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Health & Place 15 (2009) 568–577
Contents lists available at ScienceDirect
Health & Place
1353-82
doi:10.1
� Corr
E-m
journal homepage: www.elsevier.com/locate/healthplace
County variation in use of inpatient and ambulatory psychiatric care in NewYork State 1999–2001: Need and supply influences in a structural model
Sarah Curtis a,�, Peter Congdon b, Michael Almog c, Raymond Ellermann d
a Department of Geography, Durham University, South Road, Durham DH1 3LE, UKb Queen Mary, University of London, UKc New York University, USAd Office of Mental Health, New York State, USA
a r t i c l e i n f o
Article history:
Received 14 December 2007
Received in revised form
19 August 2008
Accepted 18 September 2008
Keywords:
Psychiatric hospital services
Psychiatric ambulatory services
Geography
New York State
Population needs
Spatial access
92/$ - see front matter & 2008 Elsevier Ltd. A
016/j.healthplace.2008.09.009
esponding author. Tel.: +441913341830; fax
ail address: [email protected] (S. Curtis
a b s t r a c t
This study investigates the potential for ecological studies to contribute useful information on variations
in service use, both across areas and across different types of psychiatric care. The analysis uses data for
the 62 counties of New York State, which include both urbanised and rural areas, with widely differing
social, household and ethnic structures. We analysed data on service use by patients aged 15–64 years
for several psychiatric conditions combined. The research reported here used an approach which for
several reasons is innovative, compared with other ecological studies of psychiatric service use. First,
the impact of population variables on both ambulatory and hospitalisation rates is considered, whereas
many previous studies are confined to hospital use. Second, our method combines and weights
population variables in the ‘need index’ in a way that (a) reflects geographical variations in service use
rates in both hospital and ambulatory sectors (b) controls for service configuration and access as well as
(c) allowing for spatial autocorrelation in the need index. To demonstrate this method, four simple
indicators of poverty, social isolation, concentration of racial minorities and population density, were
used in combination to define a ‘needs’ index that predicts use of psychiatric services at county level.
Comparison with alternative methods of measuring need, using the same data but based on more
conventional strategies, resulted in significantly different need rankings of areas. Our composite index
of ‘underlying need’ showed a positive association with service use (hospital and ambulatory care for
men and for women). This relationship controls for access to services, and allows for spatial correlation
in the need construct. Controlling for underlying population ‘need’, a measure of spatial proximity to
hospitals with psychiatric beds had an independent effect, being associated positively with hospital
inpatient use, and negatively with ambulatory referral rates. For women, after allowing for population
characteristics and proximity to hospital beds, there was no strong relationship between county level
indicators of hospitalisation and rate of use of ambulatory care. For men, at the county population level
considered in this ecological study, relatively high rates of admission in the inpatient sector were
associated with higher rates of referral in the ambulatory care sector. The analysis highlights the
importance of considering a set of socio-geographic factors that affect need for care (as well as simple
measures of population size and age/sex structure) when making ecological comparisons of levels of
mental health service use. It also demonstrates that the geographical relationship between psychiatric
hospital use and population ‘need’ indicators should to be evaluated in ways that take into account a
functionally complex ‘matrix’ of local conditions including population characteristics, service
configuration, access and possible interrelationships between various psychiatric care sectors.
& 2008 Elsevier Ltd. All rights reserved.
Introduction
There is an international trend towards more strategicgeographic service planning in health service systems, particularly
ll rights reserved.
: +441913341801.
).
in countries with advanced health care systems. In these places ithas become increasingly important to monitor variations in use ofservices from one local area to another and investigate the factorsthat seem to explain the variation. Geographical variability in therelative rate of psychiatric service use is important for planning ofmental health services because it may affect the pressure ofdemand placed on local services and the types of serviceconfigurations that may most effectively meet these demands.
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In particular, planners need to clarify the relative importance forlocal service utilisation of the existing supply of available services,the balance of provision of different types of services, and thecharacteristics of the population that may affect populationpropensity to use mental health care in a particular area.
There is also a growing tendency in the international literatureto view regional and national health care systems as complexsystems (e.g. Cilliers, 1998; Sweeney and Griffiths, 2002). Formental health care this idea of a complex system accords withTansella and Thornicroft’s vision of a ‘matrix model’ of mentalhealth care involving different types of services operating togetherat different geographical scales and over time to meet to provideservices to people with mental illnesses that are often chronic.They comment that ‘ythe local level is usually the best level ofanalysis to consider the components of the general adult mentalhealth systemy. A series of questions arise at this level, forexample, yare the main components of adult mental healthservices mutually substitutabley’ (Tansella and Thornicroft, 1998,p. 505). This vision of a functionally, spatially and temporallycomplex mental health system is consistent with conceptualdevelopments in health geography that are increasingly movingtowards approaches which can more effectively model andanalyse the spatial organisation of such complex health caresystems (e.g. Cummins et al., 2007) In this paper we argue that inlight of these developments we need to develop more advancedways of modelling the geographical interrelationships betweenservice provision, service use and population variables and wedemonstrate an example of a statistical method designed to bebetter adapted to do this. We demonstrate this approach usingdata from a specific regional health care system, though theprincipals of the method could be applicable in other systemsinternationally.
Modelling complexity of a mental health care system in a specificpolicy context
These international trends are reflected, for example, in recentdevelopments in mental health care planning in the USA. The USPresident’s New Freedom Commission on Mental Health (2003)emphasised the need for a strategic approach to health care forstates and localities. This implies that within states, plans willneed to be informed about local variations in resource use andwill be able to interpret these variations in terms of aims forstrategic development. Although the majority of mental healthcare is now delivered in ambulatory settings, for purposes ofstrategic planning it is still important to consider use of inpatientservices, not least because acute service use is a significant part ofthe mental health service. For example, as noted in OMH NYS(2004) in New York State in 2002, 12.2% of Medicaid fundedmental health service users in a typical week were inpatients butinpatient services accounted for 52.7% of annual Medicaidexpenditures. In the US generally, it is reported that in 2003 over$24 billion of mental health expenditures were for inpatientservices, representing over one third of total expenditures and anincrease of about $4 billion dollars since 1993 (Mark et al., 2007).
