Explicit Estimates for Cell Counts and Modeling the Missing Data Indicators in a Three-Way Contingency Table by Log-Linear Models

Missing observations in cross-classified data are an extremely common problem in the process of research in clinical studies, observational studies and public health. Ignorance of missing values in the analysis can produce biased results and low statistical power. The focus of this research is to expand Baker, Rosenberger and Dersimonian (BRD) model approach to compute the explicit maximum likelihood estimates for cell counts for three-way cross-classified data. In case of missing observations, derivation of explicit cell counts for three-way table with supplementary margins can be obtained by controlling the missingness in third variable and by modeling the missing-data indicators using homogeneous log-linear models. Previous methods for contingency tables with supplementary margins required an iterative algorithm, however, expected cell counts for complete cells as well as missing cells can be obtained by simple algebraic formula. We conduct a simulation study with Neuropatholody data to illustrate that the explicit maximum likelihood estimates can produce consistent results.