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2017, Volume 7, Issue 1: 107-112. Doi: 10.3934/naco.2017007
This issue Previous Article Adaptive order of block backward differentiation formulas for stiff ODEs Next Article

Rank-based inference for the accelerated failure time model in the presence of interval censored data

  • Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

  • * Corresponding author: M. Karimi

    * Corresponding author: M. Karimi 
Received:  April 2016
Revised:  November 2016
Published:  May 2017
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    Abstract

  • Semiparametric analysis and rank-based inference for the accelerated failure time model are complicated in the presence of interval censored data. The main difficulty with the existing rank-based methods is that they involve estimating functions with the possibility of multiple roots. In this paper a class of asymptotically normal rank estimators is developed which can be acquired via linear programming for estimating the parameters of the model, and a two-step iterative algorithm is introduced for solving the estimating equations. The proposed inference procedures are assessed through a real example. The results of applying the proposed methodology on the breast cancer data show that the algorithm converges after three iterations, and the estimations of model parameter based on Log-rank and Gehan weight functions are fairly close with small standard errors.

    Mathematics Subject Classification: Primary: 62N01, 62N02; Secondary: 62G09, 90-08.

    Citation:
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  • Figure 1.  Line chart of Gehan and Log-rank estimating functions versus failure time

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    Table 1.  Accelerated failure time analysis for the breast cancer data

    WeightCovariateParameterStandardConfidence
    functionestimateerrorinterval
    Log-ranktreatment-0.8210.210(-1.232, -0.409)
    Gehantreatment-0.6770.196(-1.061, -0.293)
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