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Comparing conditional survival functions with missing population marks in a competing risks model

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  • Bandyopadhyay, Dipankar
  • Jácome, M. Amalia

Abstract

In studies involving nonparametric testing of the equality of two or more survival distributions, the survival curves can exhibit a wide variety of behaviors such as proportional hazards, early/late differences, and crossing hazards. As alternatives to the classical logrank test, the weighted Kaplan–Meier (WKM) type statistic and their variations were developed to handle these situations. However, their applicability is limited to cases where the population membership is available for all observations, including the right censored ones. Quite often, failure time data are confronted with missing population marks for the censored observations. To alleviate this, a new WKM-type test is introduced based on imputed population marks for the censored observations leading to fractional at-risk sets that estimate the underlying risk for the process. The asymptotic normality of the proposed test under the null hypothesis is established, and the finite sample properties in terms of empirical size and power are studied through a simulation study. Finally, the new test is applied on a study of subjects undergoing bone marrow transplantation.

Suggested Citation

  • Bandyopadhyay, Dipankar & Jácome, M. Amalia, 2016. "Comparing conditional survival functions with missing population marks in a competing risks model," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 150-160.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:150-160
    DOI: 10.1016/j.csda.2015.10.001
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    References listed on IDEAS

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    1. Isha Dewan & J. V. Deshpande & S. B. Kulathinal, 2004. "On Testing Dependence between Time to Failure and Cause of Failure via Conditional Probabilities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 79-91, March.
    2. Lee, Seung-Hwan & Lee, Eun-Joo & Omolo, Bernard Oguna, 2008. "Using integrated weighted survival difference for the two-sample censored data problem," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4410-4416, May.
    3. Susan Murray, 2001. "Using Weighted Kaplan-Meier Statistics in Nonparametric Comparisons of Paired Censored Survival Outcomes," Biometrics, The International Biometric Society, vol. 57(2), pages 361-368, June.
    4. Anastasios A. Tsiatis, 2002. "Multiple imputation methods for testing treatment differences in survival distributions with missing cause of failure," Biometrika, Biometrika Trust, vol. 89(1), pages 238-244, March.
    5. Datta, Somnath & Satten, Glen A., 2000. "Estimating future stage entry and occupation probabilities in a multistage model based on randomly right-censored data," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 89-95, October.
    6. Yu Shen & Jianwen Cai, 2001. "Maximum of the Weighted Kaplan-Meier Tests with Application to Cancer Prevention and Screening Trials," Biometrics, The International Biometric Society, vol. 57(3), pages 837-843, September.
    7. Satten, Glen A. & Datta, Somnath, 1999. "Kaplan-Meier representation of competing risk estimates," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 299-304, April.
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