Case/control studies with follow-up: Constructing the source population to estimate effects of risk factors on development, disease, and survival

Abstract

If individuals in a case/control study are subsequently observed as a cohort of cases and a cohort of controls, weighted regression analyses can be used to estimate the association between the exposures initially recorded and events occurring during the follow-up of the 2 cohorts. Such analyses can be conceptualized as being undertaken on a reconstructed source population from which cases and controls stem. To simulate this population, the cohort of cases is added to the cohort of controls expanded with the reciprocal of the case disease incidence odds (the sampling weight) to include all individuals in the source population who did not develop the case disease. We use a simulated dataset to illustrate how weighted generalized linear model regression can be used to estimate the association between an exposure captured during the case/control study component and an outcome that occurs during follow-up.

Figure 1.

Venn diagram showing the distribution of 2400 cases and 2400 controls in relation to an exposure and an outcome in a population of 100 000 individuals. The numbers were generated using functions found in the Supplementary Appendix. Abbreviations: CoCa, cohort of cases; CoCo, cohort of controls.

Figure 2.

Schematic presentation of associations between an exposure (E), a case disease (D), and an outcome (O) in a population, where arrows indicate the direction of causality.

Figure 3.

Regression lines reflecting the relative risk for an outcome during follow-up for (A) the cohort of cases (CoCa) + the cohort of controls (CoCo) and (B) the reconstructed population (CoCa + noncases that have been reconstructed from the CoCo × sampling weight [rNC]). The data underlying each line corresponds to the 2 × 2 tables in Table 1 and Table 2, so that (T1B) is the 2 × 2 in row B of Table 1, and (T2A) is the 2 × 2 table in row A of Table 2. Notice that the change in weights, or individuals, between (A) and (B) alters the end-point positions, and thus the slope of the middle line. (A) depicts the ill-advised approach to analyze the combined CoCo and CoCa data (Table 1, row H). The area of each circle is proportional to the number of exposed (Exposure = 1) and unexposed (Exposure = 0) individuals in the CoCa and the CoCo. (B) depicts the reconstructed population method (Table 2, row B). The area of each circle is proportional to the number of exposed and unexposed individuals in the CoCa and the rNC. Abbreviations: CoCa, cohort of cases; CoCo, cohort of controls; rNC, noncases that have been reconstructed from the CoCo × sampling weight; RR, relative risk.