Heterogeneous causal effects of neighborhood policing in New York City with staggered adoption of the policy

Communities often self select into implementing a regulatory policy, and adopt the policy at different time points. In New York City, neighborhood policing was adopted at the police precinct level over the years 2015-2018, and it is of interest to both (1) evaluate the impact of the policy, and (2) understand what types of communities are most impacted by the policy, raising questions of heterogeneous treatment effects. We develop novel statistical approaches that are robust to unmeasured confounding bias to study the causal effect of policies implemented at the community level. Using techniques from high-dimensional Bayesian time-series modeling, we estimate treatment effects by predicting counterfactual values of what would have happened in the absence of neighborhood policing. We couple the posterior predictive distribution of the treatment effect with flexible modeling to identify how the impact of the policy varies across time and community characteristics. Using pre-treatment data from New York City, we show our approach produces unbiased estimates of treatment effects with valid measures of uncertainty. Lastly, we find that neighborhood policing decreases discretionary arrests, but has little effect on crime or racial disparities in arrest rates

Robust inference for geographic regression discontinuity designs: assessing the impact of police precincts

We study variation in policing outcomes attributable to differential policing practices in New York City (NYC) using geographic regression discontinuity designs (GeoRDDs). By focusing on small geographic windows near police precinct boundaries we can estimate local average treatment effects of precincts on arrest rates. The standard GeoRDD relies on continuity assumptions of the potential outcome surface or a local randomization assumption within a window around the boundary. These assumptions, however, can easily be violated in realistic applications. We develop a novel and robust approach to testing whether there are differences in policing outcomes that are caused by differences in police precincts across NYC. In particular, our test is robust to violations of the assumptions traditionally made in GeoRDDs and is valid under much weaker assumptions. We use a unique form of resampling to identify new geographic boundaries that are known to have no treatment effect, which provides a valid estimate of our test statistic's null distribution even under violations of standard assumptions. This procedure gives substantially different results in the analysis of NYC arrest rates than those that rely on standard assumptions, thereby providing more robust tests of the effect of police precincts on arrest rates in NYC

Statistical Methods for Analyzing Complex Spatial and Missing Data

In chapter 1, we develop a novel two-dimensional wavelet decomposition to decompose spatial surfaces into different frequencies without imposing any restrictions on the form of the spatial surface. We illustrate the effectiveness of the proposed decomposition on satellite based PM2.5 data, which is available on a 1km by 1km grid across Massachusetts. We then apply our proposed decomposition to study how different frequencies of the PM2.5 surface adversely impact birth weights in Massachusetts. In chapter 2, we study the impact of monitor locations on two stage health effect studies in air pollution epidemiology. Typically in these studies, estimates of air pollution exposure are obtained from a first stage model that utilizes monitoring data, and then a second stage outcome model is fit using this estimated exposure. The location of the monitoring sites is usually not random and their locations can drastically impact inference in health effect studies. We take an in-depth look at the specific case where the location of monitors depends on the locations of the subjects in the second stage model and show that inference can be greatly improved in this setting relative to completely random allocation of monitors. In chapter 3, we introduce a Bayesian data augmentation method to control for confounding in large administrative databases when additional data is available on confounders in a validation study. Large administrative databases are becoming increasingly available, and they have the power to address many questions that we otherwise couldn't answer. Most of these databases, while large in size, do not have sufficient information on confounders to validly estimate causal effects. However, in many cases a smaller, validation data set is available with a richer set of confounders. We propose a method that uses information from the validation data to impute missing confounders in the main data and select only those confounders which are necessary for confounding adjustment. We illustrate the effectiveness of our method in a simulation study, and analyze the effect of surgical resection on 30 day survival in brain tumor patients from Medicare.Biostatistic

Principal stratification with continuous treatments and continuous post-treatment variables

In causal inference studies, interest often lies in understanding the mechanisms through which a treatment affects an outcome. One approach is principal stratification (PS), which introduces well-defined causal effects in the presence of confounded post-treatment variables, or mediators, and clearly defines the assumptions for identification and estimation of those effects. The goal of this paper is to extend the PS framework to studies with continuous treatments and continuous post-treatment variables, which introduces a number of unique challenges both in terms of defining causal effects and performing inference. This manuscript provides three key methodological contributions: 1) we introduce novel principal estimands for continuous treatments that provide valuable insights into different causal mechanisms, 2) we utilize Bayesian nonparametric approaches to model the joint distribution of the potential mediating variables based on both Gaussian processes and Dirichlet process mixtures to ensure our approach is robust to model misspecification, and 3) we provide theoretical and numerical justification for utilizing a model for the potential outcomes to identify the joint distribution of the potential mediating variables. Lastly, we apply our methodology to a novel study of the relationship between the economy and arrest rates, and how this is potentially mediated by police capacity