Spatial structural equation Spatial structural equation models for representing the models for representing the

impact of area social constructs impact of area social constructs on psychiatric outcomeson psychiatric outcomesPeter Congdon, Geography, Peter Congdon, Geography,

QMUL p.congdon@qmul.ac.ukQMUL p.congdon@qmul.ac.uk

Ecological (Population Scale) Ecological (Population Scale) FrameworkFramework

The talk will concern ecological The talk will concern ecological (geographical) variations. (geographical) variations.

Effects of area level constructs on area Effects of area level constructs on area level health outcomes represent combined level health outcomes represent combined impact of population composition & ‘true’ impact of population composition & ‘true’ contextual influences (effects of place per contextual influences (effects of place per se)se)

Caveat: ideal framework is multilevelCaveat: ideal framework is multilevel

Benefits of Ecological AnalysisBenefits of Ecological AnalysisVital statistics and hospitalisation data for Vital statistics and hospitalisation data for areas much less affected than surveys by areas much less affected than surveys by issues of nonresponse . Essentially total issues of nonresponse . Essentially total coverage of rare mortality events coverage of rare mortality events Difficulties (for surveys or panel studies) of Difficulties (for surveys or panel studies) of sampling rare populations (e.g. ONSPMS sampling rare populations (e.g. ONSPMS and psychotics)and psychotics)Infeasibility of follow up studies of rare Infeasibility of follow up studies of rare events such as suicideevents such as suicide

Spatial Correlation in Ecological Spatial Correlation in Ecological StudiesStudies

Statistical techniques taking areas as Statistical techniques taking areas as independent are inappropriate for independent are inappropriate for spatially configured dataspatially configured dataIf not accounted for, residual spatial If not accounted for, residual spatial correlation can bias regression correlation can bias regression parameter estimates & cause parameter estimates & cause standard errors to be standard errors to be underestimated,leading to incorrect underestimated,leading to incorrect inferencesinferences

Define spatial correlationDefine spatial correlation

Various ways to define spatial Various ways to define spatial correlation (distance decay, 1correlation (distance decay, 1stst & 2 & 2ndnd order neighbours)order neighbours)

Popular at moment (esp. in Bayes Popular at moment (esp. in Bayes applications) are conditional applications) are conditional autoregressive (CAR) models. autoregressive (CAR) models. Usually correlation simply based on Usually correlation simply based on whether areas adjacent or notwhether areas adjacent or not

Spatial Correlation in Psychiatric Outcomes Spatial Correlation in Psychiatric Outcomes & in Risk Factors& in Risk Factors

Mortality/disease/hospitalisation outcomes Mortality/disease/hospitalisation outcomes in areas that are geographically close in areas that are geographically close typically display spatial dependence. typically display spatial dependence. Geographically defined risk factors (e.g. Geographically defined risk factors (e.g. census indices such as unemployment or census indices such as unemployment or one person households) also spatially one person households) also spatially correlated correlated Such dependence should be acknowledged Such dependence should be acknowledged in developing latent constructs (e.g. in developing latent constructs (e.g. deprivation, fragmentation, mental illness deprivation, fragmentation, mental illness needs) as in other spatial regression needs) as in other spatial regression contextscontexts

Spatial SEMsSpatial SEMsSEM has measurement model (defining SEM has measurement model (defining latent constructs from information latent constructs from information contained in measured indicators), & contained in measured indicators), & structural model using constructs in structural model using constructs in explanatory modelexplanatory modelIn applications here, social indicator In applications here, social indicator measurement model uses area census measurement model uses area census variables as indicators of latent variables as indicators of latent constructs, which are allowed to be constructs, which are allowed to be spatially correlatedspatially correlatedThe structural model relates observed The structural model relates observed area health outcomes to latent constructs. area health outcomes to latent constructs.

Structural (Dependent Variables) Structural (Dependent Variables) Model ComponentModel Component

This takes the form of a regression of area This takes the form of a regression of area health outcomes (e.g. hospitalisations, health outcomes (e.g. hospitalisations, mortality) on the needs constructs. mortality) on the needs constructs. Nonlinear effects of need are allowed.Nonlinear effects of need are allowed.

