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http://dx.doi.org/10.5351/CKSS.2009.16.4.713

Effective Computation for Odds Ratio Estimation in Nonparametric Logistic Regression  

Kim, Young-Ju (Department of Information Statistics, Kangwon National University)
Publication Information
Communications for Statistical Applications and Methods / v.16, no.4, 2009 , pp. 713-722 More about this Journal
Abstract
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.
Keywords
Bayesian confidence interval; case-control; odds ratio; smoothing splines;
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1 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   DOI   ScienceOn
2 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   DOI   ScienceOn
3 Luo, Z. and Wahba, G. (1997). Hybrid adaptive splines, Journal of the American Statistical Association, 92, 107-116   DOI   ScienceOn
4 Wang, Y. (1997). Odds ratio estimation in bernoulli smoothing spline ANOVA models, Statistician, 48, 49-56   DOI   ScienceOn
5 Wahba, G. (1983). Bayesian “confidence interval” for the cross-validated smoothing spline, Journal of the Royal Statistical Society Series B, 45, 133-150
6 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   DOI   ScienceOn
7 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
8 Kim, Y.-J. (2003). Smoothing spline regression: scalable computation and cross-validation, Ph.D. diss., Purdue University
9 Kim, I., Cohen, N. D. and Carroll, R. J. (2003). Semiparametric regression splines in matched case-control studies, Biometrics, 59, 1158-1169   DOI   ScienceOn
10 Gu, C. (1992). Penalized likelihood regression: a Bayesian analysis, Statistica Sinica, 2, 255-264
11 Gu, C. (2002). Smoothing Spline ANOVA models, Springer-Verlag
12 Gu, C. and Kim, Y.-J. (2002). Penalized likelihood regression: General formulation and efficient approximation, Canadian Journal of Statistics, 30, 619-628   DOI   ScienceOn
13 Gu, C. and Wahba, G. (1993). Smoothing spline ANOVA with component-wise Bayesian confidence intervals, Journal of computational and graphical statistics, 2, 97-117   DOI   ScienceOn
14 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   DOI   ScienceOn