Title: Multivariate analysis of non-commensurate outcomes
Description: In health care research it is common to collect multiple outcomes in order to, for example, characterize treatment effectiveness or to evaluate quality of care delivered by health providers. These outcomes may be non-commensurate, i.e., measured in different scales such as binary and continuous responses. While multivariate methods for multiple commensurate outcomes are commonly used, methods for the analysis of non-commensurate responses in a multivariate framework are not as well developed. The common strategy is to ignore the multivariate structure of the data and analyze each outcome separately using univariate models. This approach is less efficient in the sense that it discards the additional information contained in the correlation between the outcomes. This thesis focuses on the development, evaluation and application of multivariate methods for the analysis non-commensurate outcomes. In Chapter 1 we review several full likelihood and quasi-likelihood approaches to model a binary and continuous outcomes, and introduce a new latent variable model for this setting. We show that the factorization approach of Catalano and Ryan (1992) is equivalent to assuming a latent variable. We use Monte Carlo simulations to compare consistency, efficiency and coverage of the multivariate models with the univariate approach. We show that all models give consistent estimates of the parameters and similar coverage levels of the confidence intervals. When the mean structure of the outcomes is modeled with the same set of covariates, the gains in efficiency by taking a multivariate approach are negligible. However, if each outcome has a different set of associated covariates, then some of the parameter estimators are more efficient if a multivariate approach is used. Three real examples are used to illustrate the different approaches.

In Chapter 2 we propose methods to analyze non-commensurate outcomes with data missing for some outcomes. We describe the properties of the latent variable models proposed in Chapter 1 under missing data, and we extend the weighted GEE (WGEE) methodology to multiple non-commensurate outcomes for data missing at random. We also discuss the situation of missing data not at random and present some strategies to this problem. We show that, when outcomes are analyzed separately, there is a loss of efficiency as well as bias in parameters estimates. The methodology is illustrated in a study investigating the association between participation in a managed behavioral health care carve-out and quality of health care measured using bivariate mixed outcomes. In Chapter 3 we develop and apply a latent variable model for evaluation of quality of hospital care using multiple outcomes. In contrast to the work in Chapters 1 and 2, the goal here is to learn about the underlying latent variable. Recently in the United States and United Kingdom there have been several initiatives that financially reward health care providers that provide superior quality of care. The estimation of quality of care is typically based on the raw average of multiple outcomes collected at each hospital. We discuss some disadvantages of this scoring approach and argue that a model based score is more appropriate. Finally we propose a methodology to classify hospitals as superior taking into account the precision of the score estimates. The methods are illustrated using national data collected to evaluate quality of care delivered by acute care hospitals in the United States.