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Activity Number:
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59
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Type:
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Contributed
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Date/Time:
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Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
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Sponsor:
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Biometrics Section
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| Abstract - #302287 |
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Title:
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Chi-square-Type Goodness-of-Fit Statistic for Survival Time Model as Calibration
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Author(s):
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Byung-Ho Nam*+ and Ralph B. D'Agostino, Sr.
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Companies:
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Boston University and Boston University
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Address:
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185 Freeman St. Apt. 540, Brookline, MA, 02446-3547,
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Keywords:
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calibration ; Poisson log-linear model ; generalized linear model ; chi-square distribution
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Abstract:
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Calibration measures are often statistics that partition a dataset into groups and assess how the average predicted probability compares with the outcome prevalence in each group. Common forms of calibration statistics are based on the Pearson c2 statistic which summarize model fit by comparing observed and expected outcomes within M groups defined by the rank ordering of the predicted probabilities. Hosmer and Lemeshow's chi-square statistics are widely used for goodness of fit for logistic regression. We present a chi-square type statistic for the survival time data with censored observations. Poisson log-linear model was employed in developing the statistic based on the theoretical framework of goodness-of-fit statistic for generalized linear models. Asymptotic behavior of the statistic is examined by investigating the asymptotic null distribution of the statistic. The null distribution of the statistic is a weighted sum of independent c2(1) distributions, where the weights are the eigenvalues of the covariance matrix. A large number of numerical examples were generated in various conditions. The c2(M-1) is shown to be appropriate approximate null distribution.
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