Estimating a marginal causal odds ratio in a case-control design: analyzing the effect of low birth weight on the risk of type 1 diabetes mellitus

Abstract

Estimation of marginal causal effects from case-control data has two complications: (i) confounding due to the fact that the exposure under study is not randomized, and (ii) bias from the case-control sampling scheme. In this paper, we study estimators of the marginal causal odds ratio, addressing these issues for matched and unmatched case-control designs when utilizing the knowledge of the known prevalence of being a case. The estimators are implemented in simulations where their finite sample properties are studied and approximations of their variances are derived with the delta method. Also, we illustrate the methods by analyzing the effect of low birth weight on the risk of type 1 diabetes mellitus using data from the Swedish Childhood Diabetes Register, a nationwide population-based incidence register.