## Impact Metrics per HCP

The ultimate business KPI in this solution is **prescriptions (Rx)** for a given brand. However, at the level of a single HCP × single action, we cannot reliably observe:

> "This specific email caused +X prescriptions from Dr. Smith."

The main reasons are that HCPs receive multiple touches across channels over time so Rx is driven by the whole journey, not one action; Rx data comes from third-party sources (IQVIA, etc.) that are often lagged, aggregated, and noisy; and external factors such as guidelines, competitive activity, and seasonality also influence prescribing.

Because of this, the NBA engine does not try to predict exact prescription lift for individual actions. Instead it uses two complementary metrics to rank, select, and communicate recommendations.

### Expected Impact

The optimizer's objective - expressed in absolute incremental Rx units. Ensures budget flows to where it generates the most prescribing uplift, not just to the most responsive or highest-volume HCPs.

```
expected_impact = p_engage × avg_rx_8w × channel_uplift
```

- `p_engage` — predicted probability that HCP i will successfully engage 
  with channel c in the next cycle (output of the ML model)
- `avg_rx_8w` — rolling 8-week average weekly Rx volume for this HCP — 
  reflects current prescribing level, smoothed against single-week noise
- `channel_uplift` — fractional Rx lift when an engagement on this channel 
  succeeds. Sourced from expert judgment initially; should be replaced with 
  causal estimates from Marketing Mix Modeling (MMM) as evidence accumulates

This metric is used internally by the optimizer and is not surfaced directly to reps or managers.


### Expected Lift (%)

The human-facing metric - expressed as a percentage above the HCP's own weekly baseline. Volume-neutral and immediately interpretable.

```
expected_lift_pct = p_engage × channel_uplift × 100
```

A value of 5% for an HCP writing 200 prescriptions per week means the action is projected to generate approximately 10 additional prescriptions above their usual weekly volume. Used in dashboards, rep briefings, and CRM notes.

### How to Interpret

**Expected Impact** answers: *how big is the absolute opportunity?* Higher for high-volume prescribers even at the same engagement probability - which is correct, because the same percentage lift generates more incremental Rx for a higher-volume HCP.

**Expected Lift (%)** answers: *how significant is this action relative to what this HCP already does?*  Volume-neutral - directly comparable across HCPs of different sizes and useful for rep-facing communication.

Key points:
- Both are relative scores, not exact Rx counts or causal predictions
- Sorting by expected_impact produces a portfolio that should, on average, 
  drive more Rx uplift than the bottom portion of the ranked list
- Channel uplift coefficients are static in this version and should be 
  validated against a holdout group over time