IMPUTATION FOR EXPOSURE HISTORIES WITH GAPS, UNDER AN EXCESS RELATIVERISK MODEL

In reconstructing exposure histories needed to calculate cumulative ex posures, gaps often occur. Our investigation was motivated by case con trol studies of residential radon exposure and lung cancer, where half or more of the targeted homes may not be measurable. Investigators ha ve adopted various schemes for imputing exposures for such gaps. We fi rst undertook simulations to assess the performance of five such metho ds under an excess relative risk model, in the presence of random miss ingness and under assumed independence among the true exposure levels for different epochs of exposure (houses). Assuming no other source of measurement error, one of the methods performed without bias and with coverage of nominally 95% confidence intervals that was close to 95%. This method assigns to the missing residences the arithmetic mean acr oss all measured control residences. We show that its good properties can be explained by the fact that this approach produces approximate ' 'Berkson errors.'' To take advantage of predictive information that mi ght exist about the missing epochs of exposure, one might prefer to ca rry out the imputations within strata. In further simulations, we aske d whether the method would still perform well if imputations were carr ied out within many strata. It does, and much of the lost statistical power/precision can be recovered if the stratification system is moder ately predictive of the missing exposures. Thus, observed control mean imputation provides a way to impute missing exposures without corrupt ing the study's validity; and stratifying the imputations can enhance precision. The technique is applicable in other settings where exposur e histories contain gaps.