Bias due to differential participation in case-control studies and review of available approaches for adjustment

Low response rates in epidemiologic research potentially lead to the recruitment of a non-representative sample of controls in case-control studies. Problems in the unbiased estimation of odds ratios arise when characteristics causing the probability of participation are associated with exposure and outcome. This is a specific setting of selection bias and a realistic hazard in many case-control studies. This paper formally describes the problem and shows its potential extent, reviews existing approaches for bias adjustment applicable under certain conditions, compares and applies them.

We focus on two scenarios: a characteristic C causing differential participation of controls is linked to the outcome through its association with risk factor E (scenario I), and C is additionally a genuine risk factor itself (scenario II). We further assume external data sources are available which provide an unbiased estimate of C in the underlying population. Given these scenarios, we (i) review available approaches and their performance in the setting of bias due to differential participation; (ii) describe two existing approaches to correct for the bias in both scenarios in more detail; (iii) present the magnitude of the resulting bias by simulation if the selection of a non-representative sample is ignored; and (iv) demonstrate the approaches' application via data from a case-control study on stroke.

The bias of the effect measure for variable E in scenario I and C in scenario II can be large and should therefore be adjusted for in any analysis. It is positively associated with the difference in response rates between groups of the characteristic causing differential participation, and inversely associated with the total response rate in the controls. Adjustment in a standard logistic regression framework is possible in both scenarios if the population distribution of the characteristic causing differential participation is known or can be approximated well.