Rank regression for accelerated failure time model with clustered and censored data

For clustered survival data, the traditional Gehan-type estimator is asymptotically equivalent to using only the between-cluster ranks, and the within-cluster ranks are ignored. The contribution of this paper is two fold: - (i) incorporating within-cluster ranks in censored data analysis, and; - (ii) applying the induced smoothing of Brown and Wang (2005, Biometrika) for computational convenience. Asymptotic properties of the resulting estimating functions are given. We also carry out numerical studies to assess the performance of the proposed approach and conclude that the proposed approach can lead to much improved estimators when strong clustering effects exist. A dataset from a litter-matched tumorigenesis experiment is used for illustration.

Parametric accelerated failure time models with random effects and an application to kidney transplant survival

Accelerated failure time models with a shared random component are described, and are used to evaluate the effect of explanatory factors and different transplant centres on survival times following kidney transplantation. Different combinations of the distribution of the random effects and baseline hazard function are considered and the fit of such models to the transplant data is critically assessed. A mixture model that combines short- and long-term components of a hazard function is then developed, which provides a more flexible model for the hazard function. The model can incorporate different explanatory variables and random effects in each component. The model is straightforward to fit using standard statistical software, and is shown to be a good fit to the transplant data. Copyright (C) 2004 John Wiley Sons, Ltd.

On the Accelerated Failure Time Model for Current Status and Interval Censored Data

This paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time (AFT) model for current status and interval censored data. The estimator is constructed by inverting a Wald type test for testing a null proportional hazards model. A numerically efficient Markov chain Monte Carlo (MCMC) based resampling method is proposed to simultaneously obtain the point estimator and a consistent estimator of its variance-covariance matrix. We illustrate our approach with interval censored data sets from two clinical studies. Extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators.

Change Point Estimation in Monitoring Survival Time

Precise identification of the time when a change in a hospital outcome has occurred enables clinical experts to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for survival time of a clinical procedure in the presence of patient mix in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the mean survival time of patients who underwent cardiac surgery. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. The proposed estimator shows a better performance where a longer follow-up period, censoring time, is applied. In comparison with the alternative built-in CUSUM estimator, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Modelling total duration of traffic incidents including incident detection and recovery time

Traffic incidents are key contributors to non-recurrent congestion, potentially generating significant delay. Factors that influence the duration of incidents are important to understand so that effective mitigation strategies can be implemented. To identify and quantify the effects of influential factors, a methodology for studying total incident duration based on historical data from an ‘integrated database’ is proposed. Incident duration models are developed using a selected freeway segment in the Southeast Queensland, Australia network. The models include incident detection and recovery time as components of incident duration. A hazard-based duration modelling approach is applied to model incident duration as a function of a variety of factors that influence traffic incident duration. Parametric accelerated failure time survival models are developed to capture heterogeneity as a function of explanatory variables, with both fixed and random parameters specifications. The analysis reveals that factors affecting incident duration include incident characteristics (severity, type, injury, medical requirements, etc.), infrastructure characteristics (roadway shoulder availability), time of day, and traffic characteristics. The results indicate that event type durations are uniquely different, thus requiring different responses to effectively clear them. Furthermore, the results highlight the presence of unobserved incident duration heterogeneity as captured by the random parameter models, suggesting that additional factors need to be considered in future modelling efforts.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

UNIFORMLY ACCELERATED FINITE-TIME DETECTORS

The behavior of uniformly accelerated detectors in the Minkowski and Rindler vacua is analyzed when the detector is coupled to a scalar field during a finite amount of time T. We point out that the logarithmic ultraviolet divergences reported in the literature are due to the instantaneous switching of the detector. We explicitly show this by considering a detector switched on and off continuously. The usual Planckian spectrum for the excitation probability is recovered in the limit T --> infinity.

Quantifying and Comparing the Accuracy of Binary Biomarkers When Predicting a Failure Time Outcome

The positive and negative predictive value are standard measures used to quantify the predictive accuracy of binary biomarkers when the outcome being predicted is also binary. When the biomarkers are instead being used to predict a failure time outcome, there is no standard way of quantifying predictive accuracy. We propose a natural extension of the traditional predictive values to accommodate censored survival data. We discuss not only quantifying predictive accuracy using these extended predictive values, but also rigorously comparing the accuracy of two biomarkers in terms of their predictive values. Using a marginal regression framework, we describe how to estimate differences in predictive accuracy and how to test whether the observed difference is statistically significant.

BNP-guided vs symptom-guided heart failure therapy: the Trial of Intensified vs Standard Medical Therapy in Elderly Patients With Congestive Heart Failure (TIME-CHF) randomized trial

CONTEXT: It is uncertain whether intensified heart failure therapy guided by N-terminal brain natriuretic peptide (BNP) is superior to symptom-guided therapy. OBJECTIVE: To compare 18-month outcomes of N-terminal BNP-guided vs symptom-guided heart failure therapy. DESIGN, SETTING, AND PATIENTS: Randomized controlled multicenter Trial of Intensified vs Standard Medical Therapy in Elderly Patients With Congestive Heart Failure (TIME-CHF) of 499 patients aged 60 years or older with systolic heart failure (ejection fraction < or = 45%), New York Heart Association (NYHA) class of II or greater, prior hospitalization for heart failure within 1 year, and N-terminal BNP level of 2 or more times the upper limit of normal. The study had an 18-month follow-up and it was conducted at 15 outpatient centers in Switzerland and Germany between January 2003 and June 2008. INTERVENTION: Uptitration of guideline-based treatments to reduce symptoms to NYHA class of II or less (symptom-guided therapy) and BNP level of 2 times or less the upper limit of normal and symptoms to NYHA class of II or less (BNP-guided therapy). MAIN OUTCOME MEASURES: Primary outcomes were 18-month survival free of all-cause hospitalizations and quality of life as assessed by structured validated questionnaires. RESULTS: Heart failure therapy guided by N-terminal BNP and symptom-guided therapy resulted in similar rates of survival free of all-cause hospitalizations (41% vs 40%, respectively; hazard ratio [HR], 0.91 [95% CI, 0.72-1.14]; P = .39). Patients' quality-of-life metrics improved over 18 months of follow-up but these improvements were similar in both the N-terminal BNP-guided and symptom-guided strategies. Compared with the symptom-guided group, survival free of hospitalization for heart failure, a secondary end point, was higher among those in the N-terminal BNP-guided group (72% vs 62%, respectively; HR, 0.68 [95% CI, 0.50-0.92]; P = .01). Heart failure therapy guided by N-terminal BNP improved outcomes in patients aged 60 to 75 years but not in those aged 75 years or older (P < .02 for interaction) CONCLUSION: Heart failure therapy guided by N-terminal BNP did not improve overall clinical outcomes or quality of life compared with symptom-guided treatment. TRIAL REGISTRATION: isrctn.org Identifier: ISRCTN43596477.