A post-hoc Unweighted Analysis of Counter-Matched Case-Control Data.

Informative sampling based on counter-matching risk set subjects on exposure correlated with a variable of interest has been shown to be an efficient alternative to simple random sampling; however, the opposite is true when correlation between the two covariates is absent. Thus, the counter-matching design will entail substantial gains in statistical efficiency compared to simple random sampling at a first stage of analyses focused by design on variables correlated with the counter-matching variable but will lose efficiency at a second stage of analyses aimed at variables independent of the counter-matching variable and not conceived as a part of the initial study. In an effort to recover efficiency in such second stage of analyses scenarios, we considered a naive analysis of the effect of a dichotomous covariate on the disease rates in the population that ignores the underlying counter-matching sampling design. We derive analytical expressions for the bias and variance and show that when the counter-matching and the new dichotomous variable of interest are uncorrelated and a multiplicative main effects model holds, such an analysis is advantageous over the standard "weighted" approach, especially when the counter-matching variable is rare and in such scenarios the efficiency gains exceeds 80%. Moreover, we consider all possible conceptual violations of the required assumptions and show that moderate departures from the above-mentioned requirements lead to negligible levels of bias; numerical values for the bias under common scenarios are provided. The method is illustrated via an analysis of BRCA1/2 deleterious mutations in the radiation treatment counter-matched WECARE study of second breast cancer.