This study investigates the potential for ecological studies tocontribute useful information on variations in service use, bothacross areas and across different types of psychiatric care. Itconsiders the factors affecting acute and ambulatory service use,in particular need for care and supply measures, and uses aregression model to assess how far use of ambulatory care reducesthe demand for acute care. It also considers how census indicatorscan be combined in a single spatially correlated needs index, insuch a way that the index also takes account of service usepatterns. We explain how this compares with more conventional
methods for constructing psychiatric service need measures atpopulation level. The geographic focus is the 62 counties of NewYork State (NYS), which include both urbanised and rural areas,with widely differing social, household and ethnic structures.Counties were chosen as a unit of analysis primarily because ofthe role that they play in the NYS planning process. They have theadded advantage that census data are available on a countywidebasis. (A major disadvantage in using county data is that thecounties are extremely variable in composition, ranging from ruralcounties with low population densities that are primarily white tolarge urban counties with large minority populations, and weaimed to use modelling techniques which would be robust in forsuch diverse geographical units.)
The planning process in NYS is described in Section 5.07 of theNYS Mental Hygiene Law. Under the Mental Hygiene Law theplanning process begins with a statement of goals and objectivesfrom a statewide mental health service council. Counties arerequired to develop plans consistent with these goals andobjectives and provide input to OMH based on local planningefforts. A number of issues relating to service supply andutilisation have emerged as a result of this process, whichhighlight the need to develop ways to model the complexinterrelationships in the mental health service system. Some ofthese are as follows:
�
There are substantial disparities in county based per capitaservice rates. � Counties sometimes use services in adjoining or nearbycounties.
� Disparities in county based per capita service rates differ fordifferent services. There is a need to reduce reliance oninpatient services and more information is needed on whetherthis may best done by increasing community based services.
� Relative disparities in service use partly reflect the relativeneed for services in the population i.e. some counties haveargued that because of their populations they ‘need’ higherservice levels.
� Any approach to a reduction or expansion of services shouldtake into account the allocation of existing resources to specificservices within each locality, how they influence each otherand the ‘unmet need’ for services in each county.
The current fiscal environment in NYS, suggests that resourcesfor all public services will become increasingly scarce, making itmore likely that there will be reduction in services, so a betterunderstanding of the factors associated with relative need forservices in different populations and the equitable distribution ofexisting services will play increasingly important roles. Previousneeds assessment methodologies used in NYS to distributeresources (OMH NYS, 1992) did take into consideration theinfluence of socio-economic variables on need for service.However, it did so for specific parts of the service in isolation(e.g. only for acute hospital beds). The basic assumption under-lying these needs assessment methodologies was that the relative(i.e. equitable) need for each the service in each county (e.g. acuteinpatient beds) was proportional to estimates of the relativeprevalence of serious mental illness in that county. The actualamount of each service which could be attributed in relation torelative need was determined by the total state supply of eachservice. The methodologies did not consider spatial correlationsbetween counties nor did they consider possible interdependen-cies between services, nor the relative levels of access to servicesin the county.
The approach taken in this paper takes all of these factors intoconsideration so that it has the potential to develop county based
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relative ‘need’ measures based on population variables thatpredict service use in the region. It has the potential to identifycounties whose use patterns make them ‘outliers’ from thegeneral pattern of provision and use, which could prove helpfulin making fairer decisions regarding the reduction or expansion ofservices. At the outset, we emphasise that we do not aim todevelop a measure of unmet and ‘absolute’ need for service. Wedo however provide an approach by which a meaningful relativeneeds index for small areas can be developed using routinelyavailable administrative data and using a method of modellingwhich reflects more accurately the complexity of the mentalhealth system in the region. The use of administrative data is notmeant to suggest that individual risk factors are not important inpredicting psychiatric morbidity. Indeed, there is some evidenceto suggest that, with the exception of area based economic rank,individual factors may be more important (Goldsmith et al., 1998).However, the use of individual risk factors to predict psychiatricmorbidity for planning purposes requires that their measures bereadily available and updated on a regular basis. This is not oftenthe case so that the use of administrative population based data isoften the most practical solution to developing indices ofestimated psychiatric morbidity and likely demand for services.In the absence of precise and up to date measures of ‘true’population need, based on morbidity surveys, a ‘needs index’ maybe constructed from area based socio-economic variables whichhave been shown to be associated with psychiatric morbidity, andwhich can also be shown to have an actual association withservice use in the specific region in question.
Measuring need: approaches in ecological studiesof psychiatric use
Our analysis therefore aims to demonstrate how variations inhealth service activity between New York counties are associatedwith population variables, taking into account the ecologicalrelationship between mental health service use in the inpatientand ambulatory sectors.
Our approach to modelling relevant population characteristicswas informed by other research, mainly from studies of urban areasin North America and Europe: Schweitzer and Kierszenbaum(1978), Dear and Wolch (1987), Almog et al. (2004), Curtis et al.(2006), Dean and James (1981), Glover et al. (1998, 2004), Johnsonet al. (1998), Congdon et al. (1998), Jarman et al. (1992), Smith et al.(1996), Dekker et al. (1997), Driessen et al. (1998), Koppel andMcGuffin (1999), and Maylath et al. (1999, 2000).
