The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 60:804-810 (2005)
© 2005 The Gerontological Society of America
Stature Prediction Equations for Elderly Hispanics in Latin American Countries by Sex and Ethnic Background
Alberto Palloni and
Abdelhani Guend
Center for Demography and Ecology, University of Wisconsin–Madison.
Address correspondence to Alberto Palloni, Center for Demography and Ecology and Center for Demography of Health and Aging, Department of Sociology, University of Wisconsin-Madison, 4426 Social Science Bldg., 1180 Observatory Dr., Madison, WI 53706-1320. E-mail: palloni{at}ssc.wisc.edu
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Abstract
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Background. We estimate prediction equations of stature from knee height for elderly Hispanic Blacks, Mulattos, Mestizos, Mexicans, and Whites. We test the predictive power of estimated equations, assess the magnitude of relative errors in measures of body mass index (BMI), quantify errors committed when using predicted rather that observed height, and evaluate the differences in the strength of the relation between BMI and diabetes.
Methods. Using data collected in 1999–2000, we split each sex and/or ethnic group into validation and cross-validation groups, estimate equations from the validation groups, then test them on the cross-validation groups. We use robust linear regression to assess the sex- and/or ethnic-specific relation between knee height and stature. We evaluate the accuracy of classifications by obesity and of estimates of risk of diabetes when using estimated versus observed height.
Results. Our equations are slightly less accurate than those obtained from U.S. data (
4), although ethnic-specific parameters are comparable. Classification of subpopulations by obesity has high sensitivity and specificity. The estimated measure of BMI strongly attenuates estimated effects of obesity on diabetes. Thus, although the predicted heights fall within acceptable error bounds, their utilization in modeling relations to other health outcomes may give misleading inferences.
Conclusions. Knee height is a good surrogate for current height for elderly populations. It is always preferable to use ethnic-specific predictions, because the relation differs by ethnicity. Great care has to be exercised when classifying populations using surrogate measures of height, or in estimating relations between measures that are functions of surrogate height and health outcomes.
HEIGHT of elderly persons and their body mass index (BMI) defined as the ratio of weight (in kilograms) to the square of height (in meters) are two anthropometric measures frequently used to determine current nutritional status of the individual as well as to assess their likely nutritional status when growing up (1–3). For a number of reasons, height of an elderly person is not always obtained; even when it is, it may be systematically biased due to skeletal compression. In its place researchers have proposed to use surrogate measures which are easier to collect and less subject to distortion while being simultaneously important components or constituents of height itself (4,5). One such surrogate is knee height (6). Estimating equations relating knee height and height have been developed for elderly non-Hispanic Whites, Hispanic Blacks, and Mexican American individuals using data from the Third National Health and Nutrition Examination Survey (NHANES III) (5). Similar equations for Black males and females from a sample of 21 Black males and 98 Black females over 60 years old were also estimated (7). Pini and colleagues (8) highlighted the importance of geographic factors as determinants of differences in body height, confirmed the importance of knee height as the best predictor of height, and corroborated the findings of Chumlea and Guo (5) suggesting that controlling for age does not alter the predictive power of knee height. Similar conclusions are reached by Prothro and Rosenbloom (7) for their Black sample.
In all cases, past studies have focused on populations residing in the United States or Europe. Because it is possible that the relation between stature and one or more of its components, such as knee height, varies across populations, it is relevant to verify whether there are important differences in the estimated relations and, if so, to identify the factors that explain such differences. From a purely pragmatic point of view, however, estimating relations in a heterogeneous population base has a value in itself; in fact, it will increase the strength of inferences regarding height that could be made from surrogate measures in populations that are potentially different from those in which most of the work has been done up to now.
