thirteen methods for computing binomial confidence intervals are compared based on their coverage properties, widths and errors relative to exact limits. The use of the standard textbook method, x/n ± 1.96√[(x/n) (1 − x/n)/n], or its continuity corrected version, is strongly discouraged. A commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p̂ is such that np̂ and n(1 − p̂) both exceed 5 does not ensure adequate accuracy. Score limits are easily calculated from closed from solutions to quadratic equations and can be used at all times. Based on coverage functions, the continuity corrected score method is recommended over exact methods. Its conservative nature should be kept in mind, as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction.
A conditional analysis for two‐treatment multiple‐period crossover designs with binomial or poisson outcomes and subjects who drop out
Authors: McKnight Barbara , Van Den Eeden Stephen K.
Published: April 2007

We propose a conditional analysis for outcome data on numbers of recurrent symptoms arising in a two‐treatment, multiple‐period crossover trial. Conditioning on subject‐specific totals removes any dependence on mean subject‐specific symptom rates and permits the use of standard software to perform regression analysis to examine treatment, period, carryover and interaction effects. The addition of offsets to the regression equations allows the incorporation of data from subjects who do not complete all period in the trial. We apply the proposed method to data from a crossover trial and discuss its advantages and disadvantages.
Marker‐dependent hazard estimation: An application to AIDS
Authors: Fusaro Robert E. , Nielsen Jens P. , Scheike Thomas H.
Published: April 2007

The acquired immunodeficiency syndrome (AIDS) results from infection with the human immunodeficiency virus (HIV). The time of infection is generally unknown since transmission usually occurs during the course of repeated sexual contacts or needle sharing. Brookmeyer and Gail describe the biases that may arise in survival analyses using the recruitment time rather than the unknown infection time as the origin in prevalent cohorts of HIV‐infected individuals. We apply a non‐parametric hazard estimator, introduced by Nielsen, that assumes the hazard of an AIDS diagnosis depends upon the unknown time of infection solely through the value of possibly multidimensional markers of HIV‐disease progression such as CD4+ T lymphocyte cell counts. Essentially, we estimate the hazard for a specific marker value y by dividing the number of occurrences among subjects with marker measurements in a neighbourhood of y by the total risk time in that neighbourhood. We present this estimator, which relies upon kernel estimator techniques to produce a smooth estimate, within a counting process framework. We apply this method to marker data from the San Francisco Men's Health Study.
Pitfalls inherent in retrospective time‐to‐event studies: The example of time to pregnancy
Authors: Weinberg Clarice R. , Baird Donna Day , Rowland Andrew S.
Published: April 2007

Retrospective studies of time from initiation of risk (for example, transfusion of HIV‐infected blood) to the occurrence of an endpoint of interest are useful in epidemiology. One example is studies of time to pregnancy, which have evaluated exposures that may affect human fertility. One can reconstruct the non‐contracepting interval required for each woman's most recent pregnancy and then treat the data as if the couples had been studied prospectively. As we illustrate, however, failure‐time models can be dangerously misleading when there have been trends over calendar time in exposures under study. We propose anad hocmethod for evaluating possible effects on fertility despite this bias, by making use of external data on trends in the exposure over time. This approach applies a prospective model and generates an empiricalp‐value, based on comparing the data‐based estimated exposure coefficient with its null distribution estimated by simulation. A second method maximizes a conditional likelihood, and we show that this is equivalent to logistically modelling the relative odds for the subject's exposure as related to the reported time she required to achieve pregnancy.
Generalized logistic models for low—dose response data
Authors: Devidas Meenakshi , George E. Olusegun , Zelterman Daniel
Published: April 2007