In these studies direct measures of psychiatric morbidity insmall area populations were not available and in most casesindicators of socio-demographic conditions were instead used asproxies for variations in psychiatric morbidity likely to influenceuse of services. The research generally shows that higher rates ofuse of psychiatric inpatient services in small areas are positivelyassociated with higher local levels of poverty and socio-economicdeprivation. Some studies (e.g. Congdon et al., 1998; Almog et al.,2004; Curtis et al., 2006) also report a positive association withuse of psychiatric services for measures of social isolation andfragmentation, operationalised using Congdon’s (1996) index thatcombines proportions of people living alone, unmarried adults,resident population ‘turnover’ and rented housing tenure. In someresearch, though not in all studies higher concentrations of certainminority racial groups (e.g. African Americans in the US) alsoshow a positive ecological association with hospital use (Barnes,2004; Harvey et al., 1996).
Independently of these relationships with socio-demographicvariables, small area rates of inpatient admissions also vary withgeographical proximity to hospitals (e.g. see review by Curtis
et al., 2006). Thus distance from area of residence to hospitalswith psychiatric beds is often taken as an indicator of varyingaccess to inpatient services at the population level.
Most ecological research to produce indicators of populationfactors relating to use of psychiatric services has employed dataon inpatient admissions, but has not been able to incorporateinformation on services provided outside hospitals. This is alimitation, partly because in countries like the US a large part ofmental health services are now delivered outside hospital settingsand the population factors influencing outpatient or ambulatoryservice use may not be the same as for inpatient care.
Also, levels of inpatient service use by psychiatric patients maybe affected by differing provision of ambulatory care. If ambula-tory services have a strong preventive role in most areas, reducinggeneral risk of admission in the population, then areas with higherrates of use of ambulatory mental health services would havelower rates of hospital admission (after allowing for populationcharacteristics and proximity to hospitals). Burns et al. (2002)have conducted a systematic review of evidence from the US andthe UK and comment that controlled trials in the US have oftenshown a significant reduction in inpatient use for individualpatients who receive home treatment services. This suggests thatambulatory care can ‘prevent’ some inpatient episodes, or at leastreduce lengths of inpatient stays. Some forms of communityprovision (e.g. assertive outreach and crisis intervention) may beparticularly effective in reducing risk of admission (Johnson et al.,2001). In New York State studies on the impact of mandatedtreatment (OMH NYS, 2005) have shown that an increasedparticipation in community based services is accompanied by adecrease in the use of inpatient services. A few studies haveexamined the question using an ecological approach, with data forarea populations. In the US, Fortney et al. (1999) showed that ruralpopulations in closer proximity to ambulatory services had lowerrates of inpatient admissions than those living further from awayambulatory services. If, alternatively, ambulatory provision gen-erally plays a complementary role with respect to inpatient care,areas with higher rates of use of ambulatory services might havehigher rates of hospital admission. This might occur, for example,if greater levels of ambulatory provision tend to uncover morecases of mental illness, leading to greater demand for all forms ofmental health care, or if patients discharged from hospital aregenerally referred to community services. Hendryx and Rohland(1994) found that hospital psychiatric admissions were greater inareas closer to ambulatory services. Naish et al. (2001) showedthat in one part of London, UK, there appeared to be a positiveassociation between referrals to community based mental healthcare teams and rates of admission to hospitals. It is also possiblethat both processes are operating to varying degrees in differentareas, in which case it may be difficult to determine this clearlyfrom an ecological analysis of the type used in the present study.
In the analysis presented below we have developed a prototypemodel which incorporates information relating to all the elementsdiscussed above. As well as relevant population socio-economicvariables, and measures of proximity to hospitals, we include dataon provision of ambulatory services.
In addition, we have applied a novel strategy in which aseparate measurement model is used to derive the needs indexfrom the area population variables, while a structural model usesthe same index to model service use variations. Therefore theneeds measure selects and weights component census indicatorsfor the ‘needs index’ in the way that is most relevant forpsychiatric service use. This is an advance on previous studiesthat have related mental health service use to existing deprivationindices derived from other research, not necessarily related topsychiatric service use (e.g. Jarman et al., 1992), or have relatedservice use to several census indicators to derive weights for a
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composite index using more conventional regression (e.g. Gloveret al., 1998, 2004). The latter strategy runs the risk of multi-collinearity between several census indicators, which makes theregression coefficients difficult to interpret. If, for example,poverty, ethnic composition and social isolation are geographi-cally intercorrelated, the conventional regression coefficientsobtained by including all three in a model may not represent asuitable weighting for these variables in a ‘needs’ index.
A further innovation in this study is the way that we build onthe approach of Hogan and Tchernis (2004) and derive a needsindex that incorporates selected US Census 2000 indices whilealso taking spatial correlation into account. In this way the needsindex takes into account ‘unobserved’ (unmeasured) determi-nants of service use, that are themselves likely to be spatiallycorrelated. Previous psychiatric care needs research has notrecognised that health need is likely to be spatially correlated,in the sense of explicitly incorporating such correlation in themethodology for formulating the needs score. For instance, theMental Illness Needs Index (MINI) proposed by Glover et al.(2004) for England shows a Moran’s I statistic of 0.54 over 354English local authorities, which suggests that there is significantgeographical clustering of areas with similar MINI scores. Suchclustering affects statistical modelling of associations found inecological studies because it implies that conditions in eachindividual area may not be independent of conditions in adjacentareas.
We explain below in more detail the modelling strategy thatwe have used to introduce these innovations.
Modelling strategy
In the following analysis we address the limitations of previousresearch discussed above and report an ecological model whichincorporates: (a) indicators of use of both inpatient andambulatory psychiatric services, (b) information on proximity toservices and (c) measures of population variables likely to affectservices. The model aims to control for spatial correlation and forpossible overdispersion in relation to the Poisson model oftenused to model health events. We also aim through the model todevelop a clearer understanding of how different interrelated setsof variables in a complex mental health care system affect oneanother.
