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Estimation of probabilities by classical maximum likelihood estimators can give unreliable results when the number of cases is small. A Bayesian approach, where prior probabilities with Dirichlet distributions are used to temper the estimates, can reduce the variance enough to make the estimates useful. This is demonstrated by using this approach to estimate mortalities of severe infections from different sites, lungs, skin urinary tract, etc. The prior probabilities are provided in a hierarchical way, i.e. by deriving them from the same database, but without distinguishing between different sites of infection.

Empirical antibiotic treatment with broad-spectrum antibiotics provides a high probability of covering treatment, but is associated with unnecessary costs as high drug prices, side-effects, and facilitated development of antibiotic resistance. A decision support system (DSS) based upon a causal probabilistic network (CPN) was constructed from a database with 491 cases (1992-94) of urosepticaemia and validated on 426 cases (1995-96). The CPN uses decision theory to balance the gain in life-years due to therapy against the costs of the antibiotic therapy, i.e. price, side-effects and ecological cost. The DSS selected antibiotics of an overall lower price, higher coverage and less ecological cost than the antibiotics actually chosen for empirical treatment. Thus, a DSS incorporating the CPN could achieve a desirable antibiotic policy, and it holds promise for improving empirical antibiotic therapy.