HLTH 5013 Module 4 Descriptive and Inferential Data Analysis Example

Older, Heavier and Lower Starting A1c: A Descriptive and Inferential Analysis of 2,400 Adults in a County Diabetes Prevention Data Set

Student Name

American College of Education

HLTH5013: Epidemiology and Statistics

Module 4 Assignment

Instructor Name

October 26, 2026

Purpose and Data

The previous module found that adults in a composite county who enrolled in a lifestyle program for prediabetes developed diabetes less often over three years, and that part of the difference reflected enrollees' lower starting A1c. This module analyzes the full data set of 2,400 adults, adding age, body mass index, sex and insurance, to describe the two groups and to estimate the program's association with diabetes after accounting for several factors at once. The outcome is the same as before, diabetes by diagnosis or by laboratory value over the three years of follow-up; 347 adults, 14.5%, reached it.

Body mass index was missing for 142 adults, about 6%. The main analysis uses the 2,258 with complete data, and a sensitivity analysis described below checks whether the missing records change the result.

Describing the Groups

Descriptive statistics come first because they show whether the groups being compared are alike. The 620 enrolled adults had a mean age of 56.2 years with a standard deviation of 10.8, compared with 51.9 years and 12.4 among the 1,780 not enrolled. Mean body mass index was 33.1 among enrollees and 31.4 among non-enrollees. Mean baseline A1c was 5.96% and 6.03%. Women made up 71% of enrollees and 54% of non-enrollees, and 22% of enrollees had Medicaid or no insurance, compared with 38% of non-enrollees.

The profile is informative. Enrollees were older and heavier, which would raise their diabetes risk, but they had lower starting A1c and were more often women and privately insured, which may lower it. The groups differ in ways that pull the comparison in opposite directions, which is exactly why a single crude comparison cannot be trusted.

Testing Baseline Differences

Two-sample t-tests compared continuous variables. The difference in mean baseline A1c, 0.07 percentage points, has a standard error of about 0.009 using the unequal-variance formula, giving a t statistic near 7.8 and a p-value well below .001. The age difference of 4.3 years gives a t statistic of about 8.2. Chi-square tests showed that sex and insurance also differed between groups, each with a p-value below .001.

These p-values need careful reading. With groups this large, even small differences produce very small p-values. A difference of 0.07 in A1c is statistically clear but small clinically; what matters for the analysis is that it is consistent in direction and that A1c strongly predicts the outcome, so even a small baseline difference can confound the comparison. Greenland et al. (2016) list common misinterpretations of such tests, including treating a small p-value as a measure of the size or importance of an effect, which it is not.

Multivariable Logistic Regression

To estimate the program's association with diabetes while accounting for several differences at once, a logistic regression modeled the odds of diabetes as a function of enrollment, age in ten-year units, body mass index in five-unit steps, baseline A1c in tenths of a percentage point, sex and insurance. With 347 outcome events and six predictors, the model has well over the ten events per predictor commonly recommended for stable estimates.

The adjusted odds ratio for enrollment was 0.64, with a 95% confidence interval of 0.47 to 0.87. Each additional 0.1 in baseline A1c was associated with higher odds of diabetes, an odds ratio of 1.38 with an interval of 1.29 to 1.48, and each five-unit increase in body mass index with an odds ratio of 1.24, 1.12 to 1.37. Medicaid or no insurance had an odds ratio of 1.29, 1.00 to 1.66. Age, with an odds ratio of 1.08 and an interval of 0.97 to 1.20, and female sex, 0.91 with 0.71 to 1.17, had intervals that included 1.0.

Checking the Model

A regression result is only as good as the model behind it, so four checks were run before interpreting the estimates. First, continuous predictors were entered in grouped categories as well as linearly; the pattern for A1c rose steadily across tenths, supporting the linear term, while body mass index showed a steeper rise above 35, which the five-unit coding captures reasonably. Second, an interaction term between enrollment and baseline A1c tested whether the program's association differed by starting A1c; it did not clearly differ, with a p-value of about .41, consistent with the similar stratum ratios in the previous module. Third, the model's discrimination, its ability to separate people who developed diabetes from those who did not, was moderate, with a c-statistic of about 0.71. Fourth, predicted and observed risks were compared across tenths of predicted risk and agreed closely, indicating acceptable calibration. None of these checks revealed a problem that would change the interpretation of the enrollment estimate, and all four are reported so that a reader can judge the model rather than take it on trust.

Interpreting the Results

Because diabetes developed in about 16% of non-enrollees, the odds ratio overstates the relative risk. Converting it with the baseline risk gives an approximate adjusted relative risk of 0.68, close to the Mantel-Haenszel estimate of 0.69 from the previous module. Two different adjustment approaches, one stratifying on A1c alone and one modeling five covariates, arrive at nearly the same answer, which increases confidence that the measured confounders have been handled.

Two cautions apply. The interval for age includes 1.0, but Altman and Bland (1995) warn that failing to detect an effect does not show that none exists; the data are compatible with a modest effect of age as well as none. And p-values are better read as graded evidence than as a pass or fail at .05 (Sterne & Davey Smith, 2001), which is why this paper reports intervals throughout. The insurance estimate, whose lower bound sits at 1.00, is best described as suggestive rather than dismissed or overstated.

Sensitivity Analysis and Limits

Excluding the 142 adults with missing body mass index could bias the result if they differed systematically. Refitting the model without body mass index on all 2,400 adults gave an enrollment odds ratio of 0.62, close to the main estimate, so the missing values do not appear to change the conclusion. The analysis still cannot account for unmeasured factors, such as motivation, diet and physical activity before enrollment, that may differ between people who choose the program and those who do not. It also treats enrollment as attending four sessions, a threshold chosen in advance; a dose-response analysis by sessions attended would be a useful next step.

Summary for the Health Department

Enrollees and non-enrollees differed at baseline in ways that matter, but after adjusting for age, body mass index, starting A1c, sex and insurance, enrollment remained associated with about 32% lower risk of developing diabetes within three years. The finding is consistent across two methods and robust to missing data, but it is an association from observational data. The department can reasonably continue and expand the program while using the randomized clinic rollout recommended earlier to confirm the effect.

References

Altman, D. G., & Bland, J. M. (1995). Absence of evidence is not evidence of absence. BMJ, 311(7003), 485. https://doi.org/10.1136/bmj.311.7003.485

Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: A guide to misinterpretations. European Journal of Epidemiology, 31(4), 337-350. https://doi.org/10.1007/s10654-016-0149-3

Sterne, J. A. C., & Davey Smith, G. (2001). Sifting the evidence: What's wrong with significance tests? Another comment on the role of statistical methods. BMJ, 322(7280), 226-231. https://doi.org/10.1136/bmj.322.7280.226