The model involves two main components and amounts to aform of structural equation model (SEM). One component of thismodel can be seen as a form of factor analysis, although, asapplied here, it is more adaptive to the aims of this analysis. Inconventional factor analysis, the idea is to concentrate or reducethe information in a set of different, but inter-correlatedindicators into latent constructs that summarise their variabilityand the relationships between them. Here we use such constructsas proxy measures, subject to measurement error, of the ‘need’ formental health care-hence the term ‘measurement model’.
The second element of our model provides the structuralcomponent of our SEM approach. This involves regressionmodelling of relationships between constructs (such as our ‘need’measure), and observable outcomes (such as rates of hospital use),while also taking account of access and supply variables.
Previous approaches to ecological service utilisation modelingthat use composite area ‘need’ measures to predict psychiatricservice use (e.g. Koppel and McGuffin, 1999; Jarman et al., 1992)typically had two stages; a data reduction stage to produce acomposite area ‘need’ indicator, followed by a regression analysiswhich seeks to predict service use using the ‘need’ indicator.Koppel and McGuffin (1999) employed factor analysis in the firststage to produce factor ‘loadings’ for each area summarizing
variability in a number of separate socio-economic indicators.Other studies (e.g. Jarman et al., 1992; Almog et al., 2004) havecombined standardized values on different ‘needs’ indicators in asummative ‘need’ score. These may not the most efficientstrategies to use in order to represent the ecological associationsbetween service use and socio-economic conditions. One short-coming is that the socio-economic ‘construct’ measure of ‘needs’is derived using methods that are independent of the statisticalrelationships between the constituent ‘need’ variables and theoutcome of interest (variation in service use). Therefore the needsmeasure may not select and weight components in the way that ismost relevant for psychiatric service use. Also these earlier studiesdid not take account of the spatial correlation in the variousmeasured indicators when deriving the overall needs construct.
In the prototype measurement model used here, we derive asingle ‘latent’ need for care index using four observed socio-economic indicators (theoretically selected and empiricallyderived as described in the data section below). These represent,respectively: % of persons aged over 18 living in poverty; % of totalpopulation living alone; % of total population non-white; andpopulation per hectare (represented in Fig. 1 as Z1, Z2, Z3, Z4). Ourmodel summarizes these into a single ‘construct’ and in contrastto previous studies, the loadings (weightings) of the observedindicators on this construct are adaptive in the sense that theyboth summarise the complex variability and correlations amongthe four need indicators and also optimise the relevance for theoutcome variables (rates of service use).
Also, in our model, the needs factor is assumed to be spatiallycorrelated, showing clustering among adjacent areas (Hogan andTchernis, 2004). The model therefore reflects spatial correlation inboth ‘observed’ socio-economic indicators and in unmeasured riskfactors that affect need.
In the structural (SEM) part of the model (see Fig. 1), we use anegative binomial regression for referral counts with meansobtained as the product of relative referral rates (r) by expectedreferrals (E), obtained by multiplying county age–sex populationsby New York statewide age–sex referral rates). The relativereferral rates r are specific to county and to each of four referraloutcomes: female and male hospitalisations (HOSPF and HOSPM);female and male ambulatory referrals (AMBF and AMBM). Theseare all related to the latent needs index (F) which combinesinformation from four socio-economic variables (Z1, Z2, Z3, Z4)from the 2000 US Census and to a measure of hospital access(explained in the next section).
The model for hospital use explicitly includes features of thepsychiatric care system. These include the measure of access tohospital care (AXS) and a binary indicator of whether a countycontains a psychiatric hospital (OWNHOSP). We expected thatAXS and OWNHOSP would raise hospitalisation rates whileambulatory referrals would be negatively related to AXS. Inaddition, included in the modelling of hospitalisation are therelative rates of ambulatory service use (AMBF or AMBM) (whichare therefore treated here both as outcome variables and aspossible predictors of hospitalisation rates).
Fig. 1 represents graphically the model for predicting hospita-lisation and ambulatory use rates; ambulatory referrals are takento depend on the need factor F and on the spatially correlatedresidual term just discussed. Appendix A contains a formaldescription of the model in terms of constituent equations andparameters.
Data
Hospital admission data is from the Statewide Planning andResearch Cooperative System (SPARCS) for three years, 1999–2001,
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‘Need’index(F)
Z1 poverty
Z2 livingalone
Z3 race
Z4 popndensity
GeographicAccess (AXSS) Hospitalisat-
ion rates(HOSPM,HOSPF)
Hospital in County (OWNHOSP)
AmbulatoryService Use (AMBM,AMBF)
Fig. 1. Structural equation model in graph form.
S. Curtis et al. / Health & Place 15 (2009) 568–577572
for patients aged 15–64 years, and includes schizophrenia, mooddisorder, delusional disorder, anxiety disorder, and other mentalillness in ICD9 categories 290–319, but excludes organic anddevelopmental mental illness, substance-addiction diagnoses andeating disorders (ICD-9 780). Community ambulatory service usedata are derived from the 1999 and 2001 Patient CharacteristicsSurveys (PCS) conducted by the New York Office of Mental Health.These relate to ambulatory services comprising ‘outpatient’ and‘community support non-residential’ service categories as definedby the Office of Mental Health. The PCS is a ‘census’ survey ofnumbers of users reported by service providers across New YorkState and data from two surveys conducted in 1999 and 2001.
