Gengsheng Qin

Comparison of non-parametric confidence intervals for the area under the ROC curve of a continuous-scale diagnostic test

The accuracy of a diagnostic test with continuous-scale results is of high importance in clinical medicine. It is often summarised by the area under the ROC curve (AUC). In this article, we discuss and compare nine non-parametric confidence intervals of the AUC for a continuous-scale diagnostic test. Simulation studies are conducted to evaluate the relative performance of the confidence intervals for the AUC in terms of coverage probability and average interval length. A real example is used to illustrate the application of the recommended methods.

Empirical Likelihood for Censored Linear Regression

In this paper we investigate the empirical likelihood method in a linear regression model when the observations are subject to random censoring. An empirical likelihood ratio for the slope parameter vector is defined and it is shown that its limiting distribution is a weighted sum of independent chi-square distributions. This reduces to the empirical likelihood to the linear regression model first studied by Owen (1991) if there is no censoring present. Some simulation studies are presented to compare the empirical likelihood method with the normal approximation based method proposed in Lai et al. (1995). It was found that the empirical likelihood method performs much better than the normal approximation method.

Empirical likelihood inference for median regression models for censored survival data

Recent advances in median regression model have made it possible to use this model for analyzing a variety of censored survival data. For inference on the model parameter vector, there are now semiparametric procedures based on normal approximation that are valid without strong conditions on the error distribution. However, the accuracy of such procedures can be quite low when the censoring proportion is high. In this paper, we propose an alternative semiparametric procedure based on the empirical likelihood. We define the empirical likelihood ratio for the parameter vector and show that its limiting distribution is a weighted sum of chi-square distributions. Numerical results from a simulation study suggest that the empirical likelihood method is more accurate than the normal approximation based method of Ying et al. (J. Amer. Statist. Assoc. 90 (1995) 178).

EMPIRICAL LIKELIHOOD FOR COX REGRESSION MODEL UNDER RANDOM CENSORSHIP

In this paper we investigate the empirical likelihood method for Cox regression model when the failure times are subject to random censoring. An empirical likelihood ratio for the vector of regression coefficients is defined and it is shown that its limiting distribution is a chi-square distributions with p degrees of freedom. Some simulation studies are presented to compare the empirical likelihood method with the normal approximation method.

New intervals for the difference between two independent binomial proportions

Abstract In this paper we gave an Edgeworth expansion for the studentized difference of two binomial proportions. We then proposed two new intervals by correcting the skewness in the Edgeworth expansion in a direct and an indirect way. Such the bias-correct confidence intervals are easy to compute, and their coverage probabilities converge to the nominal level at a rate of O(n−1/2), where n is the size of the combined samples. Our simulation results suggest that in finite samples the new interval based on the indirect method have the similar performance to the two best existing intervals in terms of coverage accuracy and average interval length and that the another new interval based on the direct method had the best average coverage accuracy but could have poor coverage accuracy when two true binomial proportions are close to the boundary points.

Optimal Combinations of Diagnostic Tests Based on AUC

When several diagnostic tests are available, one can combine them to achieve better diagnostic accuracy. This article considers the optimal linear combination that maximizes the area under the receiver operating characteristic curve (AUC); the estimates of the combinations coefficients can be obtained via a nonparametric procedure. However, for estimating the AUC associated with the estimated coefficients, the apparent estimation by re-substitution is too optimistic. To adjust for the upward bias, several methods are proposed. Among them the cross-validation approach is especially advocated, and an approximated cross-validation is developed to reduce the computational cost. Furthermore, these proposed methods can be applied for variable selection to select important diagnostic tests. The proposed methods are examined through simulation studies and applications to three real examples.

Inference for the Mean Residual Life Function via Empirical Likelihood

In addition to the distribution function, the mean residual life (MRL) function is the other important function which can be used to characterize a lifetime in survival analysis and reliability. For inference on the MRL function, some procedures have been proposed in the literature. However, the coverage accuracy of such procedures may be low when the sample size is small. In this article, an empirical likelihood (EL) inference procedure of MRL function is proposed and the limiting distribution of the EL ratio for MRL function is derived. Based on the result, we obtain confidence interval/band for the MRL function. The proposed method is compared with the normal approximation based method through simulation study in terms of coverage probability.

Asymptotic properties for estimation of partial linear models with censored data

Abstract Consider a partial linear model Y i = X i β + g ( T i )+ e i . Here g is an unknown smooth function on [0,1], β is a one-dimensional parameter to be estimated and e i is an unobserved error. When Y i is censored on the right by another random variable W i with unknown distribution G , the estimators β n ∗ and g ∗ n for β and g are constructed by kernel smoothing and the synthetic data methods. The asymptotic normality and the law of the iterated logarithm for β n ∗ and the convergent rates for g n ∗ are established under some mild conditions.

EMPIRICAL LIKELIHOOD RATIO CONFIDENCE INTERVAL FOR THE TRIMMED MEAN

ABSTRACT The method of empirical likelihood is extended to make inference for the asymptotic mean of the trimmed mean. In this case, the limiting distribution of the empirical likelihood ratio is not the usual but a scaled . Simulation results indicate that the empirical likelihood ratio confidence interval is more reliable than the normal approximation based interval when the underlying distribution is skewed.

Confidence intervals for the difference in paired Youden indices

Comparison of accuracy between two diagnostic tests can be implemented by investigating the difference in paired Youden indices. However, few literature articles have discussed the inferences for the difference in paired Youden indices. In this paper, we propose an exact confidence interval for the difference in paired Youden indices based on the generalized pivotal quantities. For comparison, the maximum likelihood estimate-based interval and a bootstrap-based interval are also included in the study for the difference in paired Youden indices. Abundant simulation studies are conducted to compare the relative performance of these intervals by evaluating the coverage probability and average interval length. Our simulation results demonstrate that the exact confidence interval outperforms the other two intervals even with small sample size when the underlying distributions are normal. A real application is also used to illustrate the proposed intervals.