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Point processes are probabilistic tools for modelling event data. While there exists a fast-growing literature on the relationships between point processes, how such relationships connect to causal effects remains unexplored. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation to deal with point process treatment and outcome, showing that it should be performed after a Fourier transform of the intention-to-treat effects on the treatment and outcome, and thus takes the form of deconvolution. We refer to this approach as generalized Wald estimation and propose an estimation strategy based on well-established deconvolution methods. [ABSTRACT FROM AUTHOR]

Two‐stage randomized experiments become an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two‐stage randomized experiments. Under the randomization‐based framework, we consider the estimation of a new direct effect of interest as well as the average direct and spillover effects studied in the literature. We provide unbiased estimators of these causal quantities and their conservative variance estimators in a general setting. Using these results, we then develop hypothesis testing procedures and derive sample size formulas. We theoretically compare the two‐stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the randomized evaluation of the Indian National Health Insurance Program. An open‐source software package is available for implementing the proposed methodology. [ABSTRACT FROM AUTHOR]

Despite an increasing reliance on fully-automated algorithmic decision-making in our day-to-day lives, humans still make consequential decisions. While the existing literature focuses on the bias and fairness of algorithmic recommendations, an overlooked question is whether they improve human decisions. We develop a general statistical methodology for experimentally evaluating the causal impacts of algorithmic recommendations on human decisions. We also examine whether algorithmic recommendations improve the fairness of human decisions and derive the optimal decision rules under various settings. We apply the proposed methodology to the first-ever randomized controlled trial that evaluates the pretrial Public Safety Assessment in the United States criminal justice system. Our analysis of the preliminary data shows that providing the PSA to the judge has little overall impact on the judge's decisions and subsequent arrestee behaviour. [ABSTRACT FROM AUTHOR]

Causal inference concerns not only the average effect of the treatment on the outcome but also the underlying mechanism through an intermediate variable of interest. Principal stratification characterizes such a mechanism by targeting subgroup causal effects within principal strata, which are defined by the joint potential values of an intermediate variable. Due to the fundamental problem of causal inference, principal strata are inherently latent, rendering it challenging to identify and estimate subgroup effects within them. A line of research leverages the principal ignorability assumption that the latent principal strata are mean independent of the potential outcomes conditioning on the observed covariates. Under principal ignorability, we derive various nonparametric identification formulas for causal effects within principal strata in observational studies, which motivate estimators relying on the correct specifications of different parts of the observed‐data distribution. Appropriately combining these estimators yields triply robust estimators for the causal effects within principal strata. These triply robust estimators are consistent if two of the treatment, intermediate variable and outcome models are correctly specified, and moreover, they are locally efficient if all three models are correctly specified. We show that these estimators arise naturally from either the efficient influence functions in the semiparametric theory or the model‐assisted estimators in the survey sampling theory. We evaluate different estimators based on their finite‐sample performance through simulation and apply them to two observational studies. [ABSTRACT FROM AUTHOR]

In many social science experiments, subjects often interact with each other and as a result one unit's treatment influences the outcome of another unit. Over the last decade, a significant progress has been made toward causal inference in the presence of such interference between units. Researchers have shown that the two-stage randomization of treatment assignment enables the identification of average direct and spillover effects. However, much of the literature has assumed perfect compliance with treatment assignment. In this article, we establish the nonparametric identification of the complier average direct and spillover effects in two-stage randomized experiments with interference and noncompliance. In particular, we consider the spillover effect of the treatment assignment on the treatment receipt as well as the spillover effect of the treatment receipt on the outcome. We propose consistent estimators and derive their randomization-based variances under the stratified interference assumption. We also prove the exact relationships between the proposed randomization-based estimators and the popular two-stage least squares estimators. The proposed methodology is motivated by and applied to our own randomized evaluation of India's National Health Insurance Program (RSBY), where we find some evidence of spillover effects. The proposed methods are implemented via an open-source software package. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

The matched-pairs design enables researchers to efficiently infer causal effects from randomized experiments. In this paper, we exploit the key feature of the matched-pairs design and develop a sensitivity analysis for missing outcomes due to truncation by death, in which the outcomes of interest (e.g., quality of life measures) are not even well defined for some units (e.g., deceased patients). Our key idea is that if 2 nearly identical observations are paired prior to the randomization of the treatment, the missingness of one unit's outcome is informative about the potential missingness of the other unit's outcome under an alternative treatment condition. We consider the average treatment effect among always-observed pairs (ATOP) whose units exhibit no missing outcome regardless of their treatment status. The naive estimator based on available pairs is unbiased for the ATOP if 2 units of the same pair are identical in terms of their missingness patterns. The proposed sensitivity analysis characterizes how the bounds of the ATOP widen as the degree of the within-pair similarity decreases. We further extend the methodology to the matched-pairs design in observational studies. Our simulation studies show that informative bounds can be obtained under some scenarios when the proportion of missing data is not too large. The proposed methodology is also applied to the randomized evaluation of the Mexican universal health insurance program. An open-source software package is available for implementing the proposed research. [ABSTRACT FROM AUTHOR]

Principal stratification is a causal framework to analyse randomized experiments with a post-treatment variable between the treatment and end point variables. Because the principal strata defined by the potential outcomes of the post-treatment variable are not observable, we generally cannot identify the causal effects within principal strata. Motivated by a real data set of phase III adjuvant colon cancer clinical trials, we propose approaches to identifying and estimating the principal causal effects via multiple trials. For the identifiability, we remove the commonly used exclusion restriction assumption by stipulating that the principal causal effects are homogeneous across these trials. To remove another commonly used monotonicity assumption, we give a necessary condition for the local identifiability, which requires at least three trials. Applying our approaches to the data from adjuvant colon cancer clinical trials, we find that the commonly used monotonicity assumption is untenable, and disease-free survival with 3-year follow-up is a valid surrogate end point for overall survival with 5-year follow-up, which satisfies both causal necessity and causal sufficiency. We also propose a sensitivity analysis approach based on Bayesian hierarchical models to investigate the effect of the deviation from the homogeneity assumption. [ABSTRACT FROM AUTHOR]