The recommended therapy is Paxlovid (utility = 3.585174).
Full posterior distribution:
COVID19 posterior = 0.483883 (unnormalized = 0.00928200)
Influenza posterior = 0.427894 (unnormalized = 0.00820800)
AllergicRhinitis posterior = 0.006686 (unnormalized = 0.00012825)
BacterialPneumonia posterior = 0.081538 (unnormalized = 0.00156408)
Therapy utility scores:
Paxlovid expectedSuccess = 0.388517 adverse = 0.10 utility = 3.585174
Oseltamivir expectedSuccess = 0.285141 adverse = 0.08 utility = 2.611410
Antihistamine expectedSuccess = 0.100269 adverse = 0.03 utility = 0.912689
Antibiotic expectedSuccess = 0.110953 adverse = 0.07 utility = 0.899526
SupportiveCare expectedSuccess = 0.291512 adverse = 0.01 utility = 2.885120
Evidence: Fever=present, DryCough=present, LossOfSmell=absent, Sneezing=absent, ShortBreath=absent.
Evidence total (normalizing constant) = 0.01918233.
The posterior for each disease is computed as:
posterior(d) = prior(d) × ∏ P(symptom|d) / evidenceTotal
where for an absent symptom the factor is 1 − P(symptom|d).
For each therapy, expected success is:
expectedSuccess(t) = Σ_i posterior(i) × successByDisease(i)
and utility = benefitWeight × expectedSuccess − harmWeight × adverse.
The recommended therapy is the one with the highest utility.