89 replies to this topic

[color red]

Not at all, even though there is a vast body of litterature explaining why some statistical protocols related to drug acceptance tests are inadequate (eg overreliance on parametric tests, like Student or similar statistics, which discard the possibility of "large outliers" in the underlying distribution), these drug test protocols are relatively reliable. First because, as you mentioned the samples are larger and random. Splitting them into subgroups via a controlled experience plan is part of the statistical theory, it actually improves, not decrease, the reliability of the results (in a nutshell, it incorporates external knowledge, eg placebos are placebos, into the test protocol). Besides, the aim of medical treatment by drugs is to save lives, so there probably is some kind of risk-benefit trade-off at work here.

Outliers are for the quantitative measurements, not a simple measure like allells, or microsattelites. Allowances for the correspondence are usually too broad for any biological random events. Nature of these studies also require the presence or absence of some patterns. Anyway, ask me any questions if you don't understand these, I can explain each in details.

Regarding drug test, you are not surely increasing power by splitting them, as you can clearly see by increasing the degree of freedoms. (I can show you how it works, but please post another thread to discuss)

But there is a very big difference between a controlled experience plan of 10 000 persons, and an uncontrolled surveys on a few hundred samples, split into groups of 10 or 50. The problem is twofold. First, the sampling is probably not random, nor controlled, which means that statistical laws hold less well. Second, the samples are below the minimal limits for basic theorems of probability to hold (ie the various forms of the law of large number, convergence of empirical means to expectations, uniform convergence of frequencies to distributions, or convergence of the underlying residuals to a normal law).

Weak convergence is sufficient, and as I told you, normality assumption does not need to hold because of the discrete nature of nucleotides. Do you think we need an almost sure sense of random variable? no, we don't even need an estimate of the powers.

Random sampling is not that considered important, as it means less in genome studies. Human genome won't mutate in the same generation, and mutation rate is extremely low for Y-chromosomes. That's why we can even "infer" that human is out of africa, because of the constant behaviours across the samples within the same group.

The sample you presented is not very small in itself, but its splitting into very small groups (of less than 100 persons, and sometimes less than 10), sort of prevent any proper statistics to be done.

My impression is that such isolated cases are good for inducing general hypotheses, which is what the papers you quote probably do. But in order for them to become proof, or evidence, larger samples, and statistical tests are needed.

Not necessarily. You assumption is at the moment on the laws of random variables which you can model. Bootstrapping is just enough in most cases.

In all fairness, there are a few theories on induction from small samples (you could search for Vapnik as a starter), but samples are often much larger than a few units, and they are quite complex to design and use (this branch of statistics is in infancy too)

Francois

You are making assumptions again. You seem to assume that I understand little about the theory which might be true, as has been a while I studied last time, but in reality, all these college stuffs are useless, and mostly statisitcs remains arts rather than a complete beautiful mathematics.

That's why scientist call "scientific evidences". But these are usually good enough estimates, that you might not be aware of.

Edited by color red, 23 October 2006 - 06:16 AM.

[fcharton]

Hi Color Red,

I changed the order of your paragraphs so as to adress them in a more logical fashion. Sorry about that...

Regarding drug test, you are not surely increasing power by splitting them, as you can clearly see by increasing the degree of freedoms. (I can show you how it works, but please post another thread to discuss)

Actually, I think we would agree on this. What I was trying to say is that experience plans are a way to "make the best" out of a certain sample size. Of course, a larger sample is always better than a smaller one, but given a fixed sample size, experience plans provide better test power.

Outliers are for the quantitative measurements, not a simple measure like allells, or microsattelites. Allowances for the correspondence are usually too broad for any biological random events. Nature of these studies also require the presence or absence of some patterns. Anyway, ask me any questions if you don't understand these, I can explain each in details.

Weak convergence is sufficient, and as I told you, normality assumption does not need to hold because of the discrete nature of nucleotides. Do you think we need an almost sure sense of random variable? no, we don't even need an estimate of the powers.

Random sampling is not that considered important, as it means less in genome studies. Human genome won't mutate in the same generation, and mutation rate is extremely low for Y-chromosomes. That's why we can even "infer" that human is out of africa, because of the constant behaviours across the samples within the same group.

My impression is that random sampling and convergence serve two purposes. First, they even out the possible variance in the data measured. This seems not to be the problem here. But they also act as a guarantee against possible sampling errors. For instance, the above survey tested one tibetan, and a score of japanese. But how do we know they are "typical" tibetan and japanese, once we want to trace back their lineage over tens or hundreds of generations? It seems to me that the only way out of this question is the sample size.

