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2 IRD and Institut Pasteur, Paris, France; 3 IRD, Montpellier, France; 4 WHO, Geneva, Switzerland; and 5 IRD, Geneva, Switzerland
* To whom correspondence should be addressed. E-mail: mgarenne{at}pasteur.fr.
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ABSTRACT |
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 TOP ABSTRACT IntroductionMethodsResultsDiscussionAppendix: Derivations of true...LITERATURE CITED |
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5000 children, 6–59 mo of age. The anthropometric indicators used were Z-scores of weight-for-age, weight-for-height, height-for-age, head circumference-for-age, arm circumference-for-age, triceps skinfold-for-age, and subscapular skinfold-for-age, plus arm circumference, body mass index, and 2 composite indicators. Population attributable fraction varied according to indicators selected and ranged from 31% (head circumference) to 65% (arm circumference). The 2 composite indicators summarizing the whole nutritional status provided the same value for the population attributable fraction (59 and 60%, respectively). Classic thresholds of mild, moderate, and severe malnutrition are presented, as well as the bivariate distribution of wasting and stunting. Whatever the indicator used, mortality attributable risks appeared evenly distributed along the scale of low nutritional status. Our findings question the value of using classic thresholds of mild, moderate, and severe malnutrition (developed by clinicians for practical purposes) for nutritional epidemiology.
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Introduction |
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TOPABSTRACTIntroductionMethodsResultsDiscussionAppendix: Derivations of true...LITERATURE CITED |
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Using a different approach in a study conducted in Bangladesh, Fauveau et al. (20) found that 34% of all deaths were attributable to severe malnutrition, including 49% of diarrhea deaths. In this study, severe malnutrition was assessed by a family report of rapid wasting or the appearance of tibial edema prior to death. This definition was validated by an independent measure of mid-upper–arm circumference (MUAC)6 (<11.0 cm) on a small subsample of children.
Among the unresolved questions are the theoretical basis for these calculations and the role of the various components of malnutrition. In particular, the role of severe or very severe malnutrition remains poorly analyzed.
The aim of this study is to present a method to calculate the distribution of the population attributable risks, and to apply this method to a study conducted in Senegal in the mid-1980s by the same authors.
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Methods |
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TOPABSTRACTIntroductionMethodsResultsDiscussionAppendix: Derivations of true...LITERATURE CITED |
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Earlier approaches have used arbitrary values of thresholds under which children are considered malnourished (18). We propose here another approach: to consider both nutritional status and relative risk of death as continuous variables, and to estimate directly the PAR by calculating the integral values of continuous distributions. This calculation can be applied to any variable measuring nutritional status compared with a reference population of well-nourished children. In formulae, it can be written as:
x0 x0
The population attributable risk can be written as:
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Prevalence of malnutrition and population below a given threshold.
Relative risks and prevalence of malnutrition have to be derived from empirical data based on a classification of nutritional status. This implies that the relative risk calculated from empirical data RR(x) is associated with a given value of (x), the nutritional indicator, and therefore relates to C(x) the proportion of the population at this given threshold, and not to the true prevalence of malnutrition C(x) x k(x) in the population. If one would consider the true proportion of malnourished children to estimate the true prevalence, one should therefore correct the relative risk accordingly. We show formally in the appendix that under simple assumptions this leads to a new relative risk RR'(x) such as:
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In other words, the calculation of the attributable risk can be done directly from the empirical data, using the empirical C(x) and RR(x) and is independent from the proportion malnourished at any given threshold. This is the approach followed in this article.
Adjusting the distribution of C(x). In practice, because most anthropometric measurements are approximately normally distributed, C(x) was calculated after adjusting the empirical distribution with a normal curve with the same mean and variance. More precisely, the mean should be taken as the median of the empirical distribution, and the variance should be calculated as the left variance, that is, the variance below the median, as it is done in reference populations. With this procedure, knowledge of median and left variance of the distribution of the anthropometric indicator is enough to calculate all indices. Note that the right side (above median) of the distribution has no influence on the calculations, which depend only on the distribution below the median. All calculations were done with a spreadsheet, although they could have been done with a basic computer program. Estimations of integrals were done with small steps of 0.1 Z-scores from –7 to +4, or equivalent small steps for absolute values. The precision of the calculations is therefore likely to be higher than with larger steps, such as 2 or 3 strata, and in particular, would affect the lower end of the distribution, which represents the most severely malnourished children who bear the highest mortality burden.
