Lin LI, Hedayat AS, Sinha B, et al. Statistical methods for evaluating the agreement: models, problems and instruments. J Am Stat Assoc. 2002;97:257–70. In addition to the above studies, chakraborti and Li presented a numerical comparison of several methods of estimating the interval of normal percentiles . They adopted a standardized minimum and unbiased estimate as a precise regime quantity and proposed accurate and approximate confidence intervals of ordinary percentiles. Their simulation study showed that the expected width and probability of coverage of the exact and approximate methods proposed are almost identical to those described in Lawless (, p. 231). Despite the analytical arguments and empirical results in Chakraborti and Li , the following two attentions should be recalled to their illustration. First, while Lawless` confidence intervals  have been shown to be identical to the existing formulas in Owen  and Odeh and Owen , they have not discussed the theoretical implications between their precise method and the precise established procedure. Second, unlike the asymmetry of exact confidence intervals, the approximate confidence intervals of Chakraborti and Li  are equal to an unbiased estimate of the minimum variance. Note that both ends of a bilateral confidence interval can also be interpreted as the limits of the unilateral confidence interval.
It is therefore appropriate to continue to evaluate the performance of the two limits of the approximate interval method of Chakraborti and Lis  with respect to the ownership of egaltailed. The analytical and numerical results in Chakraborti and Li  are not detailed enough to address these fundamental issues. It is wise to shed light on these essential aspects of their methods, which are accepted as a viable technique. Shieh, G. The adequacy of Bland-Altman`s approximate confidence intervals for The Limits of the Agreement. BMC Med Res Methodol 18, 45 (2018). doi.org/10.1186/s12874-018-0505-y Barnhart HX, Haber MJ, Lin LI. An overview of the assessment of compliance with ongoing measures.
J Biopharm Stat. 2007;17:529-69. The simple 95% limits of the agreement method are based on the assumption that the average value and standard deviation of differences are constant, i.e. they do not depend on the size of the measurement. In our original documents, we described the usual situation where the standard deviation is proportional to size, and described a method using a logarithmic transformation of the data. In our 1999 review paper (Bland and Altman 1999), we described a method to avoid any relationship between the average and the SD of the differences and magnitude of the measurement. (It was Doug Altman`s idea, I can`t take recognition.) In general, the actual distribution of the T-plan is distorted, particularly when the sample size is small and p deviates significantly from 0.5. This means that the procedure intervals asymmetric confidence intervals for . It should be noted that the exact estimates of the interval ” (`widehat`uptheta`) L , `widehat`uptheta` ` are not equal to the sample average, with the exception of the particular case p – 0.5. On the other hand, the approximate confidence intervals of Chakraborti and Li  are equally far removed from UB`s unbiased estimate.
Therefore, the interval method is probably inadequate, and the two confidence limits, AL and (largehat, upthetian) are methodically imprecise when one takes into account the probability of unilateral coverage.