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==Of Mice and Males==
Telomeres Tell A Lot


Conventional wisdom, indeed wisdom of any form, indicates that physical activity, a.k.a. regular exercise, is good for you.  In particular, intuition would imply that the risk factors for age-related diseases such as diabetes, cancer, hypertension, obesity and osteoporosis would be reduced if people were engaged in physical activity.  To make a direct connection between ageing and physical activity, consider a paper in the Archives of Internal Medicine (Vol.168, No. 2, January 28, 2008), “The Association Between Physical Activity in Leisure Time and Leukocyte Telomere Length” by Cherkas, et al.


Authors are not responsible for what journalists write about a research articleLacking knowledge of statistics, reporters tend to act like stenographers when they aren't extrapolating far beyond the limits of the researchTake a look at what the lay press had to say about [http://journals.royalsociety.org/content/j151602t103q3h76/?p=8b1ffc09760a4f009a01e070823d6d3e&pi=0 Experimental alteration of litter sex ratios in a mammal] which appeared in the Proceedings of the Royal Society (B).
“Telomeres consist of tandemly repeated DNA sequences that play an important role in the structure and function of chromosomes.”  Leukocyte telomere length (LTL) is a proxy variable for one’s biological age as opposed to one’s chronological ageThat is, the longer one’s telomeres, the younger one actually isConversely, the shorter the telomeres, the more aged.


The Daily Mail:
This study measured the telomeres of 2401 twins who were put into four mutually exclusive categories of physical activity: “Inactive,” “Light,” “Moderate,” and “Heavy” corresponding to “16 minutes, 36 minutes, 102 minutes and 199 minutes” physical activity per week, respectively.  The result after adjusting for “Age, sex, and extraction year” was that the “LTL of the most active subjects (group 4) was an average 200 (SE, 79) nt [nucleotides] longer than that of the inactive subjects (group 1)” producing a p-value of .006.  “This difference suggests that inactive subjects had telomeres the same length as sedentary individuals up to 10 years younger, on average.”  When more complete information was available concerning BMI (biomass index), smoking and SES (socioeconomic status) this reduced the number of subjects to 1531 from the 2401; the LTL difference increased to 213 nt and the p-value increased to .02.  Below are a summary table and Figure 1.


<blockquote>Red meat and salty snacks are said to lead to boys while chocolate is thought to help to produce girls.  Now science suggests the stories may be true: mice with low blood-sugar levels - a good indicator of a sugar-rich diet - produce more female than male offspring. </blockquote>
[[Image:wallis1.png|500px|center]]


The Independent:
   
 
<blockquote>Boy or girl? Battle of the sexes Are you desperate for a daughter or dying for a son? The solution could lie in a mother's diet - before she even conceives.</blockquote>
 
New Scientist:
 
<blockquote>Findings lend credence to traditional beliefs that eating certain foods can influence the sex of offspring.</blockquote>
 
Discover:
 
<blockquote>The Biology of . . . Sex Ratios. Want a boy at all costs? The secret may lie in your glucose levels.</blockquote>
 
FoxNews.com:
 
<blockquote>Can what a mother-to-be eats influence the sex of her unborn baby? Maybe, says new research.</blockquote>
 
The research itself looks at a very important issue in biology: the influence of nutrition on reproductive strategy and the ensuing evolutionary advantage.  To carry out their research, they had 20 female mice in a control group and 20 female mice in the treatment group which was given "a steroid [DEX] that inhibits glucose transport and reduces plasma glucose concentrations."  The original paper does not give a table whereby for each of the 40 mice is recorded the number in the litter, number of males and which arm of the study it was in.  Instead, we have to relay on the given summary data: average litter size for control is 10.45 with a standard error of .60, and the average litter size for the treatment is 9.17 with a standard error of .62.
 
According to the article, "The sex ratio differed significantly between the treatment and control groups (rank-sum test: Z= -2.18, p=0.03), with DEX females giving birth to fewer sons (41.9%) than control females (53.5%)."  With this information, it would appear that the control group produced a total of 10.45 * 20 = 209 mice resulting in 209*.535 = 112 males.  The treatment group is more difficult to determine because two of the 18 "failed to conceive;" thus, if only 18 are relevant, then the treatment group has 9.17 * 18 = 165 mice and 165 * .419 = 69 males.  Using these numbers, a Minitab printout yields a (Fisher exact because of the relatively small samples) p-value of .029 which is close to the "p=.03" mentioned in the article.
 
