Survival models for exploring tuberculosis clinical trial data-an empirical comparison
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The proportional hazard (PH) model and its extension are used comprehensively to assess the effect of an intervention in the presence of covariates. The assumptions of PH model may not hold where the effect of the intervention is to accelerate the onset of an event. The accelerated failure time (AFT) model is the alternative when the PH assumption does not hold. The aim of this paper is to formulate a model that yields biological plausible and interpretable estimates of the effect of important covariates on survival time. The data consists of 1236 tuberculosis patients admitted in randomized controlled clinical trial. A total of six covariates are considered for modeling. The AFT model gives better prediction than the Cox PH model. Keywords: Accelerated failure time model; proportional hazards model; time dependent covariate, tuberculosis.Abstract The Cox proportional hazards model (CPH) is normally applied in clinical trial data analysis, but it can generate severe problems with breaking the proportion hazard assumption. An accelerated failure time (AFT) is considered as an alternative to the proportional hazard model. The model can be used through consideration of different covariates of interest and random effects in each section. The model is simple to fit by using OpenBugs software and is revealed to be a good fit to the Chemotherapy data.
Hazard model
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Abstract Background : When estimating survival functions and hazard ratios during theanalysis of cohort data, we often choose one time-scale, such as time-on-study, asthe primary time-scale, and include a xed covariate, such as age at entry, in themodel. However, we rarely consider the possibility of simultaneous effects ofmultiple time-scales on the hazard function. Methods : In a simulation study, within the framework of exible parametricmodels, we investigate whether relying on one time-scale and xed covariate asproxy for the second time-scale is sucient in capturing the true survivalfunctions and hazard ratios when there are actually two underlying time-scales. Result : We demonstrate that the one-time-scale survival models appeared toapproximate well the survival proportions, however, large bias was observed in thelog hazard ratios if the covariate of interest had interactions with the secondtime-scale or with both time-scales. Conclusion : We recommend to exercise caution and encourage tting modelswith multiple time-scales if it is suspected that the cohort data have underlyingnon-proportional hazards on the second time-scale or both time-scales.
Survival function
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We study the properties of test statistics for a covariate effect in Aalen's additive hazard model and propose several new test statistics. The proposed statistics are derived by using the weights from linear rank statistics for comparing two survival curves. We compare these statistics with the two statistics proposed by Aalen using Monte Carlo simulations. Several different survival configurations are considered in the simulation study: proportional hazards; crossing hazards; hazard differences early in time, and hazard differences for large survival times. Of the proposed test statistics, one is superior for detecting hazard differences for large survival times and another is superior for detecting early hazard differences and crossing hazards. © 1998 John Wiley & Sons, Ltd.
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The most widely used model in multivariate analysis of survival
data is proportional hazards model proposed by ox. While it is easy
to get and interpret the results of the model, the basic assumption of
proportional hazards model is that independent variables assumed
to remain constant throughout the observation period. Model can
give biased results in cases which this assumption is violated. ne
of the methods used modelling the hazard ratio in the cases that the
proportional hazard assumption is not met is to add a time-dependent
variable showing the interaction between the predictor variable and
a parametric function of time. In this study, we investigate the factors
that affect the survival time of the firms and the time dependence of
these factors using ox regression considering time-varying variables.
The firm data comes from Business evelopment enters (ISG M)
which is a prominent business incubation center operating in urkey.
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Proportional Hazard regression model for censored survival data often specifies that covariates have a proportional fixed effect on the hazard function of the lifetime distribution of a subject. A modification of the proportional hazards model of Cox (1972) to accommodate the non-proportional effect on hazard with a time-varying covariate and the introduction of guarantee time into the Weibull distributed baseline hazard function. Simulations were conducted to investigate properties of the models. Our approach had shown to have the best asymptotic properties in a simulation study with mean, Absolute Bias (AB) and Mean Square Error (MSE) of the parameter estimates for the models (under different levels of censoring and sample sizes) using simulated data.
Censoring (clinical trials)
Survival function
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Aim: To compare their prediction performance of BP neural network model and Cox proportion hazard model in survival analysis and to explore the superiority of BP neural network model in survival analysis. Methods: Monte Carlo was used to generate the data sets under the condition of different sample size,different degree of censoring,number of variable and interactions,non-linear effect,distinct distribution of covariate and proportional vs non-proportional hazard.Then BP neural network model and Cox model were built,and their prediction performance was compared using concord-ance index C. Results: In the research on simulation data sets,when the sample size of 100,proportion of censoring of60%,80%,and sample size of 300,proportion of censoring of 80%,BP neural network model performed superior to Cox model( P 0. 05). And when the covariates don' t meet PH assumption and had three-way interaction,non-linear effect,BP neural network performed superior to Cox model( P 0. 05). In the real data,BP neural network model's concordance index was 0. 835,which performed superior to Cox model( tpaired= 4. 311,P 0. 001). Conclusion: For the small sample size,high and the covariates don't meet PH assumption and has three-way interaction,non-linear effect data sets,BP neural network has better advantage than Cox model. It is worth to popularize further in survival analysis.