These sampling outliers will have an even larger effect, I think, it the data you observe is stable over time (and you tell me it is). Also, I have the impression that these studies do much more than just testing one hypothesis : they build whole phylogenetic maps, a very complex modelling process, do you think that such sampling errors (even a small number of them) would have no effect?

To me, the out of africa theory is different, because it is supported by a number of studies on large samples.

Not necessarily. You assumption is at the moment on the laws of random variables which you can model. Bootstrapping is just enough in most cases.

You are making assumptions again. You seem to assume that I understand little about the theory which might be true, as has been a while I studied last time, but in reality, all these college stuffs are useless, and mostly statisitcs remains arts rather than a complete beautiful mathematics.

Well, bootstrapping works because the data is random, else it would reproduce the original biases in the sample... Besides, you can't really bootstrap a very small sample (well, you always can, I suppose, but I don't think it can provide any meaningful result).

I must say I disagree with your point about statistics being an art. It is often used informally, because the underlying theorems which make it work are deep and not well understood, but this informal approach only works when the samples are large enough for the "nice theorems" to set in (and in fact, these theorems do explain why statistics can be seen as an art, ie why informal methods often work, this is the gist of the strong law of large numbers). Which boils down to my original point, sample sizes... can you really infer something on groups of 10 or 50 persons, which are taken as representative of a whole population?

Francois

Edited by fcharton, 23 October 2006 - 06:57 AM.

[color red]

Hi Color Red,

I changed the order of your paragraphs so as to adress them in a more logical fashion. Sorry about that...

That's not a problem. Your response has been quiet fast, and I couldn't honestly keep up with your speed, since I have some other things to do. The structure of my reply could be broken down as you wish.

Actually, I think we would agree on this. What I was trying to say is that experience plans are a way to "make the best" out of a certain sample size. Of course, a larger sample is always better than a smaller one, but given a fixed sample size, experience plans provide better test power.

It is of course possible to estimate the power of sample, but experimentalists aren't supposed to increase the power more than they needed it. Surely, there must be a well-planned experimental plan, but that's not as much need as in the case of high variability population. As I will explain below, there will be tiny within population-variability, and even negligible experimental biases in Y-chromosome results, which aren't the case with other studies.

My impression is that random sampling and convergence serve two purposes. First, they even out the possible variance in the data measured. This seems not to be the problem here. But they also act as a guarantee against possible sampling errors. For instance, the above survey tested one tibetan, and a score of japanese. But how do we know they are "typical" tibetan and japanese, once we want to trace back their lineage over tens or hundreds of generations? It seems to me that the only way out of this question is the sample size.

Well, let me take a more didatic approach in giving you the clear problem statement. Until you clearly understands the problem, our discourse never meets on the same grounds. Take the above article for example. We have about 68 for European, 243 for Asian, and 72 for African for each. The sampling number is comparative low where the total sample number usually varies around 1000.

Natural biological assumption is:

(1) Genes within groups will be homogeneous (e.g., Y-chromosome is not disease linked, age independent, only male population allowed)
(2) Mutation rate is extremely low and negligible (Y does not recombine)
(3) Each of our sample has 58 million base pairs (sample points) or less.

For each sample, we have extensive univariate systems. A(1) will rule out the concerns of "typical tibetans". A(2) will eliminate the concerns for the generations.

These sampling outliers will have an even larger effect, I think, it the data you observe is stable over time (and you tell me it is). Also, I have the impression that these studies do much more than just testing one hypothesis : they build whole phylogenetic maps, a very complex modelling process, do you think that such sampling errors (even a small number of them) would have no effect?

To me, the out of africa theory is different, because it is supported by a number of studies on large samples.

See Assumption (2) above.

Phylogeny is an independent science, and more of computational mathematics than statistics. It shares the underlying framework with statistics, but the procedures are much different. Modelling schemes are remarkably simple for all the articles I cited in this thread. (Complex modelling are used for the ab initio experiments where you try to fit the models based on limited information and assumptions).

Well, bootstrapping works because the data is random, else it would reproduce the original biases in the sample... Besides, you can't really bootstrap a very small sample (well, you always can, I suppose, but I don't think it can provide any meaningful result).

A(3) mentions that we have say the replication of at least 1 million bases. Experimental biases are usually very low when we tests the correspondence of the low mutation rate sequences. Bootstrapping tests are used for the quality checks and to ensure that samples are selected radomly. For your information, some experimentalists use Bayesian arguements for variance reduction by using the simulation scheme, but in my opinion, it's only for the ab initio studies, where you know little about the true responses.