To calculate population adjusted area measures of relativerates of use of both hospital and amubulatory services, the UScensus population for the year 2000 was used to compile data onpopulation numbers in counties by sex and 5 year age group. Wethen derived age standardized referral ratios (analogous tostandard mortality ratios), namely ratios of observed hospital orambulatory referrals to expected referrals. Differences in levels ofhospital and ambulatory service use were significant between thedifferent counties, allowing for population size and age composi-tion. The areas with the lowest hospitalisation ratios for malesincluded Hamilton, Livingston, Madison, Orleans and Tiogacounties (standardized referral ratios were 30% or more belowthe State average). Counties with relatively high hospitalisationrates for men include Bronx, Chemung, New York, Niagara andSullivan, where age standardized ratio measures of use were atleast 35% above the state average. The range of variability inambulatory use rates was less extreme than for inpatient care:areas with the lowest levels of use of these ambulatory serviceswere Saratoga, Oswego, Essex counties, where ratio measures ofuse were all between 40% and 50% of the State Average. Sullivan,Bronx, New York and Chemung counties were the highest users ofthese ambulatory services, all with ratios over 30% of the averagefor New York State.
For the health needs measurement model, we selected the fourcomponent socio-economic variables (Z1,y, Z4 in Fig. 1) on whichto base the composite population need index to explain variationin use, while also accounting for service configuration. Thesevariables were intended to represent attributes of populationsthat influence demand for psychiatric care, independently of theorganisation of services or access opportunity to services. They arerelative measures for populations and are not intended torepresent clinically assessed need for specific services by
individual persons. The variables taken as measures of populationneed are material poverty, social fragmentation, and racialcomposition of the population which (according to previousresearch reviewed above) are likely to be independently asso-ciated with varying use of psychiatric care. We also included ameasure of rural vs. urban conditions because rurality as well aspoverty may be important for mental health care use. The 2000population census was used to derive a selected set of indicatorsassociated with these population attributes:
�
% individuals age 18+ below poverty line as a measure ofmaterial poverty; � % total population living alone as a measure of social isolation; � % of population reporting themselves to be in non-white racialgroups to assess concentrations of racial/ethnic minorities and
� persons per square mile as a measure of urban versus ruralconditions.
These variables were converted from percentages to standar-dized indicators (z scores).
It may be noted that data on county level variation inpsychiatric morbidity in the resident county populations werenot available. However, the population indicators we have usedmay also be predictors of varying levels of psychiatric morbidity incommunities (Weich et al., 2003; Congdon, 2006; Allardyce et al.,2005).
As noted above, other research suggests that proximity to thelocal supply of hospital beds can influence demand. We measuredaccessibility of acute psychiatric beds, for county populations,using two indicators:
�
a binary indicator of whether or not psychiatric beds werelocated in the county; � an ‘access opportunity’ score for each county of proximity to allpsychiatric beds in New York State. Information on numbers ofpsychiatric hospital beds located in general hospitals (article28) in 2000 was produced by aggregating age-appropriate beds(for adolescents and adults) by hospital, and mapping hospitalzip codes to the counties in which they are located. For caseswhere capacity changes were made during 2000, these figuresrepresent an average for that year. Zip Code data for hospitalsenabled us to link the hospital addresses to Zip Code Areas(ZCAs) for which the US Census Bureau provides a ‘centroid’
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point location. Straight line distances between hospitals andeach ZCA centroid were obtained.
For each ZCA ‘access opportunity’ is then summed across allhospitals, but adjusted for intervening populations in other ZCAs,to give an overall access score. This is calculated as follows:
Ai ¼X
k½BkgðdikÞ=ð
Xm
PmgðdmkÞ�
where Ai is the access score for ith ZCA, Bk the no of psychiatricbeds at kth hospital, dik the distance from ith ZCA to hospital k, dmk
the distance from mth ZCA to hospital k, Pm the population in mthZCA; and g a function of distance. For each county a populationweighted average of scores for all ZCAs within the county (labelledAXSS in Fig. 1) is then used to indicate proximity to psychiatricbeds for the county population as a whole.
Analysis and interpretation of coefficients
As explained above, the structural component of the SEM wasapplied to investigate:
(a)
how rates of use of ambulatory and inpatient services areassociated with the population ‘need’ construct,(b)
how usage rates are related to measures of spatial proximityto hospitals and(c)
whether use of inpatient services varies in relation to use ofambulatory services.The measurement sub-model of the SEM generates a compositeindicator (construct measure) of socio-economic health ‘need’ inthe population, based on four ‘manifest’ variables from the 2000Census. Appendix A provides a formal description of the modelequations and coefficients.
The omega coefficients reported below (corresponding to theoj in Appendix A) are loadings (analogous to other sorts of factoranalysis) showing how the different census indicators Z1, Z2, Z3, Z4
relate to the composite needs construct (F). The omega coefficientfor Zj shows whether it contributes significantly to the overallneeds index and whether the loading is positive or negative.
The ‘usage to need’ (beta) coefficients show the relationshipbetween the composite needs construct (F) and each type ofmental health service use, after controlling for sex and agecomposition, the pattern of the other outcome variables and themeasures of access to beds. The ‘access’ (gamma) coefficientsshow (for each service use outcome, AMBM, AMBF, HOSPM,HOSPF) whether service use is independently associated with the‘access opportunity score’ (AXSS), after controlling for othervariables in the model. The ‘hospital in county’ (eta) coefficientsshow whether having a hospital with psychiatric beds locatedwithin the county (OWNHOSP) influences use of inpatient care,after controlling for other factors in the model. The ‘sectorinterplay’ (delta) coefficients show whether there is a significantassociation between inpatient admission rates and ambulatoryservice use, after controlling for population need and access.
We compare a model with the needs-use relationships onlywith a full model also including the access and sector interplayeffects. This will show whether introducing the service contextvariables affects the needs loadings and ‘usage to need’ coeffi-cients. Models are compared using the ‘DIC’ criterion of Spiegel-halter et al. (2002), where the DIC is the average deviance plus ameasure of complexity de. The latter also provides an estimate ofthe effective parameters in the model (reflecting the poolingstrength under random effects). It is estimated as the difference
between the average deviance and the deviance DevðyÞ at theposterior mean of the full parameter set y.
