Robustness of a parametric model for informatively censored bivariate longitudinal data under misspecification of its distributional assumptions: A simulation study

Abstract

Repeated measurements of surrogate markers are frequently used to track disease progression, but these series are often prematurely terminated due to disease progression or death. Analysing such data through standard likelihood-based approaches can yield severely biased estimates if the censoring mechanism is non-ignorable. Motivated by this problem, we have proposed the bivariate joint multivariate random effects (JMRE) model, which has shown that when correctly specified it performs well in terms of bias reduction and precision. The bivariate JMRE model is fully parametric and belongs to the class of shared parameters joint models where a survival model for the dropouts and a mixed model for the markers' evolution are linked through a multivariate normal distribution of random effects. As in every parametric model, robustness under violations of its distributional assumptions is of great importance. In this study we generated 500 simulated data sets assuming that random effects jointly follow a heavy-tailed distribution, two skewed distributions or a mixture of two normal distributions. Moreover, we generated data where level-1 errors or residuals in the survival part of the model follow a skewed distribution. Further sensitivity analysis on the effects of reduced sample size, increased level-1 variances and altered fixed effects values was also performed. We found that fixed effects estimates are almost unaffected, but their standard errors (SEs) may be underestimated especially under heavily skewed distributions. The proposed model seems robust enough, but its performance on smaller data sets or under more extreme departures of its assumptions needs further investigation.

Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues

“…Despite this, it has translated into only limited model innovation in the MVJM framework, with Tang and Tang [49] considering using the multivariate skew-normal distribution. The robustness of model estimates to misspecification of errors, error structures, and magnitude of errors, has been examined through several simulation studies [40, 43, 49, 50]. Dantan et al [44] and Proust-Lima et al [45, 57] considered a model for [0, 1]-bounded continuous data using the Beta transformation link function, as it is parsimonious and offers very flexible shapes.…”

“…Nonetheless, multivariate normal distributions are the standard modelling choice for random effects in the longitudinal submodel. Several simulation studies have generated data under misspecified random effects [43, 49, 60, 68]. Pantazis and Touloumi [43] explored misspecification by fitting their proposed model [40] to data simulated under a range of heavy tailed, skewed, and mixture distributions.…”

“…Several simulation studies have generated data under misspecified random effects [43, 49, 60, 68]. Pantazis and Touloumi [43] explored misspecification by fitting their proposed model [40] to data simulated under a range of heavy tailed, skewed, and mixture distributions. They concluded that fixed effect parameter estimates were quite robust to misspecification with the exception of those in the time-to-event submodel, but standard errors may be underestimated for heavily skewed distributions.…”

“…Parametric models considered in the MVJM framework include the Weibull [20, 45, 52, 53, 55, 57, 62, 64, 65], exponential [20, 52, 62, 65], log-normal [40, 41, 43, 55, 64], log-logistic [55], and Gompertz [57, 62]. Hu et al [48] used a Weibull model for imputing composite event times, but used a conditional multinomial logistic regression model to then impute the cause type.…”

Vol. 11, No. 1 (Full Issue)

“…The JMRE model allows the modeling of mixed effects and bivariate outcomes. There are several advantages of modeling bivariate outcomes (see Laird and Ware, 1982;Dempster, et al, 1984;Bagiella, 2000;Pantazis & Touloumi, 2007;McCulloch, 2008;Atem, et al,. 2010).…”