We discuss a generalization of the logistic response function of the form Pr(y = 1|x) = {1 + exp( − θ − β'x)}−α, where α > 0. This function coincides with the usual logistic response when the shape parameter α is equal to one. We describe the use of this model for analysing cancer rates in mice for low‐dose exposure to a known carcinogen. When estimating the low‐dose responses, the errors associated with extrapolation are reduced when a priori knowledge about the rates among unexposed individuals is incorporated into the fitting procedures.
Time‐period effects in longitudinal studies measuring average rates of change
Authors: Roe Denise J. , Korn Edward L.
Published: April 2007

Random time‐period effects are unexplained increases or decreases in the observed value for all individuals measured at a particular time point in a longitudinal study. They can be caused by learning effects, changes in equipment, personnel and overall subject co‐operation. We investigate the consequences of time‐period effects in random coefficient regression models, where interest is in the average rate of change (slope) of a continuous outcome. In a study with a single group of subjects, they can lead to conditionally biased estimates of the mean slope and its variance (conditional on the time‐period effects). Calculations suggest that the increase in sample size required to maintain a specified precision of the mean slope estimate over repeated studies may be substantial. In a study with a concurrent control group, however, time‐period effects do not distort the expectation, estimated variance or the distribution of the difference between the mean slopes. With missing data, in addition to time‐period effects, an unbaised estimate of a single mean slope remains problematic, but one can use standard maximum likelihood techniques to obtain consistent estimators of the difference in mean slopes and its variance. This suggests the importance of a concurrent control group when potential time‐period effects are of concern.
Solving the cluster puzzle: Clues to follow and pitfalls to avoid
Authors: Wartenberg Daniel , Greenberg Michael
Published: April 2007

Dozens of methods have been proposed for the identification of disease clusters, although only a few are used routinely in published investigations. New methods, although designed to exploit some particular aspect of the data or use some specific statistical tool, are rarely compared thoroughly in terms of power or performance. Users, when confronted with the multitude of methods available, often select methods arbitrarily, basing choices on software availability, ease of implementation, or use experience rather than considerations of statistical power, possible alternative hypotheses )that is, cluster structure( and likely confounding. In this review, we extend our typology of disease clustering methods and apply it to many of the extant methods identifying strengths, weaknesses and unique features of the methods. We conclude with recommendations for which methods should be applied to which types of situations.
Disease clusters, maxima, and P‐values
Authors: Grimson Roger C.
Published: April 2007

This paper presents combinatorial )exact( methods that are useful in the analysis of disease cluster data obtained from small environments, such as buildings and neighbourhoods. Maxwell–Boltzmann and Fermi–Dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns )space and/or time( in these environments. The methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring. One of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models.
Assessing directional effects in spatial data
Authors: Oden Neal L.
Published: April 2007

A variable is measured at two locations separated by a given distance. Are the values more similar to each other if the locations are oriented in one direction than another? This question has application to studies of human genetics, epidemics, and acid rain. One obvious analytic approach, regression on latitude and longitude, fails when data are non‐directional )isotropic( but spatially autocorrelated. Moreover, although non‐zero slope implies similarity between neighbours, the converse is not true. IDIFF, a statistic derived from Moran's coefficient of spatial autocorrelation, is developed to detect general directional effects that apply to the collection of data points. Simulations suggest that, when data have isotropic spatial autocorrelation but are incorrectly assumed to be independent, IDIFF will at worst reject too little. IDIFF has good power to distinguish epidemics that spread non‐directionally from those that spread in a favoured direction.
Analysing post‐alarm data in a monitoring system in order to accept or reject the alarm
Authors: Chen R. , Connelly R. R. , Mantel N.
Published: April 2007

In a disease monitoring system embracing several diseases and communities, alarms indicating a significant increase in disease incidence will frequently occur even though the false alarm rate has been set quite low. An approach is presented by which an alarm is determined as either confirmed or rejected according to data observed subsequent to the alarm. The suggested procedure is expected to weed out a substantial proportion )say about 75 per cent( of the false alarms at the expense of some delay in detecting a true alarm.
Properties of Tango's index for detecting clustering in time
Authors: Rayens Mary Kay , Kryscio Richard J.
Published: April 2007

