Smoothed nonparametric estimation for current status competing risks data

We study the nonparametric estimation of the cumulative incidence function and the cause-specific hazard function for current status data with competing risks via kernel smoothing. A smoothed naive nonparametric maximum likelihood estimator and a smoothed full nonparametric maximum likelihood estimator are shown to have pointwise asymptotic normality and faster convergence rates than the corresponding unsmoothed nonparametric likelihood estimators. Using the smoothed estimators and the plug-in principle, we can estimate the cause-specific hazard function, which has not been studied previously. We also propose semi-smoothed estimators of the cause-specific hazard as an alternative to the smoothed estimator and demonstrate that neither is uniformly more efficient than the other. Numerical studies show that a smoothed bootstrap method works well for selecting the bandwidths in the smoothed nonparametric estimation. The use of the estimators is exemplified by an application to cumulative incidence and hazard of subtype-specific HIV infection from a sero-prevalence study in injecting drug users in Thailand. Copyright 2013, Oxford University Press.

[1]  M. Pike,et al.  Estimation of the distribution of age at natural menopause from prevalence data. , 1983, American journal of epidemiology.

[2]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.

[3]  J. Wellner,et al.  Information Bounds and Nonparametric Maximum Likelihood Estimation , 1992 .

[4]  M. Larson,et al.  Covariate analysis of competing-risks data with log-linear models. , 1984, Biometrics.

[5]  J. Esparza,et al.  Continued high HIV-1 incidence in a vaccine trial preparatory cohort of injection drug users in Bangkok, Thailand , 2001, AIDS.

[6]  Robert Gray,et al.  A Proportional Hazards Model for the Subdistribution of a Competing Risk , 1999 .

[7]  James Stephen Marron,et al.  Bootstrap selection of the smoothing parameter in nonparametric hazard rate estimation , 1996 .

[8]  Marloes H. Maathuis,et al.  Current status data with competing risks: Consistency and rates of convergence of the MLE , 2006 .

[9]  Nicholas P. Jewell,et al.  Nonparametric estimation from current status data with competing risks , 2003 .

[10]  Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times. , 2009, Biometrika.

[11]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[12]  S. Sheather.  A data-based algorithm for choosing the window width when estimating the density at a point , 1983 .

[13]  I M Longini,et al.  Nonparametric Maximum Likelihood Estimation for Competing Risks Survival Data Subject to Interval Censoring and Truncation , 2001, Biometrics.

[14]  P. Groeneboom,et al.  MAXIMUM SMOOTHED LIKELIHOOD ESTIMATION AND SMOOTHED MAXIMUM LIKELIHOOD ESTIMATION IN THE CURRENT STATUS MODEL , 2010, 1001.1829.

[15]  Piet Groeneboom,et al.  CURRENT STATUS DATA WITH COMPETING RISKS: LIMITING DISTRIBUTION OF THE MLE. , 2006, Annals of statistics.

[16]  D. D. Des Jarlais,et al.  Infection with HIV-1 subtypes B and E in injecting drug users screened for enrollment into a prospective cohort in Bangkok, Thailand. , 1998, Journal of acquired immune deficiency syndromes and human retrovirology : official publication of the International Retrovirology Association.

[17]  Martin L. Hazelton.  Bandwidth Selection for Local Density Estimators , 1996 .

[18]  R. Gray.  A Class of $K$-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk , 1988 .