Depicting Time-Dependent Changes in Environmental Data 

 for Prospective Uses in Personalized Medicine 

 Turkan K. Gardenier, Ph.D., Pragmatica Corporation 

 115 Saint Andrews Drive, Vienna, VA 22180 

 

Abstract

Estimating environmental exposure is a crucial component of health risk assessment. With the 

recent emphasis on personalized medicine and patient participation, data submitted to analysis 

and evaluation need to clear, retrievable and easy to merge. Patients, physicians, and public 

health officials may all be interested in individuals’ exposure histories. Large databases are now 

available and accessible to the public including, patients and caregivers. Some environmental 

data are monitored under mandate and are available for many years, thus making it feasible to 

trace change over time. When merging data over time, it is also important to remember that 

there is uncertainty in data elements; for example, discretized continuous data, incorporate a 

region of uncertainty between adjacent categories. A step-function based 3-category approach 

(trinary) is presented and discussed with reference to data collected between 1990-2010 for two 

criteria pollutants: Carbon Monoxide (CO) and Nitrogen Dioxide (NO2) in a rural and an urban 

city in northeastern United States. Correlation and regression analysis was applied, as well as a 

trace of successive data in a step-assignment of +1, 0 or -1 delineated using distance from the 20-

year average for each city. Various distance allotments of bandwidth, were explored, including 

mean + or minus 1⁄2 standard deviation, 3rd minus 1st quartiles, 90th minus 10th percentiles and 

visual inspection. Switching patterns from +1 to 0 range and from 0 to -1 range were examined 

for the rural and urban areas with a view to quantifying a decision rule for stability of shifting 

pattern. This paper demonstrates how three-level categorizations of environmental exposure 

data (and potentially other measurement data as well) can simplify and clarify health related 

exposure histories. The analytic approach has broad applications in personalized medicine, 

epidemiology and public health policy. 

 

KEY WORDS: Step-Function; Environmental exposure; Air Quality; Regression analysis; 

Geographic Information Science (GIS); Trinary categories; Time-series; Uncertainty; 
2 

1. Introduction 

 

 In parallel with rapid advances in computer technology, databases in multiple disciplines 

have increased in number and magnitude. Interactive features of retrieval now enable the user to 

query data for a specific geographic location, for a specific time interval, and for specific 

demographic or age groups. Yet this process of delving into such diverse databases exploring 

linkages among multiple variables which relate to health and environment raises challenges. 

 When new types of data are added to each record, e.g., genomic findings, the number of 

variables for each individual increases. When the same individual is evaluated over time, there 

are multiple measurements, some for the same attribute and some for the new variables added to 

the database over time. Similarly, for environmentally-oriented databases such as air or water 

quality, data are compiled differently, such that the measurement of magnitude of pollution 

differs in precision. For example, air quality measurements are obtained at monitoring stations 

which are often distant from the specific location of interest to the researcher who is trying to 

analyze the exposure level of a specific individual. Or, data may be analog, later to be

discretized into “per-hour” or “per day” basis, later to enter into monthly averages. Thus

associating data from different record types, although necessary and worthy of merit, introduces 

uncertainties which demand recognition and integration with analytical procedures. 

 The field of Geographic Information Science (GIS) uses the term “locational 

analytics” addressing the issue of multiple attributes for the same location, similar to that in 

personalized medicine, whereby analysis is directed to all available data for a given individual 

( Gardenier, 2011). For a specific person or record, data may be obtained at different times, 

 with missing values interspersed. They may emanate from a single measurement or may be 
3 

 

averages of multiple measurements. They may arrive from a specific laboratory or 

different laboratories, creating other sources of error or uncertainty. Thus, although researchers 

strive for precision, the inherent lack of uniformity due to a variety of reasons, such as 

the way in which data are measured, processed, and associated with each individual record 

 

or a location, needs to be recognized and reflected in the analytics. 

