Identification of the most informative items
The Fisher information functions in Equation 3 and Equation 4 were used
to estimate the information content across the entire severity
range13:
\(I_{\text{jk}}\left(S_{i\left(t\right)}\right)=-\frac{\partial^{2}}{{\partial S}^{2}}\log P_{\text{jk}}{(S=S}_{i\left(t\right)})\)Equation 3\(I_{j}\left(S_{i\left(t\right)}\right)=\sum_{n=0}^{K}{I_{\text{jk}}\left(S_{i\left(t\right)}\right)P_{\text{jk}}{(S}_{i\left(t\right)})}\)Equation 4
In these equations,Pjk (Si (t ))
is the probability of responding with score k of item j by
subject i with severitySi (t ) at time t .
Thus, Ijk(Si (t )) is the information
for score k of item j from subject i at timet , andIj (Si (t ))
is the total information for all scores (from the lowest score of0 to the highest score of K ) of item j from subjecti at time t .
The items were ranked according to their overall informativeness, which
was Ij (S ) integrated over time and summed
for all subjects.