Adjusting the relative risk. Similarly, the relative risks RR(x) were calculated directly from empirical data. In malnourished populations, mortality is increasing in a Logit-linear way below a threshold, taken as the median of the reference population, whether anthropometric indicators are calculated as Z-score (threshold = 0), or in absolute values for selected indicators. Therefore, the relative risk can be calculated from the Logit regression line of the relation between mortality and nutritional status below the threshold. In practice, we coded the anthropometric indicator as the reference value above the threshold (e.g., 0 for a Z-score), and estimated the Logit equation directly from empirical data. Relative risks were then calculated after fitting with the Logit adjustment by dividing the fitted mortality estimate q(x) by the baseline value q(x0).
In our study, we have used a further refinement. Indeed, all indicators considered here have an age pattern, and therefore a correlation with age, as in the case for mortality. For instance, among children 6–59 mo of age, most of the wasting and most of the deaths were below 36 mo of age, whereas most of the stunting was above 36 mo of age. In the empirical analysis of Niakhar data, correlation with age was positive for most indicators and negative for height-for-age and head circumference-for-age. This effect was dealt with by introducing age as a cofactor in the linear-logistic model, and calculating a new regression equation to be used for calculating the relative risk RR(x) independent of age. We provide the 2 calculations in the empirical analysis, although final estimates were completed after controlling for age. The relation used in the regression can be written as:
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where (x) is a Z-score or an absolute value of an anthropometric measure. Final estimates of relative risks were obtained for the mean value of age (32 mo).
Application to Niakhar data.
The integral approach was applied to the data collected in Niakhar in 1983–1984, an area under demographic surveillance and covering 30 villages in the Fatick region of central Senegal. The study was approved by the ORSTOM health department and by the European Union DG-XII directorate. Data and methods have been presented elsewhere (10–12). In brief, a sample of 5000 children were measured 4 times every 6 mo and were followed up for survival for at least 18 mo. The anthropometric measures included weight, height, mid-upper–arm circumference, head circumference, triceps skinfold, and subscapular skinfold. For the present study we used the classic indicators presented as Z-scores (Table 1). In addition we used the absolute values for MUAC and BMI for comparison with other studies. We added 2 composite indicators: 1) height and weight index (HWI), defined as the mean of Z-scores for height-for-age and weight-for-height. This index corresponds to the classic distinction between stunting and wasting; and 2) anthropometric composite index (ACI), defined as the mean Z-scores for height-for-age, muscle circumference, and subscapular skinfold. This indicator was derived from an in-depth multivariate analysis of the relations between all the anthropometric indicators and child survival and will be presented formally in a companion paper. It summarizes stunting, muscle mass, and fat mass.
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We also used a dual index, as recommended by Waterlow (22), classifying height-for-age and weight-for-height. This led to an extension of the method using 2 variables instead of 1. The dual index was studied the same way in a 3-dimension space: the relative risk was estimated with a similar multivariate analysis model to compute RR(x,y), prevalence was fitted with a bivariate normal distribution C(x,y), and the PAR(x,y) by taking a double integral on x and y.
Reference sets for calculating percentages of median and Z-scores were taken from international references. For weight-for-age, height-for-age, weight-for-height, head circumference, and BMI we used the CDC-2000 reference set (23). The CDC-2000 set was preferred to the more classic NCHS-1977 set primarily because its SD were more stable than in the other set, although the medians were virtually identical. For MUAC, we used the WHO recommended reference set (24), and for the skinfolds and muscle circumference we used the Jelliffe reference set (25). The Jelliffe sets do not provide SD. These were calculated from the Frisancho reference set (26) by applying the same CV (SD/median) and interpolating for monthly values. Age was calculated in months with 2 decimals, and proper interpolations were completed for each case.
For this study, mortality was defined as the risk of death for any cause within 6 mo of the nutritional assessment. We plan to provide in the future a sensitivity analysis for other delays, either shorter (1, 2, 3 mo) or longer (9, 12, 18 mo) after the nutritional assessment.
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Results |
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TOPABSTRACTIntroductionMethodsResultsDiscussionAppendix: Derivations of true...LITERATURE CITED |
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Main characteristics of the nutritional assessment are given in Table 1. Mean and SD as well as median and left-of-median SD are presented. For practical purposes means and SD were providing basically the same estimates of PAR as median and left-of-median SD, because most distributions were close to a normal curve (Fig. 1).
