Targeted Estimation of Marginal Absolute and Relative Associations in Case-Control Data: An Application in Social...

Case-control studies are useful for rare outcomes, but typical analyses limit investigators to parametric estimation of conditional odds ratios. Several methods exist for obtaining marginal risk differences and risk ratios in a case-control setting, including a recently described semiparametric targeted approach optimized for rare outcomes.

Using case-control data from a study of neighborhood poverty and very preterm birth, we demonstrate estimation of marginal risk differences and risk ratios and compare a parametric substitution estimator based on maximum likelihood estimation with targeted maximum likelihood estimation (TMLE), and a refinement of TMLE for rare outcomes that incorporates bounds on the conditional risk.

In this illustration, living in a neighborhood with high poverty was associated with a higher risk of very preterm birth for white women. The estimated risk differences (cases/100) were 0.6 (95% confidence interval [CI]: 0.1, 1.1) from maximum likelihood estimation, 0.5 (95% CI: -1.1, 2.1) from TMLE, and 0.5 (95% CI: 0.0, 1.0) from the rare outcomes refinement. The rare outcomes refinement, which incorporates knowledge that the conditional risk is small, produced more precise estimates than TMLE. A similar pattern was observed for the relative risk.

Absolute and relative associations estimated from case-control data using a semiparametric targeted approach allow the scientific question to determine the analysis and avoid unwarranted parametric assumptions. A rare outcomes refinement provided more precise estimates than TMLE, and thus is well suited for the study of rare outcomes.