I must say I disagree with your point about statistics being an art. It is often used informally, because the underlying theorems which make it work are deep and not well understood, but this informal approach only works when the samples are large enough for the "nice theorems" to set in (and in fact, these theorems do explain why statistics can be seen as an art, ie why informal methods often work, this is the gist of the strong law of large numbers). Which boils down to my original point, sample sizes... can you really infer something on groups of 10 or 50 persons, which are taken as representative of a whole population?

Most usual genetic studies have the total population size of 1000, and these studies devote more shares of the pie to, say, japanese, korean, mongolian, indian, lebanese, etc. Your point of 10-50 persons are least happening in genetic experiments.

LLN is useful for the mathematical modelling, but I see little applications, and i don't think you've discussed enough how that applies to the sampling issues.

Edited by color red, 23 October 2006 - 08:50 AM.

[fcharton]

Thanks for your patience, here is what I understand (trying to summarise in case other neophytes, like me, are interested in the subject).

We are looking at the sequence of genes, which are present on the Y chromosome of men. The idea is that one’s version of this chromosome is inherited from one’s father, from which it is a “perfect copy”, because these genes are copied at birth, and very rarely change over time. As such, all male descendents of the same ancestors should have the same Y chromosome, unless a mutation of the gene has occurred, which is very unlikely over short periods of time.

As such, when looking at the genetic patrimony of two individual we can, by focusing on the differences between their Y chromosomes, get an idea of the closeness between them (how far back is their common ancestor).

Better still, and I think this is what you call phylogeny, by looking at a specific differences (ie past mutations), you can draw some kind of “family tree” of groups of people, by classifying them according to the presence in their patrimony of certain specific differences (mutations). I believe this is what is called a “marker”. The idea behind phylogeny is that mutations are so rare, and we have so many genes, that the possibility of the same “marker” happening twice in an unrelated manner is extremely low.

The only aspect which is more difficult is to be able to date these mutations, as it implies the estimation of a very low probability, and slight changes in the estimate can produce big changes in the derived chronology.

So, what is being done in this survey is to test 841 males, of various regions for a specific marker, and see where the marker is more or less prevalent. Right? And the results are as follows.

“In this article, only three asian group (japanese, tibetan, jew), african, and a few European have a genetic marker YAP+ on the non-recombining portion of Y-chromosomes. Tibetan (Central Asian): 1 out of 1 sample Japanese: 4 out of 13 samples Chinese: 0 out of 23 samples Laotian: 0 of 7 samples Cambodian: 0 out of 3 samples South East Asians: 0 out of 16 samples South Asians: 0 out of 152 samples West Asians: Jews: 4 out of 18 samples Lebanese: 0 out of 2 samples Syrian: 0 out of 6 samples Melanesian: 0 out of 2 samples African: 37 out of 72 samples European: 3 out of 68 samples”

A short observation is passing, the results you quote here correspond to a total sample of 383 persons… What happened to the 458 others? (more than half of the sample)

Now, the first thing I’d like to observe is that if the populations were as homogeneous as you seem to say, then the marker would either be present or absent in all a population (except probably in the “original source”) the fact that you can measure something like 4 out of 13 on the Japanese, or 3 out of 68 for Europeans, shows that inside each of these populations, there is some diversity, ie people with and people without the marker.

This creates my first problem: the conclusion says that only three asian groups have the marker
1 tibetan out of 1
4 japanese out of 13
4 Western Asian Jews out of 18

But note that these proportions are very low, on such samples it is impossible to estimate precisely the proportion of this marker (is it really 100% of the Tibetans? Probably not, or just 30% of the Japanese? We don’t know, but it seems unlikely, we just don’t have enough data).

Now is it so certain that the gene is absent from Laotian (0 out of 7), or Cambodians (0 out of 3), it could be because the marker is absent, or because we were unlucky, and just didn't measure the "right person"

Now look at the Europeans, we see 3 out of 68 having the marker, this is an even lower probability, but the result is "the marker is present".

Now note that we have 23 chinese in the sample, none of which have the marker. What if was had asked 68?I think there could quite be a low prevalence of this marker among chinese, in a proportion equivalent to Europeans, or maybe even larger, but that, as the sample is small, it failed to appear. Yet the conclusion will be, the marker is absent in China.

This is where the law of large numbers sets in, it gives probabilities that this is likely or unlikely to happen, but it needs larger samples.

Just as an example, if I aggregate a bit more the information:
Suppose I try to “recut” the sample into Africans, Europeans, Northern Asians and Southern Asians, I get
Africans 37/72
Europeans 3/68
Northern and western Asians (Chinese, Japanese, Tibetans, West Asians) 9/65
South+SouthEast Asians 0/178

I get observations which are slightly less probant. Note though that I didn’t doctor the data, I tried to find groups which are geographically close.