Tango proposed an index for detecting disease clustering in time applicable to grouped data obtained from a population that remains fairly stable over the study period. In this paper, we show that Tango's index is a two‐dimensional U‐statistic having an asymptotic normal distribution. To apply this result in the finite sampling situation, an Edgeworth expansion is used and is shown to be at least as accurate as Tango's best result in approximating the tails of his test statistic under the null hypothesis. This is extended to show that the Edgeworth expansion can be used to approximate the power of Tango's test statistic under selected alternatives to randomness. A power study based on simulations is conducted to compare the power of Tango's index to that of three of its competitors.
Power of the scan statistic for detection of clustering
Authors: Wallenstein Sylvan , Naus Joseph , Glaz Joseph
Published: April 2007

The scan statistic is the maximum number of events in an interval of fixed length w as the subinterval moves over the entire time frame. Previous research derived the null distribution of the scan statistic under the conditional model which assumed that the total number of events was fixed, and under the unconditional model which let the total number of events be a random variable. This paper derives approximations for the power of the scan test for a pulse alternative. Under this alternative, the relative risk of disease on a subinterval )τ, τ + w(, τ unknown, is θ‐fold as high as it is for other subintervals of length w. Two sets of approximations are given for each model. The first approximation gives highly accurate results, but requires use of a personal computer. The second procedure can be performed on a hand‐held calculator and appears very accurate for the cases examined.
Approximations for the tail probabilities and moments of the scan statistic
Authors: Glaz Joseph
Published: April 2007

The scan statistic is used to test the hypothesis that the observed events occur at random )uniformly distributed( in time or space versus the hypothesis that they cluster within a moving window of sizew. To implement the testing procedure based on the scan statistic its tail probabilities have to be effectively evaluated. In this article a survey of results on the approximations of the distribution of the scan statistic and its moments is presented. Numerical results comparing these approximations are also given. Numerous references with applications in epidemiological studies using the scan statistics are mentioned. Related scan statistics that have been used in many other interesting applications are listed in the reference section. The article concludes with the presentation of unsolved problems related to the scan statistic.
Effect of relative risk and cluster configuration on the power of the one‐dimensional scan statistic
Authors: Sahu Sujit K. , Bendel Robert B. , Sison Cristina P.
Published: April 2007

The scan test for clustering in time is based on the maximum number of events in an interval )window( of width w as the window moves across the entire time frame. Power estimates of the scan statistic are simulated for a variety of epidemiologically motivated situations. Two cluster configurations are used: a rectangular pulse, and a triangular pulse designed to emulate environmental contamination. For a rectangular pulse, the relative risk R of disease in the cluster region in R‐fold as high as it is for the background region. The power is strongly influenced by the sample size, the relative risk, and the width or duration of the cluster region, whereas the effect of the cluster configuration is small. Using a 5 per cent significance level, a relative risk of 4, a standardized cluster duration of 0·10, a relative window width of 1·5, and a )non‐random( sample size of 50, the simulated power is approximately 80 per cent, indicating that the minimum sample size in the cluster region for adequate power is in the 12–32 range for values of the parameters used in this study.
The effects of scale on tests for disease clustering
Authors: Waller Lance A. , Turnbull Bruce W.
Published: April 2007

Surveillance of a large geographic region for ‘clusters’ of adverse health events, particularly cancers, often involves searching for raised incidence in the vicinity of prespecified putative sources of hazard. For reasons of practicality or of confidentiality, incidence and population data are usually only available aggregated over subregions or ‘cells’. The performance of statistical procedures designed to detect the presence of clusters can be highly sensitive to the level of aggregation, that is to the choice of partition of the region into the cells. We investigate this sensitivity in the cases of three recently proposed procedures, namely those of Besag and Newell, Stone, and Waller et al. For illustration, we use leukaemia incidence data for 1978–82 in a region of upstate New York, with inactive hazardous waste sites containing trichloroethylene acting as suspected sources.
Assessing spatial patterns in disease rates
Authors: Walter S. D.
Published: April 2007

