Alessandra Mattei

Causal inference on multiple non-independent outcomes raises serious challenges, because multivariate techniques that properly account for the outcome's dependence structure need to be considered. We focus on the case of binary outcomes framing our discussion in the potential outcome approach to causal inference. We define causal effects of treatment on joint outcomes introducing the notion of product outcomes. We also discuss a decomposition of the causal effect on product outcomes into intrinsic and extrinsic causal effects, which respectively provide information on treatment effect on the intrinsic (product) structure of the product outcomes and on the outcomes' dependence structure. We propose a log-mean linear regression approach for modeling the distribution of the potential outcomes, which is particularly appealing because all the causal estimands of interest and the decomposition into intrinsic and extrinsic causal effects can be easily derived by model parameters. The method is illustrated in two randomized experiments concerning (i) the effect of the administration of oral pre-surgery morphine on pain intensity after surgery; and (ii) the effect of honey on nocturnal cough and sleep difficulty associated with childhood upper respiratory tract infections.

SUMMARY: We conduct principal stratification and mediation analysis to investigate to what extent the positive overall effect of treatment on postoperative pain control is mediated by postoperative self administration of intra-venous analgesia by patients in a prospective, randomized, double-blind study. Using the Bayesian approach for inference, we estimate both associative and dissociative principal strata effects arising in principal stratification, as well as natural effects from mediation analysis. We highlight that principal stratification and mediation analysis focus on different causal estimands, answer different causal questions, and involve different sets of structural assumptions.

The opportunity to assess short term impact of air pollution relies on the causal interpretation of the exposure-response association. However, up to now few studies explicitly faced this issue within a causal inference framework. In this paper, we reformulated the problem of assessing the short term impact of air pollution on health using the potential outcome approach to causal inference. We considered the impact of high daily levels of particulate matter ≤10 μm in diameter (PM10) on mortality within two days from the exposure in the metropolitan area of Milan (Italy), during the period 2003–2006. Our research focus was the causal impact of a hypothetical intervention setting daily air pollution levels under a pre-fixed threshold. We applied a matching procedure based on propensity score to estimate the total number of attributable deaths (AD) during the study period. After defining the number of attributable deaths in terms of difference between potential outcomes, we used the estimated propensity score to match each high exposure day, namely each day with a level of exposure higher than 40 μg/m3, with a day with similar background characteristics but a level of exposure lower than 40 μg/m3. Then, we estimated the impact by comparing mortality between matched days. During the study period daily exposures larger than 40 μg/m3 were responsible for 1079 deaths (90% CI: 116; 2042). The impact was more evident among the elderly than in the younger age classes. Exposures ≥ 40 μg/m3 were responsible, among the elderly, for 1102 deaths (90% CI: 388, 1816), of which 797 from cardiovascular causes and 243 from respiratory causes. Clear evidence of an impact on respiratory mortality was found also in the age class 65–74, with 87 AD (90% CI: 11, 163). The propensity score matching turned out to be an appealing method to assess historical impacts in this field, which guarantees that the estimated total number of AD can be derived directly as sum of either age-specific or cause-specific AD, unlike the standard model-based procedure. For this reason, it is a promising approach to perform surveillance focusing on very specific causes of death or diseases, or on susceptible subpopulations. Finally, the propensity score matching is free from issues concerning the exposure-confounders-mortality modeling and does not involve extrapolation. On the one hand this enhances the internal validity of our results; on the other, it makes the approach scarcely appropriate for estimating future impacts.

Regression discontinuity (RD) designs are often interpreted as local randomized experiments: a RD design can be considered as a randomized experiment for units with a realized value of a so-called forcing variable falling around a pre-fixed threshold. Motivated by the evaluation of Italian university grants, we consider a fuzzy RD design where the receipt of the treatment is based on both eligibility criteria and a voluntary application status. Resting on the fact that grant application and grant receipt statuses are post-assignment (post-eligibility) intermediate variables, we use the principal stratification framework to define causal estimands within the Rubin Causal Model. We propose a probabilistic formulation of the assignment mechanism underlying RD designs, by re-formulating the Stable Unit Treatment Value Assumption (SUTVA) and making an explicit local overlap assumption for a subpopulation around the threshold. A local randomization assumption is invoked instead of more standard continuity assumptions. We also develop a model-based Bayesian approach to select the target subpopulation(s) with adjustment for multiple comparisons, and to draw inference for the target causal estimands in this framework. Applying the method to the data from two Italian universities, we find evidence that university grants are effective in preventing students from low-income families from dropping out of higher education.

Summary: The paper investigates the relationship between fertility and women's education in Italy, using data from the 2009 Household Multipurpose Survey of Family and Social Subjects. We use event history models, adopting a Bayesian approach for inference to study the association between fertility and women's education in the presence of a time varying unobserved component. Our analysis shows that either disregarding the unobserved component or assuming a time constant unobserved heterogeneity can lead to misleading results, at least in the context studied.

In many observational studies, the treatment may not be binary or categorical but rather continuous, so the focus is on estimating a continuous dose– response function. In this article, we propose a set of programs that semiparametrically estimate the dose–response function of a continuous treatment under the unconfoundedness assumption. We focus on kernel methods and penalized spline models and use generalized propensity-score methods under continuous treatment regimes for covariate adjustment. Our programs use generalized linear models to estimate the generalized propensity score, allowing users to choose between alternative parametric assumptions. They also allow users to impose a common support condition and evaluate the balance of the covariates using various approaches. We illustrate our routines by estimating the effect of the prize amount on subsequent labor earnings for Massachusetts lottery winners, using data collected by Imbens, Rubin, and Sacerdote (2001, American Economic Review, 778–794).

Even in randomized experiments the identification of causal effects is often threatened by the presence of missing outcome values, with missingness possibly being non ignorable. We provide sufficient conditions under which the availability of a binary instrument for non response allows us to non parametrically point identify average causal effects in some latent subgroups of units, named Principal Strata, defined by their non response behavior in all possible combinations of treatment and instrument. Examples are provided as possible scenarios where our assumptions may be plausible.

We consider a new approach to identify the causal effects of a binary treatment when the outcome is missing on a subset of units and dependence of nonresponse on the outcome cannot be ruled out even after conditioning on observed covariates. We provide sufficient conditions under which the availability of a binary instrument for nonresponse allows us to derive tighter identification intervals for causal effects in the whole population and to partially identify causal effects in some latent subgroups of units, named Principal Strata, defined by the nonresponse behavior in all possible combinations of treatment and instrument. A simulation study is used to assess the benefits of the presence versus the absence of an instrument for nonresponse. The simulation design is based on real health data, coming from a randomized trial on breast self-examination (BSE) affected by a large proportion of missing outcome data. An instrument for nonresponse is simulated considering alternative scenarios to discuss the key role of the instrument for nonresponse in identifying average causal effects in presence of nonignorable missing outcomes. We also investigate the potential inferential gains from using an instrument for nonresponse adopting a Bayesian approach for inference. In virtue of our theoretical and empirical results, we provide some recommendations on study designs for causal inference.