My Dominant Hemisphere

Courtesy Lydia Elle @ Flickr (by-nc license)

I just finished a great lecture series on the history of mathematics by Dr. David Bressoud recently¹. Remember how I once spoke about elegance in inelegance? How some people have argued (eg: Lee Smolin) that the universe just might be complex by nature? How mankind might just be wrong about looking for simple and thus elegant solutions to explain physical phenomena?

Well, I was pretty intrigued by some of the stuff I learned about Henri Poincare‘s work in this regard. Poincare is famous for a number of things, his Poincare conjecture being the most obvious of them. A Russian math guru, Grigori Perelman, apparently proved this conjecture some years back and among other peculiar things, not only declined the Fields medal but also a million dollar prize for solving one of the toughest math problems ever known.

But I was particularly piqued by how Poincare was fascinated by this idea of finding elegance and hidden patterns even where one might expect junk. Here are what might be interesting questions as crude examples:

Take a random set of 100 beads. Throw these beads on the floor. They scatter randomly. How many throws would be needed to find at least three beads on the floor that yield an equilateral triangle when they are connected? How many throws would you need to find a cluster of beads that is of a certain shape or size?

That there is some sense of order even in randomness and chaos, is truly an enchanting concept.

Have any thoughts of your own? Do send in your feedback !
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1. Queen Of The Sciences (Lectures by David Bressoud)
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Copyright © Firas MR. All rights reserved.

zaveqna@flickr (by-nc-sa license)

I’ve been studying mathematics lately and really enjoying it. Here’s an interesting story about the history of the trigonometric function, ‘sine‘.

Early in the 1st millenium A.D., a new way of thinking about chords was coming about. The chord is defined as the straight line that joins two points on the circumference of a circle. The ancient Greeks had developed trigonometric functions to calculate the length of arbitrary chords. But several centuries later, by the early 1st millenium A.D., mathematicians in India began to think about calculating and working with half-chord lengths instead. For this, they developed the familiar ‘sine’ and ‘cosine‘ functions that we still use to this day. The earliest accounts of the use of the half-chord in Indian texts, is from the Surya Siddhanta (c. 300 – 400 AD), written in Sanskrit. The sound of the Sanskrit word used for ‘half-chord’ was ardha-jya [ardha = half, jya = chord]. Perhaps they found this word too long and eventually it was shortened to jya or jiva for all practical purposes.

By roughly the end of the 1st millenium A.D., the vanguard of scientific growth was now in the hands of the Arab world. In translating the works from Sanskrit into Arabic, scholars in the Arab world transliterated and pronounced jiva as jiba [جب]. The sound ‘jiba‘ is recorded in Arabic as two consonants j [ج] and b [ب] with no vowels explicitly written between them. The vowel sounds are merely implied.

Several centuries later, after the decline of scientific growth in the Arab world, came the Europeans. When they in turn came upon the Arabic word for jiva and tried to translate it, they of course ended up with a word, ‘jb‘ [pronounced as 'jay bee']. Apparently, they were oblivious of the implied vowel sounds. Things were dandy for the Arab scientists, but the Europeans couldn’t make any sense of the sound ‘jay bee‘ because such a sound doesn’t exist in any of the words in the Arabic language. They found that the closest sound to ‘jay bee‘, was the sound ‘jaib‘ or ‘ja-eeb‘, in the Arabic word for the mammary gland! And so the Europeans assumed that the half-chord was to be referred to with a Latin word that meant mamma, mammary gland or any of its other synonyms. Perhaps out of modesty, it was ultimately instead decided that the word used for the fold of a cloth utilized to cover a mamma would be appropriate to refer to a half-chord. This word was ‘sinus’. And from this Latin word ‘sinus‘, ultimately came the English word ‘sine‘ that is in use today!

Remarkable, isn’t it?

Feel free to send in your feedback, corrections and comments .

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References:

1. Queen Of The Sciences (Lectures by David Bressoud)

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Copyright © Firas MR. All rights reserved.

Remember Wilson the volleyball, from the movie ‘Castaway‘? In a dash of newfound creativity and imagination, I shot a couple of photographs today of a coconut that shared an uncanny resemblance to Wilson! Seemed like the perfect opportunity for some prop-photography .

Wilson reads for the USMLE.

