WWW-publications from the WHO MONICA Project
October 2004
Adrian G. Barnett1 and Annette J. Dobson1, for the WHO MONICA Project2
1 School of Population Health, University of Queensland, Heston,
QLD 4006, Australia. Phone: +61-7-3365 5559. E-mail: a.barnett@sph.uq.edu.au
2 Annex: Sites and key personnel of the WHO
MONICA Project
Correspondence to Adrian Barnett (a.barnett@sph.uq.edu.au)
This document is the method appendix to the paper titled "Cold periods and coronary events: an analysis of populations worldwide" published in journal in 200? [1].
Standardising the rates of coronary events in each population facilitates comparison between populations and with data from other sources. It also makes the result robust to changes in population demographics. The age- and sex-standardised coronary-event rate is given by
where cht is the total count of coronary events (combining fatal and non-fatal events) for five-year age- and sex-group h, on day t; n is the total number of days; pht is the size of the corresponding age- and sex-population group (collected annually in each population); and {w} = {6, 6, 6, 5, 4, 4} were the weights used to standardise the rates to a common population distribution (using the World Standard Population [2] age-groups: 35-39, 40-44, 45-49, 50-54, 55-59 and 60-64 years).
The data from some weather stations contained small amounts of missing data on daily temperatures or humidities. In Belfast the amount of missing temperature data was 4.9%, in every other population the amount of missing data was less than 0.4 %. To make a complete data set these missing values were imputed using a linear regression with the covariates of the previous day's temperature (or humidity) and the month, as these variables had strong correlations with known values. These regressions had R-squared values that were greater than 90%.
The aim of this analysis was to compare changes in daily temperature with changes in the daily age- and sex-standardised rates of coronary events in each population.
We investigated possible delayed associations between temperature and daily event rates using a distributed lag model [3]. Daily rates per 100,000 of coronary events were assumed to have a Poisson distribution with possible over-dispersion. The delayed effects of temperature and humidity (where available) were modelled using unconstrained (independent) variables. The distributed model can be written as:
where rt is the standardised rate of daily coronary events given in Equation (1); E(rt) = µt and var(rt) = λµt, so that λ is the over-dispersion parameter; L is the maximum delay between exposure and disease onset; α0 is the mean rate of events; the other covariates are discussed below; xt is the temperature on day t; and yt is the humidity on day t. The sum of the lagged effects,
is an unbiased estimate of the overall risk due to temperature [4]. The percent change in events was calculated using,
The other covariates included in model (2) were day of the week and time.
Coronary events in the MONICA populations have been shown to increase on Mondays
[5], and trends in coronary-event rates changed slowly
over time with the magnitude and direction of the trend depending on the
population [6]. Coronary event rates also change
seasonally, and some of this seasonal change is likely due to effects other than
temperature (e.g. changes in diet and activity) [7]. To
account for these sources of variability in the coronary event rates - that were
not due to changes in temperature - we included a categorical explanatory
variable for day of the week, and used a cubic spline with two degrees of
freedom per year to capture both the long-term trend and seasonal changes in
coronary-event rates. To ensure that the seasonal variation had been fully
captured, the time series of residuals
were tested for autocorrelation using the cumulative periodogram test [8].
The parameters λ,
α0,
β and γ from model (2), and the day
of the week effect and cubic spline function were estimated using the methods
described in Hastie and Tibshirani [9]. The
analysis was made using the ‘mgcv’ library in the R statistical package [10].
Model (2) does not include a subscript for population as the model is run
separately in each population.
As humidity was not available in every population we also ran a temperature only version of model (2), in which γ1,...,γL = 0.
The estimated effect of temperature in each population, Equation (3), was
entered into a hierarchical model to explore the population-level effect
modifiers of average temperature and average humidity. This meta-regression
analysis
was calculated using a mixed effects model, with a random intercept for each
population. The regression was weighted using the inverse standard errors of
as the weights. The explanatory variables used were the mean daily temperature
and humidity in each population. The estimated changes in events (C%) and the
meta-regression line were plotted against mean temperature.
The optimal value of L in model (2) was estimated by examining the Akaike Information Criteria for L = 1, . . . , 14. To ensure that the same set of rates (r) were used by each model, we set the first 14 values of r equal to missing. To ensure that every population was included we ran this analysis using the temperature only model.
The optimal estimates (
) from each population were regressed against mean
temperature. The estimate of L used in the hierarchical analysis was the mean
value across populations.
The aim of this analysis was to identify subject-level variables that might be associated with an increased risk in cold periods. Cold periods were defined using the average temperature over the previous 0-3 days.
Confidence intervals (CIs) for the overall percentage of coronary events in the coldest periods were calculated using the normal approximation to the binomial distribution.
A Bayesian hierarchical multiple logistic regression model was used to estimate the effects of the subject-level variables. The outcome variable for the logistic regression was an event during a cold period. The subject-level explanatory variables were: age, sex, fatality of the event (fatal/non-fatal), previous myocardial infarction (yes/no/insufficient data). These variables were chosen because they could plausibly mark biological or behavioural associations for increased risk in cold periods. The final model was selected using a forward stepwise procedure with a significance level of 10%. There was a random intercept for each population, the other covariates were modelled as fixed or random effects depending on the deviance information criteria (DIC - a criterion of the model fit that controls for over-fitting [11]).
Bayesian methods consider the probability of a hypothesis given observed data, whereas standard statistical methods (frequentist) consider the probability of the data given a hypothesis. Results using Bayesian methods are reported with a 95% posterior interval (PI), and results using standard methods are reported with a 95% confidence interval. Both intervals estimate the likely range of the parameter of interest, but the PI has the simpler interpretation that it has a high probability of containing the true parameter value.
The hierarchical analysis was conducted using a generalised linear mixed model in WinBUGS Version 1.2 [12].
This work was funded by the National Health and Medical Research Council of Australia (grant numbers 100954 and 252834).
The MONICA Centres were funded predominantly by regional and national governments, research councils, and research charities. Coordination was the responsibility of the World Health Organization (WHO), assisted by local fund raising for congresses and workshops. WHO also supported the MONICA Data Centre (MDC) in Helsinki. Not covered by this general description is the generous support of the MDC by the National Public Health Institute of Finland, and a contribution to WHO from the National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland, USA for support of the MDC and the Quality Control Centre for Event Registration in Dundee. The completion of the MONICA Project was generously assisted through Concerted Action and Shared Cost Grants from the European Community. Likewise appreciated are grants from ASTRA Hässle AB, Sweden, Hoechst AG, Germany, Hoffmann-La Roche AG, Switzerland, the Institut de Recherches Internationales Servier (IRIS), France, and Merck & Co. Inc., New Jersey, USA, to support data analysis and preparation of publications.