title: Likelihood methods for incomplete longitudinal binary responses with incomplete categorical covariates.
abstract: We consider longitudinal studies in which the outcome observed over time is binary and the covariates of interest are categorical. With no missing responses or covariates, one specifies a multinomial model for the responses given the covariates and uses maximum likelihood to estimate the parameters. Unfortunately, incomplete data in the responses and covariates are a common occurrence in longitudinal studies. Here we assume the missing data are missing at random (Rubin, 1976, Biometrika 63, 581-592). Since all of the missing data (responses and covariates) are categorical, a useful technique for obtaining maximum likelihood parameter estimates is the EM algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association 85, 765-769). In using the EM algorithm with missing responses and covariates, one specifies the joint distribution of the responses and covariates. Here we consider the parameters of the covariate distribution as a nuisance. In data sets where the percentage of missing data is high, the estimates of the nuisance parameters can lead to highly unstable estimates of the parameters of interest. We propose a conditional model for the covariate distribution that has several modeling advantages for the EM algorithm and provides a reduction in the number of nuisance parameters, thus providing more stable estimates in finite samples.
authors.affiliation: Department of Biostatistics, Harvard School of Public Health, and Dana Farber Cancer Institute, Boston, Massachussetts 02115, USA. lipsitz@jimmy.harvard.edu
authors.forename: S R
authors.initials: SR
authors.lastname: Lipsitz
authors.forename: J G
authors.initials: JG
authors.lastname: Ibrahim
authors.forename: G M
authors.initials: GM
authors.lastname: Fitzmaurice
mesh_terms: D000339:Affect; D000465:Algorithms; D000704:Analysis of Variance; D001699:Biometry; D001943:Breast Neoplasms / Q000503:physiopathology / Q000523:psychology; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D015233:Models, Statistical