Somehow he seems quite absorbed with the book , don’t you think? Ah, nothing beats the joy of laying back, relaxing and reading a nice book.

Wilson in the Orient.

On his travels to the Orient, he received a fancy hand-held fan as a gift from a monk. In fact, that is exactly where he discovered his inner intellectual .

Wilson is a bike rider ...

… and loves his moped. How else would an intelligent coconut choose to conquer the streets?

Copyright © Firas MR. All rights reserved.

An Ongoing Surgery

Bonjour everyone! Today, I’m going to share with you some high yield keywords that should hopefully help you breeze through your surgical rotations in med school. Call it a checklist if you will. The objective is to facilitate memory recall and help you gear up with areas that you just have to familiarize yourself with, ideally before the start of your rotations. Understand that these are just keywords, with a special emphasis on surgical instruments, and you’ll really need to read some good books to develop your knowledge base. For a rapid-fire review I suggest Surgical Recall. For basic surgical skills, you might like RM Kirk’s Basic Surgical Techniques. It is also a good idea to refer to specific sections (for pictures of incisions, instruments, etc.) of a good reference book on the surgical specialty you’ll be rotating in. Finally, like we all know, surgery is an area that is incredibly skill based and different people have different preferences when carrying out the same thing – be it tying a knot, controlling a bleeder or what have you. You’ll learn to modify the way you do things depending on the specific ways of your surgical team.

I’ve also interspersed keywords specific to two areas that I have an interest in with regards to surgery, or rather surgical oncology to be exact – general thoracic surgery and colorectal surgery.

I shall be updating this list as the need comes. Comments, corrections and feedback are always welcome! Bye for now !

Copyright © Firas MR. All rights reserved.

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Romanesco broccoli - One of many examples of fractals in nature. (Wikipedia)

What do Mandelbrot and Einstein have in common?

They were/are both math aficionados. But more importantly, they both laid down the foundations for thinking about abstract natural phenomena in a geometrical way. The impact was reverberating.

Before Einstein came along, people had no real sense of gravity at all. Yea sure, there was Newton’s universal law of gravitation. But no one really could make any sense whatsoever of how exactly gravity might operate. Was it a wave? If so, at what speed could it act? Was there something particulate about it? Gravity was so mystical. And as always, so have been the concepts of time and space. Einstein’s greatest achievement in my view is that not only was he able to lay out the underpinnings of such phenomena in the form of a couple of abstract equations, but perhaps more importantly, that he devised a method to think about them visually. In developing his theories of special and general relativity, Einstein proposed the idea of the space-time fabric. It has a 3-D structure, yet represents four dimensions – 3 in space and 1 in time. Gravity would result from distortions in this fabric. The speed with which gravity could influence an object would depend on how fast these distortions could travel. And this central notion of ‘distortions in a fabric’ would also influence our understanding of the more difficult to grasp concepts of time and space. Time and space could mean different things to different observers depending on how this fabric was warped or sliced.

Mandelbrot achieved the same thing with his theory of fractals. How can complex natural structures and phenomena be represented mathematically? How to mathematically model a plant, the form of a human or a mountain range? In spite of how incredibly difficult it all sounds, these complex shapes could all be simplified into repeating units of tiny yet geometrically simple components – fractals. Mandelbrot went on to write his epic, “The Fractal Geometry Of Nature” and there was no turning back. Suddenly so many of nature’s workings could now be analyzed mathematically. An immensely significant step for mankind indeed. What I find absolutely fascinating about fractals, is the discovery that many intangible natural phenomena also contain a fractal component. Dr. Ary Goldberger and his team of researchers at Harvard Medical School have been working on applying fractal theory to medicine and biology. For those of you who might not be familiar with Dr. Goldberger, the name might ring a bell if you’ve read his books on electrocardiography. For Dr. Goldberger, interest in electrocardiography runs in the family, his father having invented the augmented limb leads back in the day. Among some of the things I learned about his work on electrocardiography, is that his team has shown that there is a fractal nature to ECG waveforms! This isn’t something like representing the heart itself in fractal form. It’s the activities of the heart that we are talking about here. Something really quite abstract. By looking at these fractal patterns, one could potentially detect pathology at a much earlier stage. Fractal patterns and their aberrations could help detect diseases in ways that no one had ever imagined! If you want to dig what’s cool, check out what’s been going on in the world of fractals in medicine – from human vasculature, to the brain and beyond. A quick PubMed query would lead you to a lot of riveting literature on the topic. Don’t forget to also take a look at the excellent documentary on fractal theory from PBS NOVA, “Hunting The Hidden Dimensions“.

