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Locally efficient estimation of regression parameters using current status data

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  • Andrews, Chris
  • van der Laan, Mark
  • Robins, James

Abstract

In biostatistics applications interest often focuses on the estimation of the distribution of a time-variable T. If one only observes whether or not T exceeds an observed monitoring time C, then the data structure is called current status data, also known as interval censored data, case I. We consider this data structure extended to allow the presence of both time-independent covariates and time-dependent covariate processes that are observed until the monitoring time. We assume that the monitoring process satisfies coarsening at random. Our goal is to estimate the regression parameter [beta] of the regression model T=Z[inverted perpendicular][beta]+[epsilon]. The curse of dimensionality implies no globally efficient nonparametric estimator with good practical performance at moderate sample sizes exists. We present an estimator of the parameter [beta] that attains the semiparametric efficiency bound if we correctly specify (a) a model for the monitoring mechanism and (b) a lower-dimensional model for the conditional distribution of T given the covariates. In addition, our estimator is robust to model misspecification. If only (a) is correctly specified, the estimator remains consistent and asymptotically normal. We conclude with a simulation experiment and a data analysis.

Suggested Citation

  • Andrews, Chris & van der Laan, Mark & Robins, James, 2005. "Locally efficient estimation of regression parameters using current status data," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 332-351, October.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:2:p:332-351
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    References listed on IDEAS

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    1. J. Huang & J. A. Wellner, 1995. "Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(2), pages 153-163, July.
    2. Ian Diamond & John McDonald & Iqbal Shah, 1986. "Proportional hazards models for current status data: Application to the study of differentials in age at weaning in Pakistan," Demography, Springer;Population Association of America (PAA), vol. 23(4), pages 607-620, November.
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    Cited by:

    1. Jessica G. Young & Nicholas P. Jewell & Steven J. Samuels, 2008. "Regression Analysis of a Disease Onset Distribution Using Diagnosis Data," Biometrics, The International Biometric Society, vol. 64(1), pages 20-28, March.

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