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The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 60:35-38 (2005)
© 2005 The Gerontological Society of America

A Note on Age-Related Biomarkers

Robert A. Weale

Institute of Gerontology, King's College London (University of London), and Eye Department, University College London Hospital, United Kingdom.

Address correspondence to Prof. Robert A. Weale, Institute of Gerontology, King's College London (University of London), Waterloo Bridge Wing, Waterloo Rd., London SE1 9NN. E-mail: robert.weale{at}kcl.ac.uk


   Abstract
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 Abstract
Method
 Results
 Discussion
 References
 
Forty-eight randomly selected age-related human biological functions were analyzed in order to establish whether or not their (linear) regressions were modified by age-related standard errors. Possible reasons for this are advanced. Statistically significant multiple regressions were obtained in 25%, and 21% of the functions yielded statistically significant changes in the correlations between data and age when partial correlation coefficients were calculated. The conclusion is that age-related data need to be subjected to the above tests in order to minimize confounding factors.

AGE-RELATED biological functions are often called biomarkers. In many instances, they vary linearly with age, either positively or negatively, so that they can be represented with linear regressions. The latter frequently accompany plots of age-related average values together with the appropriate variances or standard errors (SEs). Computer programs designed for the easy handling of the data often also provide values for the correlation coefficient and its square value. The type of biomarker considered here needs to be distinguished from another held to be typical of a condition such as Alzheimer's disease (1) or Huntington's disease (2) on the one hand, and defining characteristics of use for example in toxicology (3,4) on the other.

Little attention seems to have been paid to the possibility that the age-related type may be affected by a special confounding factor, namely a systematic age-related variation in the SE itself. If that were found to be the case, the statistical significance of constants derived from observations might be open to debate. For example, an age-related variation of noise may distort the data. It is almost self evident when SE increases with age, but the process is somewhat harder to illustrate when the slope is negative. Let us imagine that biological functions are maintained by the action of several hypothetical repair mechanisms (5). These will have noise associated with them, and, as they progressively lose their function, their noise contribution may vanish with them.

With these possibilities in mind, I felt it would be instructive to discover whether the above speculation can be validated. Not all data on biomarkers are published with SEs, but a search revealed 48 either with SEs, or else the necessary information to enable one to calculate them for as many age groups as possible. What may apply to biomarkers may also hold for other potentially time-dependent data such as those describing risk. The inquiry would not, therefore, appear to be just academic.


   METHOD
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 Method
Results
 Discussion
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Data on biomarkers were obtained by scanning journals and searching through electronically available information in other peer-reviewed publications and a sizeable collection of relevant reprints. The choice was random in the sense that the only criterion of selection was the existence of data with SEs or with the possibility of SEs being determined. The fact that numerous studies failed to show the sought-after influence of SEs on the statistical significance of conclusions drawn from the data themselves should serve as an assurance that no conscious bias for or against the discovery of the effect was present. The data selected had to be objective; however, a handful of subjective (sensory) data were selected in order to see whether they, too, might be subject to the above-mentioned confounding factor.

Age groups for each set of averages and SEs increased by no more than 10 years. Frequently, the gap was smaller, and in some data sets it was irregular. This did not invalidate the application of the LINEST program of EXCEL.

The question had also to be faced whether small ratios of mean/SE (MSE) could affect the results. For example, while a mean value might be positive, the SE could exceed it, whence part of the distribution describing the variation of a measurement might extend into the negative space even though no corresponding measurement may be physically possible. In order to assess this, the ratio MSE was calculated for all data. They were grouped accordingly as the ratios lay between 0 and <1, 1, and <2, and so forth, and counted in each group.

It is evident that, if taking the age-related variation of SEs into consideration may modify the significance level of the slope of a regression, the correlation coefficient between the function and age may also be affected. This matters, for example, because batteries of tests were constructed (6–8) in order to deduce a generalized biological decline index from the correlations. The results of calculating partial correlation coefficients highlights possible pitfalls of such procedures.


