Transcript Talk - Personal Webspace for QMUL

Spatial structural equation
models for representing the
impact of area social constructs
on psychiatric outcomes
Peter Congdon, Geography,
QMUL [email protected]
Ecological (Population Scale)
Framework
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
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
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
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
Spatial Correlation in Psychiatric Outcomes
& in Risk Factors
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 SEMs
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.
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.
Spatial Extension of Arminger & Muthen,
Psychometrika 1998
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
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 nonfamily households (e.g. one person households),
high population turnover, extensive private renting in
‘bedsitters’.
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.
Influences on Deliberate Self Harm
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 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)
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
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
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
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.
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
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.
o 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)
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
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.
FLOW CHART FOR SUICIDE SEM
ONE PERS HH
MALE
SUIC
u1
SWD ADULTS
FEM
SUIC
u2
UNEMP
MALE
DSH
u3
FEM
DSH
u4
RESID TURNOVER
LOW SKILL
SOCIAL
HOUSING
FRAGMENTAT
ION
DEPRIVATION
LINEAR EFFECTS OF
CONSTRUCTS
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
Gradient in Outcomes (Relative Risk)
According to Rankings in Construct Scores
FRAGMENTATION
RELATIVE RISK (MALE
SUICIDE)
RELATIVE RISK (FEMALE
SUICIDE)
Minimum
-0.65
0.77
0.61
Lower Quintile
-0.35
0.87
0.77
Upper Quintile
0.37
1.16
1.32
Maximum
0.62
1.29
1.60
DEPRIVATION
RELATIVE RISK (MALE
DSH)
RELATIVE RISK (FEMALE
DSH)
Minimum
-0.66
0.85
0.88
Lower Quintile
-0.35
0.92
0.93
Upper Quintile
0.44
1.11
1.09
Maximum
0.62
1.16
1.13
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
Model 2: Linear Spline Regression with Knots
based on Sampled Factor Scores at each MCMC
Iteration
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
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
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)
Measurement Model
Six observed indicators of need for psychiatric
care from 2000 US Census
(1) proportions non white
(2) proportion of over 16s unemployed
(3) households with income < $10,000 as
proportion of total hhlds
(4) proportion of occupied housing units moving in
precensal year,
(5) proportion of over 15s not married
(6) proportion of population living alone
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
1.8
1.6
1.4
1.2
1.0
0.8
0.6
-0.5
0.0
0.5
1.0
Need Score
Relative Hospitalisation Risk & Needs
Score (Males)
Male Hospitalsations
(RR)
Nonlinear
effects of
need
score
(spline
model)
Female hospitalisations
(RR)
Relative Hospitalisation Risk & Needs
Score (Fem ales)
2.1
1.6
1.1
0.6
-0.5
0.0
0.5
Need Score
1.0
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)
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
Risk Gradients over Constructs
Male Hospitalisation
Risk
Female Hospitalisation
Risk
Minimum
0.72
0.80
1st quartile
0.89
0.92
3rd quartile
1.10
1.06
Maximum
1.62
1.39
Minimum
0.85
0.86
1st quartile
0.94
0.94
3rd quartile
1.03
1.03
Maximum
1.54
1.49
Deprivation
Fragmentation
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
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