%JM: A SAS Macro to Fit Jointly Generalized Mixed Models for Longitudinal Data and Time-to-Event Responses

Abstract

In clinical research subjects are usually observed during a period of time. Primary and secondary endpoints are often either responses measured longitudinally over time or the time at which an event of interest occurs. Joint modeling is increasingly being used for multiple purposes such as to adjust the analysis of the longitudinal response for informative dropout mechanisms.In this paper we present %JM, a SAS macro that fits jointly generalized mixed models for longitudinal data and proportional hazards models for time-to-event responses. The macro fits normal, binary, binomial and Poisson longitudinal responses and allows choosing among a range of options to fit the trajectories of the longitudinal response over time: a linear function, splines, natural cubic splines and B-splines. For the time-to-event response, that might be right-censored, the macro fits parametric, stratified or not, proportional hazards models with the following baseline risk functions: exponential, Weibull, piecewise exponential and the generalizations of the Weibull and the Gompertz models based on splines.%JM offers several options to connect the longitudinal model and the time-to-event model: current-value-dependent and slope-dependent shared parameters, lagging effects, cumulative effects, random effects coefficients as shared parameters and interaction effects.

Mixed‐effects models for slope‐based endpoints in clinical trials of chronic kidney disease

“…All estimation was carried out using the NLMIXED procedure in SAS 9.4. While there are a number of popular and flexible software packages for fitting SP models in both R and SAS, these do not, to the best of our knowledge, readily allow for the within‐subject and between‐subject heteroscedasticity assumptions as specified for the linear spline mixed‐effects model portion of our SP models. Inference under the SP model was carried out using large sample theory consistent with maximum likelihood methodology.…”

Handling informative dropout in longitudinal analysis of health-related quality of life: application of three approaches to data from the esophageal cancer clinical trial PRODIGE 5/ACCORD 17

“…In our application, we used discrete dropout times corresponding to pre-specified assessment times, but the SPM would allow researchers to take into account dropouts corresponding to clinical events such as death, which can occur at any time between the HRQoL assessment times. By contrast, the use of the SPM was facilitated by the standard statistical software [ 27 , 32 – 34 ]. Moreover, the existing programs allow for flexible models for the longitudinal outcome, more complex models for the time-to-dropout, and different association structures to capture the association between the longitudinal outcome and the time-to-dropout.…”

MMRM vs joint modeling of longitudinal responses and time to study drug discontinuation in clinical trials using a “de jure” estimand

“…Regarding the baseline hazard function, we used the Weibull distribution h 0 (t) = λ κ κt κ − 1 that includes both a scale and a shape parameter allowing the hazard risk to increase or decrease over time using a power function of time. Other more flexible baseline hazard distributions, such as the piecewise exponential, are possible and available in the existing JM software 36‐37 …”

“…Two questions that we will try to answer in Section 4 are whether we are able to distinguish from the data, the correct parameterization, and how sensitive the estimates of interest are to miss‐specification of the association between longitudinal and event processes. We should also note that other parameterizations have been considered in the literature, including, for instance, lagged effects, association via the random‐effects parameters, and the existence of cumulative effects 36‐37 . All these are not within the scope of this work.…”