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Article

Statistical Analysis of Nitrogen Balance Data with Reference to the Lysine Requirement in Adults

Department of Community Health, Tufts University School of Medicine, Boston, MA 02111 and Laboratory of Human Nutrition, School of Science, Massachusetts Institute of Technology, Cambridge, MA 02139

¹To whom correspondence should be addressed at MIT, 77 Massachusetts Ave., Room E17-434, Cambridge, MA 02139. Phone No: 617 253 5801; Fax No: 617 253 9658; E-mail: vryoung{at}mit.edu

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Statistical analysis of nitrogen balance data is an important approach to the estimation of human nutrient requirement. The usual procedure is to regress nitrogen (N) balance on intake and to define the requirement as intake that would produce zero balance. In the actual application of this methodology, there are a number of options, and in the present study we explore the sensitivity of the regression approach to those options. To put this problem into a realistic context, we examine the current controversy over the lysine requirements of healthy adults. From early N balance studies, investigators concluded that the mean requirement was generally less than 10 mg · kg^-1 · d^-1, whereas based on recent ¹³C-tracer and metabolic studies, we propose a tentative mean requirement of ~30 mg · kg^-1 · d^-1. Jones et al. (1956) conducted careful N balance studies from which they derived an estimate of lysine requirement of less than about 8 mg · kg^-1 · d^-1. We reanalyzed these data with different choices of modes of analysis, mathematical models, and different assumptions concerning the magnitude of miscellaneous N losses. We find that for these data the choice of a specific mathematical model has only a small effect on resultant estimates of requirement, while estimated requirements are very sensitive to amount of unmeasured losses that are assumed and how the model is applied (whether the aggregate data are fitted in one pass to a single model, or the data for each individual subject are fitted to that individual's unique model). Moreover, our reanalysis suggests that the population requirement for lysine is in the range of 17 to 36 mg · kg^-1 · d^-1 and strongly supports a lysine requirement value of about 30 mg · kg^-1 · d^-1. In general, our results indicate that whenever possible, N balance data should be analyzed using a square root model fitted to individual data and that the median of the individual requirements so derived be used as the estimate of population requirement. Moreover, clearly any statistical analyses of N balance data should include a sensitivity analysis to determine the influence of underlying assumptions. Finally, the finding that these estimates are highly dependent on the assumed amount of N miscellaneous losses recommends that further studies on these losses and of the factors that influence them are essential.

KEY WORDS: • N balance • lysine requirement • linear • square root • log • exponential asymptotic

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
The present study of the statistical analysis of nitrogen (N)² balance data was motivated by controversy surrounding estimates of lysine requirement. We (Young et al. 1989 , Young and El-Khoury 1996 ) proposed that the upper level of the lysine requirement in adults as suggested by FAO/WHO/UNU (1985) , namely 12 mg · kg^-1 · d^-1, is too low. This estimate was based principally on the N-balance studies by Rose and coworkers in men (Rose 1957 ) and by a number of other investigators who studied the lysine requirements in adult women (Irwin and Hegsted 1971 ). The design of the N-balance studies by Rose and collaborators (Rose 1957 ) was not adequate, as we pointed out (Young and Marchini, 1990 ). Indeed, we suggested that, as conducted and interpreted, these studies would have led to an underestimate of the actual minimal lysine requirement of healthy subjects for long-term maintenance. The N-balance studies of women were also problematical (for example, Fisher et al. 1969 ), and so the adequacy of the estimates obtained in females might also be questioned. A reanalysis of the published N balance in adult women by Hegsted (1963) , who estimated the intake required to maintain a desirable, positive balance of 0.5 mg N · d, gave specific indispensable amino acid requirement estimates that were 1.6–4.9 times those needed for N equilibrium (Fuller and Garlick 1994 ). For lysine, the difference was about threefold. From an assessment of ¹³C-tracer studies (Young et al. 1989 ) and considerations of obligatory oxidative amino acid losses (Young and El-Khoury 1995 ), we proposed a tentative mean requirement of 30 mg · kg^-1 · d^-1, or a value of about 2.5 times higher than the United Nations value.

