Accelerated failure time modeling via nonparametric mixtures.

An accelerated failure time (AFT) model assuming a log-linear relationship between failure time and a set of covariates can be either parametric or semiparametric, depending on the distributional assumption for the error term. Both classes of AFT models have been popular in the analysis of censored failure time data. The semiparametric AFT model is more flexible and robust to departures from the distributional assumption than its parametric counterpart. However, the semiparametric AFT model is subject to producing biased results for estimating any quantities involving an intercept. Estimating an intercept requires a separate procedure. Moreover, a consistent estimation of the intercept requires stringent conditions. Thus, essential quantities such as mean failure times might not be reliably estimated using semiparametric AFT models, which can be naturally done in the framework of parametric AFT models. Meanwhile, parametric AFT models can be severely impaired by misspecifications. To overcome this, we propose a new type of the AFT model using a nonparametric Gaussian-scale mixture distribution. We also provide feasible algorithms to estimate the parameters and mixing distribution. The finite sample properties of the proposed estimators are investigated via an extensive stimulation study. The proposed estimators are illustrated using a real dataset.

Semiparametric estimation for nonparametric frailty models using nonparametric maximum likelihood approach.

A consequence of using a parametric frailty model with nonparametric baseline hazard for analyzing clustered time-to-event data is that its regression coefficient estimates could be sensitive to the underlying frailty distribution. Recently, there has been a proposal for specifying both the baseline hazard and the frailty distribution nonparametrically, and estimating the unknown parameters by the maximum penalized likelihood method. Instead, in this paper, we propose the nonparametric maximum likelihood method for a general class of nonparametric frailty models, i.e. models where the frailty distribution is completely unspecified but the baseline hazard can be either parametric or nonparametric. The implementation of the estimation procedure can be based on a combination of either the Broyden-Fletcher-Goldfarb-Shanno or expectation-maximization algorithm and the constrained Newton algorithm with multiple support point inclusion. Simulation studies to investigate the performance of estimation of a regression coefficient by several different model-fitting methods were conducted. The simulation results show that our proposed regression coefficient estimator generally gives a reasonable bias reduction when the number of clusters is increased under various frailty distributions. Our proposed method is also illustrated with two data examples.

Multiple imputation for missing laboratory data: an example from infectious disease epidemiology.

PURPOSE: To present multiple imputation (MI) as an appropriate method to address missing values for a laboratory parameter (serum albumin) in an epidemiologic study. METHODS: A data set of patients who were hospitalized for invasive group A streptococcal infections was accessed. Age was the exposure of interest. The outcome was hospital mortality. Several variables, including serum albumin, were considered to be potential confounders. Of the 201 records, 91 had missing values for serum albumin. The MI procedure in SAS was used to perform 20 imputations of serum albumin by using a Markov chain Monte Carlo approach. Logistic regression was then performed on each of the 20 filled-in data sets, and the results were appropriately combined by using the MIANALYZE procedure. RESULTS: Age (> or = 55 years vs. 0-54 years) was not a risk factor for hospital mortality in the complete-case analysis (n = 110): adjusted odds ratio (OR) = 2.43 (95% confidence interval [CI]: 0.79-7.53). Age was a significant risk factor in the imputed data set (n = 201): adjusted OR = 3.08 (95% CI: 1.22-7.78). CONCLUSIONS: Epidemiologists frequently encounter data sets that contain missing values. Traditional missing data techniques such as the complete-subject analysis may lead to biased results. We have demonstrated the use of a novel technique, MI, to account for missing data.