28 © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim S13.2: Bayesian estimation of the false negative fraction in multiple screening tests Leonhard Held, Argwings Ranyimbo Otieno * Corresponding Author: Universität München, Institut für Statistik email: held@stat.uni-muenchen.de Sensitivity and specificity are two important summary measures of the accuracy of a screening or diagnostic test. Test accuracy can also be summarised in terms of the diagnostic or screening errors. The probabilities of these errors are by definition the false nega- tive fraction (FNF) which is one minus the sensitivity and the false positive fraction (FPF) which is one minus the specificity. The estimation of the above mentioned error rates when all the study subjects are verified via a gold standard procedure is simple. However due to ethical reasons or costs verification may not be feasible for all the study subjects. We consider the problem of estimating the FNF in multiple screening test under partial verification. In our case the screening test comprises K repeated applica- tions of a dichotomous kit test and only those who tested at least once positive are verified. Our approach is motivated by data from a bowel cancer screening study, discussed in Lloyd (2002). First we assume that the count of the number of positive test is (truncated) beta-binomial, to adjust for the strong overdispersion present in the data. We consider two different parametrizations of the beta-binomial distribution and use non-informative reference priors based on recent work by van der Linde (2003). Estimates of the FNF are obtained using a Metropolis-Hastings algorithm. In a second approach we use Bayesian logistic regression to estimate the FNF. Our results compare well with the estimates ob- tained using extrapolation based on classical logistic regression. Using Bayesian methods credible intervals for the FNF are directly obtained from the empirical posterior distributions; the use of an approximation based on the delta method for estimating the standard errors is avoided. This is a promising improvement on existing likelihood techniques. Finally we consider model valida- tion based on the prediction of future outcomes from the different models. In the above study, the multiple screening test has been re-applied to all verified patients and we will compare the predictive distribution of the number of positive tests with the actual observed numbers. References: Lloyd, CJ (2002) A heterogeneity model for estimating the false negative fraction from a multiple screening test when individuals who tested negative on all tests are not verified. Research Report 2002.78, Australian Graduate School of Management. van der Linde, A (2003). Personal communication. S13.3: Block Updating a Bayesian Cox Proportional Hazard Model for Interval Censored Data Volkmar Henschel*, Ulrich Mansmann * Corresponding Author: Universität Heidelberg, Institut für medizinische Biometrie email: henschel@imbi.uni-heidelberg.de In recent years there have been several frequentistic approaches for the treatment of Cox proportional hazard models for interval censored data, for example see Pan (1999). Here a bayesian approach is presented. It is based on the bayesian approach of Gamerman (1996) for generalized linear mixed models which allows a fast updating of the regression coefficients and on the block updating in Markov random field models suggested by Knorr-Held and Rue (2002) which helps to improve the sampling of the baseline hazard. Data augmentation is used to interfere unobserved event times. The performance of the proposed procedure will be assessed by simulation studies and an example from cattle breeding will be given. References: Gamerman D (1997): Sampling from the posterior distribution in generalized linear mixed models, Statistics and Computing 7, 57- 68. Knorr-Held, L and Rue, H (2002): On Block Updating in Markov Random Field Models for Disease Mapping, Scandinavian Journal of Statistics 29, 597-614. Pan, W (1999): Extending the Iterative Convex Minorant Algorithm to the Cox Model for Interval-Censored Data, Journal of Computational and Graphical Statistics 8, 109–120