Marginalized Two Part Models for Generalized Gamma Family of Distributions (original) (raw)

The Log-Beta Generalized Half-Normal Regression Model

Journal of Statistical Theory and Applications, 2013

We introduce a log-linear regression model based on the beta generalized half-normal distribution (Pescim et al., 2010). We formulate and develop a log-linear model using a new distribution so-called the log-beta generalized half normal distribution. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments and moment generating function. We characterize the proposed distribution using a simple relationship between two truncated moments. An advantage of the new distribution is that it includes as special sub-models classical distributions reported in the lifetime literature. We also show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as special cases several widely-known regression models. It therefore can be used more effectively in the analysis of survival data. We investigate the maximum likelihood estimates of the model parameters by considering censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.

Marginalized Two-Part Joint Modeling of Longitudinal Semi-Continuous Responses and Survival Data: With Application to Medical Costs

Mathematics

Non-negative continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical costs data. It is thus critical to incorporate the potential dependence of survival status and longitudinal medical costs in joint modeling, where censorship is death-related. Despite the wide use of conventional two-part joint models (CTJMs) to capture zero-inflation, they are limited to conditional interpretations of the regression coefficients in the model’s continuous part. In this paper, we propose a marginalized two-part joint model (MTJM) to jointly analyze semi-continuous longitudinal costs data and survival data. We compare it to the conventional two-part joint model (CTJM) for handling marginal inferences about covariate effects on average costs. We conducted a series of simulation studies to evaluate the superior performance of the proposed MTJM over the CTJM. To illustrate the applicability of the MTJM, we applied the model to a set ...

MTPmle: A SAS Macro and Stata Programs for Marginalized Inference in Semi-Continuous Data

Journal of Statistical Software, 2018

We develop a SAS macro and equivalent Stata programs that provide marginalized inference for semi-continuous data using a maximum likelihood approach. These software extensions are based on recently developed methods for marginalized two-part (MTP) models. Both the SAS and Stata extensions can fit simple MTP models for cross-sectional semi-continuous data. In addition, the SAS macro can fit random intercept models for longitudinal or clustered data, whereas the Stata programs can fit MTP models that account for subject level heteroscedasticity and for a complex survey design. Differences and similarities between the two software extensions are highlighted to provide a comparative picture of the available options for estimation, inclusion of random effects, convergence diagnosis, and graphical display. We provide detailed programming syntax, simulated and real data examples to facilitate the implementation of the MTP models for both SAS and Stata software users.

A Marginalized Combined Gamma Frailty and Normal Random-effects Model for Repeated, Overdispersed, Time-to-event Outcomes

Communications in Statistics - Theory and Methods, 2014

This article proposes a marginalized model for repeated or otherwise hierarchical, overdispersed time-to-event outcomes, adapting the so-called combined model for timeto-event outcomes of Molenberghs et al. (in press), who combined gamma and normal random effects. The two sets of random effects are used to accommodate simultaneously correlation between repeated measures and overdispersion. The proposed version allows for a direct marginal interpretation of all model parameters. The outcomes are allowed to be censored. Two estimation methods are proposed: full likelihood and pairwise likelihood. The proposed model is applied to data from a so-called comet assay and to data from recurrent asthma attacks in children. Both estimation methods perform very well. From simulation results, it follows that the marginalized combined model behaves similarly to the ordinary combined model in terms of point estimation and precision. It is also observed that the pairwise likelihood required more computation time on the one hand but is less sensitive to starting values and stabler in terms of bias with increasing sample size and censoring percentage than full likelihood, on the other, leaving room for both in practice. Modeling Repeated Time-to-Event Outcomes 4807 and Clayton, 1993;. This so-called combined model can flexibly handle all outcomes types commonly encountered in a generalized linear models setting . Here, we focus on time-to-event outcomes, by means of a Weibull distribution with both gamma and normal random effects. A distinctive feature is the potential occurrence of right-censoring, which needs to be incorporated. As such, this model has been studied already in Molenberghs et al. (in press). These authors fitted their combined Weibull-gamma-normal model with censoring using both full likelihood as well as pairwise likelihood ). The combined model here is different from the additive frailty model, one of the proposals by , that embeds two correlated random effects, intercept and slope, for proportional hazard models.

