Among matching techniques for observational studies, full matching is in principle the best, in the sense that its alignment of comparable treated and control subjects is as good as that of any alternate method, and potentially much better. This article evaluates the practical performance of full matching for the first time, modifying it in order to minimize variance as well as bias and then using it to compare coached and uncoached takers of the SAT. In this new version, with restrictions on the ratio of treated subjects to controls within matched sets, full matching makes use of many more observations than does pair matching, but achieves far closer matches than does matching with k ≥ 2 controls. Prior to matching, the coached and uncoached groups are separated on the propensity score by 1.1 SDs. Full matching reduces this separation to 1% or 2% of an SD. In older literature comparing matching and regression, Cochran expressed doubts that any method of adjustment could substantially reduce observed bias of this magnitude.To accommodate missing data, regression-based analyses by ETS researchers rejected a subset of the available sample that differed significantly from the subsample they analyzed. Full matching on the propensity score handles the same problem simply and without rejecting observations. In addition, it eases the detection and handling of nonconstancy of treatment effects, which the regression-based analyses had obscured, and it makes fuller use of covariate information. It estimates a somewhat larger effect of coaching on the math score than did ETS's methods.

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The propensity score collapses the covariates of an observational study into a single measure summarizing their joint association with treatment conditions; prognostic scores summarize covariates' association with potential responses. As with propensity scores, stratification on prognostic scores brings to uncontrolled studies a concrete and desirable form of balance, a balance that is more familiar as an objective of experimental control. Like propensity scores, prognostic scores can reduce the dimension of the covariate; yet causal inferences conditional on them are as valid as are inferences conditional only on the unreduced covariate. As a method of adjustment unto itself, prognostic scoring has limitations not shared with propensity scoring, but it holds promise as a complement to the propensity score, particularly in certain designs for which unassisted propensity adjustment is difficult or infeasible.

In randomized experiments, treatment and control groups should be roughly the same-balanced-in their distributions of pretreatment variables. But how nearly so? Can descriptive comparisons meaningfully be paired with significance tests? If so, should there be several such tests, one for each pretreatment variable, or should there be a single, omnibus test? Could such a test be engineered to give easily computed p-values that are reliable in samples of moderate size, or would simulation be needed for reliable calibration? What new concerns are introduced by random assignment of clusters? Which tests of balance would be optimal?To address these questions, Fisher's randomization inference is applied to the question of balance. Its application suggests the reversal of published conclusions about two studies, one clinical and the other a field experiment in political participation.

This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in samples from populations with infinitely many species. We present moments of this random variable, discuss asymptotic relations among them and with related random variables, and draw connections with regular variation, which appears in various manifestations.

The spatial segregation of the U.S. population by socioeconomic position and especially raceethnicity suggests that the social contexts or "neighborhoods" in which people live may substantially contribute to social disparities in hypertension. The Chicago Community Adult Health Study did face-to-face interviews, including direct measurement of blood pressure, with a representative probability sample of adults in Chicago. These data were used to estimate socioeconomic and racialethnic disparities in the prevalence, awareness, treatment, and control of hypertension, and to analyze how these disparities are related to the areas in which people live. Hypertension was significantly negatively associated with neighborhood affluence/gentrification, and adjustments for context eliminated the highly significant disparity between blacks/African-Americans and whites, and reduced the significant educational disparity by 10-15% to borderline statistical significance. Awareness of hypertension was significantly higher in more disadvantaged neighborhoods and in places with higher concentrations of blacks (and lower concentrations of Hispanics and immigrants). Adjustment for context completely eliminated blacks' greater awareness, but slightly accentuated the lesser awareness of Hispanics and the greater levels of awareness among the less educated. There was no consistent evidence of either social disparities in or contextual associations with treatment of hypertension, given awareness. Among those on medication, blacks were only 40-50% as likely as whites to have their hypertension controlled, but context played little or no role in either the level of or disparities in control of hypertension. In sum, residential contexts potentially play a large role in accounting for racial-ethnic, and to a lesser degree, socioeconomic disparities in hypertension

Neighborhood-level interventions provide an opportunity to better understand the impact that neighborhoods have on health. In 2004, municipal authorities in Medellín, Colombia, built a public transit system to connect isolated low-income neighborhoods to the city's urban center. Transit-oriented development was accompanied by municipal investment in neighborhood infrastructure. In this study, the authors examined the effects of this exogenous change in the built environment on violence. Neighborhood conditions and violence were assessed in intervention neighborhoods (n = 25) and comparable control neighborhoods (n = 23) before (2003) and after (2008) completion of the transit project, using a longitudinal sample of 466 residents and homicide records from the Office of the Public Prosecutor. Baseline differences between these groups were of the same magnitude as random assignment of neighborhoods would have generated, and differences that remained after propensity score matching closely resembled imbalances produced by paired randomization. Permutation tests were used to estimate differential change in the outcomes of interest in intervention neighborhoods versus control neighborhoods. The decline in the homicide rate was 66% greater in intervention neighborhoods than in control neighborhoods (rate ratio = 0.33, 95% confidence interval: 0.18, 0.61), and resident reports of violence decreased 75% more in intervention neighborhoods (odds ratio = 0.25, 95% confidence interval 0.11, 0.67). These results show that interventions in neighborhood physical infrastructure can reduce violence.

Omitted variable bias can affect treatment effect estimates obtained from observational data due to the lack of random assignment to treatment groups. Sensitivity analyses adjust these estimates to quantify the impact of potential omitted variables. This paper presents methods of sensitivity analysis to adjust interval estimates of treatment effect-both the point estimate and standard errorobtained using multiple linear regression. Central to our approach is what we term benchmarking, the use of data to establish reference points for speculation about omitted confounders. The method adapts to treatment effects that may differ by subgroup, to scenarios involving omission of multiple variables, and to combinations of covariance adjustment with propensity score stratification. We illustrate it using data from an influential study of health outcomes of patients admitted to critical care.remaining assumption is not. When regression results are questioned, it's often the nonconfounding assumption that is the focus of doubt.Because the issue arises even with the most thorough observational studies, adjusting for any number of covariates, it fuels cynicism about observational research. If the possibility of unmeasured variable bias can't be removed, then why bother with potential confounders, particularly those that are difficult to measure, or not obvious threats? It might be clear that the damage from omitting a confounder W would be reduced by adjustment for available correlates of W, yet, because introducing these correlates would draw attention to the absence of W , not at all clear that effecting the additional adjustments would enhance the credibility of the research. Plainly, the problem here is not the methodological strategy of broadly adjusting for relevant baseline characteristics but an absence of, or lack of awareness of, suitable methods with which to quantify benefits of more comprehensive confounder controls.Sensitivity analyses, procedures quantifying the degree of omitted variable bias needed to nullify or reverse key conclusions of a study, can help. Sensitivity analysis methods for various models and data structures are proposed in