Recently Millward (1997) questioned our tentative requirement values for the indispensable amino acids including lysine and Millward 1999 concluded that an inadequate lysine supply is not an issue with most cereal-based diets. His argument, in part, is based on a reanalysis of the N-balance data of Jones et al. (1956) , from which he estimated a requirement of 18.6 mg · kg^-1 · d^-1 (Millward 1998 ) with the 95% confidence limits of that estimate being 14.1 and 27 mg · kg^-1 · d^-1 (Millward 1999 ). Millward's analysis of these N-balance data involved fitting a log-linear regression model using the aggregated N-balance values obtained with the 14 women studied in that earlier investigation.

Because of the potential and very different practical significance of this conclusion in comparison with our position, and further stimulated by Millward's paper, we undertook a reexamination of the data of Jones et al. (1956) to explore how sensitive the results were to variations in the aspects of the statistical methodology involved. This reanalysis of these data permits us to make general recommendations about the statistical analysis of N-balance data.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Data.

The N-balance data of Jones et al. (1956) are shown in Figure 1 ; they represent 14 women maintained on various levels of lysine. Reported balance data were converted from g N/d to mg N · kg^-1 · d^-1 to adjust for differences in body weight among the subjects (weight range 49.7–68.0 kg). Since the original data were for observed N-balance [Intake minus (Urine and Feces)] in our analyses, we also consider the implications of different assumptions of the magnitude of the unmeasured, miscellaneous N losses.

View larger version (23K): [in this window] [in a new window]   Figure 1. Plot of lysine intake and observed nitrogen (N) balance data of Jones et al. (1956) . Points of the same individuals are connected. Horizontal lines indicate assumptions of 5 and 8 mg N · kg-1 · d-1 miscellaneous losses (dashed and solid, respectively). These data also show that more than half of the subjects (8 of 14) did not achieve a positive N balance (assuming 8 mg N losses) during the study (or about one-third of the subjects, assuming 5 mg N losses). For these individuals, requirement estimates were extrapolations.

Statistical context of estimating requirement from N-balance data.

We define the nutrient requirement of a population (Population Requirement) as the minimal intake that produces zero N balance in half of the members of the population. We define the nutrient requirement of an individual as the minimal intake that will produce zero N balance. There are two major difficulties involved in estimating the intake that will produce zero balance. The first is that requirement cannot be determined directly, and investigators must provide known amounts of the test nutrient to individuals and measure the resultant N balance. Data are gathered for responses to different levels of intake, preferably including, for each individual, levels of intake which produce negative and positive balances (since extrapolation is extremely error-prone). Requirement is estimated by interpolating these data to find the intake that produces zero balance. The assumption of a specific mathematical function to be used for interpolation is inherent in this procedure.

A second difficulty is that, as in any biological system, there is variability involved—in the measurement of N intake and output, in the change of an individual's response from day to day, and in the fact that the specifics of N metabolism differ from one individual to another. A major goal of the statistical analysis is to extract useful estimates from this variability. Ideally, a modeling approach will (i) estimate requirement in a way which minimizes the effect of the variability involved, (ii) use the variability to estimate how sure we are of estimates of population requirement, and additionally (iii) permit estimates of the variability of the requirement of the members of the population.

Modes of fitting.

We examine two general procedures for fitting the data—fitting all the data to a single equation, assuming the data are independent observations (the cross-sectional or "one-fit" mode) and fitting each subject's data to an individual equation (the two-stage or "individual-fit" mode) (see e.g., Chapter 1 of Diggle et al. 1994 ). If the data consisted of single observations on a number of individuals, we would fit all the data in one pass with a single model and use this to predict population mean requirement. However, this prediction would be influenced by both the between-individual variability (how individuals differ among themselves) and the within-individual variability (how replicate measurements on an individual at the same level of intake would differ). If the data consist of several measurements on each individual, where responses of each individual are measured at several different intake levels, then each individual's data can be used to estimate the individual requirements and these individual estimates can then used to estimate the population requirement (Rand et al. 1977 ). Since the data of Jones et al. (1956) consist of multiple measurements on the 14 individuals, we are able to use the approach of individual fitting. We contrast this with the fitting of all the data at one pass, an approach that is sometimes used to derive requirement values from balance data (e.g., Jackman et al. 1997 ; Millward 1998 , Millward 1999 ). Notably, the use of the one-fit method with the data of Jones introduces a bias due to the different numbers of measurements made on the various individuals. When the measurements are all assumed to be independent, individuals with more data will contribute more to the final estimate of requirement than do the individuals with fewer data points.

