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.

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

Interval estimation with accurate coverage for risk difference (RD) in a correlated 2 × 2 table with structural zero is a fundamental and important problem in biostatistics. The score test-based and Bayesian tail-based confidence intervals (CIs) have good coverage performance among the existing methods. However, as approximation approaches, they have coverage probabilities lower than the nominal confidence level for finite and moderate sample sizes. In this paper, we propose three new CIs for RD based on the fiducial, inferential model (IM) and modified IM (MIM) methods. The IM interval is proven to be valid. Moreover, simulation studies show that the CIs of fiducial and MIM methods can guarantee the preset coverage rate even for small sample sizes. More importantly, in terms of coverage probability and expected length, the MIM interval outperforms other intervals. Finally, a real example illustrates the application of the proposed methods.

A more efficient three-arm non-inferiority test based on pooled estimators of the homogeneous variance.

Hida and Tango established a statistical testing framework for the three-arm non-inferiority trial including a placebo with a pre-specified non-inferiority margin to overcome the shortcomings of traditional two-arm non-inferiority trials (such as having to choose the non-inferiority margin). In this paper, we propose a new method that improves their approach with respect to two aspects. We construct our testing statistics based on the best unbiased pooled estimators of the homogeneous variance; and we use the principle of intersection-union tests to determine the rejection rule. We theoretically prove that our test is better than that of Hida and Tango for large sample sizes. Furthermore, when that sample size was small or moderate, our simulation studies showed that our approach performed better than Hida and Tango's. Although both controlled the type I error rate, their test was more conservative and the statistical power of our test was higher.

An efficient test based on the inferential model for the non-inferiority of odds ratio in matched-pairs design.

Non-inferiority of one treatment to another based on odds ratio for the matched-pair design is a common issue in the medical research. Liu et al. derived two asymptotic tests, delta method and score test, which can be applicable for large samples but may tend to be liberal for small sample sizes. Jin et al. proposed an IM-based method that can control the type I risk well but may be somewhat conservative. In this paper, we extend the IM-based method to RIM-based test using the randomized plausibility function. We prove that our new proposed method is not only valid but also efficient. Simulation studies confirm that the RIM-based test is better than other methods. A numerical example illustrates the proposed method.