Conditional Tests for Multivariate One-sided Hypotheses with Missing Data

Thesis (Ph.D.)--University of Rochester. School of Medicine & Dentistry. Dept. of Biostatistics & Computational Biology, 2018.Treatment comparisons in randomized clinical trials usually involve several outcomes. Sometimes it is of interest to determine whether there is a treatment-associated improvement in disease status based on multiple outcomes, particularly if a treatment is expected to have the same directional effect on all of the outcomes. This gives rise to a multivariate onesided hypothesis. Under the multivariate normality assumption, Perlman (1969) derived the likelihood-ratio test in the one-sample case; however, its null distribution depends on the unknown covariance matrix and it is biased. Wang and McDermott (1998) derived a conditional likelihood ratio test (CLRT), conditioning on a sufficient statistic for the covariance matrix, resulting in a uniformly more powerful test. Recently, in an unpublished manuscript, Wang extended the CLRT to the two-sample case. This thesis explores the operating characteristics of the two-sample CLRT. In addition, this thesis develops practical extensions of the test such as covariate adjustment, a two-sided version, and outcome specific inference. Since the problem of missing data is ubiquitous in practical applications involving repeated measurements in multiple outcomes, this thesis proposes an observed likelihood-based approach to incorporate such missing data with a missing at random (MAR) mechanism in the CLRT. This thesis also considers the case of comparison of multiple treatments with respect to multiple outcomes and suggests a conditional test based on a statistic suggested by Sasabuchi (2003) for comparing multiple outcomes in K (> 2) samples. Derivation of the conditional test is provided and a resampling method to calculate the p-value is illustrated based on Markov Chain Monte Carlo sampling