Mathematical models.

The choice of a specific mathematical formula to which the data are fitted is an essential first step to statistical regression (see e.g., Chapter 9, Box et al. 1978 ). Theoretical considerations (Flodin et al. 1977 , Mercer et al. 1989 ) suggest a sigmoidal or at least an upper asymptotic relationship between N intake and N balance. For low intakes, balance is negative and the available intake is used efficiently with minimal N output or losses (Waterlow 1986 , Young and Marchini, 1990 ), while at high N intakes there is a promotion of whole body amino acid catabolism (Lewis 1992 ) and increased urea production (Forslund et al. 1998 ) such that N balance would be expected to approach and maintain a constant at equilibrium. Examination of existing N-balance data (Jones et al. 1956 , Young et al. 1973 , Hegsted 1976 ) shows that in general, the change of balance decreases as intake increases (see Fig. 1 ). Because there is no simple, theoretically-motivated model, we approached the problem as one of pragmatic statistical fitting (Daniel and Wood 1971 ) rather than mathematical modeling (Carson et al. 1983 , Clifford and Müller 1998 , Coburn 1992 , Coburn 1996 ). Given the multiple measurements on each individual, we need models which we can fit to individuals, and since we wish to utilize all the data, we are restricted to models with only two parameters to be estimated (several individuals have only two observations). We examined two simple curvilinear models—the natural logarithm and the square root model—and for comparison we fitted the linear model and the simplest asymptotic model that we were able to fit, namely the three parameter exponential approach to an upper asymptote (^{Eqs. 1 ,2 ,3 ,4} ).

The models examined were:

(1)

(2)

(3)

(4)

These particular models were chosen because they exhibit different types of curvature (see Fig. 2 ), they are easy to use and they can be used to fit individuals with as few as two determinations of balance (as was the case for four of the 14 subjects). Other complex models were fitted, but examination of the results showed that the variability of the data at hand did not warrant their further exploration. Since the basic models we examined are inherently linear in the transformed variable (the natural log and square root), we use least squares regression to fit the transformed data to the model and to determine estimates of the parameters (Draper and Smith 1981 ). Multiple R²'s, estimating the percentage of variability inherent in the data that the models were able to explain, were calculated as measures of how well the models fit the data, based on estimates of standard errors of fitting.

View larger version (20K): [in this window] [in a new window]   Figure 2. Plots of the one-fit regression equations relating observed nitrogen (N) balance to lysine intake (detailed in Table 1 ) and superimposed on the original data. This plot shows how well the models fit the data as well as the differing shapes of models. Models are: (A) linear, (B) square root, (C) log, and (D) exponential asymptotic. Horizontal lines (dashed and dotted, respectively) indicate assumptions of 5 and 8 mg N · kg-1 · d-1 miscellaneous losses.

The original data consist of observed N balance, calculated as the difference between N intake and N in the urine and feces. We explored the effect on requirement estimation of two different corrections for unmeasured N losses, since there is some difference of opinion as to what this correction should be. Millward (1998 , Millward 1999 ) used a value of 5 mg N · kg^-1 · d^-1, based on the review by Millward and Roberts (1996) of published values of miscellaneous N losses, which they concluded were lower than 8 mg N · kg^-1 · d^-1. The FAO/WHO/UNU (1985) report proposes a value of 8 mg N · kg^-1 · d^-1, which approximates that measured by Calloway et al. (1971) in meticulous N-balance experiments in healthy adults. It should be noted that the asymptote of the exponential asymptote model was 7.75, and thus an intake could not be calculated to allow for 8 mg N · kg^-1 · d^-1 of miscellaneous losses. For this model, requirement estimates for 7.5 mg of losses were calculated.

Estimators.

