SIMULTANEOUS MODELING OF MULTIPLE BINARY OUTCOMES: A REPEATED MEASURES APPROACH

Multiple binary outcomes are frequently encountered in epidemiologic research. This work was motivated by the Maternal Lifestyle Study, where newborns prenatally exposed to cocaine and a comparison cohort, were examined for the presence of autonomic and central nervous system (ANS/CNS) signs. Thus, each infant contributed to multiple, possibly interrelated, binary outcomes that may collectively constitute one syndrome (even though specific outcomes that are affected by cocaine are of scientific interest). Since it is neither scientifically appropriate nor statistically efficient to fit separate models for each outcome, here we adopt a multivariate repeated measures approach to simultaneously model all the ANS/CNS outcomes as a function of cocaine exposure and other covariates. This formulation has a number of advantages. First, it implicitly recognizes that all the ANS/CNS outcomes may together constitute one syndrome. Second, simultaneous modeling boosts statistical efficiency by allowing for correlations among the outcomes, and avoids multiple comparisons. Third, it allows for outcomespecific exposure effects, so that we can identify the specific signs that are affected by cocaine exposure. Introduction Binary outcome measures that indicate the presence or absence of certain medical conditions are a widely used tool in epidemiologic investigations. Moreover, public health studies frequently measure an array of such indicators for different medical conditions to make an overall assessment about an individual’s health status. For instance, overall health status in newborns is widely assessed through the APGAR test, which is often composed of a series of five binary questions about a child’s physical state at birth. The traditional approach for statistical analyses of such binary outcomes is logistic regression, where the probability of observing an ‘event’ (i.e., the prevalence of some medical condition) is modeled as a function of the principal risk factor/treatment of interest and other covariates (McCullagh and Nelder, 1989). However, the situation where multiple binary outcomes are simultaneously assessed on the same individual presents some basic statistical problems, since proper statistical modeling in this case needs to reflect that: A. Each individual contributes to multiple outcomes. Thus, the different outcomes for each individual are likely to be correlated. B. These multiple outcomes broadly purport to measure the same underlying condition or construct. C. Outcome-specific effects (i.e., which specific outcomes are associated with the effect of interest) may be of interest. Many researchers have attempted to address A and B by adding outcome indicators into scores (which can sometimes also be interpreted as the total number of adverse medical conditions), and then regressing the total score on covariates using linear or Poisson regression (Stewart and Ware, 1992). Others have used latent variable models to infer about the underlying, yet unobserved, process that these multiple outcomes purport to measure (BandeenRoche et al, 1997). However, the principal limitation in both these approaches is that, by focusing on the aggregate, they loose the ability to discern outcomespecific effects (i.e., which specific outcomes are associated with the effect of interest) which may be of interest, thus failing to address C. This is critical, since aggregation of multiple outcomes risks combining indicators of distinct processes, which could mask subtle relationships between specific outcomes and risk factors. In addition, latent variable models generally entail strong modeling assumptions which may critically impact analytic findings. Joint Statistical Meetings Section on Statistics in Epidemiology