Data and variables

We retrieved data on psychiatric inpatient admissions for select states from the State Inpatient Database (SID). The SID provides a near-census of all hospital inpatient admissions for participating states and is made available for purchase by the Agency for Healthcare Research and Quality under the Healthcare Cost Utilization Project (HCUP) [23]. SID reports individual admission-level diagnoses (ICD 9 codes) for all inpatients. We include all inpatients with a psychiatric diagnosis for mental illnesses listed within the Clinical Classification Software (CCS) categories [24] (Appendix Table A.1 of Supplementary Material). Some states also allow the SID to report whether a psychiatric admission was requested by law enforcement/court order (coded under admission source or point of origin) [24]. Among the states that participated in HCUP SID from 2006 to 2011, California, Arizona, North Carolina and New York report admission source (including law enforcement/court order), race, gender, county identifier and admission month. The most populous state in this study—California—does not provide information on race beyond 2011, hence, we restrict our analysis to 2011. These states comprise the study regions in our analysis and yield a total of 13.1 million psychiatric inpatient admissions from 2006 to 2011.

We identified 46,188 law enforcement/court order-initiated involuntary psychiatric inpatient admissions within the 13.1 million ‘universe’ of all psychiatric admissions. The SID does not directly report whether a psychiatric inpatient admission was voluntary or involuntary. We approximate this status based on whether law enforcement (or a court order) requested the admission, in keeping with the medico-legal definitions of voluntary/involuntary status of inpatient psychiatric admissions in the USA [25,26,27]. Two variables in SID, namely asource (admission source) and pointoforigin (point of origin), directly reported from the Uniform Billing form (UB04)—which is the standard claim form for billing medical and mental health claims—record whether a patient’s inpatient admission was requested by a law enforcement authority and/or a court order [28,29,30,31]. Psychiatric inpatient admissions that were transported to the hospital by emergency law enforcement responders do not receive a ‘requested by law enforcement/court order’ status on the UB04 form and in the SID [31]. This status, also referred to as a patient’s ‘legal status’ helps identify involuntary versus voluntary admissions as patients voluntarily admitted for psychiatric treatment largely originate from non-law enforcement/court order admission sources or point of origin (e.g., emergency room, another hospital, other health facility, routine, etc.) [25,26,27, 32]. Other studies use asource and pointoforigin variables for examining characteristics of psychiatric inpatient admissions and quality of care in the SID [33, 34]. Our observed count of 46,188 law enforcement/court order-initiated involuntary psychiatric admissions aligns with expected counts reported nationally by the Substance Abuse and Mental Health Services Administration and hospital/facility count in the SID [35, 36].Footnote 1

We excluded all psychiatric inpatient admissions with missing information for race, sex, month, admission source (or point of origin) or county (~10% of total observations). Our final analytic sample comprised 25,640 county-months (95 counties over 72 months, with four race and sex sub-groups per county-month). Of these, 6866 county-months reported one or more psychiatric inpatient admissions requested by law enforcement/court order.

Male African American psychiatric inpatients admitted through a request from law enforcement/court order form the main group of interest in our analysis. We aggregated the monthly count of psychiatric inpatient admissions per county over 72 months (January 2006–December 2011) by race (African American, all other races), sex (male, female) and admission status (requested by law enforcement/court order, all other admission types). We converted the monthly counts of psychiatric admissions to rates per 100,000 population using county-level race and gender population denominators from the US Census Bureau’s Population Estimates database [37]. The resulting series of monthly counts and population rates (by race, sex, admission type) form our outcome variables.

