Exact Estimation of Effect Size for Correlated Binary Outcomes

Correlated binary outcomes arise frequently in applied research. In ophthalmologic studies, measurements are often taken simultaneously on both eyes of an individual. Similar environmental and genetic exposures make it likely that measurements on the two eyes will be more similar compared to measurements taken on eyes from separate individuals. In the study of genetically transmitted diseases, measurements taken on siblings can be considered a cluster and are likely to have correlated outcomes. In longitudinal studies, subjects are tracked over time with measurements taken periodically. It is highly likely that observations taken from the same subject will be more alike than observations taken from different subjects.

The two most common tools in use today, generalized estimating equations and random effects or mixed models, rely heavily on asymptotic theory. However, in many situations, such as small or sparse samples, asymptotic assumptions may not be met. For this reason we explore the utility of the quadratic exponential model and conditional (exact) analysis to estimate the effect size of a trend parameter in small sample and sparse data settings. Further we explore the computational efficiency of two methods for conducting conditional analysis, the network algorithm and Markov chain Monte Carlo. Our findings indicate that conditional estimates do indeed outperform their unconditional maximum likelihood counterparts. The network algorithm remains the fastest tool for generating the required conditional distribution. However, for large samples, the Markov chain Monte Carlo approach accurately estimates the conditional distribution and is more efficient than the network algorithm.