Stratified proportional odds models for multilevel ordinal data with application to a knee pain severity stud

Stratified ordinal data often arise when a matched study design is applied and the response is recorded on an ordinal scale. In some situations, the matched strata can be further nested within clusters and thus be correlated. For example, in a knee pain severity study, longitudinal measurements of pain severity for a knee form a stratum and the strata/knees are correlated if they are from the same person. We refer to such data as "multilevel ordinal data" with level 1: clusters (persons), level 2: strata (knees) nested in a cluster, and level 3: observations (longitudinal measurements) matched in a stratum. To date, no analytic method can be directly applied to such data In this dissertation, we propose three types of methods to estimate the stratum-specific effects assuming a stratified proportional odds model. First, we propose the modified amalgamating conditional logistic regression (ACLR) models. ACLR has been developed for stratified ordinal data when the cluster level is absent. We take five approaches to account for the within-cluster correlation while applying ACLR: one-knee, clustered, pooled, within-cluster resampling and weighted estimating equations. Second, we propose use of parametric Bayesian hierarchical models where a wide class of parametric distributions is assumed for random intercepts, namely the normal distribution, t distribution, and skewed normal and t distributions. Third, we further explore semi-parametric Bayesian hierarchical models using truncated Dirichlet processes, which provide more flexible non-parametric distributions for random intercepts. The partitioning method is used in Bayesian models to separate the within-stratum and between-stratum effects. All of these methods are evaluated by simulation studies and applied to assess the association between bone marrow lesions and knee pain severity in the Multicenter Osteoarthritis Study. Additionally, we discuss the assessment of proportionality, a key assumption in the proportional odds model. In conclusion, our results demonstrate that multilevel ordinal data can be effectively analyzed using the conditional likelihood approaches and flexible Bayesian hierarchical models we have proposed. As future work, we plan to investigate the problems created by missing data in these analyses and Bayesian modeling of clustered and stratified ordinal data collected in retrospective study designs.