Simple optimal weighting of cases and controls in case-control studies

Abstract

Researchers of uncommon diseases are often interested in assessing potential risk factors. Given the low incidence of disease, these studies are frequently case-control in design. Such a design allows a sufficient number of cases to be obtained without extensive sampling and can increase efficiency; however, these case-control samples are then biased since the proportion of cases in the sample is not the same as the population of interest. Methods for analyzing case-control studies have focused on utilizing logistic regression models that provide conditional and not causal estimates of the odds ratio. This article will demonstrate the use of the prevalence probability and case-control weighted targeted maximum likelihood estimation (MLE), as described by van der Laan (2008), in order to obtain causal estimates of the parameters of interest (risk difference, relative risk, and odds ratio). It is meant to be used as a guide for researchers, with step-by-step directions to implement this methodology. We will also present simulation studies that show the improved efficiency of the case-control weighted targeted MLE compared to other techniques.

Figure 1:

Predicted Probabilities for Misspecified Q̂*(A, W).

Figure 2:

Simulation 1 – Bias Results. (Bias results for the case-control weighted targeted maximum likelihood with misspecified ĝ*(A | W) and the correctly specified case-control weighted targeted maximum likelihood were excluded since those values were the same as those for the targeted maximum likelihood with correctly specified Q̂*(A, W) and ĝ*(A | W).)

Figure 3:

Simulation 2 – Bias Results for the Odds Ratio. (Bias results for the case-control weighted targeted maximum likelihood with misspecified ĝ*(A | W) were excluded since those values were the same as those for the targeted maximum likelihood with correctly specified Q̂*(A, W) and ĝ*(A | W).)