Regression Analysis for Ordinal Outcomes in Matched Study Design: Applications to Alzheimer's Disease Studies
Creators: name: Austin, Elizabeth 
Publisher: name: University of Massachusetts Amherst
Year: 2018

description: Alzheimer's Disease (AD) affects nearly 5.4 million Americans as of 2016 and is the most common form of dementia. The disease is characterized by the presence of neurofibrillary tangles and amyloid plaques [1]. The amount of plaques are measured by Braak stage, post-mortem. It is known that AD is positively associated with hypercholesterolemia [16]. As statins are the most widely used cholesterol-lowering drug, there may be associations between statin use and AD. We hypothesize that those who use statins, specifically lipophilic statins, are more likely to have a low Braak stage in post-mortem analysis.
In order to address this hypothesis, we wished to fit a regression model for ordinal outcomes (e.g., high, moderate, or low Braak stage) using data collected from the National Alzheimer's Coordinating Center (NACC) autopsy cohort. As the outcomes were matched on the length of follow-up, a conditional likelihood-based method is often used to estimate the regression coefficients. However, it can be challenging to solve the conditional-likelihood based estimating equation numerically, especially when there are many matching strata. Given that the likelihood of a conditional logistic regression model is equivalent to the partial likelihood from a stratified Cox proportional hazard model, the existing R function for a Cox model, coxph<em>( </em>), can be used for estimation of a conditional logistic regression model. We would like to investigate whether this strategy could be extended to a regression model for ordinal outcomes.
More specifically, our aims are to (1) demonstrate the equivalence between the exact partial likelihood of a stratified discrete time Cox proportional hazards model and the likelihood of a conditional logistic regression model, (2) prove equivalence, or lack there-of, between the exact partial likelihood of a stratified discrete time Cox proportional hazards model and the conditional likelihood of models appropriate for multiple ordinal outcomes: an adjacent categories model, a continuation-ratio model, and a cumulative logit model, and (3) clarify how to set up stratified discrete time Cox proportional hazards model for multiple ordinal outcomes with matching using the existing <em>coxph( )</em> R function and interpret the regression coefficient estimates that result. We verified this theoretical proof through simulation studies. We simulated data from the three models of interest: an adjacent categories model, a continuation-ratio model, and a cumulative logit model. We fit a Cox model using the existing <em>coxph( )</em> R function to the simulated data produced by each model. We then compared the coefficient estimates obtained. Lastly, we fit a Cox model to the NACC dataset. We used Braak stage as the outcome variables, having three ordinal categories. We included predictors for age at death, sex, genotype, education, comorbidities, number of days having taken lipophilic statins, number of days having taken hydrophilic statins, and time to death. We matched cases to controls on the length of follow up. We have discussed all findings and their implications in detail.