   RESULTS
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 Method
 Results
Discussion
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Figure 1 shows an example of a correlation between data and their SEs, the raison d'être of this study. Table 1 lists six sets of calculations (cf. top line). Asterisks (*, **, ***) in the first column indicate linked sets of data; it can be shown that this interdependence does not affect the conclusions drawn from this study. The first numerical column indicates the levels of the significance of the slopes of function versus age, the second the corresponding data for variance versus age. The two differ in that the limiting value for the functions is the customary 5%, whereas a more tolerant 10% was adopted for the SEs. Column three contains the significance values for the F values assessing the ratios of the variance of the variable of the multiple regressions and that of the independent variable (i.e., age). F-values were obtained for all sets of data, that is, whether either or both of the slopes differed significantly from zero or not. Column four lists the significance levels (≤0.05) for the multiple regressions. Finally, the last two columns in Table 1 contain significance values for the correlation coefficients r (≤0.05) with age for the functions and variances, respectively. The signs of the correlations with age are indicated after each value, and also double for the values in numerical columns one and two. An upward arrow in the last but one column indicates that, resulting from calculating partial correlations, a nonsignificant value of r becomes significant, and vice versa. Note that 21% of variances correlated significantly with age. Figure 2 shows the counts for values of MSE, which peak at ~3. The functions with at least two values <3 were marked MSE in Table 1. The significance, if any, of the relation between the proportion of MSE values and F and m(1)m(2), respectively, was tested on the assumption that MSE and the other two variables were not independent (43). [Note: References (9–42) appear in Table 1.]



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  		Figure 1. An example of the correlation between function (abscissa) and standard error (ordinate) (16)

 

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  		Table 1. Results of the LINEST Analysis.

 


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  		Figure 2. Numbers of given ratios of mean/SE (standard error) to indicate that low values of the ratios are very frequent, which may contribute to the observed effects

 
A study on tongue pressure (44) showed an age-related variation for men but not for women; however, when the above procedure was applied to the results, the data for women also became statistically significant. Furthermore, although measurements on the accommodation of the eye (18) are objective, they contain a subjective element in that the person accommodating has the will to focus on an optical target. These examples serve to show that the confounding effect is not linked only to purely objective measurements.

Finally, determinations were made of the probabilities of occurrence of the frequencies of significant F-values, of multiple regressions, and of changes in the significance levels of the correlation coefficients between function and age after calculations of partial correlation coefficients. They are summarized in Table 2.


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  		Table 2. Significance Levels of Classes in Table 1.

 

   DISCUSSION
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 Method
 Results
 Discussion
References
 
The notion that the SE of age-related human biological functions may affect the significance level of data appears to be vindicated: 25% of the studies in Table 1 justify the determination of a multiple regression involving the SE, and the correlation coefficients between data and age of another 21% of the functions show a change in significance level when the age variation of the SE is taken into consideration.

In regard to the influence of MSE, whereas the test ratio for F (0.067) is teetering on a level of significance of 0.05 (one result could make a difference), the result for the multiple regressions (0.8) appears to be unambiguous: MSE plays no role in their formation. More functions could have been included in this analysis, the guideline for choosing the present ones being the existence of an age-relation of the function and the possibility of determining SEs for each datum point. It can, however, be shown that, for the 12 statistically significant m1m2 values to rise from a significance level of 0.0024 to one of 0.05, more than 60 new functions would have to be added without one of them showing a statistically significant value in the column headed m(1)m(2) in Table 1.

The fact that more than 20% of the correlation coefficients change their significance levels in either direction over the threshold of 5% may play a role in assessments of combinations of correlation coefficients (cf. 7, 8, 28). Thus, the analysis of 48 studies of human biomarkers has shown that 25% of the appropriate linear regressions are changed when the variation with age of the SEs is considered. While it does not seem possible to offer more than the hypothesis mentioned in the introductory paragraph to explain this effect, it would seem that an interpretation of age-related (or time-related) data may benefit from the type of analysis outlined above. This view is supported when the correlation factors between biological function and age are subjected to calculations of partial correlation coefficients.

It would seem to follow that data showing a systematic age-related variation of SEs ought to be subjected to the LINEST program of the EXCEL system or similar programs. It amounts to little more than the determination of a multiple regression with two components, which permits a before-and-after comparison of the calculated constants.


   Acknowledgments
 
This study was supported from the author's private resources.


   Footnotes
 
Decision Editor: James R. Smith, PhD

Received September 24, 2004

Accepted September 28, 2004


   References
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 Abstract
 Method
 Results
 Discussion
 References
 

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