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No description available.

Cox Proportional Hazard Model is one of the most popular tools used in the study of Survival Analysis. Empirical Likelihood (EL) method has been used to study the Cox Proportional Hazard Model. In recent work by Qin and Jing (2001), empirical likelihood based confidence region is constructed with the assumption that the baseline hazard function is known. However, in Cox’s regression model the baseline hazard function is unspecified. In this thesis, we re-formulate empirical likelihood for the vector of regression parameters by estimating the baseline hazard function. The EL confidence regions are obtained accordingly. In addition, Adjusted Empirical Likelihood (AEL) method is proposed. Furthermore, we conduct extensive simulation studies to evaluate the performance of the proposed empirical likelihood methods in terms of coverage probabilities by comparing with the Normal Approximation based method. The simulation studies show that all the three methods produce similar coverage probabilities.

The receiver operating characteristic, or the ROC curve, is widely utilized to evaluate the diagnostic performance of a test, in other words, the accuracy of a test to discriminate normal cases from diseased cases. In the biomedical studies, we often meet with missing data, which the regular inference procedures cannot be applied to directly. In this thesis, the random hot deck imputation is used to obtain a 'complete' sample. Then empirical likelihood (EL) confidence intervals are constructed for ROC curves. The empirical log-likelihood ratio statistic is derived whose asymptotic distribution isproved to be a weighted chi-square distribution. The results of simulation study show that the EL confidence intervals perform well in terms of the coverage probability and the average length for various sample sizes and response rates.

In biomedical research and lifetime data analysis, the comparison of two hazard functions usually plays an important role in practice. In this thesis, we consider the standard independent two-sample framework under right censoring. We construct efficient and useful confidence intervals for the ratio and difference of two hazard functions using smoothed empirical likelihood methods. The empirical log-likelihood ratio is derived and its asymptotic distribution is a chi-squared distribution. Furthermore, the proposed method can be applied to medical diagnosis research. Simulation studies show that the proposed EL confidence intervals have better performance in terms of coverage accuracy and average length than the traditional normal approximation method. Finally, our methods are illustrated with real clinical trial data. It is concluded that the empirical likelihood methods provide better inferential outcomes.

The mean residual life (MRL) function is an important function in survival analysis, actuarial science, economics and other social sciences and reliability for characterizing lifetime. Different methods have been proposed for doing inference on the MRL but their coverage probabilities for small sample sizes are not good enough. In this thesis we apply the empirical likelihood method and carry out a simulation study of the MRL function using different statistical distributions. The simulation study does a comparison of the empirical likelihood method and the normal approximation method. The comparisons are based on the average lengths of confidence intervals and coverage probabilities. We also did comparisons based on median lengths of confidence intervals for the MRL. We found that the empirical likelihood method gives better coverage probability and shorter confidence intervals than the normal approximation method for almost all the distributions that we considered. Applying the two methods to real data we also found that the empirical likelihood method gives thinner pointwise confidence bands.

Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. More accurate tests lead to improved treatment and thus reduce medical mistakes. The sensitivity and specificity are two important measurements for the diagnostic accuracy of a diagnostic test. When the test results are continuous, it is of interest to construct a confidence interval for the sensitivity at a fixed level of specificity for the test. In this thesis, we propose three empirical likelihood intervals for the sensitivity. Simulation studies are conducted to compare the empirical likelihood based confidence intervals with the existing normal approximation based confidence interval. Our studies show that the new intervals had better coverage probability than the normal approximation based interval in most simulation settings.

In biomedical research and lifetime data analysis, the comparison of two hazard functions usually plays an important role in practice. In this thesis, we consider the standard independent two-sample framework under right censoring. We construct efficient and useful confidence intervals for the ratio and difference of two hazard functions using smoothed empirical likelihood methods. The empirical log-likelihood ratio is derived and its asymptotic distribution is a chi-squared distribution. Furthermore, the proposed method can be applied to medical diagnosis research. Simulation studies show that the proposed EL confidence intervals have better performance in terms of coverage accuracy and average length than the traditional normal approximation method. Finally, our methods are illustrated with real clinical trial data. It is concluded that the empirical likelihood methods provide better inferential outcomes.

In this thesis, we study two independent samples under right censoring. Using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two samples and construct the pointwise confidence intervals from it as well. The empirical log-likelihood ratio is proposed and its asymptotic limit is shown as a chi-squared distribution. In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation method. It is concluded that the empirical likelihood method has a better performance. At last, a real clinical trial data is used for the purpose of illustration. Numerical examples to illustrate the efficacy of the method are presented.