Generalized log-gamma regression models with cure fraction

Lifetime Data Analysis, 2008

In this paper, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to event follows a generalized gamma distribution. We define the negative binomial-generalized gamma distribution, which can be used to model survival data. The new model includes as special cases some of the well-known cure rate models discussed in the literature. We consider a frequentist analysis and nonparametric bootstrap for parameter estimation of a negative binomial-generalized gamma regression model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, we analyze a real data set from the medical area.

New Flexible Regression Models Generated by Gamma Random Variables with Censored Data

International Journal of Statistics and Probability, 2016

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.

The cross-product ratio in bivariate lognormal and gamma distributions, with an application to non-randomized trials

Journal of Applied Statistics, 2010

Non-randomised trials can give a biased impression of the effectiveness of any intervention. We consider trials in which incidence rates are compared in two areas over two periods. Typically, one area receives an intervention whilst the other does not. We outline and illustrate a method to estimate the bias in such trials under two different bivariate models. The illustrations use data in which no particular intervention is operating. The purpose is to illustrate the size of the bias that could be observed purely due to regression towards the mean. The illustrations show that the bias can be appreciably different from zero, and even when centered on zero, the variance of the bias can be large. We conclude that the results of non-randomised trials should be treated with caution, as interventions which show small effects could be explained as artifacts of regression towards the mean.

Doubly Robust and Efficient Estimation of Marginal Structural Models for the Hazard Function

The International Journal of Biostatistics, 2016

In social and health sciences, many research questions involve understanding the causal effect of a longitudinal treatment on mortality (or time-to-event outcomes in general). Often, treatment status may change in response to past covariates that are risk factors for mortality, and in turn, treatment status may also affect such subsequent covariates. In these situations, Marginal Structural Models (MSMs), introduced by Robins (1997. Marginal structural models Proceedings of the American Statistical Association. Section on Bayesian Statistical Science, 1-10), are well-established and widely used tools to account for time-varying confounding. In particular, a MSM can be used to specify the intervention-specific counterfactual hazard function, i. e. the hazard for the outcome of a subject in an ideal experiment where he/she was assigned to follow a given intervention on their treatment variables. The parameters of this hazard MSM are traditionally estimated using the Inverse Probability Weighted estimation Robins (1999. Marginal structural models versus structural nested models as tools for causal inference. In: Statistical models in epidemiology: the environment and clinical trials.

DPpackage: Bayesian Semi- and Nonparametric Modeling inR

Journal of Statistical Software, 2011

Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian nonparametric and semiparametric models in R, DPpackage. Currently, DPpackage includes models for marginal and conditional density estimation, receiver operating characteristic curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison and for eliciting the precision parameter of the Dirichlet process prior, and a general purpose Metropolis sampling algorithm. To maximize computational efficiency, the actual sampling for each model is carried out using compiled C, C++ or Fortran code.

Bayesian Flexible Hierarchical Skew Heavy-Tailed Multivariate Meta Regression Models for Individual Patient Data with Applications

Statistics and Its Interface, 2020

A flexible class of multivariate meta-regression models are proposed for Individual Patient Data (IPD). The methodology is well motivated from 26 pivotal Merck clinical trials that compare statins (cholesterol lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline. The research goal is to jointly analyze the multivariate outcomes, Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG). These three continuous outcome measures are correlated and shed much light on a subject’s lipid status. The proposed multivariate meta-regression models allow for different skewness parameters and different degrees of freedom for the multivariate outcomes from different trials under a general class of skew t-distributions. The theoretical properties of the proposed models are examined and an efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for carrying out Bayesian inference under the proposed multivariate meta-regression model. In addition, the Conditional Predictive Ordinates (CPOs) are computed via an efficient Monte Carlo method. Consequently, the logarithm of the pseudo marginal likelihood and Bayesian residuals are obtained for model comparison and assessment, respectively. A detailed analysis of the IPD meta data from the 26 Merck clinical trials is carried out to demonstrate the usefulness of the proposed methodology.