You are currently browsing the tag archive for the ‘multiple testing’ tag.
When I was a teenager I broke all the rules on Friday night. After dinner I would watch Louis Rukeyser’s Wall Street Week at 8:30pm, and I would be in bed an hour later. On new year’s eve, he had a special “year-end review”, during which he hosted “financial experts” who would opine on the stock market and make predictions for the coming year.
What I learned from Louis Rukeyser was:
1. Never trust men in suits (or tuxedos).
2. It’s easier to perpetrate the 1024 scam than one might think!
Here are the experts in 1999 all predicting increases for the stock market in 2000:
As it turned out, the NASDAQ peaked on March 10, 2000, and within a week and a half had dropped 10%. By the end of the year the dot-com bubble had completely burst and a few years later the market had lost almost 80% of its value.
Predictions on the last day of the 20th century represented a spectacular failure for the “pundits”, but by then I had already witnessed many failures on the show. I’d also noted that almost all the invited “experts” were men. Of course correlation does not imply causation, but I remember having a hard time dispelling the notion that the guests were wrong because they were men. I never wanted to be sexist, but Louis Rukeyser made it very difficult for me!
Gender issues aside, the main lesson I learned from Louis Rukeyser’s show is that it’s easy to perpetrate the 1024 scam. The scam goes something like this: a scammer sends out 1024 emails to individuals that are unlikely to know each other, with each email making a prediction about the performance of the stock market in the coming week. For half the people (512), she predicts the stock market will go up, and for the other half, that it will go down. The next week, she has obviously sent a correct prediction of the market to half the people (this assumes the market is never unchanged after a week). She ignores the 512 people who have received an incorrect prediction, dividing those who received the correct prediction into two halves (256 each). Again, she predicts the performance of the market in the coming week, sending 256 individuals a prediction that the market will go up, and the other 256 a prediction that it will go down. She continues this divide-and-conquer for 10 weeks, at which time there is one individual that has received correct predictions about the movement of the stock market for 2.5 months! This person may believe that the scammer has the ability to predict the market; after all, which looks like a very significant p-value. This is when the scammer asks for a “large investment”. Of course what is missing is knowledge of the other prediction emails sent out, or in other words the multiple testing problem.
The Wall Street Week guest panels essentially provided a perfect setting in which to perpetrate this scam. “Experts” that would err would be unlikely to be invited back. Whereas regular winners would be back for another chance at guessing. This is a situation very similar to the mutual fund management market, where managers are sacked when they have a bad year, only to have large firms with hundreds of funds on the books highlight funds that have performed well for 10 years in a row in their annual glossy brochures. But that is not the subject matter of this blog post. Rather, it’s the blog itself.
I wrote and posted my first blog entry (Genesis of *Seq) exactly a year ago. I began writing it for two reasons. First, I thought it could be a convenient and useful forum for discussion of technical developments in computational biology. I was motivated partly by the seqanswers website, which allows users to share information and experience in dealing with high-throughput sequence data. But I was also inspired by the What’s New Blog that has created numerous bridges in the mathematics community via highly technical yet accessible posts that have democratized mathematics. Second, I had noticed an extraordinary abuse of multiple testing in computational biology, and I was desperate for a forum where I could bring the issue to peoples attention. My initial frustration with outlandish claims in papers based on weak statistics had also grown over time to encompass a general concern for lack of rigor in computational biology papers. None of us are perfect but there is a wide gap between perfect and wrong. Computational biology is a field that is now an amalgamation of many subjects and I hoped that a blog would be able to reach the different silos more effectively than publications.
And thus this blog was born on August 19th 2013. I started without a preconception of how it would turn out over time, and I’m happy to say I’ve been surprised by its impact, most notably on myself. I’ve learned an enormous amount from reader feedback, in part via comments on individual posts, but also from private emails to me and in personal conversations. For this (selfish) reason alone, I will keep blogging. I have also been asked by many of you to keep posting, and I’m listening. When I have nothing left to say, I promise I will quit. But for now I have a backlog of posts, and after a break this summer, I am ready to return to the keyboard. Besides, since starting to blog I still haven’t been to Las Vegas.
In reading the news yesterday I came across multiple reports claiming that even casually smoking marijuana can change your brain. I usually don’t pay much attention to such articles; I’ve never smoked a joint in my life. In fact, I’ve never even smoked a cigarette. So even though as a scientist I’ve been interested in cannabis from the molecular biology point of view, and as a citizen from a legal point of view, the issues have not been personal. However reading a USA Today article about the paper, I noticed that the principal investigator Hans Breiter was claiming to be a psychiatrist and mathematician. That is an unusual combination so I decided to take a closer look. I immediately found out the claim was a lie. In fact, the totality of math credentials of Hans Breiter consist of some logic/philosophy courses during a year abroad at St. Andrews while he was a pre-med student at Northwestern. Even being an undergraduate major in mathematics does not make one a mathematician, just as being an undergraduate major in biology does not makes one a doctor. Thus, with his outlandish claim, Hans Breiter had succeeded in personally offending me! So, I decided to take a look at his paper underlying the multiple news reports:
- J.M. Gilman et al., Cannabis Use Is Quantitatively Associated with Nucleus Accumbens and Amygdala Abnormalities in Young Adult Recreational Users, Journal of Neuroscience (Neurobiology of Disease section), 34 (2014), 5529–5538.