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Mortality risk ratios. Goodness of fit of the Logit model was verified graphically for each indicator (see Fig. 1, weight-for-age), and corresponding curves were presented elsewhere (11). The Logit slopes for all indicators available, both before and after controlling for age, are provided in Table 2. The Logit slopes allow for the computation of death rates at any threshold. All anthropometric indicators were closely related with child survival and statistical validity was not an issue with 303 deaths, because P-values for slope estimates were in the range of 10–11 to 10–33. Slopes were steep and translated into high relative risks at low levels of nutritional status. For instance, the relative risk of mortality for weight-for-age Z-scores ranged from 1.7 at –1 Z, 2.9 at –2 Z, 4.9 at –3 Z, 8.2 at –4 Z, 13.6 at –5 Z, to 21.9 at –6 Z. Similar values of high risk ratios were found at low values of nutritional status for all indicators considered. Controlling for age tended to reduce the slope for many indicators but increased the slope for those inversely related to age (height-for-age, muscle circumference, subscapular skinfold, and BMI).
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–1.9, and shows the same importance of mild malnutrition (defined as between –1.0 and –1.99) and moderate malnutrition (defined as between –2.0 and –2.99) with a small residual of severe malnutrition. The HWI is lower and centered at –2.4. In this case, using the same thresholds leads to different estimates and a higher role of severe malnutrition (18% of PAR). If weight-for-age is used with the same thresholds, then severe malnutrition appears as dominant, accounting for 61% of the total attributable risk, and only a small contribution of mild malnutrition (11%) (Fig. 2).
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Discussion |
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TOPABSTRACTIntroductionMethodsResultsDiscussionAppendix: Derivations of true...LITERATURE CITED |
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Overall, our estimates of total PAR appear similar to earlier estimates. For instance, Pelletier et al. (18) and Caulfield et al. (19) provided PAR of weight-for-age that falls within the range of our estimates. We ran Pelletier's computations to our data and found a PAR of 58.3%, which is close to our estimate (63.2%). Differences are due to the inclusion of some cases above –1 Z-score (very mild category), to small differences in relative risks, and to more accurate calculations of RR at very low thresholds. The main advantage of the integral approach is to allow many thresholds and to provide a more global picture. The gain in precision seems of little interest compared with the other gains.
Estimations of PAR could be produced for any population distribution of nutritional status simply from mean and variance (or median and left variance for optimal precision). Fitting a normal curve with the same mean and standard deviation is a simple procedure, and applying corresponding risk ratios is straightforward. However, these data might not be available everywhere, and concrete application of this procedure might be limited.
Our estimates of the contribution of severe and very severe malnutrition appear higher than previous estimates. This is in part due to the choice of thresholds (for MUAC and weight-for-height) but not for weight-for-age, because classic thresholds were used there. For instance, Pelletier et al. (18), using regression models linking PAR and proportion of children below the weight-for-age threshold of 60 or 80%, found that 83% of deaths attributable to malnutrition were due to mild and moderate forms and 17% to the severe forms. Our figures clearly show the important role of severe and very severe malnutrition in Senegal, despite a moderate overall prevalence of malnutrition. Of course, these estimates are context specific and depend upon the distribution of malnutrition (e.g., kwashiorkor vs. marasmus), the mortality level in the population, prevalent infectious diseases, cause of death patterns, as well as available preventive and curative services. Indeed, even in places with high prevalence of malnutrition, mortality from severe malnutrition can be kept at low levels if appropriate treatments are offered to children in need.
Pelletier (18) used a log slope of –0.550 for weight-for-age, and we used an empirical estimate of –0.548 after controlling for age. These slopes are obviously equivalent and are found to be similar to the 8 studies reviewed by Pelletier. One could take this further and select a standard value of log-slope for weight-for-age, as well as for other nutritional indicators, to provide a standard for international comparisons.
Our finding that any nutritional status variable is contributing significantly to mortality indicates that any indicator could be used as criteria, either for screening malnourished children or for evaluating the impact of malnutrition. We consider the composite indices as the most robust indicators for estimating PAR because they integrate the various dimensions of nutritional status. In this respect, arm circumference-for-age and weight-for-age appeared as the closest indicators together with subscapular skinfold, which is more difficult to use in the field. Arm circumference-for-age and weight-for-age tend to give somewhat higher values, partly because of high relative risks associated with low values of nutritional status, and partly because of lower absolute risk associated with values above the median (baseline mortality). Formal analysis of sensitivity and specificity had revealed the same effect, however without controlling for age (11,12).