This article contributes to the extant literature in two distinctive ways. First, the samples of elderly people we use in this study are drawn from countries in the Caribbean (Barbados and Cuba), North and Central America (Mexico), and South America (Argentina, Brazil, Chile, and Uruguay). A few of these (Argentina, Chile, and Uruguay) are ethnically quite homogeneous with a dominant White population. Others have a strong component of African origin populations (Brazil and Cuba), and still others (Mexico) are influenced by indigenous populations. We can take advantage of this remarkable heterogeneity to test conjectures about differences in the relationships between height and knee height, and thus extend the work done by other researchers in more homogeneous populations. Admittedly, however, because the samples are all from urban populations, there might be factors producing more homogeneity than what one would find had the samples also included persons living in rural areas. Yet, as we argue below, most of the countries in our study are almost completely urban, as the rural population is a rapidly vanishing component (9).
Second, rather than stopping at the point where one verifies that errors of prediction in a measure of height fall within reasonable boundaries, we also assess the estimated relation between knee height and height by showing that the use of surrogate measures does not alter inferences regarding a well known and well established relation between obesity and diabetes. This assessment is important because from first principles of measure theory we know that, to the extent that independent variables in a relation are subject to (random) errors, the estimated effects will be systematically biased downward. If this is so, using a surrogate measure of height (even with acceptable measurement errors) may conceal relations that exist between height (or derived measures) and health outcomes such as diabetes.
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METHODS
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SABE (10,11) is a data collection project anchored in seven major cities (six of them capital cities) of the region: Buenos Aires (Argentina), Bridgetown (Barbados), San Paulo (Brazil), Santiago (Chile), Havana (Cuba), Mexico City (Mexico), and Montevideo (Uruguay). All seven surveys were administered to representative samples of populations aged 60 years or older in each city, and were strictly comparable although translated to three different languages (Spanish, Portuguese, and English). In some cases, interviewers selected a target older person and his or her surviving spouse. All sample frames were drawn either from recent population censuses or from nationally representative surveys carried out periodically in the capital cities of the region. The fieldwork took place between June 1999 and June 2000, and a preliminary final report was completed in December 2002. An important feature of the survey is that, with one exception (Buenos Aires), the rates of response were significantly higher than those in similar surveys in other countries. Additional clarifying information on the data appears in Appendix 3. Table 1 displays basic information on sample sizes, rates of response, as well as selected dimensions of the demographic profile (composition by age, sex, marital status, and race) and of the socioeconomic composition of the samples (by education). As shown elsewhere, the basic demographic profile accords well with national figures (11). Table 2 summarizes pertinent information on age, height, and knee height.
In what follows, we first describe our choices of subpopulations; the procedures to estimate the relations between knee height, height, and corresponding measures of accuracy; and the nature of two applications, one to infer BMI to classify the subpopulations by obesity and the other to estimate the relation between obesity and self-reported diabetes.
To enhance comparability with the analyses carried out by other researchers (4) we partitioned the pooled samples of elderly persons into the following ethnic groups: non-Mexican Whites, Mexicans, Mestizos, Mulattos, and Blacks. Identification of ethnicity (Black, Mulatto, Mestizo, and White) was derived from self-reports in each of the surveys that were elicited from strictly comparable questions. The group corresponding to Mexicans is composed of the entire sample of elderly persons from Mexico except for those who reported themselves as Mestizo. Thus defined, the category Mexican encompasses individuals of Mexican origin, and all our ethnic categories become comparable to the groups of Mexican-Americans used by Chumlea and colleagues. Relations and error analysis was carried out within each of the above defined ethnic groups.
The method we used is similar to that of Chumlea and colleagues (4). For each ethnic subsample, we randomly assigned observations to either validation or cross-validation group as follows. First, we assigned a random number to each observation. Second, we sorted the data set by that random variable. Third, we assigned the first half of the group to the validation group and the second half to the cross-validation group.
Two equations were used to estimate the relation between knee height and actual height. The first equation includes knee height and age as predictors. The second equation includes knee height as sole predictor of stature. In both equations we also control for sex. To assess the accuracy of the equations estimated in the validation group, we defined three types of errors. The algebraic expressions appear in Appendix 1, and their magnitudes are reported in Table 3.