Copyright © Firas MR. All rights reserved.

Readability grades for this post:

Flesch reading ease score: 61.1
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Flesch-Kincaid grade level: 8.2
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Gunning fog index: 11.6
SMOG index: 11

Bronze balance pans and lead weights from the Vapheio tholos tomb, circa 15th century BC. National Museum, Athens. Shot courtesy dandiffendale@Flickr. by-nc-sa license.

Objectives and talking points:

• To recap basic concepts of hypothesis testing in scientific experiments. Readers should read-up on hypothesis testing in reference works.
• To contrast drug vs. placebo and drug vs. standard drug study designs.
• To contrast non-equivalence and equivalence studies.
• To understand implications of these study designs, in terms of interpreting study results.

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Howdy readers! Today I’m going to share with you some very interesting concepts from a fabulous book that I finished recently – “Designing Clinical Research – An Epidemiologic Approach” by Stephen Hulley et al. The book speaks fairly early on, on what are called “equivalence studies”. Equivalence studies are truly fascinating. Let’s see how.

When a new drug is tested for efficacy, there are multiple ways for us to do so.

A Non-equivalence Study Of Drug vs. Placebo

A drug can be compared to something that doesn’t have any treatment effect whatsoever – a ‘placebo’. Examples of placebos include sugar tablets, distilled water, inert substances, etc. Because pharmaceutical companies try hard to make drugs that have a treatment effect and that are thus different from placebos, the objective of such a comparison is to answer the following question:

Is the new drug any different from the placebo?

Note the emphasis on ‘any different’. As is usually the case, a study of this kind is designed to test for differences between drug and placebo effects in both directions¹. That is:

Is the new drug better than the placebo?

OR

Is the new drug worse than the placebo?

The boolean operator ‘OR’, is key here.

Since we can not conduct such an experiment on all people in the target ‘population’ (eg. all people with diabetes from the whole country), we conduct it on a random and representative ‘sample’ of this population (eg. randomly selected diabetes patients from the whole country). Because of this, we can not directly extrapolate our findings to the target population without doing some fancy roundabout thinking and a lot of voodoo first – a.k.a. ‘hypothesis testing’. Hypothesis testing is crucial to take in to account random chance (error) effects that might have crept in to the experiment.

In this experiment:

• The null hypothesis is that the drug and the placebo DO NOT differ in the real world².
• The alternative hypothesis is that the drug and the placebo DO differ in the real world.

So off we go, with our experiment with an understanding that our results might be influenced by random chance (error) effects. Say that, before we start, we take the following error rates to be acceptable:

1. Even if the null hypothesis is true in the real world, we would find that the drug and the placebo DO NOT differ only 95% of the time, purely by random chance. [Although this rate doesn't have a name, it is equal to (1 - Type 1 error)].
2. Even if the null hypothesis is true in the real world, we would find that the drug and the placebo DO differ 5% of the time, purely by random chance. [This rate is also called our Type 1 error, or critical level of significance, or critical α level, or critical 'p' value].
3. Even if the alternative hypothesis is true in the real world, we would find that the drug and the placebo DO differ only 80% of the time, purely by random chance. [This rate is also called the 'Power' of the experiment. It is equal to (1 - Type 2 error)].
4. Even if the alternative hypothesis is true in the real world, we would find that the drug and the placebo DO NOT differ 20% of the time, purely by random chance. [This rate is also called our Type 2 error].

The strategy of the experiment is this:

If we are able to accept these error rates and show in our experiment that the null hypothesis is false (that is ‘reject‘ it), the only other hypothesis left on the table is the alternative hypothesis. This has then, GOT to be true and we thus ‘accept’ the alternative hypothesis.

Q: With what degree of uncertainty?

A: With the uncertainty that we might arrive at such a conclusion 5% of the time, even if the null hypothesis is true in the real world.

Q: In English please!

