Peter Congdon, Geography, QMUL p.congdon@qmul.ac.uk

1. Spatial structural equation models for representing the impact of area social constructs on psychiatric outcomes Peter Congdon, Geography, QMUL p.congdon@qmul.ac.uk

2. The talk will concern ecological (geographical) variations. Effects of area level constructs on area level health outcomes represent combined impact of population composition & ‘true’ contextual influences (effects of place per se) Caveat: ideal framework is multilevel Ecological (Population Scale) Framework

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

4. Spatial Correlation in Ecological Studies • Statistical techniques taking areas as independent are inappropriate for spatially configured data • If not accounted for, residual spatial correlation can bias regression parameter estimates & cause standard errors to be underestimated,leading to incorrect inferences

5. Define spatial correlation • Various ways to define spatial correlation (distance decay, 1st & 2nd order neighbours) • Popular at moment (esp. in Bayes applications) are conditional autoregressive (CAR) models. Usually correlation simply based on whether areas adjacent or not

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

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

8. Structural (Dependent Variables) Model Component • This takes the form of a regression of area health outcomes (e.g. hospitalisations, mortality) on the needs constructs. Nonlinear effects of need are allowed. • Both census and area health outcomes play a role in defining the needs scores – both types of data used in defining latent constructs.

9. Spatial Extension of Arminger & Muthen, Psychometrika 1998

10. Case Studies • Describe three applications. 1st application considers impact of two latent constructs (deprivation & social fragmentation) on male/female suicide deaths & self harm hospitalizations in 32 London boroughs. • 2nd application considers impact of psychiatric need construct on hospital & ambulatory (community) referrals in 62 counties of New York state. • 3rd application considers impact of fragmentation & deprivation on hospitalisations for serious mental illness in 354 English local authorities 2002-3 to 2004-5

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

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

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

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

15. Scores in Spatial SEM • In spatial SEM deprivation & fragmentation scores determined both by census indicator measurement model and health outcomes model. • Latent constructs summarise population composition indicators (e.g. census indices), but estimation method means scores obtained are also those most relevant for predicting patterns of mortality/health use that are being analyzed

16. Scores in Other Schemes • Construct Scores based on factor analysis or summed Z scores using census or benefit indices only (e.g. Townsend, IMD). Need scores do not then include information on morbidity provided by health “responses” (e.g. mortality, hospital use) • Construct scores based on regression of service use on bundle of census indices (York Psychiatric Need Index, Mental Illness Need Index). Problems with this approach: multicollinearity, unexpected negative signs

17. Spatial SEM for Suicide & DSH in London • Four responses SUICM, SUICF, DSHM, DSHF over 32 London Boroughs (i=1,..,32) Denote outcomes j=1,..,4. Counts Yij of mortality or hospitalisation (rare in relation to population so Poisson). Expected deaths/hospitalisations Eij • Yij ~ Poisson(Eijij) • ij are relative risks of mortality/self harm over areas i and outcomes j

18. Measurement Model • There are P=6 indicators of M=2 latent social area constructs: Fragmentation F1 & Deprivation F2 • Census indicators of social fragmentation are 2001 Census one person hhlds, rate of residential turnover & adults not married. • Indicators of deprivation are 2001 Census low skill workers, renting from social landlords, and % unemployment among economically active.

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

20. Leroux, Lei, Breslow (1999) Fi|F[i]~ N(ai∑j≠iFj,Vi) ai=λ/(1-λ+λ∑j≠icij) Vi=2F/(1-λ+λ∑j≠icij) Reduces to unstructured heterogeneity when =0; CAR when =1. • Under binary adjacency, cij=1 if areas {i,j} adjacent, Mi=# areas next to area i, ai=λ/(1-λ+λMi); Vi=2F/(1-λ+λMi)

21. Structural Model • Relate area relative risks ij for suicide and DSH to M area social constructs Fim • Linear effects bjm of M factors on J health outcomes; also residuals to account for remaining over-dispersion

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

24. FLOW CHART FOR SUICIDE SEM

25. Correlation between deprivation and fragmentation around 0.7, but distinct spatial pattern shows in maps of scores Deprivation has strongest effects on DSH, fragmentation has strongest effects on suicide Female suicide variation more strongly affected by fragmentation than male suicide variation LINEAR EFFECTS OF CONSTRUCTS

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

29. NONLINEAR CONSTRUCT EFFECTS • Structural model allows both linear and nonlinear impacts of constructs on suicide relative risks • Use spline regression to model nonlinear construct effects • Relative risk effects mostly similar to linear model and fit very similar also

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

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

32. Influences on service use other than population morbidity (true need) • Actual service use in different areas reflects interplay between supply/configuration of care & genuine differences in morbidity. Discrepancies between service use & need for care likely: populations in some areas under-served. • Residual factors useful for measuring: aspects of service configuration; local imbalances between need & care; aspects of morbidity that cannot be proxied by observed indicators. • Of course, may also have observed measures of supply

33. Structural Model • So have both indicator based constructs & residual constructs • The structural model relates the referral outcomes to both types of construct in a Poisson regression (and to measurable influences on service use such as geographic access) • For instance, for hospital use in county LOG(RELRISK)=f(Latent Need Construct, Hospital in County, Common Residual Spatial Effect, Common Residual Unstructured Effect)

34. Measurement Model Six observed indicators of need for psychiatric care from 2000 US Census • proportions non white • proportion of over 16s unemployed • households with income < $10,000 as proportion of total hhlds • proportion of occupied housing units moving in precensal year, • proportion of over 15s not married • proportion of population living alone

35. Choice of Indicators for Measurement Model • These indicators are all expected to be positively linked to psychiatric health care need • Some are indicators of social isolation/fragmentation • Some are indicators of material deprivation • Ethnicity also relevant to need – complex issues of psychiatric hospitalisation by ethnicity • Multiple construct model is obvious development

37. Nonlinear effects of need score (spline model)

38. English Local Authorities (N=354) • Impact of deprivation and fragmentation on hospitalisations for schizophrenia & bipolar disorder for 354 English local authorities over 2002-3 to 2004-5. Ages 15-64 (adult population) • Fragmentation Score (F1) based on one person hhlds, private renting, residential turnover, SWD adults • Deprivation (F2) based on unemployment, social housing, low skill • J=2 responses (SMI=schizophrenia & BPD combined) for males (Y1) and females (Y2)

39. Structural Model • Structural model at LA level also includes observed risk factor (% nonwhite) as well as latent constructs • Multi level aspect: beds per head of adult population and mental illness standard prevalence ratio (from 2004-05 QOF) in Strategic HA that LA is located in

41. Risk Gradients over Constructs

42. PATTERN OF SCORES • Correlation between deprivation and fragmentation scores is 0.60. • Deprivation effect stronger for male SMI admissions than female SMI admissions • Spatial pattern for two scores differs

44. Final Remarks • Construct overlaps: interrelated developments in measuring social capital, social cohesion, and social fragmentation • Other latent constructs (e.g. urbanity-rurality) not discussed here but can be important for psychiatric outcomes • Lots of scope for deprivation constructs based on updatable (non-census) indices • Admittedly quite a complicated technology but important to recognize spatial configuration in developing area needs indices/area social constructs