Test and CI for Two Proportions
 
<table width="41%" height="77" border="1">
  <tr>
    <td width="20%"><div align="center">Sample</div></td>
    <td width="19%"><div align="center">X</div></td>
    <td width="16%"><div align="center">N</div></td>
    <td width="45%"><div align="center">Sample p</div></td>
  </tr>
  <tr>
    <td><div align="center">1</div></td>
    <td><div align="center">112</div></td>
    <td><div align="center">209</div></td>
    <td><div align="center">.0.535885</div></td>
  </tr>
  <tr>
    <td><div align="center">2</div></td>
    <td><div align="center">69</div></td>
    <td><div align="center">165</div></td>
    <td><div align="center">0.418182</div></td>
  </tr>
</table>
 
 
Difference = p (1) - p (2)
 
Estimate for difference:  0.117703
 
95% CI for difference:  (0.0165306, 0.218876)
 
Test for difference = 0 (vs not = 0):  Z = 2.28  P-Value = 0.023
 
Fisher's exact test: P-Value = 0.029


Discussion
Discussion


1. No confidence interval for the difference in proportion of males is given in the article itself.  Does the 95% CI suggest any guarantee for reduction in male mice?  Male humans?
1. The article states, “The results of this study can be extrapolated to other white individuals (men and women) of North European origin.”  Find a biologist or a helpful librarian to determine whether it is suspected that non-whites have different telomere lengths and/or have a different distribution. If so, what does this imply about telomere length and ageing?
 
2. There were about nine times as many women in the study as men. Why might this be a concern?
2. Regarding the treatment arm, the article states : "42%, two-tailed binomial test, p=.04."  Using the summary data, Minitab reports
3. Something important is missing in Figure 1 and its absence serves to magnify the average differenceWhat is it?
 
4. The subjects in the study were twins and therefore, attracted extra lay media attentionSix of the ten authors are affiliated with Kings College, LondonFrom the Kings College website, “Comparing the telomere lengths of twins who were raised together but take different amounts of exercise, reduces the effect of genetic and environmental variation and so provides a more powerful test of the hypothesis.” Obtain the article and reference #21 to determine why twins as subjects as opposed to non-twins are sort of beside the point.
Test and CI for One Proportion
5. There was a “discordant twin-pair analysis” performed “as a further confirmation of the larger analysis.  A paired 2-tailed t test for 67 twin pairs, separated by at least a two category difference is displayed in Figure 2.  What defect does it share with Figure 1? Why is it even more misleading given that a paired t test is being done?  
 
Test of p = .05 vs p not = 0.5
 
<table width="80%" border="1">
<tr>
<td>Sample</td>
<td>X</td>
<td>N</td>
<td>Sample p</td>
<td>95% CI</td>
<td>P-Value</td>
</tr>
<tr>
<td>1</td>
<td>69</td>
<td>165</td>
<td>0.418182</td>
<td>(0.341979,0.497378)</td>
<td>0.043</td>
</tr>
</table>
 
Does this 95% CI suggest any guarantee for reduction in the number of male mice? Male humans?
 
3. Thus far, offspring production has been treated as a Bernoulli processThat is, each offspring is considered to be independentIn other words, no use has been made of the number of female parents (20 in the control and 18 in the treatment arm)Using the summary data given in the article, Minitab obtains for the difference in means of males a somewhat different p-value, .05 rather than the .03 mentioned in the article and thus a wider interval.  
 
Two-Sample T-Test and CI
 
<table width="43%" border="1">
  <tr>
    <td width="17%"><div align="center">Sample</div></td>
    <td width="14%"><div align="center">N</div></td>
    <td width="21%"><div align="center">Mean</div></td>
    <td width="23%"><div align="center">StDev</div></td>
    <td width="25%"><div align="center">SE Mean</div></td>
  </tr>
  <tr>
    <td><div align="center">1</div></td>
    <td><div align="center">20</div></td>
    <td><div align="center">5.59</div></td>
    <td><div align="center">2.68</div></td>
    <td><div align="center">0.60</div></td>
   </tr>
  <tr>
    <td><div align="center">2</div></td>
    <td><div align="center">18</div></td>
    <td><div align="center">3.84</div></td>
    <td><div align="center">2.63</div></td>
    <td><div align="center">0.62</div></td>
   </tr>
</table>
 
Difference = mu (1) - mu (2)
 
Estimate for difference: 1.750
 
95% CI for difference: (-0.000, 3.500)


T-Test of difference = 0 (vs not =): T-Value = 2.03  P-Value = 0.050  DF = 35


Ask a biologist whether or not the Bernoulli assumption is valid.


