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Estimation with Cox models: cause-specific survival analysis with misclassified cause of failure.

ABSTRACT: While epidemiologic and clinical research often aims to analyze predictors of specific endpoints, time-to-the-specific-event analysis can be hampered by problems with cause ascertainment. Under typical assumptions of competing risks analysis (and missing-data settings), we correct the cause-specific proportional hazards analysis when information on the reliability of diagnosis is available. Our method avoids bias in effect estimates at low cost in variance, thus offering a perspective for better-informed decision making. The ratio of different cause-specific hazards can be estimated flexibly for this purpose. It thus complements an all-cause analysis. In a sensitivity analysis, this approach can reveal the likely extent and direction of the bias of a standard cause-specific analysis when the diagnosis is suspect. These 2 uses are illustrated in a randomized vaccine trial and an epidemiologic cohort study, respectively.

SUBMITTER: Van Rompaye B

PROVIDER: S-EPMC3903130 | biostudies-literature | 2012 Mar

REPOSITORIES: biostudies-literature

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Estimation with Cox models: cause-specific survival analysis with misclassified cause of failure.

Van Rompaye Bart B Jaffar Shabbar S Goetghebeur Els E

Epidemiology (Cambridge, Mass.) 20120301 2

While epidemiologic and clinical research often aims to analyze predictors of specific endpoints, time-to-the-specific-event analysis can be hampered by problems with cause ascertainment. Under typical assumptions of competing risks analysis (and missing-data settings), we correct the cause-specific proportional hazards analysis when information on the reliability of diagnosis is available. Our method avoids bias in effect estimates at low cost in variance, thus offering a perspective for better ...[more]

PMID: 22317803

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Project description:BackgroundSeparation or monotone likelihood may exist in fitting process of the accelerated failure time (AFT) model using maximum likelihood approach when sample size is small and/or rate of censoring is high (rare event) or there is at least one strong covariate in the model, resulting in infinite estimates of at least one regression coefficient.MethodsThis paper investigated the properties of the maximum likelihood estimator (MLE) of the regression parameters of the AFT models for small sample and/or rare-event situation and addressed the problems by introducing a penalized likelihood approach. The penalized likelihood function and the corresponding score equation is derived by adding a penalty term to the existing likelihood function, which was originally proposed by Firth (Biometrika, 1993) for the exponential family models. Further, a post-hoc adjustment of intercept and scale parameters is discussed keeping them out of penalization to ensure accurate prediction of survival probability. The penalized method was illustrated for the widely used log-location-scale family models such as Weibull, Log-normal and Log-logistic distributions and compared the models and methods uisng an extensive simulation study.ResultsThe simulation study, performed separately for each of the log-location-scale models, showed that Firth's penalized likelihood succeeded to solve the problem of separation and achieve convergence, providing finite estimates of the regression coefficients, which are not often possible by the MLE. Furthermore, the proposed penalized method showed substantial improvement over MLE by providing smaller amount of bias, mean squared error (MSE), narrower confidence interval and reasonably accurate prediction of survival probabilities. The methods are illustrated using prostate cancer data with existence of separation, and results supported the simulation findings.ConclusionWhen sample size is small (≤ 50) or event is rare (i.e., censoring proportion is high) and/or there is any evidence of separation in the data, we recommend to use Firth's penalized likelihood method for fitting AFT model.

Project description:BACKGROUND:Thanks to the advances in genomics and targeted treatments, more and more prediction models based on biomarkers are being developed to predict potential benefit from treatments in a randomized clinical trial. Despite the methodological framework for the development and validation of prediction models in a high-dimensional setting is getting more and more established, no clear guidance exists yet on how to estimate expected survival probabilities in a penalized model with biomarker-by-treatment interactions. METHODS:Based on a parsimonious biomarker selection in a penalized high-dimensional Cox model (lasso or adaptive lasso), we propose a unified framework to: estimate internally the predictive accuracy metrics of the developed model (using double cross-validation); estimate the individual survival probabilities at a given timepoint; construct confidence intervals thereof (analytical or bootstrap); and visualize them graphically (pointwise or smoothed with spline). We compared these strategies through a simulation study covering scenarios with or without biomarker effects. We applied the strategies to a large randomized phase III clinical trial that evaluated the effect of adding trastuzumab to chemotherapy in 1574 early breast cancer patients, for which the expression of 462 genes was measured. RESULTS:In our simulations, penalized regression models using the adaptive lasso estimated the survival probability of new patients with low bias and standard error; bootstrapped confidence intervals had empirical coverage probability close to the nominal level across very different scenarios. The double cross-validation performed on the training data set closely mimicked the predictive accuracy of the selected models in external validation data. We also propose a useful visual representation of the expected survival probabilities using splines. In the breast cancer trial, the adaptive lasso penalty selected a prediction model with 4 clinical covariates, the main effects of 98 biomarkers and 24 biomarker-by-treatment interactions, but there was high variability of the expected survival probabilities, with very large confidence intervals. CONCLUSION:Based on our simulations, we propose a unified framework for: developing a prediction model with biomarker-by-treatment interactions in a high-dimensional setting and validating it in absence of external data; accurately estimating the expected survival probability of future patients with associated confidence intervals; and graphically visualizing the developed prediction model. All the methods are implemented in the R package biospear, publicly available on the CRAN.

Dataset Information

Estimation with Cox models: cause-specific survival analysis with misclassified cause of failure.

Publications

Estimation with Cox models: cause-specific survival analysis with misclassified cause of failure.

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