Both census and area health outcomes Both census and area health outcomes play a role in defining the needs scores – play a role in defining the needs scores – both types of data used in defining latent both types of data used in defining latent constructs.constructs.

Spatial Extension of Arminger & Muthen, Spatial Extension of Arminger & Muthen, Psychometrika 1998Psychometrika 1998

Case StudiesCase Studies

Describe three applications. Describe three applications. 11stst application considers application considers impact of two latent constructs (deprivation & social impact of two latent constructs (deprivation & social fragmentation) on male/female suicide deaths & self fragmentation) on male/female suicide deaths & self harm hospitalizations in 32 London boroughs. harm hospitalizations in 32 London boroughs. 22ndnd application considers impact of psychiatric need application considers impact of psychiatric need construct on hospital & ambulatory (community) construct on hospital & ambulatory (community) referrals in 62 counties of New York state. referrals in 62 counties of New York state. 33rdrd application considers impact of fragmentation & application considers impact of fragmentation & deprivation on hospitalisations for serious mental deprivation on hospitalisations for serious mental illness in 354 English local authorities 2002-3 to illness in 354 English local authorities 2002-3 to 2004-52004-5

Ecological Suicide VariationsEcological Suicide Variations

Work on geographical suicide variations has Work on geographical suicide variations has highlighted impact of factors associated with highlighted impact of factors associated with elevated psychiatric morbidity in general, esp. social elevated psychiatric morbidity in general, esp. social deprivation (Gunnell et al, Br Med J, 1995). deprivation (Gunnell et al, Br Med J, 1995). However, analysis of area suicide data also shows However, analysis of area suicide data also shows excess risk associated with social fragmentation. excess risk associated with social fragmentation. Fragmentation higher in areas characterised by non-Fragmentation higher in areas characterised by non-family households (e.g. one person households), family households (e.g. one person households), high population turnover, extensive private renting in high population turnover, extensive private renting in ‘bedsitters’. ‘bedsitters’.

Social FragmentationSocial Fragmentation

An index summarising such factors is used by An index summarising such factors is used by Whitley et al (Br Med J 1999) and Congdon Whitley et al (Br Med J 1999) and Congdon (Urban Studies, 1996) to analyse suicide (Urban Studies, 1996) to analyse suicide variations. variations. Social fragmentation may occur in affluent areas Social fragmentation may occur in affluent areas (e.g. central London) as well as deprived areas, (e.g. central London) as well as deprived areas, Deprivation & fragmentation not necessarily highly Deprivation & fragmentation not necessarily highly correlated. correlated. Fragmentation scores tend to be high in inner city Fragmentation scores tend to be high in inner city areas; and in coastal resorts with transient areas; and in coastal resorts with transient workforces.workforces.

Influences on Deliberate Self HarmInfluences on Deliberate Self Harm

Analysis of ecological DSH variations Analysis of ecological DSH variations (hospitalisations) shows deprivation to be (hospitalisations) shows deprivation to be important influence. important influence. Gunnell et al (2000, Psychol Med) find Gunnell et al (2000, Psychol Med) find deprivation effects on DSH stronger than deprivation effects on DSH stronger than fragmentation effectsfragmentation effectsThough Hawton et al (Psychol Med. 2001) find Though Hawton et al (Psychol Med. 2001) find associations between DSH rates and social associations between DSH rates and social fragmentation scores were similar to those fragmentation scores were similar to those observed for socio-economic deprivationobserved for socio-economic deprivation

Influences on psychiatric hospitalisationsInfluences on psychiatric hospitalisationsSuch admissions concentrated in psychosis Such admissions concentrated in psychosis diagnoses (schizophrenia, bipolar disorder). diagnoses (schizophrenia, bipolar disorder). Some analyses derive single need index for Some analyses derive single need index for allocating resources (e.g. Mental Illness Need allocating resources (e.g. Mental Illness Need Index; Glover et al, 2004, Soc Psych Psych Epid)Index; Glover et al, 2004, Soc Psych Psych Epid)No account of spatial correlation in deriving such No account of spatial correlation in deriving such indicesindicesSingle need index may conflate multiple distinct Single need index may conflate multiple distinct constructs underlying need for psychiatric care.constructs underlying need for psychiatric care.Fragmentation distinct influence on psychiatric Fragmentation distinct influence on psychiatric hospitalisations (Allardyce/Boydell,Schiz Bull. hospitalisations (Allardyce/Boydell,Schiz Bull. 2006)2006)

