The trade-off between bias and precision: Some statistical considerations

Very often biostatisticians are confronted with the problem of trade-off between bias and precision. Specifically, subjects are often divided into several strata (cluster) so that the legitimate within stratum comparison can be made. A typical example in public health research is the stratified case-control studies for disease-risk factors associations. To reflect the design consideration, one assigns a cluster-specific parameter to each cluster to assure that the comparison is made on the within cluster basis. This approach has the potential drawback of being unstable when many strata are uninformative about the within stratum comparison. Alternatively, one may simply ignore the heterogeneity among clusters so that an overall comparison among all subjects is made regardless their cluster assignment. As a result, one increases the precision of estimates and pays the price for being biased due to more stringent assumptions. A familiar trade-off between bias and precision is clearly presented.;In this thesis, two estimating procedures for handling this type of problem are proposed. One is based on the asymptotic properties of estimators, and the other takes the advantage of estimating functions' superior properties. A key novelty of this dissertation is the second compromising estimating procedure which uses the concept of estimating functions as a middle road between two estimating procedures, one known to be asymptotically optimal but unstable in finite samples; whereas the other procedure is more precise yet subject to bias. Some comparisons with two previous methods via simulation are presented for the problem of estimating a common odds-ratio in the one-to-one matched case-control study. The applicability to the estimation of a common risk factor effect in the stratified proportional hazard model is also demonstrated. A Baltimore What's Happening Drug Use Study provides a proper example of exhibiting the motivation of this dissertation. A Diabetic Retinopathy Study provides an interesting example of such an application. Extension to the multidimensional case is also provided.