Appendix 4: Statistical Notes for Sections 1.1, 1.2, and 1.3
1.1: Intrauterine Growth Retardation (IUGR)
In 1998 de Onis and collaborators made the first attempt to quantify the magnitude and describe the geographical distribution of IUGR in developing countries at the global level.1 They estimated the incidence of infants born at term (≥ 37 weeks of gestation) with low birthweight (LBW), referred to as IUGR-LBW, using a linear regression equation proposed by Villar et al.2
Incidence of IUGR-LBW = -3.2452 + 0.8528 total rate of LBW
This equation was derived from 60 populations of developing countries where gestational ages and birth-weights were recorded and has an r of 0.96. The IUGR-LBW predictive equation was validated against observed values in 17 selected data sets not included in the development of the model. The equation underestimates the incidence of IUGR-LBW by a mean difference of -1.46% (95% confidence intervals of this mean difference: -2.51% to -0.40%).
The overall rate of LBW in developing countries was obtained from an updated version (September 1996) of the WHO Database on Low Birthweight.3 These estimates were based on studies identified in the database as nationally representative and carried out between 1985 and 1995. Thirty-eight per cent of the selected data points were derived from monitoring systems, 17% from registration data, 13% from the Western Pacific region data bank, 10% from UNICEF field offices’ estimates, 9% from hospital data, 4% from government reports, 3% from community-based studies, and 6% of unknown source. Data were available for 106 out of 146 developing countries.
For the Fourth Report the WHO Database on Low Birthweight was reviewed in January 1999 to assess the possible effects of new data having been added to the database since the de Onis review. Also, changes in the WHO estimates of LBW prevalence for 1979 to 1990 as set out in WHO (1992)3 were examined. Both reviews indicated that LBW estimates published by de Onis et al. in 1998 are still applicable for producing estimates for the year 2000. The analysis presented in this Fourth Report does not include any country data points in addition to those included by de Onis et al.
1.2 and 1.3: Stunting and Underweight
Multilevel modelling refers to a generalization of regression that uses multiple levels as sources of variability in the prevalence of stunting or underweight.4 These levels are between regions, between countries within regions, and between surveys over time within countries. Countries that had only one survey did not contribute to the estimate of a trend but only to the mean prevalence. Mean prevalence was estimated for each country, while averages were used to estimate trends in prevalence over time across all countries. A simplified version of a random coefficient model with only random intercepts was used.5 Each region and sub-region was analyzed separately. It was assumed that the availability of data for countries was not related to the prevalence of undernutrition.
To estimate the trends in the prevalence of under-nutrition by region, a random coefficient model was fit for each region and sub-region with sufficient data, using the country population as sample weights. Therefore, the effect of a country was proportional to its population.
The multilevel models specified a linear (that is, straight line) relationship between prevalence of under-nutrition and survey year. In other words, these models assumed that the rate of change in the prevalence is constant. To determine if any regional trends were speeding up or slowing down, possible nonlinear relationships were examined by including quadratic and cubic polynomial terms. No evidence of nonlinear relationships was found for any region or sub-region. Thus, there was no justification in any region for fitting a curvilinear model for past or future trends.
The fitted equations were used to predict region and sub-region prevalences for the years 1980,1985, 1990,1995,2000, and 2005. Uncertainty in the forecasts was assessed by 95% confidence intervals estimated by SAS Proc Mixed.6 The predictions for 2010 and beyond were discarded because the 95% confidence intervals were too wide.
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