Analysis of matched case-control data with multiple ordered disease states: possible choices and comparisons

In an individually matched case-control study, effects of potential risk factors are ascertained through conditional logistic regression (CLR). Extension of CLR to situations with multiple disease or reference categories has been made through polychotomous CLR and is shown to be more efficient than carrying out separate CLRs for each subgroup. In this paper, we consider matched case-control studies where there is one control group, but there are multiple disease states with a natural ordering among themselves. This scenario can be observed when the cases can be further classified in terms of the seriousness or progression of the disease, for example, according to different stages of cancer. We explore several popular models for ordered categorical data in this context. We first adopt a cumulative logit or equivalently, a proportional-odds model to account for the ordinal nature of the data. The important distinction of this model from a stratified dichotomous and polychotomous logistic regression model is that the stratum-specific nuisance parameters cannot be eliminated in this model via the conditional-likelihood approach. We discuss a Mantel-Haenszel approach for analysing such data. We point out possible difficulties with standard likelihood-based approaches with the cumulative logit model when applied to case-control data. We then consider an alternative conditional adjacent-category logit model. We illustrate the methods by analysing data from a matched case-control study on low birthweight in newborns where infants are classified according to low and very low birthweight and a child with normal birthweight serves as a control. A simulation study compares the different ordinal methods with methods ignoring sub-classification of the ordered disease states.