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Actuarial statistics uses probability theory and statistical inference to quantify insurance claims, premiums, and the uncertainty of future losses. Aggregate claims model describes portfolios, reinsurance redistributes losses, and the Bühlmann model combines experience with population information.

Mathematical epidemiology uses mathematical models and statistical inference to study the occurrence, transmission, and control of disease in populations.

Response-adaptive randomization can assign a larger proportion of later participants to the treatment currently estimated to be better, improving outcomes for participants within the trial. Its allocation probabilities depend on earlier outcomes, which complicates statistical inference; delayed responses and calendar-time trends can also make adaptation ineffective or biased, and an allocation aimed at patient benefit need not maximize power.