For the one-fit method of fitting (using all the data to fit one equation), the estimate of the population requirement was calculated as the intersection of the estimated mean regression equation with zero balance (corrected for miscellaneous losses). Notably this is neither a mean nor a median estimate of the population requirement; it is merely the intake that gives zero balance, assuming a certain response equation for the population. Asymptotic standard errors of this estimate of population requirement were calculated using standard Taylor expansions as a guide to the precision of these estimates.

For the method of individual fittings, we estimate individual requirements as the intersection of individual regression lines with zero balance. These 14 requirements were then used as a sample of requirements within the population. In order to explore the population distribution of individual requirements, histograms of the data were examined and three methods of estimating population requirement were used: the mean, a minimally trimmed mean (the mean calculated with the largest and smallest observations removed), and the median. For the log and square root models, estimates were calculated from the transformed variables and transformed back to produce the tables values. From the individual requirements, we calculate 95% confidence intervals for our estimate, using the standard error for the mean. Additionally, from the individual estimates, we are able to calculate the range of levels which are likely to include 95% of the individuals in the population as the interpolated 2.5 and 97.5 percentiles.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 
Figure 2 shows the results of the one-pass fitting of all the data for each of the four models; the actual best fit equations are shown in Table 1. From the summary given, Table 2 it can be seen that fitting all the data in one pass explained 50–60% of the variability in the data, while fitting each subject's data to an individual model explained 15–20% more of the variability. While the exponential asymptotic model explained the highest percentage of the variability, it was not significantly different from the other models. Table 3 summarizes the estimates of population requirement for different modes of fitting, specific models, and levels of assumed miscellaneous N losses and shows:

1. For the same modes of fitting and with constant assumed miscellaneous N losses, the specific model made little difference to the requirement estimates, with the exception that the asymptotic model estimates were lower than the others for 5 mg N losses and higher for 8 mg N losses. For the 8 mg N level of miscellaneous losses, the lysine requirement estimates were 26–28 mg · kg^-1 · d^-1 for one-fit while they were 30–36 mg · kg^-1 · d^-1 for individual fits. These estimates were all (within each mode of fitting) statistically indistinguishable [with overlapping (confidence interval)]. Notably, for the higher level of assumed losses, 7.5 mg N was used for the asymptotic model vs. 8 mg of N for the other models. The problem is that at assumed losses near the asymptote the estimated requirement becomes large and imprecise. For example, for 7.75 mg of N miscellaneous losses the estimated lysine requirement is 60.8 mg · kg^-1 · d^-1 with a standard error of about four thousand.
   
   

   View this table: [in this window] [in a new window]   Table 1. Results of one-fit equations for the aggregated N-balance data for the 14 individuals studied by Jones et al. (1956)

    
   
   

   View this table: [in this window] [in a new window]   Table 2. Result of one-fitting and individual fitting of N-balance data for subjects studied by Jones et al. (1956)

    
   
   

   View this table: [in this window] [in a new window]   Table 3. Estimation of requirement (lysine mg · kg-1 · d-1) for the subjects studied by Jones et al. (1956) 1

    
   
2. The one-fit procedure consistently produced requirement estimates that were in the same range as the individual-fit procedure. Again the asymptotic model is an exception; this is due to the fact that curves could not be fitted to a number of individuals, and those individuals that could be fitted were those with lower requirements (for 5 mg of N losses, only seven individuals could be fitted, while for 7.5 mg of N losses only four individuals could be fitted.)
   
3. The factor which had major effect on the estimate of population lysine requirement was the magnitude of the assumed miscellaneous N losses. For example, for the square root model, the assumption of 5 mg N · kg^-1 · d^-1 gave requirements that were from 6 to 12 mg · kg^-1 · d^-1 less than those which assumed 8 mg · kg^-1 · d^-1. The asymptotic exponential model shows the strongest effect of magnitude of the correction, since, as Figure 2 shows, change of requirement estimates depends inversely on the slope of the regression, which are lowest for this model.
   
4. In general, means and medians show little difference. Additional trimmed means were calculated (not shown) and found to be consistent. The estimates for the log model, with 8 mg of N miscellaneous losses assumed, are the major exception to this, with the median being 7 mg N · kg^-1 · d^-1 below the mean estimate. However, the broad confidence intervals for these values show that even this difference is not significant.
   