We describe the empirical performance of three indices of spatial autocorrelation )Moran'sI, Geary'scand a rank adjacency statisticD( in the analysis of regional cancer incidence data. Heterogeneity in regional population sizes and age structure leads to variable precision in estimated rates; the usual methods for assessingI, candD, which ignore such heterogeneity, are shown to be liberally biased, especially forcandD. The power of these indices to detect likely disease patterns is estimated by simulation; the power is quite variable, depending on the exact pattern assumed, althoughItends to have the highest power. The null distributions appear quite robust in small samples, even when several regions have no observed case. Preliminary work on the Ontario cancer registry showed generally unimportant effects on the spatial analysis of variation in case registration rates or missing residence data.
Disease mapping using empirical bayes and bayes methods on mortality statistics in the Netherlands
Authors: Heisterkamp S. H. , Doornbos G. , Gankema M.
Published: April 2007

Data from the 64 public health service districts in the Netherlands, describing the health status of the Dutch population, were used to construct maps for several causes of deaths. The choice and estimation of the relative risk measure is described. The prior expected number of deaths was modelled using a Poisson regression approach based on a model with main effects of district and age. Desirable properties of risk parameters for disease mapping are that they both reflect the level of risk and cope with the instability in the observed measure caused by the numbers at risk in each district. Different techniques for estimation of parameters were applied: empirical Bayes estimation )EB( using a non‐parametric prior and a gamma prior, and a Bayesian approach )B( with a uniform prior. For the parametric EB also a constrained estimator was used. The EB techniques studied in this paper shift or smooth the values of the risk parameter towards a global mean. In the Bayesian method applied here, spatial dependence among districts can be modelled, that is the estimates are smoothed towards a local mean. The three EB estimates gave by and large similar results, although the constrained EB estimate smoothed less, as was expected. The Bayesian estimates smoothed the estimates more or less similarly to the constrained EB.
Aggregation of existing geographic regions to diminish spurious variability of disease rates
Authors: Morris Robert D. , Munasinghe Rajika L.
Published: April 2007

The availability of large data sets together with the growth in power and storage capabilities of computers have made the analysis of the spatial distribution of disease rates an increasingly important tool in public health research. Use of existing geographic divisions or groupings tends to result either in unstable estimates of disease rates if the corresponding populations are small or in loss of spatial resolution if the areas are unnecessarily large. This paper describes a computer algorithm for combining existing geographic areas into regions with populations large enough to diminish spurious variability in disease rates while limiting the loss in resolution. The method is demonstrated using Medicare hospital admissions data for pneumonia and central nervous system cancer. Disease rates were calculated for both predefined regions and those generated by the algorithm and their frequency distributions were compared. The algorithm produces more stable rates over a variety of diseases and provides substantially more flexibility than the use of predefined aggregations.
Synthetic cancer variables and the construction and testing of synthetic risk maps
Authors: Jacquez Geoffrey M. , Kheifets Leeka I.
Published: April 2007

Cancer cluster investigations are usually univariate in nature; they focus on a particular cancer, such as leukaemia, and attempt to determine whether excess risk is associated with a suspected cancer‐causing agent. Although several causes of death )such as leukaemia, lymphoma, Hodgkin's( may be considered, the approach is univariate because the causes of death are analysed sequentially and independently of one another. This approach is consistent with a one‐cause one‐effect model. Rarely, however, is the action of a carcinogen manifested at only one body site, and correlations among causes of death are the norm rather than the exception. A multiple effects model is therefore appropriate, and the multivariate nature of cancer mortality data should be exploited when exploring geographic pattern in cancer risks. This paper describes such an approach. We construct maps based on a principal components analysis of cancer mortality rates from different geographic areas. The resulting principal components are called synthetic cancer variables )SCVs(, and maps of the SCV scores are synthetic risk maps )SRMs(. These maps quantify geographic variation in cancer risk at several body sites simultaneously, and may be analysed for )1( spatial structure and )2( geographic association with potential risk factors. As an example, we use synthetic risk maps to determine whether high‐risk counties in Illinois cluster near nuclear facilities. Much work remains to be done, but synthetic cancer risk maps appear to be a useful tool for quantifying geographic pattern and multivariate structure in cancer mortality.
Mixture models and disease mapping
Authors: Schlattmann Peter , Böhning Dankmar
Published: April 2007