Some sensitivity analyses were also carried out to explore howresults from this model compared with more conventionalmodeling approaches. These are explained below.
Results
Table 1 shows the output from the statistical modelingtogether with DIC and complexity measures. It is apparent thatthe full model provides a better fit to the data (lower DIC) and thatthe omega and beta coefficients are not greatly affected byintroducing measures of access and the relationship betweenambulatory and hospital care use.
The omega coefficients in the full model show that each of thefour socio-economic variables loads positively on the compositeneed index and that each contributes significantly to thecomposite indicator. Thus the construct is a ‘positive’ indicatorof ‘need’ for psychiatric care in the population (reflecting atendency for service use to be higher in poor, fragmented areaswith larger concentrations of racial populations). When thesesocio-economic attributes are accounted for, the compositeindicator was also higher in more densely populated urban areas,indicating greater service use compared with sparsely populated,rural areas. This construct expresses these complex and inter-related socio-geographical conditions in a single ‘score’ for eacharea.
Table 1 also shows how variations in rates of service use arepredicted by the various components of the statistical model. Thebeta coefficients demonstrate, as expected, that all types ofservice use (hospital and ambulatory care for men and forwomen) are significantly higher in counties with higher compo-site ‘need’ scores. This relationship controls for access to services,and allows for spatial correlation in the need construct.
The ‘gamma’ coefficients show the relation of access to acutebeds to service usage rates and the ‘eta’ coefficients show whetherthe presence of a Hospital within in a county affects levels ofhospitalisation. These provision effects are generally in line withprior expectations. For males, higher county access scores andhaving a hospital with psychiatric beds in the county were bothpositively associated with hospitalisation rates. For women,spatial proximity to hospital beds was also positively associatedwith inpatient hospitalisation, and the location of a psychiatrichospital in the county also has a positive effect (but is not strictlysignificant). Ambulatory service use by men and women is greaterin counties with relatively low access to hospitals (the ‘gamma’coefficients relating access scores to ambulatory service use weresignificantly negative).
As to the interrelationship between hospital referrals andambulatory care (shown by the ‘delta’ coefficients in Appendix A),the relationship for males is positive, though not quite signifi-cantly. Thus, activity in the two sectors may be complementaryand increased ambulatory care does not act to reduce hospitalreferral levels. For females there is no clear substitutive orcomplementary relationship.
Discussion and comparison of model results with alternativeanalytical options
The model here is distinctive in a number of ways from‘standard’ apparently simpler approaches often used in the healthliterature. First the model described here interrelates populationneed and service use while controlling for the fact that differenttypes of service use (ambulatory care vs. hospital care) may
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Table 1Results of statistical modelling.
Parameter Needs only model Full model
Coefficient summary
Mean St devn MC error 2.5% 97.5% Mean St devn MC error 2.5% 97.5%
Loadings on composite need score
(z4)% individuals age 18+ below poverty o1 1.758 0.064 0.009 1.671 1.906 1.854 0.279 0.035 1.524 2.239
(z16)% total population living alone o2 0.878 0.196 0.006 0.494 1.272 0.923 0.239 0.016 0.498 1.453
(z17) % total population Non-White o3 0.930 0.191 0.006 0.571 1.312 0.975 0.242 0.018 0.551 1.491
(z18) popn per sq mile o4 1.263 0.165 0.007 0.936 1.595 1.334 0.264 0.026 0.910 1.876
Predicting service use
Relation of composite need measure to county usage rates
Relation of composite need measure to female ambulatory SAR b1 0.261 0.069 0.002 0.135 0.410 0.284 0.080 0.005 0.145 0.456
Relation of composite need measure to male ambulatory SAR b2 0.234 0.058 0.001 0.128 0.351 0.250 0.069 0.004 0.133 0.403
Relation of composite need measure to female inpatient SAR b3 0.216 0.068 0.002 0.095 0.360 0.215 0.082 0.005 0.081 0.397
Relation of composite need measure to male inpatient SAR b4 0.282 0.087 0.002 0.123 0.458 0.204 0.082 0.005 0.076 0.389
Relation of access to acute beds to service usage rates
Relation of access to acute beds to female ambulatory SAR g1 �0.081 0.063 0.006 �0.245 �0.004
Relation of access to acute beds to male ambulatory SAR g2 �0.054 0.046 0.004 �0.171 �0.002
Relation of access to acute beds to female inpatient SAR g3 0.145 0.071 0.006 0.040 0.317
Relation of access to acute beds to male inpatient SAR g4 0.267 0.101 0.010 0.104 0.502
Relation of whether hospital is located in the county to hospitalisation rate
Relation of location in county to female inpatient SAR Z1 0.158 0.096 0.006 �0.030 0.347
Relation of location in county to male inpatient SAR Z2 0.290 0.101 0.007 0.089 0.485
Relation of ambulatory service use to hospitalisation rates
Relation of female ambulatory service use to female inpatient SAR d1 �0.027 0.149 0.015 �0.293 0.288
Relation of male ambulatory service use to male inpatient SAR d2 0.280 0.161 0.015 �0.055 0.548
Fit
Effective parameters 111.0 110.8
DIC 3449.0 3405.0
S. Curtis et al. / Health & Place 15 (2009) 568–577574
impact on each other. Some ‘standard’ need indices for psychiatriccare are based on a regression of hospitalisation rates onpopulation social indicators, with the need score based onsignificant coefficients. This neglects the fact that high hospitaluse in some areas may reflect not need per se but relatively lowcommunity care. Second the model here corrects for the impactthat access and hospital location have on service use, factors thatare also likely (like ambulatory use) to be confounded with theimpact of need. Third, the model here takes account ofunmeasured but spatially correlated influences on need—otheranalyses have produced need indices that are clearly spatiallycorrelated but have not included this feature in their derivation. Afinal aspect of the model here—not present in many apparentlysimpler models—is that it allows in the structural model formultiple types of service usage, such as male and female hospitalreferrals and ambulatory use. This may be important if differenttypes of service use are related differentially to population need.For example, the method developed in the present paper could bereadily extended to hospitalisations for different diagnoses.