 

2. Databases Accessed

The National Center for Health Statistics, Centers for Disease Control (NCHS,CDC) and 

National Cancer Institute, National Institutes of Health (NCI, BIH) have published maps 

 showing death rates from various causes, including many types of cancer (Pickle, L, 

Mugniole, M. et al 1996; Devesa S, Grauman, D. et al 1999). The maps now have 

friendly user retrieval interface. Simultaneous inspection of maps enables the user to visualize 

the relationship among variables and conceptualize any possible association. If the colors or 

shading are similar, forexample, if red, denotes “high” and blue “low” rates in a geographic 

location across all layers mapped, it becomes easier to identify “hot spots” for further 

exploration. Viewing the joint occurrence of high or low observations across multiple layers, or 

comparisons along the time dimension are also possible. For example, one may classifying each 

5-year interval as “high” or “low” based upon the national standards established for a specific 

pollutant, or compared to prior observations in the specific geographical area. The analysis of f 

high and low coded observations over time provides the user with a heuristic profile of whether 

time-trends are being observed If one traces other attributes in a similar fashion, an impression 

becomes available as to whether or not values are getting higher or lower jointly. This type of 

comparison of profiles yields a concise, informative overall picture of jointly occurring trends. 
4 

 

An illustration of site-specific analyses, let us use annual summaries from twenty 

successive years, 1990- 2010) for two criteria air pollutants, Carbon Monoxide (CO), Nitrogen 

Dioxide (NO2) being monitored at the national level by the U.S. Environmental Protection 

Agency (Latest Findings on National Air Quality 2000 Status and Trends 2001). These data are 

available for public use for a number of cities in the U.S. For the present analyses annual citylevel summaries were retrieved for 1990-2010 from www.epa.gov/airtrends/aqtrends.html. on 

1/18/2013. Two cities were from Eastern US, the fist with a 2009 population of 126,122, and the 

second with a 2009 population of 2,690,886. They had complete data on both contaminants, 

Carbon Monoxide (CO) and Nitrogen Dioxide (NO2) for all twenty years 1990-2000. For 

purposes of the present analyses they will be referred to as rural and urban, respectively. Data 

were analyzed using correlation and regression-based approaches, as well as a new method 

developed by the present authors.

3. Correlation and Regression Based Analyses 

Pearson Product-Moment correlations and Spearman-Brown non-parametric rank 

correlation coefficients were computed between CO and NO2 annual levels for the two 

cities. The correlation between CO and O3 levels are high for both the rural and urban cities; 

Pearson r = 0.44 and 0.66 respectively and similarly Spearman r = .56 and .73. However, NO2 

and O3 levels show a high positive correlation for the urban city (Pearson r = .53, Spearman r = 

.61, but not for the rural city (Pearson r = -.20, Spearman r = -.21). Similar results are obtained 

for the relationship between CO and O3 levels. Urban Pearson r = 0.78, Spearman r = .75; rural 

Pearson r = 0.15, Spearman r=- 0.04. This may denote high concentration of multiple pollutants 

in areas of high population. 
5 

 The annual concentrations of each pollutant were plotted for the urban and rural area 

over the 20-years. Results of the plots, along with a linear regression fit to the data are shown in 

Figure 1. Rural data are plotted on the left, urban data on the right. 

Figure 1. 20-Year Carbon Monoxide (upper two plots) and Nitrogen Dioxide (lower two plots). 

 It is apparent that a downward trend is observed over the 20 years for all except for NO2

rural data. Yet these trends cannot continue indefinitely, because they will be affected by the 
6 

regulatory standard. This challenge prompted the necessity for further analytic exploration, the 

challenge to search for a step-based approach using data available, for switches upward or 

downward and for relatively when change occurs. The step needs sufficient resolution for 

identifying change and consistency thereof. 