The analysis and recognition of disease clustering in space and its representation on a map is one of the oldest problems in epidemiology. Some traditional methods of constructing such a map are presented. An alternative approach using mixture models to identify population heterogeneity and map construction within an empirical Bayes framework is described. For hepatitis B data from Berlin in 1989, a map is presented and the different methods are evaluated using a parametric bootstrap approach.
Interfacing U.S. census map files with statistical graphics software: Application and use in epidemiology
Authors: Rizzardi M. , Mohr M. S. , Merrill D. W. , Selvin S.
Published: April 2007

In 1990, the United States Bureau of the Census released detailed geographic map files known as TIGER/Line )Topologically Integrated Geographic Encoding and Referencing(. The TIGER files, accessible through purchase or federal repository libraries, contain 24 billion characters of data describing various geographic features including coastlines, hydrography, transportation networks, political boundaries, etc. for the entire United States. Many of these physical features are of potential interest in epidemiological case studies. Unfortunately, the TIGER data base only provides raw alphanumeric data; no utility software, graphical or otherwise, is included. Recently, the S statistical software package has been extended to include a map display function. The map function augments S's high‐level approach towards statistical analysis and graphical display of data. Coupling this statistical software with the map data base developed for U.S. Census data collection will facilitate epidemiological research. We discuss the technical background necessary to utilize the TIGER data base for mapping with S. Two types of S maps, segment‐based and polygon‐based, are discussed along with methods to construct them from TIGER data. Polygon‐based maps are useful for displaying regional statistical data, such as disease rates or incidence at the census tract level. Segment‐based maps are easier to assemble and are appropriate when the data are not regionalized. Census tract data of AIDS incidence in San Francisco and lung cancer case locations relative to petrochemical refinery sites in Contra Costa County are used to illustrate the methods and potential uses of interfacing the TIGER data base with S.
Distribution‐free fitting of logit models with random effects for repeated categorical responses
Authors: Agresti Alan
Published: April 2007

This article discusses random effects models for within‐subject comparisons of repeated responses on the same categorical scale. The models account for the correlation that normally occurs between repeated responses. The standard way of fitting such models maximizes the marginal likelihood after integrating with respect to a distribution for the random effect. An alternative non‐parametric approach does not assume a distributional form for the random effects. Recent literature shows that for certain simple logit models, this approach yields essentially the same model parameter estimates as conditional maximum likelihood. Moreover, these estimates also result from fitting corresponding quasi‐symmetric log‐linear models. For simple data sets in which primary interest relates to subject‐specific comparisons of the repeated responses, one can easily obtain the estimates with standard software for log‐linear models. Examples include data from crossover designs and from comparisons of treatment and control groups regarding the change between baseline and follow‐up observations.
Controlling for a confounder monotonically related to exposure by means of isotonic quantile regression
Authors: Strömberg Ulf
Published: April 2007

We present a new approach to evaluating the effect of a continuous exposure factor when that factor increases with a covariate )for examle, age( which is regarded as a potential confounder. The basic idea is to estimate, as functions of the covariate, some selected quantiles of the exposure distribution, under the assumption that the dependence of each quantile on the covariate is monotonic. The resulting estimates are then used to divide the data into different exposure categories. This method of categorizing the data implies that the covariate distribution will be almost the same in each exposure group. We illustrate the approach with a study of blood pressure and cardiovascular mortality.
TWO‐stage sampling in pharmaceutical applications
Authors: Shao Jun , Chow Shein‐Chung
Published: April 2007