This, in my opinion, is one reason why sampling is important, especially when dealing with relatively rare events (such as the prevalence of this marker), and this is where the law of large number (weak, strong, or uniform) applies.


My second concern is linked to the methodology itself. If I were to take the test, I'd count as French, so far up in my family tree I look, we are all French, and besides, I look very French. The problem is that one of my ancient male ancestors could well not be French, in which case I could have the "wrong" Y marker. But the test would detect this, you might say. Or would it? Suppose only four French were tested, the test might also conclude that this marker is present to some proportion in the French population. My problem is that you cannot use the measured quantity as a way to detect errors in the data. This is strictly equivalent to the outliers one can observe in empirical datasets, which can result from measurement errors, or improbable events. Again, the only solution is to dilute them by increasing sample size.

Finally, a problem can happen if the original sample is biased (ie if the 13 japanese, or the 23 chinese, had some particular characteristic which made the result wrong, like them being less, or more, related (family wise) than they should in a pure random setting. The problem here is with the constitution of the sample. Ask any pollster about it, he'll probably tell you that achieving purely random samples is a daunting tasks, because biases tend to creep in many unexpected fashions, especially when the sample is small. Again, the only solution to this problem is having larger samples.

Now, don't get me wrong, I am not saying that this is not serious, or the researchers don't know what they do. I would even agree that 841 persons is not a bad sample (I've seen worse, believe me!). But I think my original problem remains. The results given here are calculated over 350 persons only, and cut into too many small parts (ie samples of 10, 20, 30…) to make a precise analysis possible.

Francois

Edited by fcharton, 23 October 2006 - 04:57 PM.

[color red]

I would like to first comment that there is one thing that you keep repetitively bringing up the same point, which I already eliminated. In this reply, I will highlight my points with bold font so that you can perhaps see what I was trying to say.

(*) This study has a roughly three major groups: Asian, African, European. Rest of the sample population has American, Oceanian, etc. All the minor breakdowns are noted for peer review which has nothing to do with what paper is trying to test.
(*) Other studies I cited are more detail focused. Say only on japanese, and chinese. therefore, do not suffer the similar problems

Thanks for your patience, here is what I understand (trying to summarise in case other neophytes, like me, are interested in the subject).

Well, I appreciate that you recognize the importance of explaining words in simple words.

We are looking at the sequence of genes, which are present on the Y chromosome of men. The idea is that one’s version of this chromosome is inherited from one’s father, from which it is a “perfect copy”, because these genes are copied at birth, and very rarely change over time. As such, all male descendents of the same ancestors should have the same Y chromosome, unless a mutation of the gene has occurred, which is very unlikely over short periods of time.

As such, when looking at the genetic patrimony of two individual we can, by focusing on the differences between their Y chromosomes, get an idea of the closeness between them (how far back is their common ancestor).

ok.

Better still, and I think this is what you call phylogeny, by looking at a specific differences (ie past mutations), you can draw some kind of “family tree” of groups of people, by classifying them according to the presence in their patrimony of certain specific differences (mutations). I believe this is what is called a “marker”. The idea behind phylogeny is that mutations are so rare, and we have so many genes, that the possibility of the same “marker” happening twice in an unrelated manner is extremely low.

I don't know how you get this "marker" idea. But, low variability idea seems ok. You should still discard using phylogeny as it's not used in the study. I'm confused because later, you seem to be using the correct notion of marker.

The only aspect which is more difficult is to be able to date these mutations, as it implies the estimation of a very low probability, and slight changes in the estimate can produce big changes in the derived chronology.

Not following you. What estimate are you talking about? Again, you are going even farther to say that mere assumptions must be an integral part of phylogeny. But we already ruled out the possibility of using phylogeny, didn't we?

A short observation is passing, the results you quote here correspond to a total sample of 383 persons… What happened to the 458 others? (more than half of the sample)

Now, the first thing I’d like to observe is that if the populations were as homogeneous as you seem to say, then the marker would either be present or absent in all a population (except probably in the “original source”) the fact that you can measure something like 4 out of 13 on the Japanese, or 3 out of 68 for Europeans, shows that inside each of these populations, there is some diversity, ie people with and people without the marker.

A seemingly correct observation of facts. But if you are interested in diversity research, this should not be a study you focus on. Take korean Y study I posted, if you like to discuss farther.

This is where the law of large numbers sets in, it gives probabilities that this is likely or unlikely to happen, but it needs larger samples.