5. Table 3 shows three different aspects of the variability of the requirement estimates. First, estimated standard errors are shown for each of the one-fit procedures, as a measure of how precisely they determine requirement. These results are consistent with the fact that these standard errors are a function of the slope of the fitted model, with lower slopes having higher standard errors. Second, 95% confidence intervals are given for the individual fit estimates of population requirement. Comparison of these with the standard errors of the one-fit standard errors shows that individual fitting gives more precise estimates of population requirement. Third, Table 3 also shows 95% confidence intervals for the population, the intervals in which we would expect to find 95% of individual requirements. Here the model chosen makes a tremendous difference, since these limits depend on the extreme individuals and range from the unrealistic negative lower limit for the linear model to the upper limit of more than a thousand for the log model. The asymptotic model cannot be compared here, since, as discussed above, so few individuals could be successfully fitted.
   

The problem of extreme individuals is highlighted in Table 4 which shows the estimates of the individual requirements for each of the 14 women of Jones, individually fitting the data to the square root and the log model. An important difficulty is illustrated by these results, namely that the procedure estimates biologically unrealistic very high and very low requirement values for some individuals. As Figure 1 shows, those individuals with the extremely high requirements are those that never came into positive balance during the experimental period (and alternatively, those with low estimated requirements never went into negative balance)—these are individuals whose requirement is based on an extrapolation of their data.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Wherever possible (where multiple measurements are taken on each individual), the data of each individual should be fitted individually to their own response curve and those individual curves used to estimate individual requirements. This follows from several considerations:

1. Theoretically, fitting all the data to a single model rests on the assumption that every individual in the population follows exactly the same response curve; this is biologically unrealistic and not supported by the data.
   
2. In general, the one-fit procedure underestimates population requirement compared to the individual fitting procedure. This is reflected in our analyses and it is also true in general. Since requirement estimates are the ratios of intercepts to slopes (of the N-balance response equation), this result follows from the mathematical inequality that the average of ratios is larger than the ratio of averages, and shows that, in general, the requirements that are derived from a one-fit procedure will underestimate population requirement.
   
3. The individual-fitting procedure permits estimation of the variability of individuals within a population. The one-fit procedure provides only estimates of how well we know the population regression line, and it does not provide information about how individuals within the population vary in their requirements.
   

The mathematical model.

With these N-balance data, it was found that the choice of the mathematical model was not a significant factor, with the exception of the asymptotic model. This model is inappropriate for these data since in the one-fit mode it requires that all individuals have the same limiting asymptote, and its use to individually fit the individuals results in discarding much of the data. Moreover, the very nature of the model as asymptotic means that the estimate is very imprecise anywhere near that asymptote.

In general, none of the models that were tried fitted the data well, and the actual responses of individuals appear too complex to be modeled, given the limited amount of data on each individual. While fitting curves to each individual removes a certain amount of the variability between individuals, a substantial amount of variability remains (Table 2) . Clearly, further experiments are needed to explore the reproducibility of, and factors that affect, individual N-balance responses, a problem which Millward and colleagues emphasized earlier (Millward et al. 1989 ). Nevertheless, we recommend that the square root model be used for data such as these, until more data are available and the underlying situation can be clarified. Of the models that we have examined we rule out the linear model due to its lack of fits both practically and theoretically (Table 2 and Fig. 2 ). As shown in Table 3 , estimates from the square root model are more consistent (less dependent on procedure) than the log model. This follows from the fact that the predicted requirements of extreme individuals are more realistic (Table 4) , since the slope of the log model is lower than that of the square root model. It should be kept in mind the statistical procedures here are pragmatic and we fit the data to an equation in order to interpolate to a criterion of nutritional adequacy (zero N balance); we are not attempting to model the underlying biological phenomenon.

Using the median instead of a mean.

