A new u-statistic with superior design sensitivity in matched observational studies

A second evidence factor for a second control group

In an observational study of the effects caused by a treatment, a second control group is used in an effort to detect bias from unmeasured covariates, and the investigator is content if no evidence of bias is found. This strategy is not entirely satisfactory: two control groups may differ significantly, yet the difference may be too small to invalidate inferences about the treatment, or the control groups may not differ yet nonetheless fail to provide a tangible strengthening of the evidence of a treatment effect. Is a firmer conclusion possible? Is there a way to analyze a second control group such that the data might report measurably strengthened evidence of cause and effect, that is, insensitivity to larger unmeasured biases? Evidence factor analyses are not commonly used with a second control group: most analyses compare the treated group to each control group, but analyses of that kind are partially redundant; so, they do not constitute evidence factors. An alternative analysis is proposed here, one that does yield two evidence factors, and with a carefully designed test statistic, is capable of extracting strong evidence from the second factor. The new technical work here concerns the development of a test statistic with high design sensitivity and high Bahadur efficiency in a sensitivity analysis for the second factor. A study of binge drinking as a cause of high blood pressure is used as an illustration.

BOUNDS ON THE CONDITIONAL AND AVERAGE TREATMENT EFFECT WITH UNOBSERVED CONFOUNDING FACTORS

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semiparametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o p n - 1 / 4 rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

Association Between Comorbid Psychiatric Disorders and Hospital Resource Use in Physically Ill Pediatric Inpatients: A Case-Matched Analysis

OBJECTIVE

To understand differences in hospital length of stay and costs associated with the presence of a comorbid psychiatric disorder among physically ill inpatients within a publicly funded pediatric hospital.

METHOD

This was a retrospective observational design using administrative data on physically ill inpatients 2 to 18 years old who were admitted over a 5-year period (n = 54,316 admissions). Records with (n = 4,953) and without (n = 49,363) documented comorbid psychiatric disorder were compared for differences in baseline characteristics. To optimize the balance of measured covariates, individuals with comorbid psychiatric disorders were matched on propensity score, case mix group, and Elixhauser comorbidities, resulting in 4,371 pairs of inpatients with and without a comorbid psychiatric disorder. Differences in length of stay and total hospital costs were assessed using generalized estimating equation models on matched patients.

RESULTS

Unmatched analyses demonstrated that inpatient admissions with comorbid psychiatric disorders were associated with higher occurrence of previous hospitalizations (69.2% versus 55.0%), unscheduled admissions (66.9% versus 60.9%), medical admissions (75.6% versus 52.7%), urgent admissions (62.5% versus 56.2%), and Elixhauser comorbidities (69.0% versus 39.0%), with standardized differences > |0.1|. Matched analyses demonstrated a 9.6% longer length of stay (95% CI = 5.7-13.7; p < .001) and 9.6% higher costs per admission (95% CI = 5.9-13.4; p < .001) in inpatients with comorbid psychiatric disorders compared to those without.

CONCLUSION

The complexity of inpatients with a comorbid psychiatric disorder, in conjunction with the approximate 10% increase in hospital resource use, highlights the need for innovative models of clinical care and research directed at improving patient outcomes and reducing hospital costs.

Nutrition status, bone mass density, and selective serotonin reuptake inhibitors

The association between selective serotonin reuptake inhibitor (SSRI) use and bone mass density (BMD) has been debated. Inadequate diet, which may occur in depressed individuals prescribed SSRIs is also associated with decreased BMD. This study seeks to determine if SSRI use in adults is associated with lower than average BMD while controlling for nutrition related variables. Further, it investigates whether there are potential interactions between micronutrients and SSRI use on BMD. Adults, 655 with an SSRI prescription ≥180 days and 12,372 non-users, were identified in the 2005-2014 National Health and Nutrition Examination Survey (NHANES) data. Survey respondents were propensity score matched on propensity to have an SSRI prescription and compared on femoral neck BMD t-scores. A sub-analysis within SSRI users was conducted to calculate the odds ratio (OR) of having a low (osteopenia or osteoporosis) BMD t-score given SSRI exposure and inadequate daily micronutrient intake. Inadequate daily micronutrient intake was common; over half of SSRI users and non-users had inadequate calcium, vitamin D, and potassium. SSRI use was associated with an absolute reduction of 0.11 in BMD t-score. Inadequate daily vitamin D intake was associated with lower BMD t-scores in both SSRI users and non-users. The interaction of SSRI use and inadequate daily intake of zinc was also associated with low BMD (OR: 1.11, 95% CI: 1.01-1.23). Patient health may be improved by nutritional education, referral to a dietitian, or by micronutrient monitoring by the prescribing physician.

Multisample adjusted U-statistics that account for confounding covariates

Multisample U-statistics encompass a wide class of test statistics that allow the comparison of 2 or more distributions. U-statistics are especially powerful because they can be applied to both numeric and nonnumeric data, eg, ordinal and categorical data where a pairwise similarity or distance-like measure between categories is available. However, when comparing the distribution of a variable across 2 or more groups, observed differences may be due to confounding covariates. For example, in a case-control study, the distribution of exposure in cases may differ from that in controls entirely because of variables that are related to both exposure and case status and are distributed differently among case and control participants. We propose to use individually reweighted data (ie, using the stratification score for retrospective data or the propensity score for prospective data) to construct adjusted U-statistics that can test the equality of distributions across 2 (or more) groups in the presence of confounding covariates. Asymptotic normality of our adjusted U-statistics is established and a closed form expression of their asymptotic variance is presented. The utility of our approach is demonstrated through simulation studies, as well as in an analysis of data from a case-control study conducted among African-Americans, comparing whether the similarity in haplotypes (ie, sets of adjacent genetic loci inherited from the same parent) occurring in a case and a control participant differs from the similarity in haplotypes occurring in 2 control participants.

Effect of the 2010 Chilean earthquake on posttraumatic stress: reducing sensitivity to unmeasured bias through study design

In 2010, a magnitude 8.8 earthquake hit Chile, devastating parts of the country. Having just completed its national socioeconomic survey, the Chilean government reinterviewed a subsample of respondents, creating unusual longitudinal data about the same persons before and after a major disaster. The follow-up evaluated posttraumatic stress symptoms (PTSS) using Davidson's Trauma Scale. We use these data with two goals in mind. Most studies of PTSS after disasters rely on recall to characterize the state of affairs before the disaster. We are able to use prospective data on preexposure conditions, free of recall bias, to study the effects of the earthquake. Second, we illustrate recent developments in statistical methodology for the design and analysis of observational studies. In particular, we use new and recent methods for multivariate matching to control 46 covariates that describe demographic variables, housing quality, wealth, health, and health insurance before the earthquake. We use the statistical theory of design sensitivity to select a study design with findings expected to be insensitive to small or moderate biases from failure to control some unmeasured covariate. PTSS were dramatically but unevenly elevated among residents of strongly shaken areas of Chile when compared with similar persons in largely untouched parts of the country. In 96% of exposed-control pairs exhibiting substantial PTSS, it was the exposed person who experienced stronger symptoms (95% confidence interval = 0.91-1.00).