PubMed · 15063219
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Gary L Grunkemeier, YingXing Wu. 2004. Bootstrap resampling methods: something for nothing?. https://doi.org/10.1016/j.athoracsur.2004.01.005
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In this paper, we are concerned with the estimation of the discrepancy between two treatments when right-censored survival data are accompanied with covariates. Conditional confidence intervals given the available covariates are constructed for the difference between or ratio of two median survival times under the unstratified and stratified Cox proportional hazards models, respectively. The proposed confidence intervals provide the information about the difference in survivorship for patients with common covariates but in different treatments. The results of a simulation study investigation of the coverage probability and expected length of the confidence intervals suggest the one designed for the stratified Cox model when data fit reasonably with the model. When the stratified Cox model is not feasible, however, the one designed for the unstratified Cox model is recommended. The use of the confidence intervals is finally illustrated with a HIV+ data set.
The standardized mean difference has been widely used as the most common index of effect magnitude in many applied fields. In this paper, we propose a novel approach using the concept of generalized variable for the confidence interval estimation and hypothesis testing of standardized mean difference. Furthermore, we extend this approach to compare standardized mean differences between two studies or between two strata. Simulation results demonstrate that the proposed approach can provide confidence intervals with excellent coverage properties and can perform hypothesis testing with satisfactory type-I error control.
The Spearman (rho(s)) and Kendall (tau) rank correlation coefficient are routinely used as measures of association between non-normally distributed random variables. However, confidence limits for rho(s) are only available under the assumption of bivariate normality and for tau under the assumption of asymptotic normality of tau. In this paper, we introduce another approach for obtaining confidence limits for rho(s) or tau based on the arcsin transformation of sample probit score correlations. This approach is shown to be applicable for an arbitrary bivariate distribution. The arcsin-based estimators for rho(s) and tau (denoted by rho(s,a), tau(a)) are shown to have asymptotic relative efficiency (ARE) of 9/pi2 compared with the usual estimators rho(s) and tau when rho(s) and tau are, respectively, 0. In some nutritional applications, the Spearman rank correlation between nutrient intake as assessed by a reference instrument versus nutrient intake as assessed by a surrogate instrument is used as a measure of validity of the surrogate instrument. However, if only a single replicate (or a few replicates) are available for the reference instrument, then the estimated Spearman rank correlation will be downwardly biased due to measurement error. In this paper, we use the probit transformation as a tool for specifying an ANOVA-type model for replicate ranked data resulting in a point and interval estimate of a measurement error corrected rank correlation. This extends previous work by Rosner and Willett for obtaining point and interval estimates of measurement error corrected Pearson correlations.