We recommend that the median value be used. What is usually defined as requirement is the minimal level of intake that satisfies the requirements of half of the population, and this, by definition, is the median. The mean, although mathematically easier to derive and perhaps use, is very dependent on the precise placement of all the data. We explored several alternatives: the mean, which is dependent on the precise level of each data point; trimmed means, calculated after leaving out the highest and lowest values; and the median, dependent only on the position of the two middle data points (the median is, of course, an extremely trimmed mean with all but these two central points trimmed away). In our data, these estimates gave similar results, except for the log model that accentuates the extreme data. The median requirement ignores the specific levels of those extreme individual requirements which are biologically unrealistically high or low. Justification for discounting these extreme data points follows examination of Figure 1 which shows that those individuals with the extremely high requirements are those that did not achieve a positive balance (and alternatively, those with low estimated requirements who did not fall into an area of negative balance) during the experimental period—these are individuals whose requirement is based on an extrapolation of their data.

Miscellaneous losses.

The most critical element in the estimation of the lysine requirement from the present N-balance data is the level of miscellaneous losses that are used in the equation. Figure 2 shows that the response curves change slowly about the requirement and so using different levels for the miscellaneous losses, to estimate true zero balance, has a major effect on the required intake. We examined two reasonable and previously assumed levels of miscellaneous losses, and it is still a matter of conjecture as to whether a value of 8 rather than 5 mg N · kg^-1 · d^-1 is more appropriate. We recommend that the higher value be accepted, since this was the figure applied in arriving at current recommendations for protein intakes (FAO/WHO/UNU 1985 ) and because true N balance is generally underestimated due to the systematic errors involved in estimating N intake and measuring N output (Fomon and Owen 1962 , Hegsted 1976 , Wallace 1959 ). We do, however, consider that this is an area which needs more careful examination and data gathering, especially with respect to correlating the magnitude of these miscellaneous losses with individual characteristics, such as body mass index.

Individual results.

The individual results that are shown in Table 4 suggest that the experimental design used by Jones et al. (1956) and followed by many other investigators since then needs to be reexamined. As shown in Figure 1 , these estimates of individual requirement are obviously consistent with the data; however, these estimates are inconsistent with our understanding of the biology of N metabolism. Thus, the very high or very low individual requirement estimates reveal problems in the data and the experimental design that produced the data rather than difficulties in the statistical analysis. Indeed, this raises the question as to how representative such data are of the "requirement phenomenon," which we do not address in this paper. Certainly, one benefit of the individual fit method is that it makes this problem explicit, revealing that there are individuals whose data, during the experimental period, are consistently out of line with biological expectations. The one-fit method obscures this problem by fitting all the data to a single curve.

General implications for statistical analysis of N-balance data.

As shown above, estimating nutrient requirements is a very complex procedure. The results of this study show that any statistical analysis of a specific set of N-balance data needs to include a sensitivity analyses—exploration of how the results will differ when alternative procedures and assumptions are made. Such analyses will not only show the confidence with which potential users can use the results, it also can show the limitations of the methodology and where additional data might be needed (e.g., as in the above where it is obvious that better information is needed for miscellaneous losses). Finally, an important point that is often overlooked is that statistical point estimates always need to be accompanied by, and interpreted in light of, the variability of those estimates.

Implications for the lysine requirement in adult women.

The N-balance values of Jones et al. (1956) produce estimates of median requirement for lysine which are in the range of 20–30 mg · kg^-1 · d^-1, depending upon the value of the N adjustment applied to account for unmeasured and miscellaneous losses. Jones et al. (1956) concluded that 0.4–0.5 g of lysine daily is adequate for the establishment of N balance in women. This would be an intake equivalent to about 6.5–8 mg · kg^-1 · d^-1 or approximately one-third to one-quarter the estimate that we derived above.

For a further comparison with our analysis, the minimal requirement for lysine, as estimated using N-balance techniques by Rose et al. (1955) , in six adult men was 8.8 mg · kg^-1 · d^-1. Also, Clark et al. (1960) concluded from N-balance experiments that the mean lysine requirement for men and women was 10 and 9 mg · kg^-1 · d^-1, respectively, but the specific N-balance data from which these values were obtained were not presented in their paper. Hence, it was not possible for us to examine the results of the investigation by Clark et al. (1960) by the approach applied here. Similarly, this limitation also applies to the study of lysine requirements in young college women by Fisher et al. (1969) , who concluded that the lysine requirement might be as low as 50 mg · d^-1 (or <1 mg · kg^-1 · d^-1).

