# Agreement Ordinal Data

Cohens – can also be used if the same counsellor evaluates the same patients at two times (for example. B to 2 weeks apart) or, in the example above, re-evaluated the same response sheets after 2 weeks. Its limitations are: (i) it does not take into account the magnitude of the differences, so it is unsuitable for ordinal data, (ii) it cannot be used if there are more than two advisors, and (iii) it does not distinguish between agreement for positive and negative results – which can be important in clinical situations (for example. B misdiagnosing a disease or falsely excluding them can have different consequences). This method is used when the evaluations of more than two observers are available for binary or ordinal data. Let us now consider a hypothetical situation in which examiners do exactly that, i.e. assign notes by throwing a coin toss; Heads – pass, tails – Table 1, situation 2. In this case, one would expect that 25% (-0.50 Ă— 0.50) of the students would receive the results of both and that 25% of the two would receive the „fail“ grade – a total approval rate „expected“ for „not“ or „fail“ of 50% (-0.25 – 0.25 – 0.50). Therefore, the observed approval rate (80% in situation 1) must be interpreted to mean that a 50% agreement was foreseen by chance. These auditors could have improved it by 50% (at best an agreement minus the randomly expected agreement – 100% 50% – 50%), but only reached 30% (observed agreement minus the randomly expected agreement – 80% 50% – 30%). Thus, their real return in agreement is 30%/50% – 60%. Two methods are available to assess the consistency between continuously measuring a variable on observers, instruments, dates, etc. One of them, the intraclass coefficient correlation coefficient (CCI), provides a single measure of the magnitude of the match and the other, the Bland-Altman diagram, also provides a quantitative estimate of the narrowness of the values of two measures.

The logistics function (ui – vj)) – 1 (1 – e ((ui-vj)) replaces the Probit function in the GLMM of logistics ordination. Wlog we put 0 to 0 for identification, With the variance of logistic distribution 2/3, and the GLMM ordinal logistics with respect to the accumulated logits is: Allsbrook et al [46] conducted a study of the agreement between 10 urological pathologists who each independently interpreted the severity of prostate cancer from 46 patient biopsies with a condensed version of the Gleason grade scale [7]. The scale had four categories defined as: category i) Gleason Points 2-4 (light illness); category (ii) Gleason scores 5-6 points; category iii) Gleason score 7; Category iv) Gleason reaches 8-9 (severe illness). Table 3 (a) shows a subset of ordinal classifications of test results of 46 patients by each of the 10 urologists. Tables 3 (b) and c) contain the observed classifications of selected pairs of urologists. Subsequently, an ordinal GLMM (2) was incorporated into the complete data set, which includes dependence between expert classifications on the structure of crossed random effects using the ordinal package in R, with less than a minute of computational time. Parameter estimates and synthesis measures are presented in Table 4. As an indicator of the prevalence of the disease, the estimated probabilities of being categorized in each of the ten categories of the ten experts are 6%, 31%, 28% and 36%, respectively, making it a high probability of being classified with a moderate to high degree of prostate cancer. The agreement observed (3) on the basis of the GLMM (2) was estimated at p0 – 0.669.

The proposed new agreement no.m-0.484 (se – 0.035) indicated a moderate and adjusted convergence of chances between the ten urologists. This value was much lower than the Kappa Vonfles Congers and the light`s kappa, LC-0.570, and kappa based on Cohen`s GLMM, estimated at GLMM-0.526 (described in sections 4.2 and 4.3) that can be attributed to the effects of a high prevalence of disease prevalence for which Cohens Kappa`s measurements are sensitive, as shown in Figure 1, while the proposed Kappa is not affected by the disease.