Proposed Summary Measure of Agreement Sample Clauses

Proposed Summary Measure of Agreement. A summary measure of agreement is derived based upon this GLMM model. A Model-Based Measure of Agreement In this section the authors propose a population-based summary measure of agreement κm based upon the ordinal GLMM model of agreement. Such that the proposed measure κm provides an overall assessment of chance-corrected agreement between many raters classifying the same sample of subjects’ test results using an ordered categorical scale. It is a linear transformation of observed (exact) agreement po, corrected for chance agreement pc and scaled to lie between 0 and 1 to allow for easy interpretation in a manner similar to Xxxxx’x kappa C κm =( ) · ∫ +∞ ΣC [Φ( Φ−1( c ) z√ρ − √C ) − Φ( Φ−1( c−1 ) z√ρ − √C )]2φ(z)dz − 1 , (3.5) C − 1 −∞ c=1 1 − ρ 1 − ρ C − 1 0 ≤ κm ≤ 1 (3.6) κm rescaled po for α∗ such that chance agreement is minimal with pc = 1/c, where ρ = σ2/(σ2 + u u σ2 + 1) and z a N (0, 1) variable. When c = 1, the second term in brackets is set to 0, and the first term in brackets for category c = C is set to 1. A value of κm close to 0 is interpreted as little or no agreement, a value around 0.5 suggests a moderate amount of agreement and a value of 1 as perfect agreement between the multiple raters, after correcting for chance agreement. The form of κm is derived from the following observations on pc, po. Derivation of observed agreement po For two raters j, xx we have Σ C po = P [(Yij = c) ∩ (Yijj = c)] c=1 = [P (Q ≤ αc − ui − vj) − P (Q ≤ αc−1 − ui − vj)] ∫ +∞ Σ ΣC −∞ c=1 ∫ Σ Σ Σ × [P (Qj ≤ αc − ui − vjj ) − P (Qj ≤ αc−1 − ui − vjj )] f (u)du +∞ C = [P (Q + vj ≤ αc − ui) − P (Q + vj ≤ αc−1 − ui)] −∞ c=1 × [P (Qj + vj ≤ α − u ) − P (Qj + vj ≤ α u 1 − u )]]φ( ) du c=1 ∫ +∞ ΣC = −∞
Sample 1
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