The variation in the requirement among the subjects in the study by Jones et al. (1956) was very high (Table 4 ). Individual requirements (based on square root model with 8 mg of N miscellaneous losses) ranged from a low of 0.1 to a high of 102 with about half of the values being in the range of 20 to 70 mg · kg^-1 · d^-1, for the 8 mg of N miscellaneous loss correction and about 18 to 40 mg · kg^-1 · d^-1 for the 5 mg of N correction. Intuitively, the very low as well as high end of this range would appear to reflect the imprecision of the N-balance technique and limitations in experimental design. We are of this opinion because it is most unlikely, for example, that an individual would require more than 1.2 g of milk protein (assuming 72 mg of lysine per g protein) (FAO/WHO/UNU 1985 ) or about 4.0 g whole wheat flour protein (assuming 24 mg of lysine per g protein) (Sikka et al. 1975 ), per kg body weight per day, to just meet the requirement for lysine and sustain an N equilibrium. Similarly, requirement values as low as 6 mg · kg^-1 · d^-1 or less are most unlikely, when it is appreciated that lysine oxidation continues during the fasting period. Thus, under conditions where subjects were adapted to a low lysine intake the rate of oxidation minimally approximates 6–12 mg · kg^-1 for the 12-h period (A. E. El-Khoury, P. Pereira and V. R. Young, unpublished MIT results). Even if during feeding the lysine oxidation was almost completely abolished, an intake of 6–12 mg of lysine per kg during the 12-h period would be far less than required to achieve the net postprandial protein synthesis or N retention (Price et al. 1994 ) that is needed to maintain body N balance (Young and El-Khoury 1996 ), when protein intakes that meet but do not exceed recommendations (FAO/WHO/UNU 1985 ).

Additionally, two long-term N-balance studies were reported and their results taken to support the relatively low lysine requirement estimates that were derived from the earlier N-balance studies (Millward 1997 , Millward 1998 ). However, in one of these studies (Bolourchi et al. 1968 ), the high dietary energy intakes provided by the experimental diet confound interpretation of the N-balance data, as was pointed earlier (Young 1998 ). In the other study (Edwards et al. 1971 ), the intake of lysine approximated 26 mg · kg^-1 · d^-1, which is close to that which the present analysis suggests as a mean requirement. Clearly, the study by Edwards et al. (1971) fails to test whether far lower intakes of lysine would be adequate.

We (Young et al. 1998 ) suggested that in those developing regions of the world where diets are based predominantly on wheat there is a risk of lysine inadequacy. Further, we propose that such diets would be improved by inclusion of food protein sources rich in lysine, such as legumes or animal proteins, or through amino acid fortification. The desirable additions of each source need only be relatively modest (Pellett and Young 1990 ). Finally, this analysis of the N-balance data of Jones et al. (1956) appears to offer support for our view that the lysine requirement of healthy adults significantly exceeds, to an extent that has significant public health and nutrition planning/policy implications, the current UN upper requirement value for lysine of 12 mg · kg^-1 · d^-1 for healthy adults (FAO/WHO/UNU 1985 ), and that it is more likely to be in the proximity of 30 mg · kg^-1 · d^-1. This is also in line with, although lower than, the lysine mean requirement value suggested by the Toronto group (Duncan et al. 1996 , Zello et al. 1993 ) based on the indicator amino acid oxidation technique (Zello et al. 1995 ).

	FOOTNOTES

 
² Abbreviations used: CI, confidence interval; N, nitrogen.

Manuscript received February 11, 1999. Initial review completed April 3, 1999. Revision accepted July 4, 1999.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

 

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7. Coburn S. P. Application of models to the determination of nutrient requirements: an overview. J. Nutr. 1992;122(3 Suppl):687-689

8. Coburn S. P. Modelling of vitamin B₆ metabolism. Adv. Food. Nutr. Res. 1996;40:107-132[Medline]

9. Daniel C., Wood F. S. Fitting equations to data 1971:5-49 Wiley-Interscience New York Chapters 2 and 3

10. Diggle P. J., Liang K.-Y., Zeger S. L. Analysis of longitudinal data 1994:1-22 Oxford Clarendon Chapter 1

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