Joint modeling of longitudinal and competing-risk data using cumulative incidence functions for the failure submodels accounting for potential failure cause misclassification through double sampling.

Most of the literature on joint modeling of longitudinal and competing-risk data is based on cause-specific hazards, although modeling of the cumulative incidence function (CIF) is an easier and more direct approach to evaluate the prognosis of an event. We propose a flexible class of shared parameter models to jointly model a normally distributed marker over time and multiple causes of failure using CIFs for the survival submodels, with CIFs depending on the "true" marker value over time (i.e., removing the measurement error). The generalized odds rate transformation is applied, thus a proportional subdistribution hazards model is a special case. The requirement that the all-cause CIF should be bounded by 1 is formally considered. The proposed models are extended to account for potential failure cause misclassification, where the true failure causes are available in a small random sample of individuals. We also provide a multistate representation of the whole population by defining mutually exclusive states based on the marker values and the competing risks. Based solely on the assumed joint model, we derive fully Bayesian posterior samples for state occupation and transition probabilities. The proposed approach is evaluated in a simulation study and, as an illustration, it is fitted to real data from people with HIV.

Misspecifying the covariance structure in a linear mixed model under MAR drop-out.

Misspecification of the covariance structure in a linear mixed model (LMM) can lead to biased population parameters' estimates under MAR drop-out. In our motivating example of modeling CD4 cell counts during untreated HIV infection, random intercept and slope LMMs are frequently used. In this article, we evaluate the performance of LMMs with specific covariance structures, in terms of bias in the fixed effects estimates, under specific MAR drop-out mechanisms, and adopt a Bayesian model comparison criterion to discriminate between the examined approaches in real-data applications. We analytically show that using a random intercept and slope structure when the true one is more complex can lead to seriously biased estimates, with the degree of bias depending on the magnitude of the MAR drop-out. Under misspecified covariance structure, we compare in terms of induced bias the approach of adding a fractional Brownian motion (BM) process on top of random intercepts and slopes with the approach of using splines for the random effects. In general, the performance of both approaches was satisfactory, with the BM model leading to smaller bias in most cases. A simulation study is carried out to evaluate the performance of the proposed Bayesian criterion in identifying the model with the correct covariance structure. Overall, the proposed method performs better than the AIC and BIC criteria under our specific simulation setting. The models under consideration are applied to real data from the CASCADE study; the most plausible model is identified by all examined criteria.

Longitudinal and time-to-drop-out joint models can lead to seriously biased estimates when the drop-out mechanism is at random.

Missing data are common in longitudinal studies. Likelihood-based methods ignoring the missingness mechanism are unbiased provided missingness is at random (MAR); under not-at-random missingness (MNAR), joint modeling is commonly used, often as part of sensitivity analyses. In our motivating example of modeling CD4 count trajectories during untreated HIV infection, CD4 counts are mainly censored due to treatment initiation, with the nature of this mechanism remaining debatable. Here, we evaluate the bias in the disease progression marker's change over time (slope) of a specific class of joint models, termed shared-random-effects-models (SREMs), under MAR drop-out and propose an alternative SREM model. Our proposed model relates drop-out to both the observed marker's data and the corresponding random effects, in contrast to most SREMs, which assume that the marker and the drop-out processes are independent given the random effects. We analytically calculate the asymptotic bias in two SREMs under specific MAR drop-out mechanisms, showing that the bias in marker's slope increases as the drop-out probability increases. The performance of the proposed model, and other commonly used SREMs, is evaluated under specific MAR and MNAR scenarios through simulation studies. Under MAR, the proposed model yields nearly unbiased slope estimates, whereas the other SREMs yield seriously biased estimates. Under MNAR, the proposed model estimates are approximately unbiased, whereas those from the other SREMs are moderately to heavily biased, depending on the parameterization used. The examined models are also fitted to real data and results are compared/discussed in the light of our analytical and simulation-based findings.

Postprocessing of genealogical trees.

We consider inference for demographic models and parameters based upon postprocessing the output of an MCMC method that generates samples of genealogical trees (from the posterior distribution for a specific prior distribution of the genealogy). This approach has the advantage of taking account of the uncertainty in the inference for the tree when making inferences about the demographic model and can be computationally efficient in terms of reanalyzing data under a wide variety of models. We consider a (simulation-consistent) estimate of the likelihood for variable population size models, which uses importance sampling, and propose two new approximate likelihoods, one for migration models and one for continuous spatial models.

Maximum-likelihood estimation of coalescence times in genealogical trees.

We develop a method for maximum-likelihood estimation of coalescence times in genealogical trees, based on population genetics data. For this purpose, a Viterbi-type algorithm is constructed to maximize the joint likelihood of the coalescence times. Marginal confidence intervals for the coalescence times based on the profile likelihoods are also computed. Our method of finding MLEs and calculating C.I.'s appears to be more accurate than alternative numerical maximization methods, and maximum-likelihood inference appears to be more accurate than other existing model-free approaches to estimating coalescent times. We demonstrate the method on two different data sets: human Y chromosome DNA data and fungus DNA data.