This is quite possibly the worst paper I’ve read all year (as some of my previous blog posts show I am saying something with this statement). Here is a breakdown of some of the issues with the paper:
1. Study design
First of all, the study has a very small sample size, with only 20 “cases” (marijuana users), a fact that is important to keep in mind in what follows. The title uses the term “recreational users” to describe them, and in the press release accompanying the article Breiter says that “Some of these people only used marijuana to get high once or twice a week. People think a little recreational use shouldn’t cause a problem, if someone is doing OK with work or school. Our data directly says this is not the case.” In fact, the majority of users in the study were smoking more than 10 joints per week. There is even a person in the study smoking more than 30 joints per week (as disclosed above, I’m not an expert on this stuff but if 30 joints per week is “recreation” then it seems to me that person is having a lot of fun). More importantly, Breiter’s statement in the press release is a lie. There is no evidence in the paper whatsoever, not even a tiny shred, that the users who were getting high once or twice a week were having any problems. There are also other issues with the study design. For example, the paper claims the users are not “abusing” other drugs, but it is quite possible that they are getting high on cocaine, heroin, or ??? as well, an issue that could quite possibly affect the study. The experiment consisted of an MRI scan of each user/control, but only a single scan was done. Given the variability in MRI scans this also seems problematic.
2. Multiple testing
The study looked at three aspects of brain morphometry in the study participants: gray matter density, volume and shape. Each of these morphometric analyses constituted multiple tests. In the case of gray matter density, estimates were based on small clusters of voxels, resulting in 123 tests (association of each voxel cluster with marijuana use). Volumes were estimated for four regions: left and right nucleus accumbens and amygdala. Shape was also tested in the same four regions. What the authors should have done is to correct the p-values computed for each of these tests by accounting for the total number of tests performed. Instead, (Bonferroni) corrections were performed separately for each type of analysis. For example, in the volume analysis p-values were required to be less than 0.0125 = 0.05/4. In other words, the extent of testing was not properly accounted for. Even so, many of the results were not significant. For example, the volume analysis showed no significant association for any of the four tested regions. The best case was the left nucleus accumbens (Figure 1C) with a corrected p-value of 0.015 which is over the authors’ own stated required threshold of 0.0125 (see caption). They use the language “The association with drug use, after correcting for 4 comparisons, was determined to be a trend toward significance” to describe this non-effect. It is worth noting that the removal of the outlier at a volume of over would almost certainly flatten the line altogether and remove even the slight effect. It would have been nice to test this hypothesis but the authors did not release any of their data.
In the Fox News article about the paper, Breiter is quoted saying ““For the NAC [nucleus accumbens], all three measures were abnormal, and they were abnormal in a dose-dependent way, meaning the changes were greater with the amount of marijuana used,” Breiter said. “The amygdala had abnormalities for shape and density, and only volume correlated with use. But if you looked at all three types of measures, it showed the relationships between them were quite abnormal in the marijuana users, compared to the normal controls.” The result above shows this to be a lie. Volume did not significantly correlate with use.
This is all very bad, but things get uglier the more one looks at the paper. In the tables reporting the p-values, the authors do something I have never seen before in a published paper. They report the uncorrected p-values, indicating those that are significant (prior to correction) in boldface, and then put an asterisk next to those that are significant after their (incomplete) correction. I realize my own use of boldface is controversial… but what they are doing is truly insane. The fact that they put an asterisk next to the values significant after correction indicates they are aware that multiple testing is required. So why bother boldfacing p-values that they know are not significant? The overall effect is an impression that more tests are significant than is actually the case. See for yourself in their Table 4:
The fact that there are multiple columns is also problematic. Separate tests were performed for smoking occasions per day, joints per occasion, joints per week and smoking days per week. These measures are highly correlated, but even so multiply testing them requires multiple test correction. The authors simply didn’t perform it. They say “We did not correct for the number of drug use measures because these measures tend not be independent of each other”. In other words, they multiplied the number of tests by four, and chose to not worry about that. Unbelievable.