The errors are defined as follows. The pure error is the square root of the weighted sum of squared differences between the observed measures and the predicted measures of height. The weight in this case is one for each observation in the sample. The mean pure error is the pure error divided by the mean stature of the ethnic and/or sex group expressed as the percentage of that mean. The mean relative error is the mean absolute value of the relative differences between observed and estimated stature, also expressed as a percentage. These errors are calculated on the observations of the cross-validation groups by comparing the observed height of individuals with the predicted value from the equations estimated in the validation groups.
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RESULTS
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The recommended equations are displayed in Table 4. For each ethnic group, these equations were estimated in the entire subsample, namely, pooling the cross-validation and validation groups. These equations ought to be associated with measures of errors that are more benign than those displayed in Table 3.
Recommended Stature Predictions Equations
Table 4 displays two sets of equations for the predictions of stature from knee height for each sex and/or ethnic group wherein more homogeneity is expected, along with pooled estimators for the non-White population, and pooled estimators for the entire sample. The first set corresponds to the model in which both age and knee height are used as predictors of stature. The second model corresponds to the case in which knee height is used as the sole predictor of stature.
Classification of Subpopulations Using Actual and Estimated BMI
BMI is calculated using observed height and estimated height, respectively, for men and women in each ethnic group. To assess the predictive value for the study of obesity, we defined as obese those individuals with a BMI greater than 30 and as underweight those individuals with a BMI less than 18.5 (12). We then calculated measures of discrepancies between predictions and observations, including specificity, sensitivity, positive predictive values (PPV), negative predictive value (NPV), and overall accuracy. These indices are reported in Table 5. All measures of discrepancy shall be read as the complement to 100. For example, the last panel of Table 4 shows the following results for the prediction of obesity among all females: 92%, 83%, 92%, 85%, and 89% for sensitivity, specificity, PPV, NPV, and overall accuracy, respectively. This means that obesity is predicted correctly in about 92% of the cases, and nonobesity is predicted correctly in about 83% of the cases. The probability that a case predicted as obese is indeed obese amounts to about 92%; conversely, the probability that a case predicted as nonobese is actually nonobese is about 85%. Finally, the overall level of accuracy, a summary index for both sensitivity and specificity, amounts to 89%. Similar assessments for a measure of underweight show the following figures: 70%, 99%, 82%, 98%, and 98% for sensitivity, specificity, PPV, NPV, and overall accuracy, respectively. Therefore, underweight prediction inaccuracy amounts to only 2%.
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Table 5. Sensitivity, Specificity, Positive Predictive Value, Negative Predictive Value, and Overall Accuracy for Body Mass Index Based on Observed Height Versus Body Mass Index Based on Estimated Height Using Prediction Equations of Model 2.
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Although these are not optimal levels of accuracy, they are all high and suggest that BMI calculated with a surrogate measure of stature is unlikely to lead to important misclassification of subpopulations.
Estimating the Relation Between Obesity and Diabetes
To identify the existence, magnitude, and pattern of error propagation associated with the use of a surrogate measure of height, we estimated robust logistic regressions of self-reported diabetes by using obesity as the main risk factor for each sex-specific or ethnic-specific subsample. We used separate sex subsamples, because it is well known that the relation between obesity and diabetes varies by sex. Two types of model were estimated. The first uses two dummy variables to capture the contrasts between obese persons, morbidly obese persons, and everybody else. The cut points are 30 and 40 for obese and morbidly obese persons, respectively (12). The second distinguishes only between obese persons and everybody else. In each case, we estimated two relationships: one between the outcomes and height when actual height was the measure for stature and another one when knee height was used to estimate stature. In all models we control for age of the subjects. To simplify presentation, the results displayed in Table 6 correspond only to the first model, that is, the one including a single dummy variable to classify the subpopulation into obese and nonobese. Two main conclusions can be drawn. The first is that, as expected, the coefficients of the dummy for obesity using estimated height is biased toward zero relative to the coefficient for the dummy of BMI calculated with the actual measure of height. In fact, in more that 90% of the cases, the p values associated with the estimated regression coefficient are larger in the former than in the latter case. Second, and perhaps more important, is that in no case does the use of the dummy for obesity using a surrogate measure of height lead to incorrect inferences regarding the influence of BMI on the probability of self-reported diabetes. Admittedly, the deck is stacked against producing incorrect inferences because, even when using actual height, only two coefficients exhibit small enough p values to assign statistical significance to them.
