Discrete proportional hazards models for mismeasured outcomes

Outcome mismeasurement can lead to biased estimation in several contexts. Magder and Hughes (1997, American Journal of Epidemiology 146, 195-203) showed that failure to adjust for imperfect outcome measures in logistic regression analysis can conservatively bias estimation of covariate effects, even when the mismeasurement rate is the same across levels of the covariate. Other authors have addressed the need to account for mismeasurement in survival analysis in selected cases (Snapinn, 1998, Biometrics 54, 209-218; Gelfand and Wang, 2000, Statistics in Medicine 19, 1865-1879; Balasubramanian and Lagakos, 2001, Biometrics 57, 1048-1058, 2003, Biometrika 90, 171-182). We provide a general, more widely applicable, adjusted proportional hazards (APH) method for estimation of cumulative survival and hazard ratios in discrete time when the outcome is measured with error. We show that mismeasured failure status in a standard proportional hazards (PH) model can conservatively bias estimation of hazard ratios and that inference, in most practical situations, is more severely affected by poor specificity than by poor sensitivity. However, in simulations over a wide range of conditions, the APH method with correctly specified mismeasurement rates performs very well.     

Accelerated hazards regression model and its adequacy for censored survival data

The accelerated hazards regression model is introduced to study the relationship between survival times and covariates through a scale change between hazard functions. The model is also compared with several other popular classes of regression models for censored survival data in statistical literature. Test statistics are proposed and studied to assess the model's adequacy. Actual data from a randomized clinical trial of biodegradable carmustine polymer for treatment of brain cancer are analyzed to demonstrate the potential application of the regression model and the proposed test statistics.     

Maximum likelihood estimation for Cox's regression model under nested case-control sampling

Nested case-control sampling is designed to reduce the costs of large cohort studies. It is important to estimate the parameters of interest as efficiently as possible. We present a new maximum likelihood estimator (MLE) for nested case-control sampling in the context of Cox's proportional hazards model. The MLE is computed by the EM-algorithm, which is easy to implement in the proportional hazards setting. Standard errors are estimated by a numerical profile likelihood approach based on EM aided differentiation. The work was motivated by a nested case-control study that hypothesized that insulin-like growth factor I was associated with ischemic heart disease. The study was based on a population of 3784 Danes and 231 cases of ischemic heart disease where controls were matched on age and gender. We illustrate the use of the MLE for these data and show how the maximum likelihood framework can be used to obtain information additional to the relative risk estimates of covariates.     

Residuals for proportional hazards models with interval-censored survival data

We develop diagnostic tools for use with proportional hazards models for interval-censored survival data. We propose counterparts to the Cox-Snell, Lagakos (or martingale), deviance, and Schoenfeld residuals. Many of the properties of these residuals carry over to the interval-censored case. In particular, the interval-censored versions of the Lagakos and Schoenfeld residuals may be derived as components of suitable score statistics. The Lagakos residuals may be used to check regression relationships, while the Schoenfeld residuals can help to detect nonproportional hazards in semiparametric models. The methods apply to parametric models and to the semiparametric model with discrete observation times.     

Model misspecification in proportional hazards regression

The proportional hazards model is frequently used to evaluatethe effect of treatment on failure time events in randomisedclinical trials. Concomitant variables are usually availableand may be considered for use in the primary analyses underthe assumption that incorporating them may reduce bias or improveefficiency. In this paper we consider two approaches to includingcovariate information: regression modelling and stratification.We focus on the setting where covariate effects are nonproportionaland we compare the bias, efficiency and coverage propertiesof these approaches. These results indicate that our intuitionbased on linear model analysis of covariance is misleading.Covariate adjustment in proportional hazards models has littleeffect on the variance but may significantly improve the accuracyof the treatment effect estimator.     

A sequential stratification method for estimating the effect of a time-dependent experimental treatment in observational studies

Survival analysis is often used to compare experimental and conventional treatments. In observational studies, the therapy may change during follow-up and such crossovers can be summarized by time-dependent covariates. Given the ever-increasing donor organ shortage, higher-risk kidneys from expanded criterion donors (ECD) are being transplanted. Transplant candidates can choose whether to accept an ECD organ (experimental therapy), or to remain on dialysis and wait for a possible non-ECD transplant later (conventional therapy). A three-group time-dependent analysis of such data involves estimating parameters corresponding to two time-dependent indicator covariates representing ECD transplant and non-ECD transplant, each compared to remaining on dialysis on the waitlist. However, the ECD hazard ratio estimated by this time-dependent analysis fails to account for the fact that patients who forego an ECD transplant are not destined to remain on dialysis forever, but could subsequently receive a non-ECD transplant. We propose a novel method of estimating the survival benefit of ECD transplantation relative to conventional therapy (waitlist with possible subsequent non-ECD transplant). Compared to the time-dependent analysis, the proposed method more accurately characterizes the data structure and yields a more direct estimate of the relative outcome with an ECD transplant.     

A marginal mixed baseline hazards model for multivariate failure time data

In multivariate failure time data analysis, a marginal regression modeling approach is often preferred to avoid assumptions on the dependence structure among correlated failure times. In this paper, a marginal mixed baseline hazards model is introduced. Estimating equations are proposed for the estimation of the marginal hazard ratio parameters. The proposed estimators are shown to be consistent and asymptotically Gaussian with a robust covariance matrix that can be consistently estimated. Simulation studies indicate the adequacy of the proposed methodology for practical sample sizes. The methodology is illustrated with a data set from the Framingham Heart Study.