Then there is Table 5, where the authors did not report the p-values at all, only whether they were significant or not… without correction:
3. Correlation vs. causation
This issue is one of the oldest in the book. There is even a wikipedia entry about it. Correlation does not imply causation. Yet despite the fact the every result in the paper is directed at testing for association, in the last sentence of the abstract they say “These data suggest that marijuana exposure, even in young recreational users, is associated with exposure-dependent alterations of the neural matrix of core reward structures and is consistent with animal studies of changes in dendritic arborization.” At a minimum, such a result would require doing a longitudinal study. Breiter takes this language to an extreme in the press release accompanying the article. I repeat the statement he made that I quoted above where I boldface the causal claim: “”Some of these people only used marijuana to get high once or twice a week. People think a little recreational use shouldn’t cause a problem, if someone is doing OK with work or school. Our data directly says this is not the case.” I believe that scientists should be sanctioned for making public statements that directly contradict the content of their papers, as appears to be the case here. There is precedent for this.
[Update April 6, 2014: The initial title of this post was “23andme genotypes are all wrong”. While that was and remains a technically correct statement, I have changed it because the readership of my blog, and this post in particular, has changed. Initially, when I made this post, the readers of the blog were (computational) biologists with extensive knowledge of genotyping and association mapping, and they could understand the point I was trying to make with the title. However in the past few months the readership of my blog has grown greatly, and the post is now reaching a wide public audience. The revised title clarifies that the content of this post relates to the point that low error rates in genotyping can be problematic in the context of genome-wide association reports because of multiple-testing.]
I have been reading the flurry of news articles and blog posts written this week about 23andme and the FDA with some interest. In my research talks, I am fond of displaying 23andme results, and have found that people always respond with interest. On the teaching side, I have subsidized 23andme testing for volunteer students in Math127 who were interested in genetics so that they could learn about personalized genomics first-hand. Finally, a number of my former and current students have worked at 23andme, and some are current employees.
Despite lots of opinions being expressed about the 23andme vs. FDA kerfuffle, I believe that two key points have been ignored in the discussions:
- All 23andme genotypes that have ever been reported to customers are wrong. This is the case despite very accurate genotyping technology used by 23andme.
- The interpretation of 23andme results involves examining a large number of odds ratios. The presence of errors leads to a huge multiple-testing problem.
Together, these issues lead to an interesting conundrum for the company, for customers, and for the FDA.
I always find it useful to think about problems concretely. In the case of 23andme, it means examining actual genotypes. Fortunately, you don’t have to pay the company $99 dollars to get your own- numerous helpful volunteers have posted their 23andme genotypes online. They can be viewed at openSNP.org where “customers of direct-to-customer genetic tests [can] publish their test results, find others with similar genetic variations, learn more about their results, get the latest primary literature on their variations and help scientists find new associations”. There are a total of 624 genotypes available at openSNP, many of them from 23andme. As an example, consider “samantha“, who in addition to providing her 23andme genotype, also provides lots of phenotypic information. Here is the initial part of her genotype file:
# This data file generated by 23andMe at: Wed Jul 20 20:37:11 2011 # # Below is a text version of your data. Fields are TAB-separated # Each line corresponds to a single SNP. For each SNP, we provide its identifier # (an rsid or an internal id), its location on the reference human genome, and the # genotype call oriented with respect to the plus strand on the human reference # sequence. We are using reference human assembly build 36. Note that it is possible # that data downloaded at different times may be different due to ongoing improvements # in our ability to call genotypes. More information about these changes can be found at: # https://www.23andme.com/you/download/revisions/ # # More information on reference human assembly build 36: # http://www.ncbi.nlm.nih.gov/projects/mapview/map_search.cgi?taxid=9606&build=36 # # rsid chromosome position genotype rs4477212 1 72017 AA rs3094315 1 742429 AG rs3131972 1 742584 AG rs12124819 1 766409 AA rs11240777 1 788822 AA rs6681049 1 789870 CC rs4970383 1 828418 CC rs4475691 1 836671 CC rs7537756 1 844113 AA rs13302982 1 851671 GG rs1110052 1 863421 GT ...
Anyone who has been genotyped by 23andme can get this file for themselves from the website (by clicking on their name, then on “Browse Raw Data” from the pull-down menu, and then clicking on “Download” in the top-right corner of the browser window). The SNPs are labeled with rsid labels (e.g. rs3094315) and correspond to specific locations on chromosomes (e.g. chr1:742429). Since every human is diploid, two bases are shown for every SNP; one came from mom and one from dad. The 23andme genotype is not phased, which means that you can’t tell in the case of rs3094315 whether the A was from mom and the G from dad, or vice versa (it turns out paternal origin can be important, but that is a topic for another post).