Scores in Spatial SEMScores in Spatial SEM

In spatial SEM deprivation & fragmentation In spatial SEM deprivation & fragmentation scores determined both by census indicator scores determined both by census indicator measurement model and health outcomes measurement model and health outcomes model. model.

Latent constructs summarise population Latent constructs summarise population composition indicators (e.g. census indices), but composition indicators (e.g. census indices), but estimation method means scores obtained are estimation method means scores obtained are also those most relevant for predicting patterns also those most relevant for predicting patterns of mortality/health use that are being analyzedof mortality/health use that are being analyzed

Scores in Other SchemesScores in Other Schemes

Construct Scores based on factor analysis or Construct Scores based on factor analysis or summed Z scores using census or benefit indices summed Z scores using census or benefit indices only (e.g. Townsend, IMD). Need scores do not only (e.g. Townsend, IMD). Need scores do not then include information on morbidity provided by then include information on morbidity provided by health “responses” (e.g. mortality, hospital use) health “responses” (e.g. mortality, hospital use)

Construct scores based on regression of service Construct scores based on regression of service use on bundle of census indices (York Psychiatric use on bundle of census indices (York Psychiatric Need Index, Mental Illness Need Index). Need Index, Mental Illness Need Index). Problems with this approach: multicollinearity, Problems with this approach: multicollinearity, unexpected negative signsunexpected negative signs

Spatial SEM for Suicide & DSH in Spatial SEM for Suicide & DSH in LondonLondon

Four responses SUICM, SUICF, DSHM, Four responses SUICM, SUICF, DSHM, DSHF over 32 London Boroughs DSHF over 32 London Boroughs (i=1,..,32) Denote outcomes j=1,..,4. (i=1,..,32) Denote outcomes j=1,..,4. Counts YCounts Yijij of mortality or hospitalisation of mortality or hospitalisation (rare in relation to population so Poisson). (rare in relation to population so Poisson). Expected deaths/hospitalisations EExpected deaths/hospitalisations E ij ij

YYijij ~ Poisson(E ~ Poisson(Eijijijij))

ijij are relative risks of mortality/self harm are relative risks of mortality/self harm over areas i and outcomes jover areas i and outcomes j

Measurement ModelMeasurement Model

There are P=6 indicators of M=2 latent social There are P=6 indicators of M=2 latent social area constructs: Fragmentation Farea constructs: Fragmentation F11 & Deprivation & Deprivation

FF22

Census indicators of social fragmentation are Census indicators of social fragmentation are 2001 Census one person hhlds, rate of 2001 Census one person hhlds, rate of residential turnover & adults not married. residential turnover & adults not married.

Indicators of deprivation are 2001 Census low Indicators of deprivation are 2001 Census low skill workers, renting from social landlords, and skill workers, renting from social landlords, and % unemployment among economically active.% unemployment among economically active.

Features of Social Indicator Features of Social Indicator Measurement ModelMeasurement Model

Allow constructs to be spatially correlated. Allow constructs to be spatially correlated. Also allow for correlation between Also allow for correlation between deprivation & fragmentationdeprivation & fragmentationSo constructs are both correlated across So constructs are both correlated across areas and with each other. Bayes aspects: areas and with each other. Bayes aspects: use bivariate version of CAR prior. use bivariate version of CAR prior. Alternative is to allow data to pick Alternative is to allow data to pick appropriate level of spatial (local) pooling appropriate level of spatial (local) pooling vs. global smoothing vs. global smoothing

Leroux, Lei, BreslowLeroux, Lei, Breslow (1999) (1999)

FFii||F[i] ~ N(a ~ N(aii∑∑j≠ij≠iFFjj,V,Vii))

aaii=λ/(1-λ+λ∑=λ/(1-λ+λ∑j≠ij≠iccijij))

