Xxxxx’x kappa Sample Clauses

Xxxxx’x kappa. We have so far used the unscaled agreement index LOA to evaluate the method agreement based upon the fitted GLMM. In this section, we will show how to calculate the scaled agreement index Xxxxx’x kappa based upon the fitted GLMM. For each i ∈ {1, 2, . . . , I} and m ∈ {1, 2}, the predicted 0-1 binary score of the ith subject by Method m is defined as xˆxx = 1, if µˆim > 0, 0, otherwise. Here, µˆim is the EBLUP that we used for the LOA approach in the previous section. Let Y1 and Y2 denote the outcomes xˆxx by Methods 1 and 2, respectively. The outcomes can then be presented as a contingency table described in Table 1. Table 1: Contingency table of outcomes. Y1 = 0 Y1 = 1 Y2 = 0 a b Y2 = 1 c d Here, ‘a’, ‘b’, ‘c’ and ‘d’ denote the numbers of patients with four possible combinations of outcomes measured by Methods 1 and 2. For example, ‘a’ denotes the number of patients whose predicted outcomes from GLMM are 0 from both measuring methods. Xxxxx’x kappa κ is given by where κ = po − pe , (2.9) 1 − pe a + d a + b a + c c + d b + d po = a + b + c + d and pe = a + b + c + d· a + b + c + d + a + b + c + d· a + b + c + d . A confidence interval for Xxxxx’x kappa is given based on the variance esti- mates discussed by Xxxxxx, Xxxxx, and Xxxxxxx[36]. The calculation of Xxxxx’x kappa together with its confidence interval is implemented using the R package ‘psych’[37]. A limitation of the original Xxxxx’x kappa is that its magnitude is sensi- tive to the underlying disease prevalence, which is described as the prevalence effect.[38] For example, older patients may experience an increased prevalence of some disease, and are more likely to be diagnosed as ‘Positive’. For rare diseases, subjects are more likely to be diagnosed as ‘Negative’. In either case, Xxxxx’x kappa would decrease due to the imbalance between a and d in Ta- ble 1. It is an overcorrection for chance agreement. If one applies Xxxxx’x kappa directly to repeated measurements, the imbalance between a and d may significantly increase due to the correlation among repeated measurements. For example, the prevalence effect for rare diseases would become severe if each sub- ject is measured at a number of time points, i.e., large Ti, because the number of ‘Negative’ a may keep increasing while the number of ‘Positive’ d remains unchanged as more observations are collected for each subject over time. It is worth noting that our predicted binary score xˆxx is a summarized predicted binary value for each sub...