Sample Size Calculation For An Agreement Study

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It is important to be aware of predefined clinically acceptable compliance limits. As with clinical equivalence or non-inferiority studies, clinical compliance limits must be set in advance by clinical researchers and biostatisticians. Defining these concordance limits can be a difficult aspect in the design of comparative measurement studies, as they depend not only on the clinical scenario, but also on other variables. Nevertheless, efforts should be made to define them; a Delphi survey (expert opinion) can be used to design the study. This survey is a group facilitation technique, which is an iterative multi-step process designed to transform an opinion into a group consensus [16]. We can obtain the upper confidence limit of the upper limit of the LOA and the lower confidence limit of the lower limit of the LOA, n being the sample size. In general, we put γ and α to 0.05. If the 95% confidence interval for 95% LOA is within the predefined agreement limits, which are clinically acceptable, the two methods are consistent enough to meet the requirements of the agreement. In fact, the correspondence between the confidence intervals for LOA and hypothesis tests is identical here.

If A is the lower limit and B is the upper limit of the LOA of population differences, we can construct the following simultaneous assumptions: H01 is A δ, H12 is B ≤ δ. If the two null hypotheses are rejected simultaneously, the two measures would be derived as concordant. The assumptions of the Bland Altman method are very similar to equivalence [13]. The standard error of the 95% limit is approximately rooted (3 s2/n), s being the standard deviation of the differences between the measurements with the two methods and n the sample size. The confidence interval is the estimate of the limit value, d plus or minus 1.96 s, plus or minus 1.96 standard error. Recently, studies on the concordance between two instruments or clinical tests have multiplied in the ophthalmological literature. McAlinden et al. used a sample size calculation method for compliance studies, based on the method proposed by Bland [19]. The sample size was calculated without taking into account the performance of the statistical method, so that the probability of obtaining the required width was only 0.50 [20]. During the design phase of the study, taking performance into account in the sample size calculations could lead to expected conclusions below the pre-established performance level. Cesana et al.

provided an additional estimate of the sample size needed to establish a pearson correlation coefficient between the differences and means of the measures [20], and we consider this method to be inappropriate. Indeed, the correlation coefficient indicated by Cesana reflected the proportional distortion. As we know, one of the assumptions about the application of the Bland Altman method is not a proportional distortion. . . .

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