Analysis of space time patterns of disease risk

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SAHSU
20 Years 1987 - 2007
Analysis of space time patterns of disease risk
Sylvia Richardson Centre for Biostatistics with
Lea Fortunato, Juanjo Abellan Linda Beale, Sam
Lefevre and Nicky Best
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Outline

• Context
• Space time models for disease risk
• Use of space time models to investigate the
  stability of patterns of disease
• Illustration on the analysis of congenital
  malformations
• Illustration on the analysis of bladder cancer in
  Utah
• Discussion

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Benefits of Space Time Analysis for chronic
diseases

• Study the persistence of patterns over time
• Interpreted as associated with stable risk
  factors, environmental effects, distribution of
  health care access
• Highlight unusual patterns in time profiles via
  the inclusion of space-time interaction terms
• Time localised excesses linked to e.g. emerging
  environmental hazards with short latency
• Variability in recording practices
• Increased epidemiological interpretability
• Potential tool for surveillance

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Case study Congenital anomalies in England

• All cases of congenital anomalies (non
  chromosomal) recorded in England for the period
  1983 1998
• Data from national post-coded registers (Office
  for National Statistics)
• Annual post-coded data on total number of live
  births, still births and terminations
• 136,000 congenital anomalies ? 84.5 per 105
  birth-years
• Congenital anomalies are sparse
• ? Grid of 970 grid squares with variable size,
  to equalize the number of birth and expected
  cases per square
• Variations could be linked to socio-economic or
  environmental risk factors or heterogeneity in
  recording practises
• ? Interest in characterising space time patterns

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Map of grid squares used in the
Congenital Anomalies study
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Expected number of congenital anomalies per year
in each square (per quintiles)
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Case study Bladder cancer
Collaboration with Sam Lefevre, Utah department
of Health

• Bladder cancer incidence in Utah (US), 1973-2004
• Spatial resolution census tracts (496)
• Between 0 and 11 new cases per year with mean
  around 0.4
• Time periods 1973-76, 1977-80,, 2001-04
• Expected counts based on sex-age incidence rates
  for the region and the total period 1973-2004

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Case study Bladder cancer
Population density in each census tract (Census
2000)
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Outline

• Context
• Space time models for disease risk
• Use of space time models to investigate the
  stability of patterns of disease
• Illustration on the analysis of congenital
  malformations
• Illustration on the analysis of bladder cancer in
  Utah
• Discussion

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Space time models in epidemiology

• Space time extensions of Bayesian hierarchical
  models for disease mapping have been considered
  by a number of authors, with models differing in
  their treatment of space time interactions
• e.g. Knorr-Held and Besag (1998), Waller et al
  (1997), Bernardinelli et al (1995), Knorr-Held
  (2000), Richardson, Abellan and Best (2006),
  Abellan, Richardson and Best (2007).

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Schematic representation
Noisy data in each area
Noise model Poisson/Binomial
Latent structure Space Time Interactions
Log scale
joint Bayesian estimation
Inference
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Notations

• Yit Observed of cases for area i, i 1,, N
  period t, t1, , T.
• nit number of person at risk in area i, period
  t
• probability of disease in area i, period t

First level binomial likelihood
Often a Poisson approximation is used
Eit expected of cases, area i, period t
relative risk, area i, period t
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Second level modelling of the structure of the
latent (random) effects or

• Prior structure for the random effects
• encodes prior epidemiological knowledge
• need to borrow strength to effect smoothing
• has to be adapted to the analysiss aim

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Prior structure for the random effects

• Overall spatial pattern account for local
  dependence due to geographical continuity of
  populations and risk factors
• use spatial autoregressive model commonly
  employed for disease mapping
• Overall time trends time dependence might be
  expected, e.g.for long latency chronic diseases
  use time structured autoregressive model
• Space time interactions capture the non
  predictable part from simple space time model
• what model to use ?

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New model for the interaction terms

• Investigating stability of patterns Aim is to
• -- Highlight true departures from the
  overall predictable space time model
• the variance of nit has to be allowed to be large
• -- Shrink idiosynchratic (non interpretable)
  interactions small variance for most nit
• ? Mixture model to characterise stable and
  unstable risk patterns over time

Component 1 small variance t12
Component 2 allows large variance t22
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Outline

• Context
• Space time models for disease risk
• Use of space time models to investigate the
  stability of patterns of disease
• Illustration on the analysis of congenital
  malformations
• Illustration on the analysis of bladder cancer in
  Utah
• Discussion

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Analysis strategy for investigating stability of
patterns

• Estimate a model
• space time interactions (mixture)
• Use the posterior probabilities of allocation pit
  into component 2 to classify areas as unstable
• Rule area i is unstable if at least for one t,
  pit is large, i.e. pit gt pcut (threshold
  probability). Other rules possible
• For stable areas, investigate spatial patterns,
  e.g. by using the rule Prob(exp(?i ) gt1) gt 0.8.
• Investigate the time profile pattern of
  unstable areas

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Statistical issues were investigated by
simulations

