Biomedical subjects

J G Ibrahim

Publications and source records attributed to J G Ibrahim.

28 records · Page 2Linked to original sources

PubMed1998

Estimating equations with incomplete categorical covariates in the Cox model.

Incomplete covariate data is a common occurrence in many studies in which the outcome is survival time. When a full likelihood is specified, a useful technique for obtaining parameter estimates is the EM algorithm. We propose a set of estimating equations to estimate the parameters of Cox's proportional hazards model when some covariate values are missing. These estimating equations can be solved by an algorithm similar to the EM algorithm. Because of the computational burden of finding a solution to these estimating equations, we propose obtaining parameter estimates via Monte Carlo methods. Asymptotic variances of the parameter estimates are also derived. We present a clinical trials example with three covariates, two of which have some missing values.

Algorithms↗

PubMed1997

Loss of lung function among sheet metal workers: ten-year study.

One hundred and twenty-two sheet metal workers in New England were examined over a 10-year interval for loss of pulmonary function and the development of asbestosis or asbestos-related pleural fibrosis. Regression models using the generalized estimating equation (GEE) approach were created to investigate the relationship between exposure and pulmonary function after adjusting for smoking status, age, height, and asbestos-related x-ray changes. A history of shipyard work was a significant contributor to the loss of forced vital capacity (FVC). Among smokers, loss in forced expiratory volume at 1 sec (FEV1) also had a significant relationship to prior shipyard work. There was a borderline significant relationship between percentage predicted FEV1 and cumulative years of asbestos exposure in smokers, as well as years-since-initial-exposure in never-smokers. This study supports previous findings of obstructive airway changes in asbestos-exposed workers and identifies shipboard work as an important predictor of loss in pulmonary function even years after shipyard exposure to asbestos has ceased.

Adult↗

PubMed1997

The large sample distribution of the weighted log rank statistic under general local alternatives.

We derive the large sample distribution of the weighted log rank statistic under a general class of local alternatives in which both the cure rates and the conditional distribution of time to failure among those who fail are assumed to vary in the two treatment arms. The analytic result presented here is important to data analysts who are designing clinical trials for diseases such as non-Hodgkins lymphoma, leukemia and melanoma, where a significant proportion of patients are cured. We present a numerical illustration comparing powers obtained from the analytic result to those obtained from simulations.

Clinical Trials as Topic↗

PubMed1997

Predictive variable selection for the multivariate linear model.

We develop a predictive Bayesian approach to variable selection in the multivariate linear model. A criterion derived from the Bayesian predictive density is proposed and a calibration is provided for it. Reference and informative priors are discussed, and an automated method that focuses on the response variable is proposed for specifying informative priors for the regression parameters. Relationships between the proposed criterion and other several well-known criteria are examined. Illustrative examples involving real data are given to demonstrate the methodology.

Asbestos↗

PubMed1997

Predictive model selection for repeated measures random effects models using Bayes factors.

The random effects model fit to repeated measures data is an extremely common model and data structure in current biostatistical practice. Modern data analysis often involves the selection of models within broad classes of prespecified models, but for models beyond the generalized linear model, few model-selection tools have been actively studied. In a Bayesian analysis, Bayes factors are the natural tool to use to explore these classes of models. In this paper, we develop a predictive approach for specifying the priors of a repeated measures random effects model with emphasis on selecting the fixed effects. The advantage of the predictive approach is that a single predictive specification is used to specify priors for all models considered. The methodology is applied to a pediatric pain data analysis.

Bayes Theorem↗

PubMed1996

Using the EM-algorithm for survival data with incomplete categorical covariates.

Incomplete covariate data is a common occurrence in many studies in which the outcome is survival time. With generalized linear models, when the missing covariates are categorical, a useful technique for obtaining parameter estimates is the EM by the method of weights proposed in Ibrahim (1990). In this article, we extend the EM by the method of weights to survival outcomes whose distributions may not fall in the class of generalized linear models. This method requires the estimation of the parameters of the distribution of the covariates. We present a clinical trials example with five covariates, four of which have some missing values.

Algorithms↗

PubMed1996

Parameter estimation from incomplete data in binomial regression when the missing data mechanism is nonignorable.

We propose a method for estimating parameters in binomial regression models when the response variable is missing and the missing data mechanism is nonignorable. We assume throughout that the covariates are fully observed. Using a logit model for the missing data mechanism, we show how parameter estimation can be accomplished using the EM algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association 85, 765-769). An example from the Six Cities Study (Ware et al., 1984, American Review of Respiratory Diseases 129, 366-374) is presented to illustrate the method.

Air Pollution↗

PubMed1996

Use of historical controls in time-adjusted trend tests for carcinogenicity.

We develop a method for incorporating historical control information into time-adjusted tests for dose effects in carcinogenicity studies. After discretizing the time scale, we use a multinomial distribution to model the number of animals dying with tumor in each interval. Data from past studies are used to estimate the parameters characterizing the prior. A score test derived from the resulting Dirichlet-multinomial generalizes the test of Tarone (1982, Biometrics 38, 215-220) and reduces, in the limit, to the log-rank test in the case of a diffuse prior. The methodology is illustrated with data from a study of the fire retardant 2,2-Bis(bromomethyl)-1,3-propanediol.

Animals↗

PubMed1991

Forecasting the number of future disabled elderly using Markovian and mathematical models.

The accuracy of forecasting the number of future disabled elderly people depends on the accuracy of projecting mortality rates and the rates of transition to and from functional disability. We describe a new two-step method for constructing mathematical models that project these future rates dynamically. (1) A Markovian model of elders' transitions between functional states is specified. (2) A mathematical model of the probability of each transition is created. We conducted pilot studies of the fundamental mathematical processes of this method using data from the Longitudinal Study of Aging. First we constructed prototypic mathematical models of the probabilities of remaining functionally able and of making transitions to disability and to death within 2 years. Then we used these models to project hypothetical rates of transition for white women of selected ages, morbidity ratings and health statuses.

Activities of Daily Living↗

PubMedDate not supplied

Non-ignorable missing covariates in generalized linear models.

We propose a likelihood method for estimating parameters in generalized linear models with missing covariates and a non-ignorable missing data mechanism. In this paper, we focus on one missing covariate. We use a logistic model for the probability that the covariate is missing, and allow this probability to depend on the incomplete covariate. We allow the covariates, including the incomplete covariate, to be either categorical or continuous. We propose an EM algorithm in this case. For a missing categorical covariate, we derive a closed form expression for the E- and M-steps of the EM algorithm for obtaining the maximum likelihood estimates (MLEs). For a missing continuous covariate, we use a Monte Carlo version of the EM algorithm to obtain the MLEs via the Gibbs sampler. The methodology is illustrated using an example from a breast cancer clinical trial in which time to disease progression is the outcome, and the incomplete covariate is a quality of life physical well-being score taken after the start of therapy. This score may be missing because the patients are sicker, so this covariate could be non-ignorably missing.

Algorithms↗