Just as an example, if I aggregate a bit more the information:
Suppose I try to “recut” the sample into Africans, Europeans, Northern Asians and Southern Asians, I get
Africans 37/72
Europeans 3/68
Northern and western Asians (Chinese, Japanese, Tibetans, West Asians) 9/65
South+SouthEast Asians 0/178

Again. you are following the wrong assumption on the study, although the division is probably more appropriate than the original study.

I get observations which are slightly less probant. Note though that I didn’t doctor the data, I tried to find groups which are geographically close.

This, in my opinion, is one reason why sampling is important, especially when dealing with relatively rare events (such as the prevalence of this marker), and this is where the law of large number (weak, strong, or uniform) applies.
My second concern is linked to the methodology itself. If I were to take the test, I'd count as French, so far up in my family tree I look, we are all French, and besides, I look very French. The problem is that one of my ancient male ancestors could well not be French, in which case I could have the "wrong" Y marker. But the test would detect this, you might say. Or would it? Suppose only four French were tested, the test might also conclude that this marker is present to some proportion in the French population. My problem is that you cannot use the measured quantity as a way to detect errors in the data. This is strictly equivalent to the outliers one can observe in empirical datasets, which can result from measurement errors, or improbable events. Again, the only solution is to dilute them by increasing sample size.

I can see how you make use of LLN. Interesting as it may be, you made several wrong description. Phenotype (eg, looks) and genotype (e.g., genes) are two different things. In Y-chromosome study, there is only a genotype. But I honestly think that this is a trivial use of LLN, as, in most studies, we do have sufficient number of samples, and idea of outliers sounds rather artificial.

Finally, a problem can happen if the original sample is biased (ie if the 13 japanese, or the 23 chinese, had some particular characteristic which made the result wrong, like them being less, or more, related (family wise) than they should in a pure random setting. The problem here is with the constitution of the sample. Ask any pollster about it, he'll probably tell you that achieving purely random samples is a daunting tasks, because biases tend to creep in many unexpected fashions, especially when the sample is small. Again, the only solution to this problem is having larger samples.

Study objective is not to conclude about the absence of YAP+ in chinese, that part of work on individual population is reserved for another research which I cited in the first page of this thread.

In summary, this article is not my liking at all. That's why I cited only in response to herousabi's request. I justified the study's perspective, and general philosophy of the researches, but there seems to be better ways to do it. I pointed out that their methods are sufficient for their study and objective, as you rather carelessly criticizes the study.

[color red]

Do you have any nice graphs or drawing that explains it? ( pictures are worth thousand words.)

Most interesting aspect of the sample space is that 37 out of 72 africans had this marker. Could you break down further as to what part of Africa the samples came from?

Because, most pop.gen. think that only small part of africans actually made outof africa to populate the globe. I want to make sure that the sample in question came from the same set of africans.

I don't have a picture for this article. This article is copyrighted, so I can use only author's peer review comments, where the figure comes from. I don't think they divided african into pieces. Their research methods are lumping all asian together, and likewise on other populations.

Anyway, I thought this is just enough to illustrate the general view of the global distributions of YAP+.

Edited by color red, 23 October 2006 - 08:53 PM.

[color red]

With the amount of information provided, I am not convinced. I will hold my original opinion.

End of discussion.

Not quiet sure what you mean though. I posted the article just for an extra reference requested by you.

As long as I have read repository of your previous posts, I do not see much disagreements though. I guess you are seeking korean genome's uniqueness, and that point can be granted with the existing references.

Korean Y-haplogroup is least studied amongst east asian populations. It is quiet easy to note the general distribution of the japanese and chinese, because of the huge sample sizes, but that luxury was not given so far to korean.

[color red]

Last chance, If you would provide sources for that copy righted article, I will look it up.

either by web link or name the journal.

Well, I thought you ended the conversation. anyway, here is a link to an article, which I already gave when I first cited for your little request. I still don't understand why you asked me this link though.

For your information, if you want to search journal, you only need to go to NCBI web site, and just search the relevant information. This is a common sense to any geneticists, so you better be familiar now.

Origin of YAP+ lineages of the human Y-chromosome
Am J Phys Anthropol. 2000 Jun;112(2):149-58. Related Articles, Links Click here to read Origin of YAP+ lineages of the human Y-chromosome. Bravi CM, Bailliet G, Martinez-Marignac VL, Bianchi NO. Multidisciplinary Institute of Cell Biology (IMBICE), 1900 La Plata, Argentina.

http://www3.intersci...n...=1&SRETRY=0