We operationalized, as our exposure, the percent change in monthly employment per metropolitan statistical area (MSA). MSAs comprise large, heavily populated urban centers of economic activity that may span one or more counties [38, 39]. MSA-level employment, measured monthly in the Current Population Survey (CPS) by the US Bureau of Labor Statistics, provides the total number of people who worked for pay (either part time or full time) during the survey reference week [38]. Employment change, defined as the difference in a month’s number of employed persons from the previous month divided by the previous month’s total employed people, gives acute changes in a local economy (i.e., MSA) in that it is zero (or of negligible value) if there is very little change in number of employed people, but high (either negative or positive) in circumstances of abrupt economic decline or expansion. Employment change accounts for changes in the civilian labor force and is well suited for modeling economic recession as ‘shocks’. Month-to-month variation in employment change overcomes the drawbacks of other macroeconomic indicators such as unemployment rate, mass layoffs and foreclosures as (a) it is not limited to only those eligible for unemployment insurance, (b) represents immediate change, accounts for inflows, outflows or changes in the civilian labor force and (c) does not present directional distortion during brief periods of economic expansion [40,41,42,43,44,45]. Its suitability as a strong, acute indicator of macroeconomic contraction is further evidenced by its use in literature documenting associations between economic downturns and health outcomes [22, 40, 46, 47]. We obtained monthly aggregated employment series from 2006 to 2011, for each metropolitan statistical area (MSA) within our study states, from the Local Area Unemployment Statistics database made available by the US Bureau of Labor Statistics [38]. We merged MSA-level data to SID counties using MSA-to-county crosswalk made available by the National Bureau of Economic Research [48]. Our final analytic sample comprised 46 MSAs (spanning 95 counties in four states) over 72 months (2006–2011).

Analysis

We hypothesize that the psychiatric inpatient admissions requested by law enforcement/court order increases among African American men, but not among other race/gender groups, in the months immediately following a decline in percent monthly employment change. Additionally, we examine whether monthly employment decline precedes changes in non-law enforcement/court order-requested inpatient psychiatric admissions among African American men and other race/ethnicity and sex groups. We use two analytic approaches based on count versus population-standardized rate outcome distributions to determine the relation between our outcomes and exposure (modeled as 0- to 3-month exposure lags):

1.

Zero inflated binomial (ZINB) regression: This approach examines the relation between county-level monthly counts of psychiatric inpatient admissions requested by law enforcement/court order (outcome) and 0- to 3-month lags of monthly employment change (exposure). ZINB models accommodate overdispersion and excessive zeros by combining a negative binomial distribution with a separate process for excess zeros (in our case, logistic regression) [49, 50]. In epidemiologic research, ZINB models tend to fare better than other approaches when excess zeros and non-zero counts in the outcome variable arise from different data generating processes, respectively (e.g., hurdle models that deem all zeros as structural, rather than a combination of structural and sampling zeros) [51]. In addition to the 0- to 3-month exposure lags, our ZINB models controlled for population, month, year fixed effects and state-specific linear time trends.

2.

Fixed effects ordinary least squares (OLS) regression: This approach uses, as the outcome, the county-level log-transformed population rate [i.e., natural logarithm of (counts/population)*100,000] of psychiatric inpatient admissions requested by law enforcement, controlling for county, month, year fixed effects and state-specific linear time trends [22]. Fixed effects OLS regression incorporates fixed effects for individual counties, capturing unobserved heterogeneity, and allows for the control of time-invariant characteristics, permitting the estimation of within county relation between the exposure and outcome over time [52].

We estimate separate regressions per admission type (requested by law enforcement/court order, all other psychiatric admissions), by race (African American, non-African American) and sex (male, female). In alignment with prior work, we contend that absent an increase in non-law enforcement/court order-requested psychiatric inpatient admissions, any observed rise in law enforcement-requested involuntary admissions among African American men following ambient macroeconomic decline would support the frustration–aggression–displacement hypothesis [4, 15]. Sensitivity checks include re-estimation of our main tests (with psychiatric inpatient admissions requested by law enforcement/court order as the outcome), controlling for all other psychiatric admissions, to account for potential confounding from overall changes in psychiatric help seeking following exposure. For tests that reject the null, we estimate the predicted counts of inpatient psychiatric admissions with incremental change in exposure. We use Stata’s ‘margins’ command to compute and graph average marginal predicted counts of psychiatric inpatient admissions (per unit increase in exposure) for race/sex groups and admission types that reject the null [53]. We conduct all analyses in Stata SE (version14.2) [54].