VVii==22FF/(1-λ+λ∑/(1-λ+λ∑j≠ij≠iccijij))

Reduces to unstructured heterogeneityReduces to unstructured heterogeneity

when when =0; CAR when =0; CAR when =1.=1.

o Under binary adjacency, cUnder binary adjacency, cijij=1 if areas {i,j} =1 if areas {i,j}

adjacent, Madjacent, Mii=# areas next to area i, =# areas next to area i,

aaii=λ/(1-λ+λM=λ/(1-λ+λMii); V); Vii==22FF/(1-λ+λM/(1-λ+λMii))

Structural ModelStructural ModelRelate area relative risks Relate area relative risks ijij for suicide and for suicide and

DSH to M area social constructs FDSH to M area social constructs F imim

Linear effects Linear effects jmjm of M factors on J health of M factors on J health

outcomes; also residuals to account for outcomes; also residuals to account for remaining over-dispersionremaining over-dispersion

RESIDUAL EFFECTSRESIDUAL EFFECTSUse unstructured effects to (a) explain residual Use unstructured effects to (a) explain residual variation in outcomes (over-dispersion) (b) variation in outcomes (over-dispersion) (b) represent procedural factors unrelated to represent procedural factors unrelated to population morbidity. population morbidity. Examples: Differences in diagnostic coding or Examples: Differences in diagnostic coding or care patterns between health agencies (e.g. how care patterns between health agencies (e.g. how far DSH treated in community). For completed far DSH treated in community). For completed suicide variations by coroners in applying criteria suicide variations by coroners in applying criteria that death self-inflictedthat death self-inflictedWithout control for process factors impact of Without control for process factors impact of population morbidity constructs may be distorted. population morbidity constructs may be distorted.

FLOW CHART FOR SUICIDE SEMFLOW CHART FOR SUICIDE SEM

FRAG-MENTATION

ONE PERS HH

RESID TURNOVER

SWD ADULTS

DEPRIV-ATION

UNEMP

LOW SKILL

SOCIAL HOUSING

MALE SUIC

FEM SUIC

MALE DSH

FEM DSH

u1

u2

u3

u4

LINEAR EFFECTS OF LINEAR EFFECTS OF CONSTRUCTSCONSTRUCTS

Correlation between deprivation and Correlation between deprivation and fragmentation around 0.7, but distinct fragmentation around 0.7, but distinct spatial pattern shows in maps of scoresspatial pattern shows in maps of scores

Deprivation has strongest effects on Deprivation has strongest effects on DSH, fragmentation has strongest DSH, fragmentation has strongest effects on suicideeffects on suicide

Female suicide variation more strongly Female suicide variation more strongly affected by fragmentation than male affected by fragmentation than male suicide variationsuicide variation

Gradient in Outcomes (Relative Risk) Gradient in Outcomes (Relative Risk) According to Rankings in Construct ScoresAccording to Rankings in Construct Scores

FRAGMENTATIONFRAGMENTATIONRELATIVE RISK (MALE RELATIVE RISK (MALE

SUICIDE)SUICIDE)RELATIVE RISK (FEMALE RELATIVE RISK (FEMALE

SUICIDE)SUICIDE)

MinimumMinimum -0.65-0.65 0.770.77 0.610.61

Lower QuintileLower Quintile -0.35-0.35 0.870.87 0.770.77

Upper QuintileUpper Quintile 0.370.37 1.161.16 1.321.32

MaximumMaximum 0.620.62 1.291.29 1.601.60

DEPRIVATIONDEPRIVATIONRELATIVE RISK (MALE RELATIVE RISK (MALE

DSH)DSH)RELATIVE RISK (FEMALE RELATIVE RISK (FEMALE

DSH)DSH)

