Mixture models and censoring by death
In examining the results of an experiment where quality of life (QOL) is to be measured, a complication is that patients who die have an undefined QOL, and similar problems occur in other contexts, with other events acting in place of death to remove observations from the pool whose QOL (or analogous measurement) is well-defined. One approach to this problem is to measure the survivor average causal effect (SACE)--the effect of the treatment on QOL among only those patients who would have lived regardless of whether they received the treatment or the control. Using principal stratification, the living individuals in each arm may be split into two groups based on whether they would have lived had they been in the other arm. If we assume that the QOL distribution of each group is normal, an EM (or, in some cases, ECM) algorithm can be used to estimate the parameters of the resulting mixtures simultaneously, from which the SACE may be computed. Normal assumptions may not be reasonable, but the method is moderately robust to certain violations of these assumptions. We consider how the sample size and the underlying parameters of a mixture may affect the bias and accuracy of the method, and the method's application to real-world data on employment training. However, graphical goodness of fit tests cast doubt on the employment data's adherence to the required parametric assumptions. We also consider the effect of covariates on the accuracy of the estimation, both in finding point estimates and confidence intervals under normal assumptions and in adapting formulas for large-sample bounds on the SACE. We perform simulation studies to test the effect of covariates on the accuracy of SACE estimates, as well as the effect of covariates on sensitivity to violations of the normal assumption, and find that a covariate can be very useful in estimating the SACE accurately, but that an irrelevant covariate, if included in the model, may increase the amount of error, thus highlighting the importance of careful variable selection.
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|Authors:||Freiman, Michael Harry|
|Type of publication:||Other|
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