Landis and Koch (1977) showed ratings by seven pathologists who separately classified 118 slides regarding the presence and extent of carcinoma of the uterine cervix, using a five-point ordinal scale. For slide i with rater t, Table 12.14 shows results of fitting model

logit[P(Y_it ‰¤ j|u_i)] = u_i + α_j + β_t

to the ordinal table (with β̂_G = 0), assuming that the {u_i} are independent N(0, σ²). It also shows GEE estimates, using independence working equations, for the corresponding marginal model. Interpret β̂_F for each model. Explain why estimates using the random effects model, for which σ̂ = 3.8, tend to be much larger in absolute value. Discuss the differences in assumptions and interpretations for the two models.

Table 13.1:

Table 12.14:

Transcribed Image Text:

Diagnoses of Carcinoma and Fits of Latent Class Models“ Fit Pathologist q = 1 B D E Count q = 2 A %3D 34 1.1 23.0 33.8 1.6 6.6 2.0 1. 2.2 12.7 6.3 2.8 1.7 1.5 1 4 3.3 3.6 3.0 1 4.7 0.5 5 4.2 1 1 2 3.0 2.1 1 1.4 1.6 0.2 0.2 1. 2.8 1.7 1.3 1 1 3.5 0.3 1.6 2 4.2 0.5 2.9 1 5.3 3.7 6.5 1 1 2.6 1.4 1 1. 1. 1.4 1.3 0.1 0.1 1 1 2.0 4.3 2.6 1 1 3 0.5 3.1 2.0 1. 1 1 1 13 3.3 11.5 9.6 1 1 1. 1 5 0.9 8.4 8.7 1 10 1.2 13.5 13.6 1 1 1 9.9 12.3 16 0.3 "Fits obtained with Latent Gold (Statistical Innovations, Belmont MA). 1, yes; 0, no. Observer Random Effect GEE Effects -0.451 (0.108) -0.391 (0.093) 0.319 (0.118) 0.632 (0.105) - 1.201 (0.300) -0.919 (0.299) 0.558 (0.301) 1.545 (0.313) - 1.379 (0.300) 2.907 (0.344) B D -0.491 (0.098) 1.252 (0.161)