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Abstract:
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In many applications of mixture models, there is often interest to conduct a test of homogeneity. Most of the existing testing procedures typically rely on common heterogeneity parameter under alternatives to homogeneity. Such procedures, albeit omnibus for general alternatives, may entail a substantial loss of power for specific alternatives such as heterogeneity varying with covariates. We introduce in this talk a novel approach that uses covariate information to improve the power to detect heterogeneity, without imposing unnecessary restrictions. With continuous covariates, the approach does not impose a regression model or rely on arbitrary dichotomizations. Instead, a scanning approach requiring continuous dichotomizations of the covariates is proposed. Empirical processes resulting from these dichotomizations are then used to construct the test statistics. We illustrate our proposals for the class of cure rate survival models, followed by simulation studies and the analysis of an ovarian cancer data. These illustrations demonstrate the efficiency gains of the scanning tests over testing procedures that neglect covariate information, or those that rely on regression models.
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