Application of pattern-mixture models to outcomes that are potentially missing not at random using pseudo maximum likelihood estimation

In this work, we fit pattern-mixture models to data sets with responses that are potentially missing not at random (MNAR, Little and Rubin, 1987). In estimating the regression parameters that are identifiable, we use the pseudo maximum likelihood method based on exponential families. This procedure provides consistent estimators when the mean structure is correctly specified for each pattern, with further information on the variance structure giving an efficient estimator. The proposed method can be used to handle a variety of continuous and discrete outcomes. A test built on this approach is also developed for model simplification in order to improve efficiency. Simulations are carried out to compare the proposed estimation procedure with other methods. In combination with sensitivity analysis, our approach can be used to fit parsimonious semi-parametric pattern-mixture models to outcomes that are potentially MNAR. We apply the proposed method to an epidemiologic cohort study to examine cognition decline among elderly.     

The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of cure

In this paper we present an extension of cure models: to incorporate a longitudinal disease progression marker. The model is motivated by studies of patients with prostate cancer undergoing radiation therapy. The patients are followed until recurrence of the prostate cancer or censoring, with the PSA marker measured intermittently. Some patients are cured by the treatment and are immune from recurrence. A joint-cure model is developed for this type of data, in which the longitudinal marker and the failure time process are modeled jointly, with a fraction of patients assumed to be immune from the endpoint. A hierarchical nonlinear mixed-effects model is assumed for the marker and a time-dependent Cox proportional hazards model is used to model the time to endpoint. The probability of cure is modeled by a logistic link. The parameters are estimated using a Monte Carlo EM algorithm. Importance sampling with an adaptively chosen t-distribution and variable Monte Carlo sample size is used. We apply the method to data from prostate cancer and perform a simulation study. We show that by incorporating the longitudinal disease progression marker into the cure model, we obtain parameter estimates with better statistical properties. The classification of the censored patients into the cure group and the susceptible group based on the estimated conditional recurrence probability from the joint-cure model has a higher sensitivity and specificity, and a lower misclassification probability compared with the standard cure model. The addition of the longitudinal data has the effect of reducing the impact of the identifiability problems in a standard cure model and can help overcome biases due to informative censoring.     

A Bayesian analysis of colonic crypt structure and coordinated response to carcinogen exposure incorporating missing crypts

This paper is concerned with modeling the architecture of colonic crypts and the implications of this modeling for understanding possible coordinated response of carcinogen-induced DNA damage between various regions of the colon. The methods we develop to address these two issues are applied to a particular important example in colon carcinogenesis. We cast the problem as an unusual and not previously studied hierarchical mixed-effects model characterized by completely missing covariates in units at a structurally base level, except for some randomly selected units. Information concerning the missing covariates is available through certain known ordering constraints and surrogate measures. Our methods use Bayesian machinery. We exploit the biological structure of this problem to generate the missing covariates simultaneously and efficiently at the base levels, as opposed to the naive practice of generating units at the base levels one-at-a-time with Metropolis-Hastings steps. We apply our methods to show that different regions of the colon have different architectures, and to estimate an important but non-standard function that measures the interrelationship of DNA damage mechanisms in different regions of the colon.     

Time-varying Markov regression random-effect model with Bayesian estimation procedures: Application to dynamics of functional recovery in patients with stroke

The rates of functional recovery after stroke tend to decrease with time. Time-varying Markov processes (TVMP) may be more biologically plausible than time-invariant Markov process for modeling such data. However, analysis of such stochastic processes, particularly tackling reversible transitions and the incorporation of random effects into models, can be analytically intractable. We make use of ordinary differential equations to solve continuous-time TVMP with reversible transitions. The proportional hazard form was used to assess the effects of an individual’s covariates on multi-state transitions with the incorporation of random effects that capture the residual variation after being explained by measured covariates under the concept of generalized linear model. We further built up Bayesian directed acyclic graphic model to obtain full joint posterior distribution. Markov chain Monte Carlo (MCMC) with Gibbs sampling was applied to estimate parameters based on posterior marginal distributions with multiple integrands. The proposed method was illustrated with empirical data from a study on the functional recovery after stroke.