• If we over-fit, (i.e. estimate a space-time model
  with interactions when the patterns are stable)
• Do we loose power to detect pure spatial
  patterns with respect to a pure spatial model ?
  NO
• Is the mixture model identifiable ? YES
• What is the performance of the classification
  rules ?
• GOOD (depends on the size of interactions and
  proportion of unstable areas)
• Can we tease out any structured patterns in the
  interactions? YES

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Results for the 2 data sets

• Map of the global spatial pattern
• Time trend
• Classification of areas
• Time profiles for unstable areas

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Congenital anomalies England, 83-98
Spatial main effect 970 grid squares Post
median of exp(?i)
Evidence of spatial heterogeneity with higher
risk in the North, NW and NE and in the Greater
London area Deprivation and maternal age are
strong determinants of congenital malformations
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Congenital anomalies England, 83-98
Time main effect exp(?t)
The downward shift picked up between pre 1990 and
post 1990 is due to the minor
anomalies exclusion policy that was implemented
in 1990 and after.
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Mixture estimation

• Using a cut off
• pcut 0.5, 125 areas (13) are classified as
  unstable

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Risk time profiles for the areas classified as
unstable

• We performed hierarchical
• clustering on the 125 areas
• Four subgroups exhibit
• smooth-like trends
• interaction terms used to
• adjust to general time trend
• One small subgroup has a
• high peak in 97
• ? warrants investigation

thanks to Mireille Toledano
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Bladder cancer, Utah, 1973-2004

• Spatial main effect (496 Census Tracts)
• Posterior median of exp(?i) spatial RR

Evidence of heterogeneity with higher risks in
central area around Salt Lake City
96 CT with Prob(exp(?i) gt 1) gt0.8
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Bladder cancer, Utah, 1973-2004

• Time main effects
• Posterior median of exp(?t) Temporal RR

Slow decrease followed by steeper increase from
97 onwards
73-76 77-80 81-84 85-88 89-92 93-96 97-00
01-04
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Bladder cancer, Utah, 1973-2004
Mixture estimation for space time interactions
Posterior distribution of pit

• Posterior distribution of ?1 and ?2

• Cut off pcut 0.6,
• 13 census tracts (3) are
• classified as unstable

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Bladder cancer, Utah, 1973-2004

• Census tracts classified as unstable using
• the rule pit gt0.6

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Bladder cancer, Utah, 1973-2004

• Space-time interactions for the 13 areas
  classified as unstable

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Bladder cancer, Utah, 1973-2004
exp(?it) overall RR for 96 Census Tracts with
elevated risks, including 3 (in blue) that are
classified as unstable
TRI sites which submitted a report for at least
10 years
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Woods Cross area Cluster of oil refineries in
this area.
Hill Air Force Base
Magna and West Valley City Disadvantaged
population, much higher smoking rates, highly
industrialized and associated with Kennecott
Copper Mine
University of Utah Young mobile population from
outside Utah (less likely to live the healthy
Mormon lifestyle, than down town Salt Lake City)
Kennecott Smelter Includes number of transfer
sites between final smelter and mine, and large
waste water lagoon
Provo and Brigham Young University. Young mobile
LDS population (take the healthy Mormon
lifestyle to the extreme)
Kennecott Copper Mine
Industrialization around the Interstate (I15)
corridor.
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Discussion

• Bayesian space time analyses allow a richer
  interpretation of patterns than purely spatial
  ones
• Models become more complex, with more choice of
  prior structure in particular, the prior
  structure for the space time interactions
• Need to relate prior structure to the different
  aims of the analyses, the time scale and the
  hypotheses on the health phenomenon under
  investigation
• To gain epidemiologic interpretability, the
  stability repeatability over time of spatial
  patterns found by a pure spatial analysis should
  be investigated
• More work on how to explore further the patterns
  showed by the space-time interactions

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References

• L. Bernardinelli, D. Clayton, C. Pascutto, C.
  Montomoli, M. Ghislandi, and M. Songini.
  Bayesian. Analysis of space-time variation in
  disease risk. Statistics in Medicine,
  1424332443, 1995.
• L. A. Waller, B. P. Carlin, H. Xia, and A. M.
  Gelfand. Hierarchical spatio-temporal mapping of
  disease rates. Journal of the American
  Statistical Association, 92607617, 1997.
• L. Knorr-Held and J. Besag. Modelling risk from a
  disease in time and space. Statistics in
  Medicine, 1720452060, 1998.
• L. Knorr-Held. Bayesian modelling of inseparable
  space-time variation in disease risk. Statistics
  in Medicine, 1925552567, 2000.
• S. Richardson, A. Thomson, N Best and P Elliott.
  Interpreting posterior relative risk estimates in
  disease-mapping studies. EHP, 112, 1016-25, 2004.
• S. Richardson, J. J. Abellan, and N. Best.
  Bayesian spatio-temporal analysis of joint
  patterns of male and female lung cancer risks in
  Yorkshire (UK). Statistical Methods in Medical
  Research, 15 385-407, 2006.
• J. J. Abellan, S. Richardson, and N. Best. Use of
  space-time models to investigate the stability of
  patterns of disease. (2007). Under revision for
  EHP
• L. Fortunato, J.J. Abellan, L. Beale, S Lefevre,
  S Richardson. Bayesian spatio-temporal analysis
  of bladder cancer incidence in Utah (1973-2004).
  In preparation