Effective Computation for Odds Ratio Estimation in Nonparametric Logistic Regression

DOI QR코드

DOI QR Code

Kim, Young-Ju

  • 발행 : 2009.07.31

초록

The estimation of odds ratio and corresponding confidence intervals for case-control data have been done by traditional generalized linear models which assumed that the logarithm of odds ratio is linearly related to risk factors. We adapt a lower-dimensional approximation of Gu and Kim (2002) to provide a faster computation in nonparametric method for the estimation of odds ratio by allowing flexibility of the estimating function and its Bayesian confidence interval under the Bayes model for the lower-dimensional approximations. Simulation studies showed that taking larger samples with the lower-dimensional approximations help to improve the smoothing spline estimates of odds ratio in this settings. The proposed method can be used to analyze case-control data in medical studies.

키워드

Bayesian confidence interval;case-control;odds ratio;smoothing splines

참고문헌

  1. Gu, C. (1992). Penalized likelihood regression: a Bayesian analysis, Statistica Sinica, 2, 255-264
  2. Gu, C. (2002). Smoothing Spline ANOVA models, Springer-Verlag
  3. Gu, C. and Kim, Y.-J. (2002). Penalized likelihood regression: General formulation and efficient approximation, Canadian Journal of Statistics, 30, 619-628 https://doi.org/10.2307/3316100
  4. Gu, C. and Wahba, G. (1993). Smoothing spline ANOVA with component-wise Bayesian confidence intervals, Journal of computational and graphical statistics, 2, 97-117 https://doi.org/10.2307/1390957
  5. Gu, C. and Xiang, D. (2001). Cross-validating non-Gaussian data: Generalized approxmate cross-validation revisited, Journal of computational and graphical statistics, 10, 581-591 https://doi.org/10.1198/106186001317114992
  6. Kim, Y.-J. (2003). Smoothing spline regression: scalable computation and cross-validation, Ph.D. diss., Purdue University
  7. Kim, I., Cohen, N. D. and Carroll, R. J. (2003). Semiparametric regression splines in matched case-control studies, Biometrics, 59, 1158-1169 https://doi.org/10.1111/j.0006-341X.2003.00133.x
  8. Kim, Y.-J. and Gu, C. (2004). Smoothing spline Gaussian regression: More scalable computation via efficient approximation, Journal of the Royal Statistical Society Series B, 66, 337-356 https://doi.org/10.1046/j.1369-7412.2003.05316.x
  9. Lin, X., G. Wabha, D. Xiang, F. Gao, R. Klein, and Klein, B. E. K. (2000). Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV, The Annals of Statistics, 28, 1570-1600 https://doi.org/10.1214/aos/1015957471
  10. Luo, Z. and Wahba, G. (1997). Hybrid adaptive splines, Journal of the American Statistical Association, 92, 107-116 https://doi.org/10.2307/2291454
  11. Wang, Y. (1997). Odds ratio estimation in bernoulli smoothing spline ANOVA models, Statistician, 48, 49-56 https://doi.org/10.1111/1467-9884.00058
  12. Wahba, G. (1983). Bayesian “confidence interval” for the cross-validated smoothing spline, Journal of the Royal Statistical Society Series B, 45, 133-150
  13. Wahba, G., Wang, Y., Gu, C., Klein, R. and Klein, B. (1995). Smoothing spline ANOVA for exponen-tial families, with application to the Wisconsin Epidemiological study of diabetic retinopathy, Annals of Statistics, 23, 1865-1895 https://doi.org/10.1214/aos/1034713638
  14. Xiang, D. and Wahba, G. (1998). Approximate smoothing spline methods for large data sets in the binary case, Proceedings of the 1997 ASA Joint Statistical Meetings, Biometrics Section, 94-98