 

4. An Aternative Approach Using Monitoring Bands and Step-Function Shifts 

 

Proceeding along this inquiry, the cumulative distributions and results of tests for Normality 

were evaluated, confirming Normality assumptions. We then proceeded to determine whether 

 it would be feasible to ascertain ranges or bands around the mean, akin to those in quality 

control (QC) charts through the use of which one can track successive observations as to 

whether a step-change could be detected during the 20-year time interval. In this effort, four 

types of alternative ranges or bands were established, as illustrated for the Nitrogen Dioxide data 

in Table 1. The first, shown in the left column, uses, as the lower limit, 0.5 standard deviation 

(1⁄2 sd) below then mean, and as the higher limit 0 .5 standard deviation above the mean. The 

second, shown in the next column to the right, uses the range between the 25th and 75th 

percentiles, often displayed in Box Plots. The third, shown in the next right column, uses visual 

inspection of the range in data—averaging the first three and the last three observations and 

inspecting the data within this range for “natural breaks,” as employed in mapping with 

Geographic Information Science (GIS). The fourth establishes the bands based upon the 10th and 

90th percentiles. The data observed are in Columns 2 and 7; the {+/0/-} allocation based on the 

alternative allocation schemes are indicated as entries in columns 3-6 (for rural) and columns 8- 

11 (for urban) locations. 

 Reviewing the monitoring bands under the four alternatives across all three air pollutants 

showed that using the mean +/-0 .5 standard deviation was preferable to the others in 
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pinpointing and isolating site-specific trend-oriented step shifts. For example, prior to 1995 

data for the urban site, data were in the {+} range; then a switch to the {0} range is observed, 

then another shift to {-} or lower values after another 10 years. For the rural location there is a 

downward shift after the first five years, but no consistent change thereafter. 90th – 10th 

percentile and Box-Plot oriented 75th – 50th percentiles resulted in wider bands, thus leaving 

more observations outside the monitoring band. They pinpointed outliers from grouped data 

and were not designed to isolate trend –oriented step shifts for the individual locations. 

Table 1. Step-Shifts in Trinary (+/0/-) Categories During Successive 20 Years (1990-2010) 

 For Nitrogen Dioxide (NO2) Annual Levels fur a Northeastern Rural and Urban Area 

 R u r a l U r b a n 

 

 
8 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

199119921993199419951996199719981999200020012002200320042005200620072008200920102011

NO2 Low 

NO2 High 

Year 

 

Figure 2. Step-Function Trinary (+/0/-) Delineation of NO2 Annual Concentrations in

 Two Cities in Notheastern U.S. during 1990-2010: Vertical Axis 0-3 Mapped 

 to 1-3 for City with Low Population; 6-8 for city with High Population 

 Figure 2 displays the data in Table 2 plotted over time. The red dots for each successive 

year refer to the trinary (+/0/-) codes for the urban city, the blue dots for the rural city. Pollution 

levels in the urban city are higher, thus a vertical shift is introduced. The primary question is: 

Does the shift to a lower “step” occur during the same time interval? For the urban city, after 

 1995, a shift to lower values is observeds, then another shift to lower values after another 10 

years. For the rual city there is a downward shift after the first 5 years, but no consistent change 

thereafter—in fact, there is a reversal. The graph depicts a novel type of portrayal. 

5. Integration with On-Line Trend Reporting

Interactive computerized access to environmental data is widely available, as shown in 

Figure 3, plots retrieved during 9/29/ 2013 from on-line EPA air quality trends website. 

The reporting shows, for the group of 89 sites for Co and 30 for NO2, the average for each year, 
9 

The national standard, and the 80% bracketed between the upper and lower 90th and 10th 

percentiles. Thus, If an individual is interested in tracing possible exposure in a certain city, 

knowing the city’s relative standing and whether relative increase or decrease appeared during 

periods of interest will provide a useful supplement to other health-related data. 

 

Figure 3. Air Quality Trends 1982-1992 for CO and NO2 showing National 

 Standard, 90th-10th Percentiles and Averages for sites. 