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Table 6. Logistic Regression of Diabetes and Obesity. Observed Height-Based Body Mass Index (BMI) Versus Predicted Height-Based BMI Controlling for Age.
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DISCUSSION
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Using a new database for elderly Latin Americans, we estimated prediction equations for individual stature using knee height, a useful tool to assess height when actual measurements are either not taken or appear to be unreliable because of the age of individuals. These equations were estimated for several ethnic groups, and for males and females, to account for as much of the heterogeneity in the relation between the two variables as is possible. We found that the equations have a good, although not excellent, predictive validity. They yield high sensitivity and specificity scores when predicted values are used to partition the population into several groups based on the calculated value of BMI. We also show that the use of surrogate height values, predicted from the relation to knee height, led to proper estimates of coefficients for the relation between diabetes and obesity, albeit with the expected downward bias.
An important feature that must be kept in mind is that equations are different across ethnic groups and sex although the differences in coefficients are not always significant. The most important distinction pertains to sex: The contrasts between equations for males and females are uniformly large and important. Thus our first recommendation is to use separate estimation equations by sex. Less import but still worthy of consideration are differences across ethnic groups. The slopes of predicting equations (see Table 3) for Blacks, Mulattos, Mestizos, and populations of Mexican origin are distinctively higher than those for Whites. Thus, the second recommendation is that, at a minimum, we should preserve a distinction between White and non-White. Further precision on ethnic group membership would be of even more help. A final remark is that the equations we estimate in this article are different from those estimated by Chumlea, but the differences are most relevant for the Black population and considerably more muted than those for the Mexican and White populations. An explanation for why this should be the case is lacking, but the finding prompts a third recommendation, namely, to ensure that if one is studying a Black population, minimal distinctions must be drawn between U.S. Blacks and those of Latin or Caribbean origin.
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APPENDIX 2
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Formulae for the Three Types of Errors Reported in Table 2
where Yi is the observed height, 
i is the predicted height, 
is the mean of observed height, and Wi, is the weight.
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APPENDIX 3
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For additional information on the nature of the samples, the reader is referred to the article by Palloni and Pelaez (11). It is important to note that, because all samples are urban samples, our ability to generalize to the total population is impaired. However, readers should bear in mind that the proportion of the total population living in urban areas in these countries is substantial, varying from close to 100% in Barbados to about 74% or 75% in Mexico and Cuba, respectively (9). This finding suggests that our results should not be too different from what we would have obtained had SABE been based on national samples. And, indeed, it has been shown that the demographic profile at least of the samples is quite close to national averages (9). In this article we use the words "country" or "city" to refer to the city samples. By using the word country, we are in no way assuming that the SABE data are exactly representative of elderly populations in each of the countries that participated in the project.
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Robust Regression Coefficients for the Prediction of Stature Models in the Validation Groups
All Models Have a p Value <.0000 for the F Statistic.
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Acknowledgments
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Research for this study was supported by The National Institute of Child Health and Human Development (core grant P30HD05876 to the Center for Demography and Ecology) and by The National Institute on Aging (core grant P30AG17266 and research grants R01AG16209, ROGAG18016, and R03AG15673 to the Center for Demography of Health and Aging).
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Footnotes
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Decision Editor: John E. Morley, MB, BCh
Received February 18, 2004
Accepted March 22, 2004
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References
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Abstract
Methods
