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A new homogeneity test of relative differences in K independent 2×2 tables arising from inverse sampling is proposed using score-based approach. Asymptotic power formula and confidence interval estimate for the common relative difference are also proposed. The methods are applied to a numerical example and a Monte Carlo simulation study is conducted to evaluate the performance of different tests with respect to size and power.

In this paper, we consider the application of the empirical likelihood for linear models under median constraints in view of robustness. For two simple median constraints, it is shown that conditions to ensure the consistency of the empirical likelihood confidence regions can be surprisingly relaxed compared with the normal approach under L norm. However, the coverage accuracy of the empirical likelihood confidence regions based on simple median constrains cannot be improved because of the discontinuity of the constraints. Therefore, a smoothed version of median constraint is proposed and a general theory is established to ensure its validity.

We propose to use mixture of geometries to model the duration Ot a spell in discrete time. The discrete hazard rate can be determined by the moments of the mixing distribution through the qd(quotient difference) algorithm, By introducing a sequence of parameters called canonical moments, we can ensure the resulting estimate of the mixing distribution is supported on [0,1]. Using the bootstrap method, we can construct, instantaneous confidence intervals for the hazard rates. For the continuous time, a mixture of exponentials is proposed. By a simple transformation, the problem can be reduced to the case for mixture of geometries. The instantaneous confidence intervals for the hazard rates can be constructed.

Given multiple binary tests, such as repeated application of a blind screening test to each individual in a sample, we attemt to estimate the prevalence, sensitivity and specificity of the test without knowing the true disease status of those tested (gold standard). This problem is equivalent to finding the mixing distribution of a mixture of binomial distributions. We suggest a new method to determine the number of latent classes. Our simulations show that the coverage probabilities of the bootstrap confidence intervals of our estimates are correct. Our methods are illustrated by examples from published medical research. © 1997 John Wiley & Sons, Ltd.

Determination of individual genotypes in DNA mixture remains a challenge in forensic science. Using an approach of mixture of distributions, this article provides formula for calculation of paternity index (PI) in cases where only tissue mixture of the mother and alleged father, the genotypes of the mother and child, but not that of the alleged father are available. The formula has been used to solve a real case using mother's vaginal tissue contaminated with semen from alleged father.

We propose to use a general mixing distribution in modeling the heterogeneity of the fecundability of couples. We introduce a sequence of parameters called canonical moments, which is in one to one correspondence with the moments, to characterize the mixing distribution. By using the bootstrap method, we can estimate the standard errors of our estimates. Our method modifies the usual moment estimates so that the resulting mixing distribution is always supported on [0, 1]. Moreover, the downward bias of the moment estimate of the number of support points would be reduced. Our approach can be used for censored data. The application of our technique in finding the sterile subpopulation is also discussed. The theory is illustrated with several data examples and simulations.

We introduce a sequence of parameters called canonical moments to characterize the predictive value of the pattern of consensus among (kappa-1) ratings to an additional rating. The usual kappa coefficient of agreement among ratings (two or more) is just the second canonical moment. By using the higher canonical moments, we can evaluate the consensus of multiple binary ratings.

A screening test is applied n times to a person with known true status. If more than k tests have positive outcomes, then the person is assigned to be screen-positive; otherwise, the person is assigned to be screen-negative. Assuming that the tests are exchangeable, we can characterize the possible dependence among tests by at most n parameters called canonical moments, which can be estimated from the data. The performance characteristics of the composite test (such as likelihood ratios, sensitivity, and specificity) can be computed based on these estimates. Thus, we can choose n and k so that the desired levels of likelihood ratios, sensitivity, and specificity can be achieved. We study the cases n = 2 and n = 3 in detail.

We point out the connection between quality control and repeated screening tests, and suggest a practical way to design the repeated screening tests so that the composite test achieves the desired level of sensitivity and specificity. We further point out the benefits of using likelihood ratios to measure the performance of a screening test. Then we investigate repeated tests when we have polytomous disease levels and polytomous diagnostic levels.