Likelihood Based Confidence Intervals for the Difference of Proportions in Two Doubly Sampled Data with a Common False-Positive Error Rate

- Journal title : Communications for Statistical Applications and Methods
- Volume 17, Issue 5, 2010, pp.679-688
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2010.17.5.679

Title & Authors

Likelihood Based Confidence Intervals for the Difference of Proportions in Two Doubly Sampled Data with a Common False-Positive Error Rate

Lee, Seung-Chun;

Lee, Seung-Chun;

Abstract

Lee (2010) developed a confidence interval for the difference of binomial proportions in two doubly sampled data subject to false-positive errors. The confidence interval seems to be adequate for a general double sampling model subject to false-positive misclassification. However, in many applications, the false-positive error rates could be the same. On this note, the construction of asymptotic confidence interval is considered when the false-positive error rates are common. The coverage behaviors of nine likelihood based confidence intervals are examined. It is shown that the confidence interval based Rao score with the expected information has good performance in terms of coverage probability and expected width.

Keywords

Profile likelihood;Rao score;information;double sampling;

Language

English

Cited by

References

1.

Agresti, A. and Caffo, B. (2000). Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures, The American Statistician, 54, 280–288.

2.

Agresti, A. and Coull, B. A. (1998). Approximation is better than “exact” for interval estimation of binomial proportions, The American Statistician, 52, 119–126.

3.

Barndorff-Nielsen, O. E. and Cox, D. R. (1994). Inference and Asymptotics, Chapman & Hall, London.

4.

Barnett, V., Haworth, J. and Smith, T. M. F. (2001). A two-phase sampling scheme with applications to auditing or sed quis custodiet ipsos custodes?, Journal of Royal Statistical Society, Serie A, 164, 407–422.

5.

Boese, D. H., Young, D. M. and Stamey, J. D. (2006). Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification, Computational Statistics and Data Analysis, 50, 3369–3385.

6.

Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion, Statistical Science, 16, 101–133.

7.

Efron, B. and Hinkley, D. V. (1978). Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information, Biometrika, 65, 457–482.

8.

Geng, Z. and Asano, C. (1989). Bayesian estimation methods for categorical data with misclassifications, Communications in Statistics, Theory and Methods, 18, 2935–2954.

9.

Hildesheim, A., Mann, V., Brinton, L. A., Szklo, M., Reeves, W. C. and Rawls, W. E. (1991). Herpes simplex virus type 2: A possible interaction with human papillomavirus types 16/18 in the development of invasion cervical cancer, International Journal of Cancer, 49, 335–340.

10.

Lee, S. C. (2010). Confidence intervals for the difference of binomial proportions in two doubly sampled data, Communications of the Korean Statistical Association, 3, 301–310.

11.

Lee, S. C. and Byun, J. S. (2008). A Bayesian approach to obtain confidence intervals for binomial proportion in a double sampling scheme subject to false-positive misclassification, Journal of the Korean Statistical Society, 37, 393–403.

12.

Lie, R. T., Heuch, I. and Irgens, L. M. (1994). Maximum likelihood estimation of proportion of congenital malformations using double registration systems, Biometrics, 50, 433–444.

13.

Moors, J. J. A., van der Genugten, B. B. and Strijbosch, L. W. G. (2000). Repeated audit controls, Statistica Neerlandica, 54, 3–13.

14.

Raats, V. M. and Moors, J. J. A. (2003). Double-checking auditors: A Bayesian approach, The Statistician, 52, 351–365.

15.

Tenenbein, A. (1970). A double sampling scheme for estimating from binomial data with misclassifications, Journal of the American Statistical Association, 65, 1350–1361.

16.

York, J., Madigan, D., Heuch, I. and Lie, R. T. (1995). Birth defects registered by double sampling: A Bayesian approach incorporating covariates and model uncertainty, Applied Statistics, 44, 227–242.