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.

Run-time model evaluation for requirements model-driven self-adaptation

A self-adaptive system adjusts its configuration to tolerate changes in its operating environment. To date, requirements modeling methodologies for self-adaptive systems have necessitated analysis of all potential system configurations, and the circumstances under which each is to be adopted. We argue that, by explicitly capturing and modelling uncertainty in the operating environment, and by verifying and analysing this model at runtime, it is possible for a system to adapt to tolerate some conditions that were not fully considered at design time. We showcase in this paper our tools and research results. © 2012 IEEE.

Smoothed rank-based procedure for censored data

A smoothed rank-based procedure is developed for the accelerated failure time model to overcome computational issues. The proposed estimator is based on an EM-type procedure coupled with the induced smoothing. "The proposed iterative approach converges provided the initial value is based on a consistent estimator, and the limiting covariance matrix can be obtained from a sandwich-type formula. The consistency and asymptotic normality of the proposed estimator are also established. Extensive simulations show that the new estimator is not only computationally less demanding but also more reliable than the other existing estimators.

Nonparametric rank regression for analyzing water quality concentration data with multiple detection limits

Environmental data usually include measurements, such as water quality data, which fall below detection limits, because of limitations of the instruments or of certain analytical methods used. The fact that some responses are not detected needs to be properly taken into account in statistical analysis of such data. However, it is well-known that it is challenging to analyze a data set with detection limits, and we often have to rely on the traditional parametric methods or simple imputation methods. Distributional assumptions can lead to biased inference and justification of distributions is often not possible when the data are correlated and there is a large proportion of data below detection limits. The extent of bias is usually unknown. To draw valid conclusions and hence provide useful advice for environmental management authorities, it is essential to develop and apply an appropriate statistical methodology. This paper proposes rank-based procedures for analyzing non-normally distributed data collected at different sites over a period of time in the presence of multiple detection limits. To take account of temporal correlations within each site, we propose an optimal linear combination of estimating functions and apply the induced smoothing method to reduce the computational burden. Finally, we apply the proposed method to the water quality data collected at Susquehanna River Basin in United States of America, which dearly demonstrates the advantages of the rank regression models.

Rank regression for analysis of clustered data: A natural induced smoothing approach

We consider rank regression for clustered data analysis and investigate the induced smoothing method for obtaining the asymptotic covariance matrices of the parameter estimators. We prove that the induced estimating functions are asymptotically unbiased and the resulting estimators are strongly consistent and asymptotically normal. The induced smoothing approach provides an effective way for obtaining asymptotic covariance matrices for between- and within-cluster estimators and for a combined estimator to take account of within-cluster correlations. We also carry out extensive simulation studies to assess the performance of different estimators. The proposed methodology is substantially Much faster in computation and more stable in numerical results than the existing methods. We apply the proposed methodology to a dataset from a randomized clinical trial.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

Assessment of the benefits of Discrete Conditional Survival Models in modelling ambulance response times

Many of the challenges faced in health care delivery can be informed through building models. In particular, Discrete Conditional Survival (DCS) models, recently under development, can provide policymakers with a flexible tool to assess time-to-event data. The DCS model is capable of modelling the survival curve based on various underlying distribution types and is capable of clustering or grouping observations (based on other covariate information) external to the distribution fits. The flexibility of the model comes through the choice of data mining techniques that are available in ascertaining the different subsets and also in the choice of distribution types available in modelling these informed subsets. This paper presents an illustrated example of the Discrete Conditional Survival model being deployed to represent ambulance response-times by a fully parameterised model. This model is contrasted against use of a parametric accelerated failure-time model, illustrating the strength and usefulness of Discrete Conditional Survival models.

Análise de resíduos em modelos de tempo de falha acelerado com efeito aleatório

We present residual analysis techniques to assess the fit of correlated survival data by Accelerated Failure Time Models (AFTM) with random effects. We propose an imputation procedure for censored observations and consider three types of residuals to evaluate different model characteristics. We illustrate the proposal with the analysis of AFTM with random effects to a real data set involving times between failures of oil well equipment

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.