Abstract:
The use of all information available on an entire cohort when fitting Cox models can be limited due to exposures of interest available only in a sample. If a case- cohort design is used, the standard estimation method (pseudolikelihood) allows for methods from survey sampling, such as calibration, to be used in order to take advantage of auxiliary information. However, under countermatching designs, the standard estimation method (partial likelihood) utilizes only one variable on the entire cohort and it does not admit the use of calibration. In this dissertation, calibrated weights are applied to countermatched designs. The calibration variables are an approximation of the influence functions of the estimator. The methods are evaluated through simulations for models with time- fixed and time varying covariates. Situations in which countermatching can be preferred over case -cohort or matching are considered. These situations include the case when a rare exposure is available for the sample, but there is a surrogate of this on the cohort. Countermatching on the surrogate leads to more efficient estimates. The new method is compared to partial likelihood and pseudolikelihood with standard weights under different designs (matching and case -cohort). Pseudolikelihood with calibrated weights returns more efficient estimators than the other methods in most situations, particularly for coeffi cients whose variables are available on the entire cohort. Partial likelihood can be more efficient than pseudolikelihood in the presence of confounding variables in the model or for variables that are unrelated to the countermatching variables. However, calibrated weights can recover the efficiency lost if suitable auxiliary information is available. The efficiency of the methods under misspecified models is also discussed. Pseudolikelihood is a more suitable method if the interest is to estimate the cohort coefficients. Furthermore, asymptotic normality of pseudolikelihood estimators with both standard and calibrated weights is discussed using an empirical processes approach. The result is attained for time -fixed Cox models. A potential information bound for under the missing at random assumption in two -phase sampling designs is studied and compared to the proposed methods .