Definition of "overtreatment" in STAT affects impact measure
Screening can have two definitions.
Was (option 1):
"any person whose last BS infection was >= 270 days ago but still received PQ", i.e. those "treated | unlikely to harbor HPZ", as per the definition of the STAT test
Is now (option 2):
"any person who doesn't have any HPZ but still receives PQ", i.e. those "treated | not carrying HPZ"
Both definitions make sense, but have different implications: the former one links overtreatment to Sp, while the latter doesn't.
For STAT, we define:
Se = P(STAT_pos == 1 | "Individual likely to carry HPZ") = P(STAT_pos == 1 | T_last_BS <= 270)
Se ~ Nb(STAT_pos == 1 && T_last_BS <= 270) / Nb(T_last_BS <= 270)
Sp = P(STAT_pos == 0 | "Individual unlikely to carry HPZ") = P(STAT_pos == 0 | T_last_BS > 270)
Sp ~ Nb(STAT_pos == 0 && T_last_BS > 270) / Nb(T_last_BS > 270)
While the definition of
PQ_overtreat_9m remains consistent with that of other interventions, the way we screen persons will have an impact on how we measure "overtreatment". With option 1, it will make overtreatment independent on sensitivity. With option 2, it introduces some correlation, allowing increasing overtreatment to increase with sensitivity (when keeping specificity fixed).
Rationale: if Sp remains constant but Se increases, we identify more persons that have
T_last_BS <= 270, and this will include more and more those how don't have HPZ (so, PQ_overtreat will increase but PQ_overtreat_9m shouldn't)
Does that make sense ?