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Semiparametric methods for survival data with measurement error under additive hazards cure rate models

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Abstract

It is well established that measurement error has drastically negative impact on data analysis. It can not only bias parameter estimates but may also cause loss of power for testing relationship between variables. Although survival analysis of error-contaminated data has attracted extensive interest, relatively little attention has been paid to dealing with survival data with error-contaminated covariates when the underlying population is characterized by a cured fraction. In this paper, we consider this problem for which lifetimes of the non-cured individuals are featured by the additive hazards model and the measurement error process is described by an additive model. Unlike estimating the relative risk in the proportional hazards model, the additive hazards model allows us to estimate the absolute risk difference associated with the covariates. To allow the model flexibility, we incorporate time-dependent covariates in the model. We develop estimation methods for the two scenarios, without or with measurement error. The proposed methods are evaluated from both the theoretical view point and the numerical perspectives. Furthermore, a real-life data application is presented to illustrate the utility of the methodology.

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References

  • Aalen OO (1989) A linear regression model for the analysis of life times. Stat Med 8:907–925

    Google Scholar 

  • Allison PD (2010) Survival analysis using SAS: a practical guide. Sas Institute, Cary

    Google Scholar 

  • Andersen PK, Borgan O, Gill RD, Keiding N (2012) Statistical models based on counting processes. Springer, Berlin

    MATH  Google Scholar 

  • Balakrishnan N, Pal S (2012) EM algorithm-based likelihood estimation for some cure rate models. J Stat Theory Pract 6:698–724

    MathSciNet  MATH  Google Scholar 

  • Balakrishnan N, Barui S, Milienos F (2017) Proportional hazards under Conway–Maxwell–Poisson cure rate model and associated inference. Stat Methods Med Res 26:2055–2077

    MathSciNet  Google Scholar 

  • Boag JW (1949) Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J R Stat Soc B 11:15–53

    MATH  Google Scholar 

  • Buzas JS (1998) Unbiased scores in proportional hazards regression with covariate measurement error. J Stat Plan Inference 67:247–257

    MathSciNet  MATH  Google Scholar 

  • Carroll RJ, Küchenhoff H, Lombard F, Stefanski LA (1996) Asymptotics for the simex estimator in nonlinear measurement error models. J Am Stat Assoc 91:242–250

    MathSciNet  MATH  Google Scholar 

  • Carroll RJ, Ruppert D, Stefanski LA, Buonaccorsi J (1997) Measurement error in nonlinear models. Metrika 45:182–183

    Google Scholar 

  • Chen IJG, Sinha D (1999) A new Bayesian model for survival data with a surviving fraction. J Am Stat Assoc 94:909–919

    MathSciNet  MATH  Google Scholar 

  • Chen K, Jin Z, Ying Z (2002a) Semiparametric analysis of transformation models with censored data. Biometrika 89:659–668

    MathSciNet  MATH  Google Scholar 

  • Chen YQ, Rohde C, Wang M (2002b) Additive hazards models with latent treatment effectiveness lag time. Biometrika 89:917–931

    MathSciNet  MATH  Google Scholar 

  • Cook JR, Stefanski LA (1994) Simulation-extrapolation estimation in parametric measurement error models. J Am Stat Assoc 89:1314–1328

    MATH  Google Scholar 

  • Cox DR, Oakes D (1984) Analysis of survival data. CRC, Boca Raton

    Google Scholar 

  • Fang HB, Li G, Sun J (2005) Maximum likelihood estimation in a semiparametric logistic/proportional-hazards mixture model. Scand J Stat 32:59–75

    MathSciNet  MATH  Google Scholar 

  • Farewell VT (1982) The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 38:1041–1046

    Google Scholar 

  • Fleming TR, Harrington DP (2011) Counting processes and survival analysis. Wiley, Hoboken

    MATH  Google Scholar 

  • Freedman LS, Fainberg V, Kipnis V, Midthune D, Carroll RJ (2004) A new method for dealing with measurement error in explanatory variables of regression models. Biometrics 60:172–181

    MathSciNet  MATH  Google Scholar 

  • Hu P, Tsiatis AA, Davidian M (1998) Estimating the parameters in the Cox model when covariate variables are measured with error. Biometrics 54:1407–1419

    MathSciNet  MATH  Google Scholar 

  • Huang Y, Wang C (2000) Cox regression with accurate covariates unascertainable: a nonparametric-correction approach. J Am Stat Assoc 95:1209–1219

    MathSciNet  MATH  Google Scholar 

  • Huber PJ et al (1967) The behavior of maximum likelihood estimates under nonstandard conditions. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, Berkeley, CA, vol 1, pp 221–233

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

    MATH  Google Scholar 

  • Kuk AY, Chen CH (1992) A mixture model combining logistic regression with proportional hazards regression. Biometrika 79:531–541

