Optimal Design of the Annual Influenza Vaccine

Seasonal influenza is a major public health concern, and the first line of defense is the flu shot. Antigenic drifts and the high rate of influenza transmission require annual updates to the flu shot composition. The World Health Organization recommends which flu strains to include in the annual vaccine based on surveillance and epidemiological analysis. There are two critical decisions regarding the flu shot design. One is its composition; currently, three strains constitute the flu shot, and they influence vaccine effectiveness. Another critical decision is the timing of the composition decisions, which affects the flu shot production. Both of these decisions have to be made under uncertainty many months before the flu season starts. We quantify the trade offs involved through multistage stochastic mixed-integer programs that determine the optimal flu shot composition and its timing in a stochastic and dynamic environment. Our first model takes the view of a social planner, and optimizes strain selections based on a production plan that is provided by the flu shot manufacturers. It also incorporates risk-sensitivity through mean-risk models. Our second model relaxes the exogenous production planning assumption and, hence, provides a more accurate representation of the hierarchical decision mechanism between a social planner, who selects the flu shot strains, and the manufacturers, who make the flu shot available. We derive structural properties of both models, and calibrate them using publicly available data. The flu shot strains are updated based on clinical, virological and immunological surveillance. In the virological surveillance, hemagglutinin inhibition assays are used to identify antigenic properties of the influenza viruses. However, this serology assay is labor-intensive and time-consuming. As an alternative, pairwise amino acid sequence comparison of influenza strains is used in statistical learning models to identify positions that cause antigenic variety. The performance of these models is evaluated by cross validation. In Chapter 5, we formulate cross validation as a bilevel program where an upper-level program chooses the model variables to minimize the out-of-sample error, and lower-level problems in each fold optimize in-sample errors according to their training data set by selecting the regression coefficients of the chosen model variables. We provide an extensive computational study using clinical data, and identify amino acid positions that significantly contribute to antigenic variety of influenza strains