A key question the FDA has asked, as it does for any diagnostic test, is whether the SNP calls are accurate. The answer is already out there. First, someone has performed a 23andme replicate experiment precisely to assess the error rate. In an experiment in 2010 with two replicates, 85 SNPs out of about 600,000 were different. Today, Illumina types around 1 million SNPs, so one would expect even more errors. Furthermore, a replicate analysis provides only a lower bound, since systematic errors will not be detected. Another way to examine the error rate is to look at genotypes of siblings. That was written about in this blog post which concluded there were 87 errors. 23andme currently uses the Illumina Omni Express for genotyping, and the Illumina spec sheet claims a similar error rate to those inferred in the blog posts mentioned above. The bottom line is that even though the error rate for any individual SNP call is very very low (<0.01% error), with a million SNPs being called there is (almost) certainly at least one error somewhere in the genotype. In fact, assuming a conservative error rate leading to an average of 100 errors per genotype, the probability that a 23andme genotype has no errors is less than 10^(-40).
The fact that 23andme genotypes are wrong (i.e. at least one error in some SNP) wouldn’t matter if one was only interested in a single SNP. With very high probability, it would be some other SNPs that are the wrong ones. But the way people use 23andme is not to look at a single SNP of interest, but rather to scan the results from all SNPs to find out whether there is some genetic variant with large (negative) effect. The good news is that there isn’t much information available for the majority of the 1 million SNPs being tested. But there are, nevertheless, lots of SNPs (thousands) to look at. Whereas a comprehensive exam at a doctor’s office might currently constitute a handful of tests– a dozen or a few dozen at most– a 23andme test assessing thousands of SNPs and hundreds of diseases/traits constitutes more diagnostic tests on an individual at one time than have previously been performed in a lifetime.
To understand how many tests are being performed in a 23andme experiment, it is helpful to look at the Interpretome website. The website allows a user to examine information on SNPs without paying, and without uploading the data. I took a look at Samantha, and the Interpretome gave information about 2829 SNPs. These are SNPs for which there is a research article that has identified the SNP as significant in some association study (the website conveniently provides direct links to the articles). For example, here are two rows from the phenotype table describing something about Samantha’s genetic predisposition for large head circumference:
Samantha’s genotype at the locus is CC, the “risk” allele is T, the odds ratios are very small (0.05,0.07) and the p-values are apparently significant. Interpretome’s results differ from those of 23andme, but looking at the diversity of phenotypes reported on gives one a sense for the possibilities that currently exist in genetics, and the scope of 23andme’s reports.
From the estimates of error rates provided above, and using the back of an envelope, it stands to reason that about 1/3 of 23andme tested individuals have an error at one of their “interesting” SNPs. Not all of SNPs arising in association studies are related to diseases, but many of them are. I don’t think its unreasonable to postulate that a significant percentage of 23andme customers have some error in a SNP that is medically important. Whether such errors are typically false positives or false negatives is unclear, and the extent to which they may lead to significant odds ratios is another interesting question. In other words, its not good enough to know how frequently warfarin sensitivity is being called incorrectly. The question is how frequently some medically significant result is incorrect.
Of course, the issue of multiple testing as it pertains to interpreting genotypes is probably a secondary issue with 23andme. As many bloggers have pointed out, it is not even clear that many of 23andme’s odds ratios are accurate or meaningful. A major issue, for example, is the population background of an individual examining his/her genotype and how close it is to the population on which the GWAS were performed. Furthermore, there are serious questions about the meaning of the GWAS odds ratios in the case of complex traits. However I think the issue of multiple testing is a deeper one, and a problem that will only be exacerbated as more disease SNPs are identified. Having said that, there are also approaches that could mitigate errors and improve fidelity of the tests. As DECODE genetics has demonstrated, imputation and phasing can in principle be used to infer population haplotypes, which not only are useful for GWAS analyses, but can also be used to identify erroneous SNP calls. 23andme’s problem is that although they have many genotypes, they are from diverse populations that will be harder to impute and phase.
The issue of multiple testing arising in the context of 23andme and the contrast with classic diagnostics reminds me of the dichotomy between whole-genome analysis and classic single gene molecular biology. The way in which customers are looking at their 23andme results is precisely to look for the largest effects, i.e. phenotypes where they appear to have high odds of contracting a disease, or being sensitive to some drug. This is the equivalent of genome scientists picking the “low hanging fruit” out of genome-wide experiments such as those performed in ENCODE. In genomics, scientists have learned (with some exceptions) how to interpret genome-wide analyses after correcting for multiple-hypothesis testing by controlling for false discovery rate. But are the customers of 23andme doing so? Is the company helping them do it? Should it? Will the FDA require it? Can looking at ones own genotype constitute too much testing?
There are certainly many precedents for superfluous harmful testing in medicine. For example, the American Academy of Family Physicians has concluded that prostate cancer PSA tests and digital rectal exams have marginal benefits that are outweighed by the harm caused by following up on positive results. Similar arguments have been made for mammography screening. I therefore think that there are serious issues to consider about the implications of direct-to-consumer genetic testing and although I support the democratization of genomics, I’m glad the FDA is paying attention.