Bias in 2-part mixed models for longitudinal semicontinuous data

Abstract

Semicontinuous data in the form of a mixture of zeros and continuously distributed positive values frequently arise in biomedical research. Two-part mixed models with correlated random effects are an attractive approach to characterize the complex structure of longitudinal semicontinuous data. In practice, however, an independence assumption about random effects in these models may often be made for convenience and computational feasibility. In this article, we show that bias can be induced for regression coefficients when random effects are truly correlated but misspecified as independent in a 2-part mixed model. Paralleling work on bias under nonignorable missingness within a shared parameter model, we derive and investigate the asymptotic bias in selected settings for misspecified 2-part mixed models. The performance of these models in practice is further evaluated using Monte Carlo simulations. Additionally, the potential bias is investigated when artificial zeros, due to left censoring from some detection or measuring limit, are incorporated. To illustrate, we fit different 2-part mixed models to the data from the University of Toronto Psoriatic Arthritis Clinic, the aim being to examine whether there are differential effects of disease activity and damage on physical functioning as measured by the health assessment questionnaire scores over the course of psoriatic arthritis. Some practical issues on variance component estimation revealed through this data analysis are considered.

A random-effects hurdle model for predicting bycatch of endangered marine species

“…This finding agrees with observations by Su, Tom and Farewell (2009), who considered two-part models for semicontinuous data, as well as those of Fulton et al (2015), who modeled multivariate binary responses. As noted, an incorrect assumption of independence between the random parts of the model produces biases in the parameter estimates, in particular, the intercept for the abundance part, because correlated random effects are informative about cluster size (since parameters in the binary part influence the number of observations FIG.…”

How to analyze longitudinal multilevel physical activity data with many zeros?

“…Alternatively, the correlation between random-effect terms can be explicitly defined within the model structure. There have been some theoretical developments in the literature (see, e.g., Su et al, 2009), but fitting such complex models is currently not feasible using standard software.…”

“…In the above formulation, if the correlation between random effects in the logistic part and the gamma part is high, ignoring such correlation can introduce selection bias in estimating the gamma regression coefficients (Su et al, 2009). The correlation can be evaluated empirically by putting the estimated random effects from the logistic part as a covariate in the gamma part and assessing its significance, as noted by Liu et al (2008).…”

Longitudinal Models for Ordinal Data With Many Zeros and Varying Numbers of Response Categories

“…Indeed, ignoring nonzero covariances between the random effects of the two model parts has been shown to result in biased parameter estimates (Su, Tom, & Farewell, 2009). Figure 1 includes a path model for a twopart latent growth model that includes two growth functions with random coefficients that covary.…”