 Source: http:www.epa.gov/airtrends Retrieved: 9/29/2013 

6. Discussion 

Einstein is said to have once remarked that not everything that can be counted counts and not 

everything that counts can be counted. In trend estimation, particularly if estimates are to be 
10 

used in forecasting, it is important to be note step changes in data, as demonstrated by the 

application of monitoring bands in Table 1. A regression line, linear or non-linear, implies that 

the function will continue beyond the present. Bands of this type do not assume steady state and 

visually smooth uncertainties implicit in the data elements, as stated in the introductory section 

of this paper. Observing successive data within a specific band over time indicates stability prior 

to a switch downward or upward. The stock bands of Energy Information Administration (Hall, 

D., Gardenier, T., Slavic A. 1984) included seasonality adjustment as well (Durbin, J. and 

Koopmans, S. J. 2001). Tracing status and change in a 3-category or trinary framework provides 

a succinct tabular representation of when change is elicited. In this paper, we have provided 

guidelines for what level of 3-way categorization is most likely to identify emerging trends in 

data and concluded that use of the mean +/- .5 standard deviation appeared to yield the best 

detection. 

 Patient engagement has taken an important role in personalized medicine (Bertakis, K. 

D., and Azari, R. 2011; Epstein, R. M., Franks, C. G. et al 2005). Not only are patients are 

encouraged to participate in their own care, but also programs such as Patients-Like-Me seek 

motivated patients to connect, research and integrate relevant data, much of which is available 

on-line. Reference guidelines for interpreting data are crucial for such evaluations. Furthermore, 

individuals are likely to inquire about the possible environmental exposures from where they 

resided or worked. 

 Not only data for geographical locations, as addressed by Dangermond (2012), but also 

time-series data for individual locations, along with any summarized interpretation provided at 

the time of data retrieval, are essential. Individuals are likely to remember the city where they 

lived or worked; it is important to integrate city-level time trends with information on the 
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national standard, national summary statistics and indices such as trinary {+/0/-} bands based 

on mean +/- .5 standard deviation, as discussed in this paper. In parallel, access to ongoing 

research as presented by Christensen and White (2011) will provide additional references. 

 The approach presented here is relevant not only to health and environmental data. In 

a report relating to climate change Washington (2011) reported annual global mean temperature 

1880-2010 not only in the form of a line graph but also as a deviation from the overall mean 

during 1901-2000 (shown as a 0.00 reference point). It was clear from this perspective how 

temperature readings were consistently below the mean during earlier years and started rising 

with time. In this paper a similar approach is being advocated, using location-specific successive 

readings for each geographic location. 

 During analyses this trend in thought also indicated a theoretical query which needs to 

be explored further. Attempting to apply a test of significance to the sequence of +1, 0, or -1 

coded successive observations, use of the non-parametric Runs Test as described in Freedman, 

 Pisani and Purves (2007), Netter, Wasserman and Whitmore (1978, p. 194-198) was 

considered. The number of switches in status, denoted by runs up and down, is used in the test 

statistic. If the observation is higher than the preceding observation, it is coded +, if it is lower, it 

is coded as -, and if two successive observation are tied, the code of the preceding evaluation 

prevails. Using a buffer zone as in the present case eliminates ties, because each successive 

observation belongs into one of 3 categories or bands: +1, 0 or -1. It is the succession of the 

codes in the three options which determines either maintenance in each step or switch from one 

step into another. Thus the non-parametric Runs Test was not applicable to the 3-category 

delineation. The test statistic is based upon a 2-category delineation for evaluating successive 

observations, thus pointing to the necessity for further methodological research. CUSUMS
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(Cumulative Sums) and MOSUMS (Moving Sums) where the sums of successive observations 

are used to detect slowly emerging trends over time; within the context of our queries early 

detection is of utmost concern and importance. 

 In conclusion, this paper demonstrates how 3-level categorizations of environmental 

exposure data (and potentially other measurement data as well) can simplify and clarify healthrelated exposure histories. The analytic approach has broad applications in personalized 

medicine, epidemiology, and public health policy. 

Acknowledgement

I wish to thank John S. Gardenier, D.B.A., National Center for Health Statistics (Retired) for 

editorial comments and encouraging the illustration and application of the 3-category index 

which I developed. 

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