Item-response model and item importance
An item-response model, including 33 graded-response logit sub-models,
one per item, was successfully developed. Figure 2 shows that the
pattern of the model-estimated severity data (upper right), including
the progression over time, the variability among patients, and the
visit-to-visit fluctuation resemble those of the observed SoS (upper
left).
The discrimination parameter and four difficulty parameters for all
items are shown in Table 2. Score value 4 (severe) was missing from five
items (1, 25, 26, 31 and 32). The probability for a patient to score
this value, and consequently the corresponding difficulty parameter,
could not be estimated for these items.
The information content varied greatly among the items (Figure 3 and
Table 2): eight items each held > 5% of the total
information, totaling 65% and with the lowest discrimination parameter
being 1.29. All seven items for the left side of the body were among the
eight top-informing items.
Conversely, 11 items each held < 1% information, with the
highest discrimination parameter being 0.46. Nine of the ten tremor
items were among the 11 least informative ones. Indeed, four of the five
items where score 4 (severe) was missing were tremor tests (Table 2).
Six items (18, 20, 21, 30, 31 and 32) had mostly score 0 (normal); three
were tremor tests (Figure 2, lower right). Several tremor items were
even estimated to have a near-zero negative discrimination parameter
value, with very wide-ranging difficult parameters. These observations
suggested that the parameters were badly estimated for these items and
revealed these items’ inability to differentiate patients with different
levels of symptom severity. Based on these findings, the longitudinal
modelling and subsequent estimation of clinical trial PoS were conducted
with or without the tremor items.