  To better understand effects of exposure to food allergens, food challenge
studies are designed to slowly increase the dose of an allergen delivered to
allergic individuals until an objective reaction occurs. These dose-to-failure
studies are used to determine acceptable intake levels and are analyzed using
parametric failure time models. Though these models can provide estimates of
the survival curve, their parametric form may misrepresent the survival
function for doses of interest, and different models that describe the data
similarly may produce different dose-to-failure estimates. Motivated by
predictive inference, we developed a Bayesian approach to combine survival
estimates based upon posterior predictive stacking, where the weights are
formed to maximize posterior predictive accuracy. The approach allows for the
inclusion of flexible models, and, in our case, allows us to include random
effects to account for frailty components entering the model through
study-to-study heterogeneity. The methodology is investigated in simulation,
and is used to estimate allergic population eliciting doses for multiple food
allergens.
