Abstract
Empirical research in the areas of health economics and medical statistics that uses a new econometric method called “partial identification” is making progress. This paper evaluates the applications of partial identification to these areas to see how effective and insightful this new method is. Section 2 presents research on partial identification for missing-data problems. For example, when infection data for COVID-19 are missing for people who have not been tested, the infection rate of the entire population cannot be accurately known. Empirical studies in this area have most commonly assumed that data are missing at random; for this particular example, the assumption would then be that the infection rate of the population at large is the same as that of people who have been tested. In contrast, research using partial identification would first apply the Law of Total Probability to the infection rate of the entire population, next assign the observed probabilities to the infection rate of the tested people and the ratio of the tested people, and finally replace the missing (counterfactual) rate of infection among those who have not been tested with 0 (its lower bound) and 1 (its upper bound) to obtain the identification region (the bound) of the infection rate of then tire population. Furthermore, the identification bounds can be narrowed by imposing credible assumptions, such as “people who are tested tend to have higher infection rates than those who are not tested” (Monotone Instrumental Variable Assumption). In Sections 3 and 4, we explain how to partially identify the causality and treatment effect using as examples(i) the effect of Swan-Ganz catheterization on mortality, and (ii) the effect of antihypertensive drugs conditional on renin response. We first explain the identification problem, i.e., the reason why the treatment effect cannot be point-identified only from the data. We then show that partial identification allows the treatment effect to be identified from the data alone as an interval (the bounds) without any assumption. We next show how the identification bounds on the treatment effect narrow when credible assumptions are imposed (Instrumental Variable Assumption and Monotone Treatment Response Assumption). The more assumptions and the stronger assumptions one imposes, the narrower are the bounds; this yields stronger conclusions, but lower credibility of inference. Thus, we are required to decide what assumptions to maintain. Finally, we consider how a decision maker who knows that the treatment effects are identified in bounds might choose an action using as examples (i) treatment of a new infection disease and (ii) choice of diagnostic testing and treatment. In the present context, the Bayesian criterion would be a good choice only when the subjective expected probability of the treatment effect is correct. The maximin criterion would be a conservative choice (which grants deference to the status quo), while the minimax-regret criterion would be a choice that balances conservatism (in deferring to the status quo) and challenge (in reflecting the innovation).
