Accurate interval estimation for the risk difference in an incomplete correlated 2 × 2 table: Calf immunity analysis

Confidence Intervals for the Risk Difference Between Secondary and Primary Infection Based on the Method of Variance Estimates Recovery

The risk difference (RD) between the secondary infection, given the primary infection, and the primary infection can be a useful measure of the change in the infection rates of the primary infection and the secondary infection. It plays an important role in pharmacology and epidemiology. The method of variance estimate recovery (MOVER) is used to construct confidence intervals (CIs) for the RD. Seven types of CIs for binomial proportion are introduced to obtain MOVER-based CIs for the RD. The simulation studies show that the Agresti-Coull CI, score method incorporating continuity correction CI, Clopper Pearson CI, and Bayesian credibility CI are conservative. The Jeffreys CI, Wilson score CI, and Arcsin CI draw a satisfactory performance; they are suitable for various practical application scenarios as they can provide accurate and reliable results. To illustrate that the recommended CIs are competitive or even better than other methods, three real datasets were used.

Comparing the variances of several treatments with that of a control treatment: Theory and applications

A common and important problem in medicine, economics and environmental studies is the comparison of the variances of several treatments with that of a control treatment. Among the existing methods, Spurrier's optimal test based on multivariate F distribution has exact type I error rates. However, it requires equal sample sizes among the treatment groups. To extend the application scope, in this paper, we propose a new efficient test for comparing several variances with a control using the marginal inferential model (MIM). Simulation studies show that the MIM test guarantees the exact type I error rate whether the sample size is equal or unequal. Moreover, the power of the MIM test is competitive with that of Spurrier's optimal test. Finally, two real examples are used to demonstrate the application of the proposed method.