Estimates for cell counts and common odds ratio in three-way contingency tables by homogeneous log-linear models with missing data
Missing observations often occur in cross-classified data collected during observational, clinical, and public health studies. Inappropriate treatment of missing data can reduce statistical power and give biased results. This work extends the Baker, Rosenberger and Dersimonian modeling approach to compute maximum likelihood estimates for cell counts in three-way tables with missing data, and studies the association between two dichotomous variables while controlling for a third variable in \( 2\times 2 \times K \) tables. This approach is applied to the Behavioral Risk Factor Surveillance System data. Simulation studies are used to investigate the efficiency of estimation of the common odds ratio.
KeywordsContingency table Cross-classified data Log-linear model Maximum likelihood method Missing data Common odds ratio Three-way table
- Agresti, A.: Wiley Series in Probability and Mathematical Statistics. Categorical data analysis, 3rd edn. Wiley, Hoboken (2002)Google Scholar
- Behavioral risk factor surveillance system: http://www.cdc.gov/brfss. Accessed 5 July 2015 (2015)
- Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B (Methodological), 1–38 (1977)Google Scholar
- Jansen, I.: Flexible model strategies and sensitivity analysis tools for non monotone incomplete categorical data. Thesis and dissertations (2005)Google Scholar
- Pregibon, D.: Typical survey data: estimation and imputation. Surv. Methodol. 2, 70–102 (1977)Google Scholar