Registered mortality data from 2006 to 2010 were procured from the Ministry of Health and Medical Education (MOH&ME). The data on the population at risk were extracted from the Statistical Centre of Iran (SCI); these data were only available from the national censuses of 2006 and 2011, so the population at risk data for the range of 2007 to 2010 was linearly estimated.
In order to avoid any misleading results and to be able to properly compare the mortality ratios, we adjusted the effect of age. Thus, using the direct method of standardization (
19), SMRs were calculated. For this standardization, Tehran’s population was used as the standard population.
Iran’s Ministry of Interior Affairs has divided the thirty-one provinces into five regions (
20). Regions three and four contain 12 provinces which are geographically located in the west (including Kordestan, Zanjan, Guilan, Ardabil, East Azarbaijan, West Azarbaijan, Kermanshah, Hamadan, Markazi, Lorestan, Ilam, and Khuzestan provinces) and region five (including Sistan and Baluchestan, Kerman, Yazd, South Khorasan, Khorasan-e-Razavi, and North Khorasan provinces) is geographically classified into the east. These divisions are shown in
Figure 1.
The eastern and western provinces’ divisions
In order to smooth the SMRs (relative risk), we utilized the Besag-York-Mollie (BYM) model (
21). In order to explore the spatio-temporal linear trend, we used Bayesian spatio-temporal model as suggested by Bernardinelli et al. (
22), shown in the following equations:
The number of mortality cases in each province yik was assumed to follow a Poisson distribution. In the model α is used to quantify the average mortality rate in all areas; eik is the number of expected mortalities for each area, which acts as an offset; ui is the spatially structured component for counting neighborhood structure by using conditional auto regressive (CAR) modeling; and vi is the unstructured component modeled. The every year mortality risk is multiplied by exp (β), so parameter β is an indicator of the global time effects and δi indicates the trend differences in each province. For all of the parameters in these models, suitable prior distributions were considered as follows: ui ~ N(0,τu), vi ~ N(0,τv) , δi ~ N(0,~τδ) and non-informative distribution N(0,1e-5) for β .We considered gamma distributions (0.5,0.0005) for all precision parameters.
The BYM model is similar to Bayesian spatio-temporal model, but it doesn’t have the β and δ
i parameters. An exposition of methodological details of the BYM model and Bayesian spatio-temporal model is presented in Lawson et al. (
23) and Blangiardo and Cameletti (
24).
We implemented the models using OpenBUGS version 3.2.3, a standard public domain package for Bayesian inference, using Markov Chain Monte Carlo (MCMC) methods (
25). ArcGIS version 9.2 (
26) was used for mapping the cases in the studied regions. Convergence for the chain was checked through graphing their traces, densities and auto-correlations. The first 1000 samples were omitted as a burn-in and the chain was run for 10000 iterations.