Mixed Effects Logistic Regression Models for Longitudinal Ordinal Functional Response Data with Multiple‐Cause Drop‐Out from the Longitudinal Study of Aging

Abstract

In the context of analyzing ordinal functional limitation responses from the Longitudinal Study of Aging, we investigate the association between current functional limitation and previous year's limitation and its modification by physical activity and multiple causes of drop-out. We accommodate the longitudinal nature of the multiple causes of informative drop-out (death and unknown loss-to-follow-up) with a mixed effects logistic model. Under the proposed model with a random intercept and slope, the ordinal functional outcome and multiple discrete time survival profiles share a common random effect structure. This shared parameter selection model assumes that the multiple causes of drop-out are conditionally independent of the functional limitation outcome given the underlying random effect representing an individual's trajectory of general health status across time. Although it is not possible to fully assess the adequacy of this assumption, we assess the robustness of the approach by varying the assumptions underlying the proposed model, such as the random effects distribution and the drop-out component. It appears that between-subject differences in initial functional limitation are strongly associated with future functional limitation and that this association is stronger for those who do not have physical activity regardless of the random effects and informative drop-out specifications. In contrast, the association between current functional limitation and previous trajectory of functional status within an individual is weaker and more sensitive to changes in the random effects and drop-out assumptions.

A mixed‐effects model for cognitive decline with non‐monotone non‐response from a two‐phase longitudinal study of dementia

“…We construct a discrete-time hazard rate model for the censoring process [10]. We assume that given that a subject has not been censored at wave j, the two sources of censoring process (death versus other reasons) compete with each other independently so that the subject stay in the study at wave j + 1 only if neither of the censoring process occurs between wave j and j + 1.…”

“…Then ! jk 's represent the cause-speciÿc 414 C. SHEN AND S. GAO discrete time hazard rates [10]. Thus, we have…”

“…Follmann and Wu [8] presented a conditional likelihood approach to approximate the full likelihood in the framework of shared parameter model. Ten-Have et al [9,10] applied similar approach to binary and ordinal longitudinal response with dropout. See References [11][12][13] for more examples.…”

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“…Fitzmaurice et al (2001) described how bias can arise in generalized estimating equations (GEE) estimators where the missingness is informative. For longitudinal binary data with non-ignorable drop-out, Ten et al (1998) proposed mixed effects logistic regression models and these models were extended to ordinal response data with multiple causes of informative drop-out by Ten et al (2000) in a later paper. Accommodating intermittent missingness in addition to monotone missingness for second order dependency, a Markov chain model was proposed by Huang and Brown (1999).…”

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“…Ten Have et al [12] proposed mixed e ects logistic regression models for longitudinal binary response data with informative drop-out. In a later paper, Ten Have et al [13] extended the binary models to ordinal response data with multiple causes of informative drop-out. Huang and Brown [14] proposed a Markov chain model for longitudinal categorical data subject to non-ignorable missingness.…”