Statistical issues in breast cancer screening and clustered survival data analysis
Shen, Yu; Yin, Guosheng
Doctor of Philosophy
This dissertation addresses certain statistical issues in two biomedical fields, namely, modeling breast cancer screening program and correlated survival data analysis. For the breast cancer screening project, this study investigates statistical approaches to quantitatively describing the age effect on screening sensitivity and sojourn time distribution. Such an investigation is directly motivated by the need to understand the inherent relationships between age and these important quantities. Age effect is incorporated through generalized linear models under a progressive disease modeling framework. Parameter estimates are obtained by maximizing conditional likelihood functions. Among a set of potential models, the Akeike's information criterion and likelihood ratio test are used in model selection and inferences. Extensive simulation studies show that the estimators have reasonable accuracy and the model selection criterion works well. The proposed methods are illustrated using data from two large breast cancer screening trials. For correlated survival data analysis, an interesting yet often ignored problem is considered, that is when cluster sizes may be informative to the outcome of interest, based on a within-cluster resampling approach and a weighted marginal model. Large sample properties for the within-cluster resampling estimators are derived under the Cox proportional hazards model, including the consistency and asymptotic normality of the regression coefficient estimators and the weak convergence property of the estimated baseline cumulative hazard function. The weighted marginal model is constructed by incorporating the inverse of cluster sizes as weights in the estimating equations. Simulation studies are conducted to assess and compare the finite-sample behaviors of the estimators and the proposed methods are applied to a dental data example as an illustration.
Biostatistics; Statistics; Oncology