Covariate Analysis of Survival Data: A Small-Sample Study of Cox's Model

Johnson, Mark E.; Tolley, H. Dennis; Bryson, Maurice C.; Goldman, A.

doi:10.2307/2530049

Cited by 47 publications

(16 citation statements)

References 5 publications

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“…If there is no true e ect the count of signiÿcant parameter estimates correspond well to the test level = 0·05. The simulated expectations as well as the count of parameter estimates with larger values than ÿ indicate a slight overestimation of the true e ect, probably resulting from the small sample properties 21 of the proportional hazards model. While the variability of parameter and risk estimates remains nearly constant when using the true cutpoint it decreases with increasing values of the true e ect when using the 'optimal' cutpoint.…”

Section: Overestimation Caused By the Minimum P-value Methodsmentioning

confidence: 87%

Resampling and cross-validation techniques: a tool to reduce bias caused by model building?

1997

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The process of model building involved in the analysis of many medical studies may lead to a considerable amount of over-optimism with respect to the predictive ability of the 'final' regression model. In this paper we illustrate this phenomenon in a simple cutpoint model and explore to what extent bias can be reduced by using cross-validation and bootstrap resampling. These computer intensive methods are compared to an ad hoc approach and to a heuristic method. Besides illustrating all proposals with the data from a breast cancer study we perform a simulation study in order to assess the quality of the methods.

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Section: Overestimation Caused By the Minimum P-value Methodsmentioning

confidence: 87%

Resampling and cross-validation techniques: a tool to reduce bias caused by model building?

1997

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“…Examining the operating characteristics of the Cox model in Table 2, Table 3, Table 4, and Table 5, it appears the conclusions of Johnson, et al [12] were upheld true hazard ratio and control median for select sample sizes. The simulation results in Table 2 assume no treatment effect (HR = 1).…”

Section: Resultsmentioning

confidence: 95%

“…The performance of Cox models, which are typically used to estimate the hazard ratio, also should not be problematic in small sample settings. Johnson, et al [12] has assessed the small sample performance of Cox models in estimating regression parameters in a two-covariate hazard function model, and they cited an earlier report that considered the simpler single variable case. The general conclusion was that in ideal conditions of balanced covariates and no censoring, results were reasonable for …”

Section: Simulation Methodsmentioning

confidence: 99%

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Inference Based on Small Randomized Oncology Clinical Trials: Is the Observed Treatment Effect True?

Cheng¹

2017

Int J Clin Biostat Biom

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“…Their study enabled the construction of confidence intervals for the survival function estimated from the Cox model. Also in 1982, Johnson et al [13] published a small-sample covariate analysis study of survival data following Cox's model, and Stewart and Pierce [14] assessed the efficiency of Cox's model in estimating regression parameters relative to parametric alternatives for grouped data settings. Bailey [15] (1983) studied the asymptotic joint distribution of the regression and survival parameter estimates in the Cox regression model.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the survival function for Gray's piecewise‐constant time‐varying coefficients model

Valenta

Weissfeld

2002

Statistics in Medicine

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Gray's extension of Cox's proportional hazards (PH) model for right-censored survival data allows for a departure from the PH assumption via introduction of time-varying regression coefficients (TVC) using penalized splines. Gray's work focused on estimation, inference and residual analyses, but no estimator for the survival function has been proposed. We derive a survival function estimator for one important member of the class of TVC models -a piecewise-constant time-varying coefficients (PC-TVC) model. We also derive an estimate for the confidence limits of the survival function. Accuracy in estimating underlying survival times and survival quantiles is assessed for both Cox's and Gray's PC-TVC model using a simulation study featuring scenarios violating the PH assumption. Finally, an example of the estimated survival functions and the corresponding confidence limits derived from Cox's PH and Gray's PC-TVC model, respectively, is presented for a liver transplant data set.In the second part of the thesis we examine the effect of model misspecification for two The effect of misspecifying the true model for the conditional hazard rate is assessed by looking at the power of the individual models to detect an existing effect, bias and mean square error observed for each conditional model-based estimator of survival. We also show that Aalen's model formulae is a first order Taylor series approximation of that of Gray's model which explains the comparably higher flexibility on part of the Aalen's model as compared to the Cox PH when the Gray's TVC model for the data is misspecified.2

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Covariate Analysis of Survival Data: A Small-Sample Study of Cox's Model

Cited by 47 publications

References 5 publications

Resampling and cross-validation techniques: a tool to reduce bias caused by model building?

Resampling and cross-validation techniques: a tool to reduce bias caused by model building?

Inference Based on Small Randomized Oncology Clinical Trials: Is the Observed Treatment Effect True?

Estimation of the survival function for Gray's piecewise‐constant time‐varying coefficients model

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