The topic of “truncation by death” in randomized experiments arises in many fields, such as medicine, economics and education. Traditional approaches addressing this issue ignore the fact that the outcome after the truncation is neither “censored” nor “missing,” but should be treated as being defined on an extended sample space. Using an educational example to illustrate, we will outline here a formulation for tackling this issue, where we call the outcome “truncated by death” because there is no hidden value of the outcome variable masked by the truncating event. We first formulate the principal stratification ( Frangakis & Rubin, 2002 ) approach, and we then derive large sample bounds for causal effects within the principal strata, with or without various identification assumptions. Extensions are then briefly discussed.

Government-sponsored job-training programs must be subject to evaluation to assess whether their effectiveness justifies their cost to the public. The evaluation usually focuses on employment and total earnings, although the effect on wages is also of interest, because this effect reflects the increase in human capital due to the training program, whereas the effect on total earnings may be simply reflecting the increased likelihood of employment without any effect on wage rates. Estimating the effects of training programs on wages is complicated by the fact that, even in a randomized experiment, wages are ''truncated'' (or less accurately ''censored'') by nonemployment, that is, they are only observed and well-defined for individuals who are employed. In this article, we develop a likelihood-based approach to estimate the wage effect of the US federally-funded Job Corps training program using ''Principal Stratification''. Our estimands are formulated in terms of: (1) the effect of the training program on wages for those who would be employed whether they were trained or not, also called the survivor average causal effect (SACE), and the proportion of people in this category; (2) the wages when trained for those who would be employed only when trained, and the proportion of people in this category; (3) the wages when not trained for those who would be employed only when not trained, and the proportion of people in this category; (4) the proportion of people who would be not employed whether trained or not. We conduct likelihood-based analysis using the EM algorithm, and investigate the plausibility of important submodels with scaled loglikelihood ratio statistics. We also conduct a sensitivity analysis with respect to specific parametric assumptions. Our results suggest that all four types of people [(1)-(4) previously] exist, which is impossible under the usual monotonicity assumptions made in traditional econometric evaluation methods.

No abstract

We investigate the estimation of subgroup treatment effects with observational data. Existing propensity score matching and weighting methods are mostly developed for estimating overall treatment effect. Although the true propensity score should balance covariates for the subgroup populations, the estimated propensity score may not balance covariates for the subgroup samples. We propose the subgroup balancing propensity score (SBPS) method, which selects, for each subgroup, to use either the overall sample or the subgroup sample to estimate propensity scores for units within that subgroup, in order to optimize a criterion accounting for a set of covariate-balancing conditions for both the overall sample and the † Jing Dong subgroup samples. We develop a stochastic search algorithm for the estimation of SBPS when the number of subgroups is large. We demonstrate through simulations that the SBPS can improve the performance of propensity score matching in estimating subgroup treatment effects. We then apply the SBPS method to data from the Italy Survey of Household Income and Wealth (SHIW) to estimate the treatment effects of having debit card on household consumption for different income groups.