Table 1.

Procedure of real-data post hoc CAT simulations in nine steps.

1. Check IRT assumptions on the full sample.

2. Randomly divide the data into 10 subsets.

3. Fit a graded response model to the data of all but the current subset and extract the estimated IRT parameters.

4. Use the IRT parameters from step 3 to calculate a full-length estimated theta (θ) of the patients in the current subset using maximum likelihood estimation.

5. Perform CAT simulations based on each patients estimated θ to estimate the θ adaptively, based on the item responses from the patients in the current subset.

6. Compare the adaptively estimated θ with the full-length θ estimates in the current subset.

7. Select optimal test length which results in the greatest similarity and accuracy between the CAT-estimated θ and full-length θ while using a minimum number of items.

8. Repeat steps 2–7 for each subset until all patients have been used in CAT simulations and combine/average the results.

9. Select items based on the selection criteria: discrimination parameters, total information, times selected in CAT simulation, and raw mean.

CAT: computerized adaptive test; IRT: item response theory.