The title of Maja’s dissertation, "Estimating the number of components in a mixture and Analysis of recurrent events with time dependent covariates in the presence of dependent censoring," reflects her two main research interests.

Her interest in estimating the number of components in a normal univariate mixture was motivated by the challenge of detecting non-responders to alendronate treatment of osteoporosis. Based on the repeat measurements of bone mineral density (BMD), she and her collaborators described a model of treatment response that is based on normal mixture models. As a part of model checking technique, the goal is to select the optimal number of mixture components. Available methods for choosing the number of components include bootstrapping the likelihood ratio test statistic and optimizing a variety of validity functionals such as AIC, BIC, MDL and ICOMP. Maja’s research interests developed in the direction of validity functionals and investigating the minimization of distance between fitted mixture model and the true density as a method for estimating the number of components. Two papers on this topic will be published soon.

Maja’s second research interest is the analysis of recurrent events, which developed as she examined the problem of modeling recurrent lung exacerbations in cystic fibrosis patients conditional on covariates of interest. She has investigated different approaches to recurrent events analysis, especially focusing on their applicability to situations with time dependent covariates and presence of dependent censoring. The general estimating function approach she considered in the recurrent events setting is presented in the soon-to-be-published book by Mark van der Laan and James Robins entitled, "Unified approach to censoring and causality." Together with Mark, Maja investigated particular cases and specific estimating functions with consistency properties in the presence of dependent censoring that reduce to estimating functions with desirable properties, when censoring is conditionally independent of the process of interest.