Bayesian Metaanalysis and Health Impact Evaluation in the Study of Heat Effect on Mortality

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Bayesian Meta-analysis andHealth Impact
Evaluation in the Study of Heat Effect on
Mortality
Mini-symposium Environmental Epidemiology
Thursday 2 August 2007

• Annibale Biggeri, Michela Baccini
• Department of Statistics, University of Florence,
  
• Biostatistics Unit, CSPO, Florence, Italy

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motivating example the PHEWE study
Epidemiological daily time series
Poisson regression

• PHEWE study (Assessment and Prevention of acute
  Health Effects of Weather conditions in Europe)
  enrolled 15 cities, about 30 million people on
  calendar years 1990-2001.
• Generalized estimating equation approach was used
  in season-specific analysis, with AR-1 error
  structure and parametric spline or segmented
  regression to model apparent temperature effects.
  
• Distributed lag and time-varying coefficient
  models were fitted.
• Effect Heterogeneity was expected, a priori two
  regions were considered (Mediterrean vs Others).

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PHEWE study 1990-2001City-specific curves (GEE
natural cubic spline)Maximum Apparent
Temperature lag03 - All natural deaths - Summer

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PHEWE 1990-2001 threshold-slope model
in red Mediterranean cities
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comments

• A pattern was evident, but with large variability
  among cities
• (we do not discuss here city-specific modelling
  issues
• restricting the analysis by season and using
  Generalized Estimating Equation approach with
  AR(k) working correlation lead to
• assure appropriate error structure for
  consistency of GEE estimates in case of few long
  time series (Xie and Yang, 2003) on the basis of
  a formalized exploratory analysis (dynamic
  regression models Pankratz, 1991 Chiogna and
  Gaetan, 2005)
• avoid use of sandwich estimator of standard
  errors (Guo et al. 2005)
• exposure effects modelling by Cubic regression
  spline with 1 knot every 8 C and straight line
  above a city-specific threshold)

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outline

• The PHEWE study documented
• heterogenous effect of heat on
• mortality across Europe
• Hierarchical Bayesian approach is used
• to estimate random-effects meta-analytic
  summaries
• to perform Multivariate random effect
  meta-analysis and
• to obtain shrunk estimates of city-specific
  parameters
• Montecarlo approach is used in Impact assessment
• sampling from city-specific posterior
  distributions and
• modelling climate change effects via
  probabilistic distributions

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Statistical modelling - 1

• In PHEWE, with exception of the description of
  the exposure-response function (where we used a
  fixed-effect approach), the city-specific results
  were combined using
• Hierarchical Bayesian random-effects
  meta-analysis.
• Separated meta-analyses performed for two a
  priori defined geographical regions
• Mediterranean cities
• Athens, Barcelona, Ljubljana, Milan, Rome, Turin,
  Valencia.
• North-Continental cities
• Budapest, Dublin, Helsinki, London, Paris, Praha,
  Stockholm,
• Zurich.

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Hierarchical Bayesian random-effects meta-analysis

• First level for each cities (c1,,C) we have a
  vector of coefficients Y and
• the associated
  variance-covariance matrix V (known)
  
• Second level the vector of true coefficients
  follows a multivariate Gaussian
• distribution with vector
  of means ß and var-cov matrix A
  
• 
  

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• Inference is based on full posterior
  distributions
• we use
• in the multivariate case direct sampling from
  the marginal posterior distribution of ß (Everson
  and Morris, 2000 TLNise library of R)
• In the univariate case MCMC methods, using
  WinBugs 1.4

marginal posterior global effect
marginal posterior het variance
marginal posterior city-specific effect
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rationale

• Hierarchical Bayesian meta-analysis was adopted
  here because
• Heterogeneity was a study objective (ML
  underestimates it)
• Multivariate effects are easy to model
• City-specific posteriors or shrinkage
  distributions which updated first stage estimates
  can be obtained
• Uncertainty can be incorporated in Impact
  evaluation phase

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PHEWE study 1990-2001Meta-analytic curves
Maximum Apparent Temperature lag 03 - All
natural deaths - Summer

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ER percent variation in mortality for 1C
increase in apparent temperature.
threshold
slope

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• Random effect meta-analysis is difficult to
  interpret because
• it assumes that the effect is not unique but
  varies among study
• the overall effect is a weighted average of
  study-specific effects, the weights include
  heterogeneity among studies
• a paradox arises because the greater the
  heterogeneity the more uniform the weights
• The purpose of a meta-analysis changes in
  presence of heterogeneity
• the interest lies in explaining it
• Ecological bias is an issue
• the meta-analysis becomes an observational study
• (the value of proof is weakened)

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effects
PHEWE 1990-2001 posteriors threshold-slope
heterogeneity among cities
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• Large heterogeneity for threshold among
  Mediterranean cities was a major result (see
  posterior for het-variance)
• (varying acclimatization ?
• east-west gradient ?)