MinimumMinimum -0.66-0.66 0.850.85 0.880.88

Lower QuintileLower Quintile -0.35-0.35 0.920.92 0.930.93

Upper QuintileUpper Quintile 0.440.44 1.111.11 1.091.09

MaximumMaximum 0.620.62 1.161.16 1.131.13

NONLINEAR CONSTRUCT NONLINEAR CONSTRUCT EFFECTSEFFECTS

Structural model allows both linear and Structural model allows both linear and nonlinear impacts of constructs on suicide nonlinear impacts of constructs on suicide relative risksrelative risks

Use spline regression to model nonlinear Use spline regression to model nonlinear construct effects construct effects

Relative risk effects mostly similar to linear Relative risk effects mostly similar to linear model and fit very similar alsomodel and fit very similar also

Model 2: Linear Spline Regression with Knots Model 2: Linear Spline Regression with Knots based on Sampled Factor Scores at each MCMC based on Sampled Factor Scores at each MCMC

IterationIteration

New York Study*New York Study*

Need for Psychiatric Care as a Latent Construct Need for Psychiatric Care as a Latent Construct underlying spatial contrasts in four (service use) underlying spatial contrasts in four (service use) outcomes: male and female psychiatric outcomes: male and female psychiatric hospitalizations (PsychHM/PsychHF) & hospitalizations (PsychHM/PsychHF) & male/female ambulatory care referrals male/female ambulatory care referrals (AmbM,AmbF) over 62 New York counties(AmbM,AmbF) over 62 New York countiesSingle latent construct based on 2000 Census Single latent construct based on 2000 Census indices taken to represent underlying population indices taken to represent underlying population morbidity or health needmorbidity or health need**Congdon P, Almog M, Curtis S, Ellerman R (2007) A Spatial Structural Equation Congdon P, Almog M, Curtis S, Ellerman R (2007) A Spatial Structural Equation

Modelling Framework for Health Count Responses. Modelling Framework for Health Count Responses. Statistics in MedicineStatistics in Medicine

Influences on service use other than Influences on service use other than population morbidity (true need)population morbidity (true need)

Actual service use in different areas reflects interplay Actual service use in different areas reflects interplay between supply/configuration of care & genuine between supply/configuration of care & genuine differences in morbidity. Discrepancies between differences in morbidity. Discrepancies between service use & need for care likely: populations in service use & need for care likely: populations in some areas under-served. some areas under-served.

Residual factors useful for measuring: aspects of Residual factors useful for measuring: aspects of service configuration; local imbalances between service configuration; local imbalances between need & care; aspects of morbidity that cannot be need & care; aspects of morbidity that cannot be proxied by observed indicatorsproxied by observed indicators. . Of course, may also have observed measures of Of course, may also have observed measures of supplysupply

Structural ModelStructural Model

So have both indicator based constructs & So have both indicator based constructs & residual constructsresidual constructs

The structural model relates the referral The structural model relates the referral outcomes to both types of construct in a Poisson outcomes to both types of construct in a Poisson regression (and to measurable influences on regression (and to measurable influences on service use such as geographic access)service use such as geographic access)

For instance, for hospital use in county For instance, for hospital use in county LOG(RELRISK)=f(Latent Need Construct, LOG(RELRISK)=f(Latent Need Construct, Hospital in County, Common Residual Spatial Hospital in County, Common Residual Spatial Effect, Common Residual Unstructured Effect)Effect, Common Residual Unstructured Effect)

Measurement ModelMeasurement Model

Six observed indicators of need for psychiatric Six observed indicators of need for psychiatric care from 2000 US Census care from 2000 US Census

(1)(1) proportions non white proportions non white (2)(2) proportion of over 16s unemployed proportion of over 16s unemployed (3)(3) households with income < $10,000 as households with income < $10,000 as

proportion of total hhlds proportion of total hhlds (4)(4) proportion of occupied housing units moving in proportion of occupied housing units moving in

precensal year, precensal year, (5)(5) proportion of over 15s not marriedproportion of over 15s not married(6)(6) proportion of population living aloneproportion of population living alone

Choice of Indicators for Choice of Indicators for Measurement ModelMeasurement Model

These indicators are all expected to be positively These indicators are all expected to be positively linked to psychiatric health care needlinked to psychiatric health care need

Some are indicators of social Some are indicators of social isolation/fragmentationisolation/fragmentation