In the pharmaceutical industry, some tests for quality assurance before, during and after the manufacture of a drug product involve a two‐stage sampling technique. We propose statistical testing procedures in a two‐stage sampling problem with large within‐class sample sizes. We also derive a two‐stage sampling plan by minimizing the expected squared volume )or the generalized variance( of the confidence region related to the test. We present two examples to illustrate the proposed methods.
Sample sizes for event rate equivalence trials using prior information
Authors: Gould A. Lawrence
Published: April 2007

Trials for demonstrating the ‘equivalence’ of active standard and test treatments generally require large sample sizes that depend on the definition of ‘equivalence’ and the overall event rate when the outcome is incidence of an event such as morality. The planning of sample sizes for such trials requires specification of a value for the overall event rate. This value often will reflect the outcomes of previous trials of the standard treatment, and is subject to uncertainty that needs some accommodation, to protect against an inadequate sample. Bayes and Empirical Bayes methods can be used to incorporate information from one or more previous trials into the sample size calculation when equivalence means high confidence that the event rate ratio is less than some specified value.
AN algorithm for robust non‐linear analysis of radioimmunoassays and other bioassays
Authors: Normolle Daniel P.
Published: April 2007

The four‐parameter logistic function is an appropriate model for many types of bioassays that have continuous response variables, such as radioimmunoassays. By modelling the variance of replicates in an assay, one can modify the usual parameter estimation techniques )for example, Gauss–Newton or Marquardt–Levenberg( to produce parameter estimates for the standard curve that are robust against outlying observations. This article describes the computation of robust )M‐( estimates for the parameters of the four‐parameter logistic function. It describes techniques for modelling the variance structure of the replicates, modifications to the usual iterative algorithms for parameter estimation in non‐linear models, and a formula for inverse confidence intervals. To demonstrate the algorithm, the article presents examples where the robustly estimated four‐parameter logistic model is compared with the logit‐log and four‐parameter logistic models with least‐squares estimates.
Testing concomitancy between two physiological pulse series
Authors: Yang Mark C. K. , Rao P. V.
Published: April 2007

Statistical methods for detecting synchronization of onsets of two physiological events, such as concomitant releases of prolactin )PRL( and luteinizing hormone )LH(, are studied in this paper. Usually, the two events are measured regularly and simultaneously and the onset times are then determined by the changes in the values of the measurements. Owing to difficulties in determining the exact onset times, a leeway is allowed for counting the onset synchronizations in most physiological studies. Using such a relaxed definition of synchronization and needing to allow for a recovery time between two episodes make the traditional hypergeometric test of concomitance inappropriate. Based on a truncated geometric inter‐arrival distribution, Clifton et al. have used simulation to construct a table of critical values for performing tests of significance of the observed number of coincidences in a series of 73 measurements. In this paper, the conditions under which their method can be used are examined from a statistical point of view. Methods for testing cases not covered by Clifton et al. are also described.
Statistics in medicine: Citations of papers in the first ten years
Authors: Campbell M. J. , Julious S. A.
Published: April 2007

All papers from Volume 1 ofStatistics in Medicinewere followed up in theScience Citation Index. There were 6.7 citations per paper in medical journals as opposed to 1.5 citations per paper in statistical journals, and overall there were 8.7 citations per paper. The average citation rate was lower than that of the first issue ofBiometrics, published in the same year, but this was partly because of a greater proportion of zero‐cited papers. Citations from medical journals increased annually, until about 5 years after publication, after which they remained steady. Volumes 2‐6 ofStatistics in Medicineand Volumes 29‐33 ofBiometrics, for the years 1983‐87, were followed up for statistical/medical source of the citations. Citations for Volumes 2‐4 ofStatistics in Medicinewere relatively low, but picked up by Volume 5.Biometricshad more citations from statistical sources than from medical, by contrast toStatistics in Medicinewhich had far more citations from medical sources than from statistical.
A comparative study of several antibiotic formulations using a design based on a combination of balanced incomplete blocks and Latin squares
Authors: Prescott Philip , Ryan Joyce , Shuttleworth Paul
Published: April 2007

