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Goodness-of-fit tests for additive mean residual life model under right censoring

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Abstract

The mean residual life (MRL) measures the remaining life expectancy and is useful in actuarial studies, biological experiments and clinical trials. To assess the covariate effect, an additive MRL regression model has been proposed in the literature. In this paper, we focus on the topic of model checking. Specifically, we develop two goodness-of-fit tests to test the additive MRL model assumption. We explore the large sample properties of the test statistics and show that both of them are based on asymptotic Gaussian processes so that resampling approaches can be applied to find the rejection regions. Simulation studies indicate that our methods work reasonably well for sample sizes ranging from 50 to 200. Two empirical data sets are analyzed to illustrate the approaches.

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References

  • Andersen PK (1982) Testing goodness of fit of Cox’s regression and life model. Biometrics 38: 67–77

    Article  MATH  MathSciNet  Google Scholar 

  • Arnold BC, Zahedi H (1988) On multivariate mean remaining life functions. J Multivar Anal 25: 1–9

    Article  MATH  MathSciNet  Google Scholar 

  • Balkema AA, de Haan L (1974) Residual life time at great age. Ann Probab 2: 792–804

    Article  MATH  Google Scholar 

  • Banerjee M (2005) Likelihood ratio tests under local alternatives in regular semiparametric problems. Stat Sin 15: 635–644

    MATH  Google Scholar 

  • Bickel PJ, Klaassen CA, Ritov Y, Wellner JA (1993) Efficient and adaptive inference in semiparametric models. Johns Hopkins University Press, Baltimore, MD

    Google Scholar 

  • Chen YQ (2007) Additive regression of expectancy. J Am Stat Assoc 102: 153–166

    Article  MATH  Google Scholar 

  • Chen YQ, Cheng SC (2005) Semiparametric regression analysis of mean residual life with censored survival data. Biometrika 92: 19–29

    Article  MATH  MathSciNet  Google Scholar 

  • Chen YQ, Cheng SC (2006) Linear life expectancy regression with censored data. Biometrika 93: 303–313

    Article  MATH  MathSciNet  Google Scholar 

  • Chen YQ, Jewell NP, Lei X, Cheng SC (2005) Semiparametric estimation of proportional mean residual life model in presence of censoring. Biometrics 61: 170–178

    Article  MATH  MathSciNet  Google Scholar 

  • Cox DR (1961) Renewal theory. Methuen, London

    Google Scholar 

  • Fleming TR, Harrington DP (1991) Counting processes and survival analysis. Wiley, New York

    MATH  Google Scholar 

  • Gill RD, Schumacher M (1987) A simple test of the proportional hazards assumption. Biometrika 74: 289–300

    Article  MATH  Google Scholar 

  • Hall WJ, Wellner JA (1984) Mean residual life. In: Csörgő M, Dawson DA, Rao JNK, Md. E. Saleh AK (eds) In: Proceedings of the international symposium on statistics and related topics. North Holland, Amsterdam, pp 169–184

  • Hollander M, Proschan F (1975) Tests for the mean residual life. Biometrika 62: 585–593

    Article  MATH  MathSciNet  Google Scholar 

  • Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data. 2. Wiley, New York

    MATH  Google Scholar 

  • Kotz S, Shanbhag DN (1980) Some new approaches to probability distribution. Adv Appl Probab 12: 903–921

    Article  MATH  MathSciNet  Google Scholar 

  • Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73: 13–22

    Article  MATH  MathSciNet  Google Scholar 

  • Lin DY, Wei LJ, Yang I, Ying Z (2000) Semiparametric regression for the mean and rate functions of recurrent events. J R Stat Soc Ser B 62: 711–730

    Article  MATH  MathSciNet  Google Scholar 

  • Maguluri G, Zhang C-H (1994) Estimation in the mean residual life regression model. J R Stat Soc Ser B 56: 477–489

    MATH  MathSciNet  Google Scholar 

  • McKeague IW, Utikal KJ (1991) Goodness-of-fit tests for additive hazards and proportional hazards models. Scand J Stat 18: 177–195

    MATH  MathSciNet  Google Scholar 

  • Oakes D, Dasu T (1990) A note on residual life. Biometrika 77: 409–410

    Article  MATH  MathSciNet  Google Scholar 

  • Pollard D (1990) Empirical processes: theory and applications. Institute of Mathematical Statistics, Hayward, CA

    MATH  Google Scholar 

  • Prentice RL (1973) Exponential survivals with censoring and explanatory variables. Biometrika 60: 279–288

    Article  MATH  MathSciNet  Google Scholar 

  • Robins JM, Ritov Y (1997) Towards a curse of dimensionality appropriate (CODA) asymptotic theory for semiparametric models. Stat Med 16: 285–319

    Article  Google Scholar 

  • Robins JM, Rotnitzky A (1992) Recovery of information and adjustment for dependent censoring using surrogate markers. In: Jewell N, Dietz K, Farewell V (eds) AIDS epidemiology: methodologic issues. Birkhauser, Boston, pp 297–331

    Google Scholar 

  • Schoenfeld D (1980) Chi-squared goodness-of-fit tests for the proportional hazards regression model. Biometrika 67: 145–153

    Article  MATH  MathSciNet  Google Scholar 

  • Shaked M, Shantikhumar J (1993) Stochastic orders and their applications. Academic Press, Boston

    Google Scholar 

  • Sun L, Zhang Z (2009) A class of transformed mean residual life models with censored survival data. J Am Stat Assoc 104: 803–815

    Article  Google Scholar 

  • Swartz GB (1973) The mean residual life function. IEEE Trans Reliab R-22: 108–109

    Article  Google Scholar 

  • Yang GL (1978) Estimation of a biometric function. Ann Stat 6: 112–116

    Article  MATH  Google Scholar 

  • Yuen KC, Burke MD (1997) A test of fit for a semiparametric additive risk model. Biometrika 84: 631–639

    Article  MATH  MathSciNet  Google Scholar 

  • Yuen KC, Zhu LX, Tang NY (2003) On the mean residual life regression model. J Stat Plan Infer 113: 685–698

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, 307 East 63rd Street, New York, NY, 10065, USA

    Zhigang Zhang

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Room HJ625, Core J, Stanley Ho Building, Kowloon, Hong Kong

    Xingqiu Zhao

  3. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Liuquan Sun

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  1. Zhigang Zhang
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  2. Xingqiu Zhao
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  3. Liuquan Sun
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Correspondence to Zhigang Zhang.

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Zhang, Z., Zhao, X. & Sun, L. Goodness-of-fit tests for additive mean residual life model under right censoring. Lifetime Data Anal 16, 385–408 (2010). https://doi.org/10.1007/s10985-010-9152-2

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  • DOI: https://doi.org/10.1007/s10985-010-9152-2

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