    MATH  Google Scholar 

  • Kulich M, Lin D (2000) Additive hazards regression with covariate measurement error. J Am Stat Assoc 95:238–248

    MathSciNet  MATH  Google Scholar 

  • Li Y, Lin X (2003) Functional inference in frailty measurement error models for clustered survival data using the simex approach. J Am Stat Assoc 98:191–203

    MathSciNet  MATH  Google Scholar 

  • Li Y, Ryan L (2004) Survival analysis with heterogeneous covariate measurement error. J Am Stat Assoc 99:724–735

    MathSciNet  MATH  Google Scholar 

  • Lin D, Ying Z (1994) Semiparametric analysis of the additive risk model. Biometrika 81:61–71

    MathSciNet  MATH  Google Scholar 

  • Liu M, Lu W, Shao Y (2006) Interval mapping of quantitative trait loci for time-to-event data with the proportional hazards mixture cure model. Biometrics 62:1053–1061

    MathSciNet  MATH  Google Scholar 

  • Lu W, Ying Z (2004) On semiparametric transformation cure models. Biometrika 91:331–343

    MathSciNet  MATH  Google Scholar 

  • Ma Y, Yin G (2008) Cure rate model with mismeasured covariates under transformation. J Am Stat Assoc 103:743–756

    MathSciNet  MATH  Google Scholar 

  • Nakamura T (1992) Proportional hazards model with covariates subject to measurement error. Biometrics 48:829–838

    MathSciNet  Google Scholar 

  • Peng Y, Dear KB (2000) A nonparametric mixture model for cure rate estimation. Biometrics 56:237–243

    MATH  Google Scholar 

  • Prentice R (1982) Covariate measurement errors and parameter estimation in a failure time regression model. Biometrika 69:331–342

    MathSciNet  MATH  Google Scholar 

  • Rodrigues J, de Castro M, Cancho VG, Balakrishnan N (2009) COM-Poisson cure rate survival models and an application to a Cutaneous Melanoma data. J Stat Plann Inference 139:3605–3611

    MathSciNet  MATH  Google Scholar 

  • Rodrigues J, de Castro M, Balakrishnan N, Cancho VG (2011) Destructive weighted Poisson cure rate models. Lifetime Data Anal 17:333–346

    MathSciNet  MATH  Google Scholar 

  • Rossi PH, Berk RA, Lenihan KJ (1980) Money, work and crime: some experimental results. Academic Press, New York

    Google Scholar 

  • Sun L, Zhou X (2008) Inference in the additive risk model with time-varying covariates subject to measurement errors. Stat Probab Lett 78:2559–2566

    MathSciNet  MATH  Google Scholar 

  • Sun L, Zhang Z, Sun J (2006) Additive hazards regression of failure time data with covariate measurement errors. Stat Neerl 60(4):497–509

    MathSciNet  MATH  Google Scholar 

  • Sy JP, Taylor JM (2000) Estimation in a cox proportional hazards cure model. Biometrics 56:227–236

    MathSciNet  MATH  Google Scholar 

  • Thurston SW, Spiegelman D, Ruppert D (2003) Equivalence of regression calibration methods in main study/external validation study designs. J Stat Plan Inference 113:527–539

    MathSciNet  MATH  Google Scholar 

  • Tsodikov A, Ibrahim J, Yakovlev A (2003) Estimating cure rates from survival data. J Am Stat Assoc 98:1063–1078

    Google Scholar 

  • Yan Y, Yi GY (2016) A class of functional methods for error-contaminated survival data under additive hazards models with replicate measurements. J Am Stat Assoc 111:684–695

    MathSciNet  Google Scholar 

  • Yi GY (2017) Statistical analysis with measurement error or misclassification: strategy, method and application. Springer, New York

    MATH  Google Scholar 

  • Yi GY, He W (2012) Bias analysis and the simulation-extrapolation method for survival data with covariate measurement error under parametric proportional odds models. Biom J 54:343–360

    MathSciNet  MATH  Google Scholar 

  • Yi YG, Lawless JF (2007) A corrected likelihood method for the proportional hazards model with covariates subject to measurement error. J Stat Plan Inference 137:1816–1828

    MathSciNet  MATH  Google Scholar 

  • Yi GY, Reid N (2010) A note on mis-specified estimating functions. Stat Sin 20:1749–1769

    MathSciNet  MATH  Google Scholar 

  • Zucker DM, Spiegelman D (2008) Corrected score estimation in the proportional hazards model with misclassified discrete covariates. Stat Med 27:1911–1933

    MathSciNet  Google Scholar 

Download references

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Correspondence to Grace Y. Yi.

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Barui, S., Yi, G.Y. Semiparametric methods for survival data with measurement error under additive hazards cure rate models. Lifetime Data Anal 26, 421–450 (2020). https://doi.org/10.1007/s10985-019-09482-0

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