Optimal Estimation for Response-Dependent Retrospective Sampling

Outcome-dependent sampling: an efficient sampling and inference procedure for studies with a continuous outcome

To characterize the relation between an exposure and a continuous outcome, the sampling of subjects can be done much as it is in a case-control study, such that the sample is enriched with subjects who are especially informative. In an outcome-dependent sampling design, observations made on a judiciously chosen subset of the base population can provide nearly the same statistical efficiency as observing the entire base population. Reaping the benefits of such sampling, however, requires use of an analysis that accounts for the outcome-dependent sampling. In this report, we examine the statistical efficiency of a plain random sample analyzed with standard methods, compared with that of data collected with outcome-dependent sampling and analyzed by either of 2 appropriate methods. In addition, 3 real datasets were analyzed using an outcome-dependent sampling approach. The results demonstrate the improved statistical efficiency obtained by using an outcome-dependent sampling, and its applicability in a wide range of settings. This design, coupled with an appropriate analysis, offers a cost-efficient approach to studying the determinants of a continuous outcome.

On the prediction and prevention of myocardial infarctions: models based on retrospective and doubly censored prospective data

Early detection of coronary heart disease (CHD) in its pre-clinical stages may offer a way to reduce the impact of this endemic disease on society. Coronary calcification accompanies the development of an atherosclerotic plaque, the pathological substrate of CHD, and its identification is currently possible by means of electron beam tomography (EBT). This is a non-invasive imaging test that quantifies the extent of coronary artery plaque calcification by means of a calcium score. In this study, we show that an age-sex based calcium score percentile (CS%) provides an invaluable predictor for myocardial infarction (MI), and examine how CS% is related to traditional risk factors. We study two separate groups of patients: 172 patients who underwent EBT screening after surviving an MI (retrospective group); and 676 asymptomatic subjects who were screened and followed for several years for the occurrence of an MI (prospective group). We use CS% with traditional risk factors in logistic regression models to: (1) compare patients in the retrospective and prospective groups, and (2) develop a mortality model for MIs that occurred in the prospective group. These logistic regressions are used to develop a joint model for the relative log-odds of an MI, which is non-linear in the covariates of the mortality model. We also use baseline covariates in the prospective group to fit an event-time regression model and estimate probabilities for 2 and 3 year exposure periods. The event-time regression provides independent estimates of the relative odds that are associated with risk factors. CS%, smoking, and their interaction were preeminent as predictors in the joint model for the relative odds of an MI and in the event-time regression, although the effects of smoking and CS% were generally subadditive. These models provide important information on the risks associated with elevated CS% levels.