Item Response Theory (IRT) is a promising concept for constructing and calibrating health related quality of life questionnaires. The most popular IRT model is the two-parameter logistic model, and its parameters are often estimated by the Marginal Maximum Likelihood method (MML). However, performance of estimation by MML is poor in a small sample, such as severe or rare disease patients. The purpose of this study was to propose a Bayesian method for improving the performance and to compare the precision and accuracy of estimates by different methods with a simulation. In the simulation, item responses were generated according to the two-parameter logistic model. The estimates obtained using a MML Program (MULTILOG) and a Bayesian program written in this study were compared with respect to the precision and accuracy. The proposed method could improve the performance about difficulty parameters using more than 100 individuals and 10 items. Though that about discrimination parameters was still poor. For example, 137 patients received the Parkinson's disease specific questionnaire (PDQ-39) and a generic one (SF-36); and we calibrated items of physical functioning in these questionnaire simultaneously. It was shown that half of the PDQ-39 items could measure the ability of patients at a little bit high level of physical functioning more efficiently than SF-36.
In the design of clinical trials in which the primary endpoint is time to occurrence of a clinical event, sample size calculation should be based on the subsequent survival analysis. This paper gives sample size formulas based on the conditional score test for the hazard ratio, which is equivalent to the normal approximation of the Cox F test. The proposed method is adopted to uniform patient entry, loss to follow-up, and treatment switching. In cancer clinical trials, it is sometimes required to show that the two treatments have equivalent survival benefit when the new treatment has apparent advantages on toxicity. Application of the proposed sample size formula to the equivalence test of two treatments is also given.
The pseudo-expectation (PE) methods for estimating variance components in the mixed linear models are equivalent to the restricted maximum likelihood (REML) procedure in the balanced case, but are a variety of the approximations in the unbalanced case. In animal breeding applications, the PE methods are used, for instance, to quickly obtain an initial value in the REML estimation. In this article, we reveal that the PE approach can never be defined under the so-called individual animal model, when each animal has only one record. We then exploit the use of another sort of animal models, or the so-called reduced animal model, in the PE approach and present sets of the possible quadratic forms. It is shown that the current PE procedure actually performs numerically, as expected, but the sampling variance of the estimator is quite likely to be relatively large, and the similarity of the current estimate to the REML estimate would considerably be affected by the given data structure, definitely indicating the necessity of further theoretical investigation for the improved procedure.