To illustrate the implications of using the more advancedmethod presented here, we consider two simpler, more conven-tional approaches to the two modeling steps reported here. Wecompared our model results with alternatives involving: (a)classic principal components analysis combining informationfrom census social and demographic indicators to derive a needindex, without any regard to psychiatric service use, and (b)regressing service use (expressed as a single measure of use of onetype of mental heath care) on a range of indicators and usingsignificant regression effects to derive an index.
Under approach (a), a principal component analysis in SPSSwas undertaken of the four indices described in the ‘Data’ sectionabove (used in a standardised form). The leading component
accounted for 56% of the variation in the four original censusvariables. [The basis for these models is very different, so it is notpossible to make a direct comparison of the variance explainedwith our model reported above.] The resulting composite indexfrom the PCA solution has a correlation of 0.73 with the indexderived using the structural model described in this paper. Itshows more extreme need scores in densely populated areas andareas with many black residents. The rank correlation betweenthe our ‘need’ score for counties reported above and the countyscores on this alternative PCA solution is relatively modest (0.44).This shows that there are some major differences in ‘needs’ranking of counties when the apparently simpler (but partial)approach is used as compared with our solution to ‘relative needs’estimates of counties.
The second alternative model illustrates the multicollinearityproblems that occur in simple regressions of service use on censusvariables (Croudace et al., 2000). Thus the log of the standardhospitalisation ratio for acute inpatient care (SHR, males andfemales combined) was regressed on the four standard scores forpoverty (ZPOV), living alone (ZALON), black people (ZBLK) andpopulation density (ZDEN). The regression equation (with tstatistics in brackets) is shown below. The b coefficientsassociated with each variable in this equation show the strengthand direction of the association with hospitalisation rate:
LogðSHRÞ ¼ 4:38þ 0:18ZPOVþ 0:01ZALON� 0:32ZBLKþ 0:42ZDEN
ð0:05Þ ð0:08Þ ð0:06Þ ð0:13Þ ð0:11Þ
This equation predicting county level use of hospital suggestssignificant positive associations with poverty and populationdensity but an implausible negative coefficient for percent blacks.Also, in this equation, the density of people living alone does not
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show a significant association independently of the othervariables. The negative coefficient associated with density of theblack population may reflect the high correlation across countiesbetween percent blacks and density or poverty, and one mayexperiment with different census predictors or stepwise selection.A similar explanation may account for the lack of significance ofthe variable indicating the density of people living alone incounties. Without reproducing the details here, stepwise selectiondid not provide a more meaningful solution either. These sortsof issue are compounded if the regression models are developed(as arguably they should be) to take account of more than oneservice outcome. The weightings associated with key variables inthis simple regression solution seem rather improbable and arequite different from those obtained using the ‘latent need index’method we describe above. For policy makers in the differentcounties of New York State, the simpler ‘standard’ type ofregression equation would therefore be unlikely to be acceptableas a relative need indicator, even though it does predict thepattern of service use to some extent.
(darker shading indicateshigher values associated withgreater levels of service use)
Need Score-0.92 - -0.37-0.36 - -0.11-0.10 - 0.030.04 - 0.210.22 - 1.92
Fig. 2. Sketch map of needs score for counties in New York State.
Conclusions
Our conclusions from this analysis need to be considered in thelight of some caveats concerning some limitations of the approachused here. In this prototype model, we have employed relativelycrude measures of spatial access to hospitals, relying on ‘straightline’ distance. Our analysis has considered service use for severalforms of psychiatric illness grouped together although we mightexpect (e.g. Curtis et al., 2006) that the associations reported heremay vary for different types of mental illness. We have used alimited set of socio-economic variables in this model andalthough these perform quite well as predictors of service use,we plan in subsequent analyses to extend this to include othersocio-economic variables that are likely to be relevant. There arealso some issues concerning identification of residential area.People who are homeless or have very insecure housing willprobably not be very well represented in this analysis. We havealso had to exclude from this study those in various forms ofinstitution (notably prisons) who may consume mental healthcare. Homeless and institutional populations may not use mentalhealth care at the same rate as the rest of the resident populationin a county. While we think that our model comes closer tocapturing the complex ‘matrix model’ of mental health caredescribed at the outset, our current model is still somewhatlimited in its description of the psychiatric care system. Otherpsychiatric services in an area such as emergency care, residentialcare and non-acute inpatient care all may have some substantialimpact on the associations reported here as well.
The results show that there were significant variations in age/sex standardized rates of use of both inpatient and ambulatorypsychiatric services among counties in New York State. Thepattern of varying use did not simply contrast New York Citycounties with ‘the rest’ since there were counties outside NewYork City with significantly higher or lower than average rates,which suggests that there are variations in local conditions acrossthe whole state that influence the age and sex adjusted levels ofuse of mental health care.
The research reported here used an approach which isinnovative compared with other ecological studies of psychiatricservice use reported elsewhere. First, it incorporated informationabout ambulatory service use for the areas studies. Second, itdeveloped and applied a comprehensive service need and usemodeling framework: this combines and weights populationvariables in the need index in a way that (a) also reflectsgeographical variations in service use rates in both hospital and
ambulatory sectors, (b) controls for service configuration andaccess, as well as (c) allowing for spatial autocorrelation in theneed index. Both geographical relationships of socio-economicconditions and relationships to service use contribute to definingneed, as compared to existing approaches that use one or other todefine a care need index.