A practical application of an experimental design, suitable for the comparison of several treatments, and based on combining balanced incomplete blocks and Latin squares balanced for carryover effects, is presented in the context of comparing a number of paediatric antibiotic formulations for taste, smell and colour. The recommended designs, originally suggested by Patterson, have the advantage of balanced incomplete blocks, in that a single trial may be used to compare a larger number of treatments than may reasonably be given to any individual subject. In addition, the incorporation of suitably chosen Latin squares allows for assessment of any effect of order of presentation of the treatments and for any simple first‐order carryover effect of one treatment into the following treatment period. Inclusion of such effects in the overall analysis could result in the reduction of bias in the comparisons of the treatments.
Estimating age, period and cohort effects using the multistage model for cancer
Authors: Holford Theodore R. , Zhang Zhongxin , McKay Lisa A.
Published: April 2007

To understand cancer aetiology better, epidemiologists often try to investigate the time trends in disease incidence with year of diagnosis (period) and birth cohort. Unfortunately, one cannot identify these factors uniquely in the usual regression model owing to a linear dependence between age, period and cohort, so that one requires additional information about the underlying biology of the disease. Carcinogenesis models provide one type of information that can result in a unique set of parameters for the effects of age, period and cohort. We use the multistage carcinogenesis model and its extensions to obtain a unique set of parameters for an age‐period‐cohort model of lung cancer trends of Connecticut males and females from 1935 to 1988. Some of these models do not seem to provide a reasonable set of model parameters, but we found that a model that included second‐order terms and a multistage mixture model both gave a good fit to the data and realistic parameter estimates.
On the analysis of life tables for dependent observations
Authors: Eriksson Bo , Adell Ragnar
Published: April 2007

Applying methods assuming independence when observations are positively correlated means that confidence intervals become too short and significance levels of statistical tests are less extreme. This paper discusses elements of life‐table analysis based on the standard product‐limit estimator and a modified Greenwood formula for its variance to be used for dependent observations. An application from oral surgery is given. Erroneously assuming independence in the analysis of a life table could have serious consequences. It is demonstrated in a simulation study that the confidence levels can be much too low. The proposed modification of the Greenwood formula for the variance of the estimated survival function most often results in confidence levels not too much below the required level. Using the upper bound for the variance will give conservative confidence intervals but also larger standard errors. Averaging individual group survival curves should only be considered for situations with large groups.
Network analytic methods for epidemiological risk assessment
Authors: Altmann Michael , Wee Beeling C. , Willard Keith , Peterson Denton , Gatewood Laël C.
Published: April 2007

The authors measure the efficacy of three methods for predicting the time to infection for susceptible individuals in a population undergoing an HIV epidemic. The methods differ in whether they require detailed information of the contact network and whether they require knowledge of the initial source of infection. Efficacy is evaluated using simulations for 20 different contact patterns. Only the risk score that uses both kinds of information accounts for more than 15 per cent of individual variability. The efficacy of this score ranges from 10 per cent in very unstructured populations to 60 per cent for spatially localized contact networks. This improved performance may be explained by the larger fraction of the total variability not due to the disease dynamics. When all variables are dichotomized, the two poorer methods produce odds ratios between 1.4 and 2.3. The odds ratio for the risk score with full information ranges from 2.5 to 17. Risk assessment protocols and intervention programmes are encouraged to assess contact patterns and detect sources of infection.