A SAS macro for the joint modeling of longitudinal outcomes and multiple competing risk dropouts

Highlights

• A SAS macro implementation of a shared parameter model for a longitudinal outcome and multiple cause-specific dropouts.

• The linear mixed effects submodel for the longidudinal outcome, with the random intercept and/or random slope specifications.

• The survival submodel allows up to three different competing causes for dropout.

• Simulation study shows the unbiased parameter estimates when informative dropout exists.

Abstract

Background and objectives

The joint modeling of longitudinal and survival data to assess effects of multiple informative dropout mechanisms on longitudinal outcomes inference has received considerable attention during recent years; related statistical programs to apply these methods have been lacking. This paper provides a SAS macro implementation of a shared parameter model to accommodate the analysis of longitudinal outcomes in the presence of multiple competing survival/dropout events.

Methods

In this macro, we assumed that the associations between the survival and the longitudinal submodels are linked through a set of shared random effects. The submodel for the longitudinal outcome takes the form of a linear mixed effects model, with specifications for the random intercept and/or random slope. The survival submodel allows up to three different competing causes for dropout, each allowing either an exponential or Weibull parametric baseline hazard function. In addition, information criterion fit statistics AIC and BIC are provided to assist with parametric baseline hazard function selection.

Results

We illustrate the SAS Macro in a cognitive decline study sensitivity analysis using data from the Atherosclerosis Risk in Communities Neurocognitive Study (ARIC-NCS). In addition, we also conduct a simulation study to show that the joint model provides unbiased parameter estimates when informative dropout exists compared against separate model approach which assumes missing at random dropout mechanisms.

Conclusions

We have presented a SAS macro to implement a shared parameter model for a longitudinal outcome and multiple cause-specific dropouts and made the macro code freely available for download.

Introduction

Long-term longitudinal studies often encounter data attrition because subjects may drop out or die before the study ends. Informative dropout due to competing risks is a critical aspect that should be taken into account when analyzing these data. For example, in the Atherosclerosis Risk in Communities Neurocognitive Study (ARIC-NCS), studying risk factors for cognitive decline is a primary interest [1], [2]. Cognitive function assessments were repeatedly measured on available participants over a 20 year study period, but many participants' cognitive function measurements were unavailable due to preceding dementia and/or death. This resulted in dropout mechanisms potentially highly correlated with participants' cognitive declines. Longitudinal analyses of cognitive function that ignore potential informative dropouts may lead to biased association estimates; determining the degree of this potential bias is of substantive import.

In the past two decades many statistical models and inference approaches have been proposed to accommodate the close relationship of repeated measurements coupled with multiple survival outcomes. The purpose of such analyses is to assess the impact on both repeated measurements and survival outcomes jointly, to improve inference for the longitudinal outcome taking into consideration the survival outcome (e.g. trajectory change assessment of longitudinal outcome in the presence of informative dropout) [3], [4], or to improve inference for the survival outcome in the presence of observed time varying covariates (e.g. effects of longitudinal biomarker measurements on the event times of interest) [5], [6]. Tsiatis and Davidian provided an excellent overview of early work on joint models [7], and Wu et al. reviewed recent progress and summarized the commonly used methods [8]. In this paper, we focus on sensitivity of the longitudinal submodel (repeated measurements) in conjunction with other researchers' recent work [9], [10], [11], [12]. Elashoff et al. proposed using a linear mixed model for the longitudinal outcome and semiparametric competing risk submodels, linked by common latent variables. The EM-based algorithm is derived to obtain the parameter estimates, and a profile likelihood method is used to estimate the standard errors [9]. Li et al. developed a joint model adopting a t- instead of normal distribution for measurement errors in the linear mixed effects submodel which is robust in the presence of outlying longitudinal observations during follow-up [10]. Ghosh et al. proposed a fully Bayesian approach to jointly model the viral RNA response and informative dropout in the presence of multiple changepoints [11], and Gueorguieva et al. constructed a joint model for the longitudinal outcome and cause-specific dropouts that allows for interval-censored dropout times [12]. Simulation studies in these references all showed that the joint analysis of longitudinal measurements and survival events gave nearly unbiased results in the presence of informative dropout, whereas standard linear mixed effects models alone did not.

Some statistical software packages have begun to appear recently to implement the aforementioned joint modeling methods (see the R package JM [13], JMbayes [14], JoineR [15] as well as Stata module STJM [16]), however, the majority of these available software packages allow only a single time-to-event outcome. We adopted the joint model proposed by Gueorguieva et al. [12], which assumes conditional independence between longitudinal and cause-specific survival outcomes given a set of underlying random effects, and we developed a SAS macro to accommodate the analysis of longitudinal outcomes in the presence of multiple competing survival/dropout events. Our proposed SAS macro allows up to three different competing events and we believe it is the first SAS program to facilitate this kind of problem.

The paper is organized as follows. Section 2 presents the shared parameter model specification. In Section 3, we introduce a SAS macro to analyze a longitudinal outcome in the presence of multiple informative competing risk dropouts. We demonstrate how to use this macro by analyzing one real ARIC-NCS data set in Section 4 and a simulation study is shown in Section 5. Section 6 provides discussion and concluding remarks.