Censoring (clinical trials)
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The restricted mean survival time is a clinically easy-to-interpret measure that does not require any assumption of proportional hazards. We focus on two ways to directly model the survival time and adjust the covariates. One is to calculate the pseudo-survival time for each subject using leave-one-out, and then perform a model analysis using all pseudo-values to adjust for covariates. The pseudo-survival time is used to reflect information of censored subjects in the model analysis. The other method adjusts for covariates using subjects for whom the time-to-event was observed while adjusting for the censored subjects using the inverse probability of censoring weighting (IPCW). This paper evaluates the performance of these two methods in terms of the power to detect group differences through a simple example dataset and computer simulations. The simple example illustrates the intuitive behavior of the two methods. With the method using pseudo-survival times, it is difficult to interpret the pseudo-values. We confirm that the pseudo-survival times are different from the actual data obtained in a primary biliary cholangitis clinical trial because of the many censored data. In the simulations, the method using IPCW is found to be more powerful. Even in the case of group differences with respect to the censor incidence rates and covariates, the method using IPCW maintains a nominal significance level for the type-1 error rate. We conclude that the IPCW method should be used to estimate the restricted mean survival time when adjusting the covariates.
Censoring (clinical trials)
Inverse probability weighting
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Cox's proportional hazard model is potentially the most used method in life data and survival analysis. Although the method is relatively simple to understand, its major difficulties in estimation are observed when time-dependent covariates with repeated events are used as input variables. An alternative approach to simplify hazard ratio prediction for repeated events is evaluated for a practical application using small appliances reliability data from an accelerated experimental design based on consumer usage.
Repeated measures design
Hazard model
Accelerated life testing
Mixed model
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Abstract Prognostic studies often involve modeling competing risks, where an individual can experience only one of alternative events, and the goal is to estimate hazard functions and covariate effects associated with each event type. Lunn and McNeil proposed data manipulation that permits extending the Cox's proportional hazards model to estimate covariate effects on the hazard of each competing events. However, the hazard functions for competing events are assumed to remain proportional over the entire follow‐up period, implying the same shape of all event‐specific hazards, and covariate effects are restricted to also remain constant over time, even if such assumptions are often questionable. To avoid such limitations, we propose a flexible model to (i) obtain distinct estimates of the baseline hazard functions for each event type, and (ii) allow estimating time‐dependent covariate effects in a parsimonious model. Our flexible competing risks regression model uses smooth cubic regression splines to model the time‐dependent changes in (i) the ratio of event‐specific baseline hazards, and (ii) the covariate effects. In simulations, we evaluate the performance of the proposed estimators and likelihood ratio tests, under different assumptions. We apply the proposed flexible model in a prognostic study of colorectal cancer mortality, with two competing events: ‘death from colorectal cancer’ and ‘death from other causes’. Copyright © 2010 John Wiley & Sons, Ltd.
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Prognostic studies often estimate survival curves for patients with different covariate vectors, but the validity of their results depends largely on the accuracy of the estimated covariate effects. To avoid conventional proportional hazards and linearity assumptions, flexible extensions of Cox's proportional hazards model incorporate non-linear (NL) and/or time-dependent (TD) covariate effects. However, their impact on survival curves estimation is unclear. Our primary goal is to develop and validate a flexible method for estimating individual patients' survival curves, conditional on multiple predictors with possibly NL and/or TD effects. We first obtain maximum partial likelihood estimates of NL and TD effects and use backward elimination to select statistically significant effects into a final multivariable model. We then plug the selected NL and TD estimates in the full likelihood function and estimate the baseline hazard function and the resulting survival curves, conditional on individual covariate vectors. The TD and NL functions and the log hazard are modeled with unpenalized regression B-splines. In simulations, our flexible survival curve estimates were unbiased and had much lower mean square errors than the conventional estimates. In real-life analyses of mortality after a septic shock, our model improved significantly the deviance (likelihood ratio test = 84.8, df = 20, p < 0.0001) and changed substantially the predicted survival for several subjects.
Survival function
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