Protocol Evaluation

We will score the protocols based on the following variables:

• Patient-Protocol Fit (PPF)

Similarity between patient profile \(P_u\) (normalized patient deficiency in clinical subscales) and protocol profile \(Q_p\) (normalized protocol attributes, on the impact of a protocol to clinical subscales improvement) for all protocols.

\[PPF = \cos(\theta) = \frac{P \cdot Q}{\|P\|\|Q\|}\]

• Recent Difficulty Modulator Changes (\(\Delta DM\)):

Exponentially weighted average increase in difficulty modulators across recent sessions, emphasizing recent performance.

\[\Delta DM_t = \frac{\sum_{i=0}^{t}(1 - \alpha)^i \cdot DM_{t - i}}{\sum_{i=0}^{t}(1 - \alpha)^i}\]

• Recent Adherence:

Session-wise adherence for all past sessions computed in minutes of protocol \(u\) for a patient \(p\).

\[\text{Adherence} = \frac{\text{Completed Duration}}{\text{Prescribed Duration}}\]

Scoring Function

Each protocol’s overall score combines these factors:

\[\text{Score} = \alpha \cdot PPF + \beta \cdot \Delta DM + \gamma \cdot \text{Adherence}\]

Coefficients \(\alpha, \beta, \gamma\) weigh factor importance.