Confidence intervals for the ratio of medians of two independent log-normal distributions

We focus on the construction of confidence intervals for the ratios of medians of two independent, log-normal distributions based on the normal approximation (NA) approach, the method of variance estimate recovery (MOVER), and the generalized confidence interval (GCI) approach. We also compare the performance of the three confidence intervals in terms of the coverage probabilities, and average lengths, using Monte Carlo simulations. The results show that the GCI confidence interval is generally preferred in terms of coverage probabilities; however, the average length for the GCI is always wider than for other approaches. The NA and MOVER approaches could be recommended on the basis of the specific values ofand/or sample sizes. The confidence intervals are illustrated using real data examples.

Automated summary

This study compares the construction of confidence intervals for the ratios of medians of two independent, log-normal distributions using different methods. The results indicate that the generalized confidence interval (GCI) performs better in terms of coverage probabilities, although it has wider average lengths. The Normal Approximation (NA) and Method of Variance Estimate Recovery (MOVER) approaches could be recommended based on specific values and sample sizes, as illustrated with real data examples.