Moreover, the impact of need on both ambulatory andhospitalisation rates is considered in this framework, whereasmany previous studies are confined to hospital use. As mentionedabove, this is important given that the majority of mental healthcare is now delivered in ambulatory settings. The modelingand conceptual framework is applicable generally, but in theapplication to New York counties there were significant associa-tions between rates of use of both inpatient and ambulatory careand socio-demographic attributes of the population. Four simpleindicators of poverty, social isolation, concentration of racialminorities and population density, used in combination, seemedrelevant for defining a needs index that predicts use of psychiatricservices at county level. The composite index of ‘underlying need’showed a positive association with service use, which wasindependent of spatial proximity to hospital care. See Fig. 2 fora map of the needs score.
Proximity to services had an independent effect after control-ling for underlying need. In particular, spatial proximity tohospital care was associated with higher rates of hospitalinpatient use, and lower ambulatory referral rates. The impact ofproximity on hospital use was greatest for men and might partlyarise from a ‘drift’ factor, if men with more severe mental healthproblems tend to migrate to areas in close proximity to inpatientservices. It might also result from referral and admission policiesthat differ for men and women and vary according to proximity toa local hospital.
For women there was no strong relationship between countylevel indicators of hospitalisation and rate of use of ambulatorycare, after allowing for population characteristics and proximity tohospital beds. However, for men the two forms of care seemcomplementary, in the population level sense that high referralsin one sector are matched by elevated referrals in the other.
The analysis highlights the importance of considering a set ofsocio-geographic factors that affect need for care (as well assimple measures of population size and age/sex structure) whenmaking ecological comparisons of levels of mental health serviceuse. It also demonstrates that the usage-need relationship needsto be evaluated in a broader context that allows for serviceconfiguration, access and possible interrelationships betweensectors. The applied analysis in the paper has considered totalambulatory and hospital referrals for all psychiatric conditionsamong relatively large populations in the counties of New York
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State; the conceptual framework of the paper could be developedto have a broader application, however, in understandingdiagnosis specific variations (e.g. schizophrenia referrals alone)and at lower spatial scales.
Finally, we draw attention to a number of elements of theapproach used here that may have wider relevance for geogra-phical modelling of mental health care systems in other regions ofthe world. First, we have argued that, variation in utilization orexpressed demand for mental health care does not necessarilyreflect variation in ‘true’ or absolute need for services, but thatdeveloping models which accurately predict variation in use canhelp us to understand the interrelationships between keyelements of complex mental health care systems, as a first steptowards managing them more effectively.
We have shown that it is possible to design a model of use ofmental health services in small areas that incorporates a numberof assumptions about the complex sets of factors relating toservice use in each area. These assumptions include the idea thatuse in one local area may be associated with rates in other nearbyareas and will be influenced by spatial access to services and theamount of services provided. In the model presented above, acutepsychiatric admissions to general hospital care and levels ofambulatory service use are regarded as jointly dependentvariables to give a better impression of how the ‘matrix of care’varies geographically. The model also represents how differencesin use are associated with population variables. These areprobably associated with complex population characteristicsincluding clinical need for services as well as cultural willingnessto access services and historic usage and referral patterns.
Acknowledgements
The research reported here was supported by the ResearchFoundation for Mental Hygiene, New York State and the Office ofMental Health, New York State. The views expressed here arethose of the authors.
Appendix A. Formal model description
Let activity counts be denoted Yi1 ¼ AMBFi, Yi2 ¼ AMBMi,Yi3 ¼ HOSPFi, Yi4 ¼ HOSPMi following the abbreviations in Fig. 1.Let Eij be expected activity counts and let age standardized referralratios (SRRs) be denoted Sij ¼ Yij/Eij. Because of the aggregatedspatial scale and relatively large death counts involved, the eventtotals are assumed to follow a negative binomial density, namely
pðYijjmij;ajÞ ¼ ½Gðaþ YijÞ=GðaÞGðYij þ 1Þ�
� ½aj=ðaj þ mijÞ�½mij=ðaj þ mijÞ�
where xij ¼ Eijrij represents the regression mean. The negativebinomial is obtained as the marginal density under an over-dispersed Poisson model namely Yij�Po(mij), with means mij
themselves following a gamma distribution, mij�G(aj,aj/xij),whereby E(mij) ¼ xij, Var(mij) ¼ xij
2/a and
VarðYijÞ ¼ E½VarðYijjmijÞ� þ Var½EðYijjmijÞ� ¼ xij þ x2ij=aj.
The relative risks rij of each activity (j ¼ 1 for femaleambulatory,y, j ¼ 4 for male hospitalisation) are modelled as
logri1 ¼ a1 þ b1Fi þ g1 logðAXSSiÞ
logri2 ¼ a2 þ b2Fi þ g2 logðAXSSiÞ
logri3 ¼ a3 þ b3Fi þ g3logðAXSSiÞ þ Z1OWNHOSPi þ d1Si1
logri4 ¼ a4 þ b4Fi þ g4logðAXSSiÞ þ Z2OWNHOSPi þ d2Si2
where Si1 and Si2 are SRRs for female and male ambulatory use.The measurement model equations relating census indicators
Zij to the need factor Fi have the form
Zij ¼ aj þojFi þ uij
where the uij are unstructured normal errors and the F scores areassumed to be spatially correlated according to the spatialconditional autoregressive (or CAR) scheme of Besag et al.(1991). The weighting scheme in the CAR model was basedon adjacency matrix, showing which counties share borders(Pascutto et al., 2000). The variance of the Fi is set to 1, and so allthe o loadings are free parameters (Skrondal and Rabe-Hesketh,2004).
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