|M.Sc Student||De Picciotto Rottem|
|Subject||Conditional and Marginal Estimates in Case-Control Family|
Data under Various Frailty Distributions
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Malka Gorfine-Orgad|
A typical case control family study includes a random sample of independent diseased individuals (cases) and non-diseased individuals (controls), along with their family members. An array of genetic and environmental risk factor measures is collected on these individuals. This design is powerful because it provides an efficient way to assess the effects of risk factors on the occurrence of a rare disease, and furthermore allows researchers to dissect genetic and environmental contribution to the disease clusters. Data analysis for this design, however, is complicated by the retrospective sampling scheme and the correlations among family members on the disease outcomes.
While family-specific hazard function is useful in, for example, genetic counseling, population-averaged marginal hazard function is also of interest from the public health perspective for devising effective strategies for preventing diseases and treating the general population. We consider two estimation techniques: under the family specific proportional hazards functions and under the population-averaged proportional hazard function. So far, these two estimation procedure were developed only for the Gamma frailty distribution mainly because of its simple interpretation and mathematical tractability. We modify both estimation procedures for other frailty distributions, such as Inverse Gaussian, Positive stable and a specific case of Discrete distribution. Finally, we investigate by a simulation study the performances of the estimation procedures under finite sample sizes and study the bias and efficiency loss under the misspecified Gamma frailty model where the true frailty is one of the above mentioned distributions.
Our main results are that under the family specific proportional hazards model, the Gamma frailty model appears to be robust to frailty distribution misspecification in terms of bias and efficiency loss in the marginal parameters. The population-averaged proportional hazard model, was found to be robust under the Gamma frailty model misspecification only under moderate or weak dependency within cluster members.