Survival Analysis: Techniques for Censored and Truncated Data

A new semiparameteric model of the receiver operating characteristic (ROC) curve based on the resilience family or proportional reversed hazard family is proposed, which is an alternative to the existing models. The resulting ROC curve and its summary indices (such as area under the curve and Youden index) have simple analytic forms. The partial likelihood method is applied to estimate the ROC curve. Moreover, the estimation methodologies of the resilience family of the ROC curve have been developed based on area under the curve estimators exploiting Mann–Whitney statistics and the Rojo approach. A simulation study has been carried out to assess the performance of all considered estimators. Real data from the American National Health and Nutrition Examination Survey has been analyzed in detail based on the proposed model and the usual binormal model prevalent in the literature. Real data in the context of brain injury-related biomarkers are also analyzed in order to compare our model with the Lehmann family of the ROC curves. Finally, we show that the proposed model may be applicable in the misspecification scenario through the Ducheme muscular dystrophy data.

Resilience Family of Receiver Operating Characteristic Curves

A new semiparameteric model of the receiver operating characteristic (ROC) curve based on the resilience family or proportional reversed hazard family is proposed, which is an alternative to the existing models. The resulting ROC curve and its summary indices (such as area under the curve and Youden index) have simple analytic forms. The partial likelihood method is applied to estimate the ROC curve. Moreover, the estimation methodologies of the resilience family of the ROC curve have been developed based on area under the curve estimators exploiting Mann–Whitney statistics and the Rojo approach. A simulation study has been carried out to assess the performance of all considered estimators. Real data from the American National Health and Nutrition Examination Survey has been analyzed in detail based on the proposed model and the usual binormal model prevalent in the literature. Real data in the context of brain injury-related biomarkers are also analyzed in order to compare our model with the Lehmann family of the ROC curves. Finally, we show that the proposed model may be applicable in the misspecification scenario through the Ducheme muscular dystrophy data. 

In the analysis of competing risks data, it is common that the exact cause of failure for certain study subjects is missing. This problem of missing failure type may be due to inadequacy in the diagnostic mechanism or reluctance to report the exact cause of failure. In the present paper, we consider the nonparametric estimation of cumulative cause specific reversed hazard rates for left censored competing risks data under masked causes of failure. We first develop maximum likelihood estimators of cumulative cause specific reversed hazard rates. We then consider the least squares type estimators for cumulative cause specific reversed hazard rates, when the information about the conditional probability of exact failure type given a set of possible failure types is available. Simulation studies are conducted to assess the performance of the proposed estimators. We illustrate the applicability of the proposed methods using a data set. Abstract

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Nonparametric Estimation of Cumulative cause Specific Reversed Hazard Rates under Masked Causes of Failure

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Two-sample nonparametric test for proportional reversed hazards

The proportional reversed hazards model explains the multiplicative effect of covariates on the baseline reversed hazard rate function of lifetimes. In the present study, we introduce a proportional cause-specific reversed hazards model. The proposed regression model facilitates the analysis of failure time data with multiple causes of failure under left censoring. We estimate the regression parameters using a partial likelihood approach. We provide Breslow's type estimators for the cumulative cause-specific reversed hazard rate functions. Asymptotic properties of the estimators are discussed. Simulation studies are conducted to assess their performance. We illustrate the applicability of the proposed model using a real data set.

S. Anjana

Papers

Proportional cause-specific reversed hazards model

Nonparametric Estimation of Cumulative cause Specific Reversed Hazard Rates under Masked Causes of Failure