DPH 810 Module 3 Measures of Occurrence and Risk Example

Counting Cases, Comparing Risks: Measures of Occurrence and Association for a Diabetes Study

Student Name

Doctor of Public Health Program, Aspen University

DPH 810: Advanced Epidemiology in Public Health

Instructor Name

Month Day, Year

Counting Cases, Comparing Risks: Measures of Occurrence and Association for a Diabetes Study

Epidemiological questions are answered with numbers that describe how often disease occurs and how strongly exposure is associated with it. Choosing the right measure matters: the wrong one can mislead. This paper reviews measures of occurrence and association and works them through with invented county figures on food swamps and diabetes.

Prevalence

Prevalence measures the share of a population living with a condition at one moment. Its size depends on how quickly new cases appear and on how long people survive with the disease. For diabetes, prevalence is useful for planning services but can mislead about causes, because exposures may affect survival as well as onset.

Incidence

Cumulative incidence is the proportion of people at risk who develop the disease over a period. The incidence rate divides new cases by person-time at risk, accommodating people followed for different lengths of time. For a cohort drawn from health records, where people enter and leave, incidence rates are more appropriate. Person-time for each participant ends at diagnosis, death, disenrollment or the end of follow-up.

A Worked Example

Composite figures for adults in the top and bottom food swamp quartiles appear in the table, each contributing about 50,000 person-years over five years.

Interpreting the Example

A rate ratio of 1.63 means adults in the highest quartile developed diabetes at about 63% higher rate than those in the lowest. The rate difference shows 5 extra cases per 1,000 person-years, or about 250 extra cases over the 50,000 person-years in the exposed group. If the association were causal and unconfounded, about 38% of cases among the exposed would be attributable to the food environment.

Hazard Ratios

Cohort studies often report hazard ratios from survival models, which compare instantaneous rates while adjusting for confounders and accounting for time. The multi-ethnic cohort that examined neighborhood resources reported its main result as a hazard ratio across the range of resource scores (Auchincloss et al., 2009). Hazard ratios are interpreted much like rate ratios. A hazard ratio of 1.3, for example, means a 30% higher rate of diagnosis at any point during follow-up.

Odds Ratios

Case-control studies and logistic regression produce odds ratios. When outcomes are rare, odds ratios approximate risk ratios; when outcomes are common, they exaggerate them. Mezuk and colleagues expressed their Swedish results as odds ratios for new diabetes among people whose areas held more unhealthy food outlets (Mezuk et al., 2016), which should be read with the outcome's frequency in mind.

Relative Versus Absolute Measures

Relative measures such as rate ratios describe the strength of association and are useful for causal questions. Absolute measures such as rate differences describe public health impact and are useful for policy. A modest ratio applied to a large exposed population may produce many cases, which is why both should be reported.

Precision

Every estimate has uncertainty. A confidence interval gives the span of effect sizes reasonably consistent with the data, given the model's assumptions. Guidance on statistical interpretation cautions against treating P values as the probability that a hypothesis is true and recommends reporting estimates with intervals (Greenland et al., 2016).

Area-Level Measures

Some studies use counties or tracts rather than individuals as units, reporting correlations or regression coefficients between area food environments and area disease rates. Such ecological measures can suggest hypotheses but risk the ecological fallacy, since area associations may not hold for individuals.

Choosing Measures for the Project

The project will report incidence rates by quartile, adjusted hazard ratios as the main measure of association and adjusted rate differences for public health impact, each with 95% confidence intervals. Population attributable fractions will be estimated cautiously, noting assumptions.

Choosing Denominators

Measures depend on correct denominators. For incidence, only people at risk, those without diabetes at baseline, belong in the denominator. Including people with existing diabetes would dilute incidence and bias comparisons. Person-time stops at diagnosis, death, loss to follow-up or the end of the study.

Standardization

Crude rates can mislead when groups differ in age. If food swamp neighborhoods have younger residents, crude diabetes incidence might look lower there. Age-standardized rates or adjustment in models address this, allowing fair comparison across quartiles.

Effect Modification

The association may differ across groups, for example stronger in lower-income neighborhoods. Measures stratified by income, or interaction terms in models, can reveal such effect modification, which has implications for targeting policy.

Population Impact Estimates

Population attributable fractions estimate the share of all cases in the population that could be prevented if exposure were removed. They depend on both the strength of association and how common exposure is, and they assume causality, so they should be presented cautiously as illustrations of potential impact.

Worked Example Caveats

The composite example assumes equal person-time in each group and no confounding. In real data, groups differ in age, income and other factors, so crude rate ratios must be adjusted. The example illustrates calculation, not a finding.

Measures for Secondary Aims

For Aim 2, stratified incidence rates and rate ratios by neighborhood income and by urban or rural setting will show whether the association varies. Ratios of hazard ratios with confidence intervals will test whether differences between strata are larger than chance would produce.

Communicating Measures to Policymakers

Planners may find absolute measures easier to use than ratios. Stating, for example, that roughly 250 additional cases over five years occurred among residents of the highest quartile makes the potential impact concrete.

Rate Versus Risk

Because follow-up varies, rates using person-time are preferred to simple risks. If everyone were followed for exactly five years with no loss, cumulative incidence would be simpler and nearly equivalent.

Conclusion

Measures of occurrence and association answer different questions. For the food swamp study, incidence rates using person-time, hazard ratios for strength of association and rate differences for impact, all with confidence intervals, best fit the design. The composite example shows how a rate ratio of 1.63 translates into a meaningful number of extra cases.

References

Auchincloss, A. H., Diez Roux, A. V., Mujahid, M. S., Shen, M., Bertoni, A. G., & Carnethon, M. R. (2009). Neighborhood resources for physical activity and healthy foods and incidence of type 2 diabetes mellitus: The Multi-Ethnic Study of Atherosclerosis. Archives of Internal Medicine, 169(18), 1698-1704. https://doi.org/10.1001/archinternmed.2009.302

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

Mezuk, B., Li, X., Cederin, K., Rice, K., Sundquist, J., & Sundquist, K. (2016). Beyond access: Characteristics of the food environment and risk of diabetes. American Journal of Epidemiology, 183(12), 1129-1137. https://doi.org/10.1093/aje/kwv318