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Multivariate meta-analysis Time-varying
coefficients model

• The temperature effect is allowed to vary
  smoothly over time within year (Peng et al., 2004)

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sensitivity of the slope to season
definitionmeta-analytic curves (time-varying
coefficient models)

some evidence of greater effect in early summer
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Multivariate meta-analysis Distributed lag models

• Where the coefficients are constrained by a
  polynomial function of grade 5, with lags
  spanning 0,40 (Almon, 1965).

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lagged effect / harvesting meta-analytic curves

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Statistical modelling 2Impact estimates
Attributable Deaths - YoLL

• To assess the impact of high summer temperatures
  on the health of European urban populations we
  estimate Attributable Deaths and Years of Life
  Lost associated with high summer temperatures,
  through secondary analysis of mortality versus
  apparent temperature functions derived as part of
  the PHEWE study.
• For each city we used a probabilistic MonteCarlo
  approach
• observed temperature by day distributions
• risk distributions (posteriors)

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model specifications and assumptions heat
attributable deaths

• Let us restrict now the attention to attributable
  number of deaths (AD).
• We assumed that all population was exposed to the
  same daily maximum apparent temperature.
• We assumed that variations in maximum apparent
  temperature under the threshold do not affect
  mortality and that the effect is linear above the
  threshold.
• The same temperature threshold by city (t0c) is
  used for all age classes. Thresholds are based on
  posterior city-specific estimates.
• Above-threshold slopes (bc) are obtained from
  age-class specific meta-analytic posterior
  distributions.
• y is the death counts

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observed temperature by day distributions PHEWE
1990-2001
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Posterior distributions of city-specific
thresholdsMaximum Apparent Temperature lag03
SummerPHEWE study 1990-2001
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Posterior distributions of city-specific slopes
by age groupsMaximum Apparent Temperature lag03
SummerPHEWE study 1990-2001
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computing heat attributable deaths

• We use a Monte Carlo approach for each city, we
  sampled values from the city-specific posterior
  distributions of the slope and from the
  city-specific posterior distributions of the
  threshold obtained from the Bayesian
  meta-analysis.
• Then, for each sample, we calculated a time
  series of daily number of attributable deaths
  from the observed time series of daily maximum
  apparent temperature at lag 0-3 and daily number
  of deaths, according to the following formula
• zero otherwise

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• Independence between threshold and slope was
  checked by sensitivity analysis.
• We obtained 10000 samples of AD time series by MC
  simulation.
• Separated AD evaluations were produced by city
  and age group (15-64, 65-74, 75) and scenarios
  (a total of 100001536).
• For each city, total number of AD was produced by
  summing AD over the three age classes.

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Heat alternative scenarios

• Temperature
• pseudo-series for
• Hottest year
• Coolest year
• Second-to-coolest
• Second-to-hottest
• Average increase
• in Temperature 1C

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details on building scenarios

• We defined scenarios selecting
• the summer with the highest mean level of
  apparent temperature.
• the summer with the lowest mean level of apparent
  temperature.
• the second to hottest day
• the second to coldest day
• for example, for the third scenario we
  considered the hypothetical summer constituted by
  the second to hottest 1st April, the second to
  hottest 2nd April.the second to hottest 30th
  Sept.
• Exposure scenarios were also defined adding to
  each observed daily apparent temperature a random
  term from a Normal distribution

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PHEWE study 1990-2001 Mean number of observed
attributable deaths by calendar day, by city.
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PHEWE study 1990-2001Heat attributable deaths /
year, people 75yrs oldobserved temperature
distribution
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PHEWE study 1990-2001Heat attributable deaths
low - high temperature scenarios
80 Credibility bands
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PHEWE study Attributable deaths observed
apparent temperature 1990-2001 versus predicted
series by 1C mean increase scenario






AD attributable deaths AveT average
temperature d days above threshold
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summary

• The PHEWE study documented
• heterogenous effect of heat on
• mortality across Europe
• Hierarchical Bayesian approach is used
• to estimate random-effects meta-analytic
  summaries
• to perform multivariate random effect
  meta-analysis and
• to obtain shrunk estimates of city-specific
  parameters
• Montecarlo approach is used in Impact assessment
• sampling from city-specific posterior
  distributions and
• modelling climate change effects via
  probabilistic distributions

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acknowledgments

• The PHEWE study group (EU DGR V Framework)
• Michelozzi, Kirchmayer, Katsouyanni, Biggeri et
  al. Assessment and prevention of acute health
  effects of weather conditions in Europe, the
  PHEWE project background, objectives, design.
• Environmental Health, 2007 6,12
• Baccini, Biggeri, Accetta, Katsouyanni et al.
  Effects of Apparent Temperature on Summer
  Mortality in 15 European Cities Results of the
  PHEWE Project. (submitted)
• Baccini, Kosatsky, Biggeri. Estimating deaths
  attributable to summer heat through climate and
  response scenarios anchored on an 11-year, 15
  European city, temperature/mortality function
  (unpublished manuscript)