4.  All of the above is from a frequentist point of view.  What would Baysians add to the discussion and why?


5. As noted, two of the 18 in the treatment arm failed to conceive while all 20 in the control arm did conceiveHow does this affect your view of the results?
6. The article states, “A limitation of this type of study is that physical activity level was self-reported.”  Why might this be a limitation?
7. Assume there is a positive association between LTL and physical activity.  Give an alternative explanation to physical activity causing greater telomere lengthGive another alternative explanation.


Submitted by Paul Alper
Submitted by Paul Alper

Revision as of 21:21, 5 February 2008

Telomeres Tell A Lot

Conventional wisdom, indeed wisdom of any form, indicates that physical activity, a.k.a. regular exercise, is good for you. In particular, intuition would imply that the risk factors for age-related diseases such as diabetes, cancer, hypertension, obesity and osteoporosis would be reduced if people were engaged in physical activity. To make a direct connection between ageing and physical activity, consider a paper in the Archives of Internal Medicine (Vol.168, No. 2, January 28, 2008), “The Association Between Physical Activity in Leisure Time and Leukocyte Telomere Length” by Cherkas, et al.

“Telomeres consist of tandemly repeated DNA sequences that play an important role in the structure and function of chromosomes.” Leukocyte telomere length (LTL) is a proxy variable for one’s biological age as opposed to one’s chronological age. That is, the longer one’s telomeres, the younger one actually is. Conversely, the shorter the telomeres, the more aged.

This study measured the telomeres of 2401 twins who were put into four mutually exclusive categories of physical activity: “Inactive,” “Light,” “Moderate,” and “Heavy” corresponding to “16 minutes, 36 minutes, 102 minutes and 199 minutes” physical activity per week, respectively. The result after adjusting for “Age, sex, and extraction year” was that the “LTL of the most active subjects (group 4) was an average 200 (SE, 79) nt [nucleotides] longer than that of the inactive subjects (group 1)” producing a p-value of .006. “This difference suggests that inactive subjects had telomeres the same length as sedentary individuals up to 10 years younger, on average.” When more complete information was available concerning BMI (biomass index), smoking and SES (socioeconomic status) this reduced the number of subjects to 1531 from the 2401; the LTL difference increased to 213 nt and the p-value increased to .02. Below are a summary table and Figure 1.

Wallis1.png


Discussion

1. The article states, “The results of this study can be extrapolated to other white individuals (men and women) of North European origin.” Find a biologist or a helpful librarian to determine whether it is suspected that non-whites have different telomere lengths and/or have a different distribution. If so, what does this imply about telomere length and ageing? 2. There were about nine times as many women in the study as men. Why might this be a concern? 3. Something important is missing in Figure 1 and its absence serves to magnify the average difference. What is it? 4. The subjects in the study were twins and therefore, attracted extra lay media attention. Six of the ten authors are affiliated with Kings College, London. From the Kings College website, “Comparing the telomere lengths of twins who were raised together but take different amounts of exercise, reduces the effect of genetic and environmental variation and so provides a more powerful test of the hypothesis.” Obtain the article and reference #21 to determine why twins as subjects as opposed to non-twins are sort of beside the point. 5. There was a “discordant twin-pair analysis” performed “as a further confirmation of the larger analysis.” A paired 2-tailed t test for 67 twin pairs, separated by at least a two category difference is displayed in Figure 2. What defect does it share with Figure 1? Why is it even more misleading given that a paired t test is being done?



6. The article states, “A limitation of this type of study is that physical activity level was self-reported.” Why might this be a limitation? 7. Assume there is a positive association between LTL and physical activity. Give an alternative explanation to physical activity causing greater telomere length. Give another alternative explanation.

Submitted by Paul Alper