Some are indicators of material deprivationSome are indicators of material deprivation

Ethnicity also relevant to need – complex issues Ethnicity also relevant to need – complex issues of psychiatric hospitalisation by ethnicityof psychiatric hospitalisation by ethnicity

Multiple construct model is obvious developmentMultiple construct model is obvious development

Nonlinear Nonlinear effects of effects of need need score score (spline (spline model)model)

Relative Hospitalisation Risk & Needs Score (Males)

0.6

1.1

1.6

2.1

-0.5 0.0 0.5 1.0

Need Score

Mal

e H

osp

ital

sati

on

s (R

R)

Relative Hospitalisation Risk & Needs Score (Females)

0.6

0.8

1.0

1.2

1.4

1.6

1.8

-0.5 0.0 0.5 1.0

Need Score

Fem

ale

ho

spit

alis

atio

ns

(RR

)

English Local Authorities (N=354)English Local Authorities (N=354)

Impact of deprivation and fragmentation on Impact of deprivation and fragmentation on hospitalisations for schizophrenia & bipolar hospitalisations for schizophrenia & bipolar disorder for 354 English local authorities over disorder for 354 English local authorities over 2002-3 to 2004-5. Ages 15-64 (adult population)2002-3 to 2004-5. Ages 15-64 (adult population)Fragmentation Score (FFragmentation Score (F11) based on one person ) based on one person hhlds, private renting, residential turnover, SWD hhlds, private renting, residential turnover, SWD adultsadultsDeprivation (FDeprivation (F22) based on unemployment, social ) based on unemployment, social housing, low skillhousing, low skillJ=2 responses (SMI=schizophrenia & BPD J=2 responses (SMI=schizophrenia & BPD combined) for males (Y1) and females (Y2)combined) for males (Y1) and females (Y2)

Structural ModelStructural Model

Structural model at LA level also includes Structural model at LA level also includes observed risk factor (% nonwhite) as well observed risk factor (% nonwhite) as well as latent constructsas latent constructs

Multi level aspect: beds per head of adult Multi level aspect: beds per head of adult population and mental illness standard population and mental illness standard prevalence ratio (from 2004-05 QOF) in prevalence ratio (from 2004-05 QOF) in Strategic HA that LA is located inStrategic HA that LA is located in

Risk Gradients over ConstructsRisk Gradients over ConstructsMale Hospitalisation Male Hospitalisation

RiskRiskFemale Hospitalisation Female Hospitalisation

RiskRisk

DeprivationDeprivation

MinimumMinimum 0.720.72 0.800.80

1st quartile1st quartile 0.890.89 0.920.92

3rd quartile3rd quartile 1.101.10 1.061.06

MaximumMaximum 1.621.62 1.391.39

FragmentationFragmentation

MinimumMinimum 0.850.85 0.860.86

1st quartile1st quartile 0.940.94 0.940.94

3rd quartile3rd quartile 1.031.03 1.031.03

MaximumMaximum 1.541.54 1.491.49

PATTERN OF SCORESPATTERN OF SCORES

Correlation between deprivation and Correlation between deprivation and fragmentation scores is 0.60.fragmentation scores is 0.60.

Deprivation effect stronger for male SMI Deprivation effect stronger for male SMI admissions than female SMI admissionsadmissions than female SMI admissions

Spatial pattern for two scores differsSpatial pattern for two scores differs

Final RemarksFinal Remarks Construct overlaps: interrelated developments Construct overlaps: interrelated developments

in measuring social capital, social cohesion, and in measuring social capital, social cohesion, and social fragmentationsocial fragmentation

Other latent constructs (e.g. urbanity-rurality) Other latent constructs (e.g. urbanity-rurality) not discussed here but can be important for not discussed here but can be important for psychiatric outcomespsychiatric outcomes

Lots of scope for deprivation constructs based Lots of scope for deprivation constructs based on updatable (non-census) indiceson updatable (non-census) indices

Admittedly quite a complicated technology but Admittedly quite a complicated technology but important to recognize spatial configuration in important to recognize spatial configuration in developing area needs indices/area social developing area needs indices/area social constructsconstructs