All our calculations are based on the selection of the median of reference norms as the threshold above which mortality is constant. We tested this hypothesis with multivariate models, including age. None of the slope above the median was significant, half of them were positive and the other half negative. However, we had only a small sample of deaths above the medians (30 deaths on the average), and confidence intervals were large. We also tested for a minimum value of mortality above the median by introducing a square term in the regression equation. The minimum value was always above median (above +1.5 Z-score for all indicators considered) and sometimes way above. This suggests that we might have under-estimated the total attributable risk, and if we had chosen a higher threshold, and considered basically all children as malnourished (the shift in mean Z-score approach), we could have found even higher values of attributable risks. In any case, calculations for attributable risk require a baseline value and graphical evidence indicated that the median was a sound one for almost all the indicators, with the exception of subscapular skinfold.
We used normal distributions of Z-scores. These are not always precisely normally distributed, and it would have been better to use the logarithm of the percentage of the median, which happened to be virtually normally distributed for all indicators considered in the Niakhar data set. However, corresponding estimates of PAR from the log percentage of the median were basically the same as with Z-scores, primarily because the left part of the distribution was the only one to play a role and most of the irregularities came from the right part (above median).
Most of the disturbances from normal distribution occurred above the median and were primarily due to the reference sets and not to the empirical data and they were primarily from the right SD being higher than the left. When using a symmetrical SD, estimated, for instance, from the 5th and the 95th percentiles, distributions were far more regular. We also tried to use more complex formulae, such as the LMS transformation used in the CDC-2000 data sets, but this led to even further erratic patterns. This suggests that the Niakhar data, originating from a very homogenous population, ethnically, socio-economically, and in terms of food intake, had normal distributions, whereas the reference sets originated from more heterogeneous populations in terms of ethnic background, socio-economic status, and feeding practices. This raises the question as to how much of a reference are those populations. If the median always appeared sound, the skewedness appeared be peculiar to the reference sets.
Controlling for age helped to better estimate the attributable risks. They did not differ much from earlier estimates except for retarded growth. Using Logit slopes without controlling for age tended to underestimate the net effect of stunting, which was an important component accounting for more than half the mortality and achieving higher attributable risks than many other previous estimates.
Composite indices tended to provide lower estimates than some of the simple indices. This was expected because cumulating all the risks is not common for individuals. Weight-for-height and height-for-age, considered separately in a 3-dimension space, or as a mean, produced similar values (59.2 and 56.4%, respectively), although these were still somewhat smaller than weight-for-age or arm circumference-for-age. Composite indices provided a closer estimate to the true effect of body composition, and 60% is probably a fair estimate of the net contribution of low nutritional status to mortality in this situation.
The symmetry of the distributions of attributable risk was remarkable but expected, given the underlying distributions of relative risk and the population distribution of nutritional status. This symmetry was also visible in the 3-dimension space of stunting and wasting. The symmetrical distributions presented here have primarily a theoretical value for nutritional epidemiology, which contrasts with the practical use of cut-offs needed by clinicians in the field. If there are only minor differences in mortality associated with values, such as say –2.9 and –3.1 Z-score, physicians have to make decisions based on a single threshold, whether for hospitalizations or for choosing specific treatments.
If our approach has no value for clinicians, it still has a value for policy makers, in addition to being of theoretical interest for nutritional epidemiology. Displaying distributions of attributable risk provides evidence on where to invest to reduce mortality. In this respect, treating severe malnutrition appears as important as preventing mild to moderate malnutrition, because both are expected to have large impacts on mortality. The fight against the various forms of malnutrition will be more efficient if it encompasses multifaceted interventions and programs adapted to each case.
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Appendix: Derivations of true relative risk in the case of 2 strata |
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TOPABSTRACTIntroductionMethodsResultsDiscussionAppendix: Derivations of true...LITERATURE CITED |
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Assuming the same mortality level in the well-nourished population and the malnourished population above the baseline threshold, and no excess mortality in the well-nourished population whatever the nutritional indicator, gives:
Similarly, prevalence in malnourished population is:
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FOOTNOTES |
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6 Abbreviations used: ACI, anthropometric composite index; HWI, height and weight index; MUAC, mid-upper arm circumference; PAR, population attributable risk; Prev, prevalence of malnutrition; RR, relative risk.
Manuscript received 23 February 2006. Initial review completed 2 May 2006. Revision accepted 3 August 2006.
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LITERATURE CITED |
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TOPABSTRACTIntroductionMethodsResultsDiscussionAppendix: Derivations of true...LITERATURE CITED |
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