Jianrong Wu

Improved interval estimation for the two-parameter Birnbaum–Saunders distribution

Abstract An improved interval estimation for the two-parameter Birnbaum–Saunders distribution is discussed. The proposed method is based on the recently developed higher-order likelihood-based asymptotic procedure. The probability coverages of confidence intervals are based on the proposed method and those procedures discussed in Ng et al. (Comput. Statist. Data Anal., (2003)) are evaluated using Monte Carlo simulations for small and moderate sample sizes. Two real life examples and some concluding remarks are also presented.

Likelihood based inference for the ratio of gamma means

Inference concerning the ratio of two means based two independent two-parameter gamma models with common shape parameter was examined in Booth et al. (1999) and a computationally intensive bootstrap calibration method was developed. In this paper, a likelihood based method is proposed for small sample inference about the ratio of two means of the two-parameter gamma models when the shape parameters may or may not be equal. The proposed method is very simple to use and, as illustrated in simulation studies, gives extremely accurate results.

Comments on ‘Sample size calculation for the proportional hazards cure model’ by Songfeng Wang, Jiajia Zhang and Wenbin Lu

In a recent issue of Statistics in Medicine, Wang et al. [1] proposed a sample size calculation for the proportional hazards cure model. The sample size formula was derived under the local alternative assumption. To investigate the performance of the sample size formula in a finite sample, they did simulation studies (Table II in their research article) and concluded that ‘the asymptotic powers derived from our sample size formula are quite close to those empirical powers under all the three scenarios’ and ‘the extensive simulations show that the proposed sample size formula performs reasonably well under different scenarios’. However, their simulations were limited in a specific parameter setting: the difference between the hazard parameters or/and cure rates under the null and alternative hypotheses was set to 0.1 only. Thus, many parameter settings for the real trial designs were not investigated in their simulations. Here, I conducted further simulations under the three scenarios similar to Wang’s research article (Table 1), but the hazard ratio of uncured patients δ was set to 1.2 − 2.0; the log odds ratio of cure rates γ0 was set to 0.4 − 1.6. In the simulated trials, patients were uniformly accrued and assigned to each treatment arm with equal probability for two arms; the survival times for uncured patients followed an exponential distribution, and no patients were loss to followup. The results based on 10,000 simulation runs showed that the sample size calculated from their formula could be either underestimated or overestimated under all the three scenarios (Table 1). The empirical powers were either as low as 81.1% or as high as 97.5% with a nominal power of 90%. Thus, the sample size formula failed to provide an adequate sample size or power for the clinical trial designs. By the way, the sample size formula (4) in Wang’s research article can not be used when β0 = 0, but it can be simply modified as follows:

Confidence Intervals of Effect Size for Randomized Comparative Parallel-Group Studies with Unequal Variances

Recent years have seen a heightened interest in estimating effect size—a common measure of effect magnitude in biomedical research—because of its direct clinical relevance. In this article, three interval estimates of effect size for randomized comparative parallel-group studies with unequal variances are discussed. Two real-life examples illustrate that confidence intervals obtained by three methods are quite different, especially when the sample sizes are small. Simulation results show that confidence intervals generated by the modified signed log-likelihood ratio method yield essentially the exact coverage probabilities, whereas the other two methods, even though they are more popular methods, yield less satisfactory results.