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General single‐index survival regression models for incident and prevalent covariate data and prevalent data without follow‐up

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  • Shih‐Wei Chen
  • Chin‐Tsang Chiang

Abstract

This article mainly focuses on analyzing covariate data from incident and prevalent cohort studies and a prevalent sample with only baseline covariates of interest and truncation times. Our major task in both research streams is to identify the effects of covariates on a failure time through very general single‐index survival regression models without observing survival outcomes. With a strict increase of the survival function in the linear predictor, the ratio of incident and prevalent covariate densities is shown to be a non‐degenerate and monotonic function of the linear predictor under covariate‐independent truncation. Without such a structural assumption, the conditional density of a truncation time in a prevalent cohort is ensured to be a non‐degenerate function of the linear predictor. In light of these features, some innovative approaches, which are based on the maximum rank correlation estimation or the pseudo least integrated squares estimation, are developed to estimate the coefficients of covariates up to a scale factor. Existing theoretical results are further used to establish the n‐consistency and asymptotic normality of the proposed estimators. Moreover, extensive simulations are conducted to assess and compare the finite‐sample performance of various estimators. To illustrate the methodological ideas, we also analyze data from the Worcester Heart Attack Study and the National Comorbidity Survey Replication.

Suggested Citation

  • Shih‐Wei Chen & Chin‐Tsang Chiang, 2018. "General single‐index survival regression models for incident and prevalent covariate data and prevalent data without follow‐up," Biometrics, The International Biometric Society, vol. 74(3), pages 881-890, September.
  • Handle: RePEc:bla:biomet:v:74:y:2018:i:3:p:881-890
    DOI: 10.1111/biom.12839
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    References listed on IDEAS

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    1. Kwun Chuen Gary Chan, 2013. "Survival analysis without survival data: connecting length-biased and case-control data," Biometrika, Biometrika Trust, vol. 100(3), pages 764-770.
    2. Chiang, Chin-Tsang & Huang, Ming-Yueh, 2012. "New estimation and inference procedures for a single-index conditional distribution model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 271-285.
    3. Bergeron, Pierre-Jerome & Asgharian, Masoud & Wolfson, David B., 2008. "Covariate Bias Induced by Length-Biased Sampling of Failure Times," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 737-742, June.
    4. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    5. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    6. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
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    Cited by:

    1. Shao‐Hsuan Wang & Chin‐Tsang Chiang, 2020. "Concordance‐based estimation approaches for the optimal sufficient dimension reduction score," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 662-689, September.

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