A: With the uncertainty that we might arrive at a conclusion that the drug DOES differ from the placebo 5% of the time, even if the drug DOES NOT differ from the placebo in the real world.

Our next question would be:

Q: How do we reject the null hypothesis?

A: We proceed by initially assuming that the null hypothesis is true in the real world (i.e. Drug effect DOES NOT differ from Placebo effect in the real world). We then use a ‘test of statistical significance‘ to calculate the probability of observing a difference in treatment effect in the real world, as large or larger than that actually observed in the experiment.  If this probability is <5%, we reject the null hypothesis. We do this with the belief that such a conclusion is within our pre-selected margin of error. Our pre-selected margin of error, as mentioned previously, is that we would be wrong about rejecting the null hypothesis 5% of the time (our Type 1 error rate)³.

If we fail to show that this calculated probability is <5%, we ‘fail to reject‘ the null hypothesis and conclude that a difference in effect has not been proven⁴.

A lot of scientific literature out there is riddled with drug vs. placebo studies. This kind of thing is good if we do not already have an effective drug for our needs. Usually though, we already have a standard drug that we know works well. It is of more interest to see how a new drug compares to our standard drug.

A Non-equivalence Study Of Drug vs. Standard Drug

These studies are conceptually the same as drug vs. placebo studies and the same reasoning for inference is applied. These studies ask the following question:

Is the new drug any different than the standard drug?

Note the emphasis on ‘any different’. As is often the case, a study of this kind is designed to test the difference between the two drugs in both directions¹. That is:

Is the new drug better than the standard drug?

OR

Is the new drug worse than the standard drug??

Again, the boolean operator ‘OR’, is key here.

In this kind of experiment:

• The null hypothesis is that the new drug and the standard drug DO NOT differ in the real world².
• The alternative hypothesis is that the new drug and the standard drug DO differ in the real world.

Exactly like we discussed before, we initially assume that the null hypothesis is true in the real world (i.e. the new drug’s effect DOES NOT differ from the standard drug’s effect in the real world). We then use a ‘test of statistical significance‘ to calculate the probability of observing a difference in treatment effect in the real world, as large or larger than that actually observed in the experiment.  If this probability is <5%, we reject the null hypothesis – with the belief that such a conclusion is within our pre-selected margin of error. Just to repeat ourselves here, our pre-selected margin of error, is that we would be wrong about rejecting the null hypothesis 5% of the time (our Type 1 error rate)³.

If we fail to show that this calculated probability is <5%, we ‘fail to reject’ the null hypothesis and conclude that a difference in effect has not been proven⁴.

An Equivalence Study Of Drug vs. Standard Drug

Sometimes all you want is a drug that is as good as the standard drug. This can be for various reasons – the standard drug is just too expensive, just too difficult to manufacture, just too difficult to administer, … and so on. Whereas the new drug might not have these undesirable qualities yet retain the same treatment effect.

In an equivalence study, the incentive is to prove that the two drugs are the same. Like we did before, let’s explicitly formulate our two hypotheses:

• The null hypothesis is that the new drug and the standard drug DO NOT differ in the real world².
• The alternative hypothesis is that the new drug and the standard drug DO differ in the real world.

We are mainly interested in proving the null hypothesis. Since this can’t be done⁴, we’ll be content with ‘failing to reject’ the null hypothesis. Our strategy is to design a study powerful enough to detect a difference close to 0 and then ‘fail to reject’ the null hypothesis. In doing so, although we can’t ‘prove’ for sure that the null hypothesis is true, we can nevertheless be more comfortable saying that it in fact is true.

In order to detect a difference close to 0, we have to increase the Power of the study from the usual 80% to something like 95% or higher. We wan’t to maximize power to detect the smallest difference possible. Usually though, it’s enough if we are able to detect the the largest difference that doesn’t have clinical meaning (eg: a difference of 4mm on a BP measurement). This way we can compromise a little on Power and choose a less extreme figure, say 88% or something.

And then just as in our previous examples, we proceed with the assumption that the null hypothesis is true in the real world. We then use a ‘test of statistical significance‘ to calculate the probability of observing a difference in treatment effect in the real world, as large or larger than that actually observed in the experiment.  If this probability is <5%, we reject the null hypothesis – with the belief that such a conclusion is within our pre-selected margin of error. And to repeat ourselves yet again (boy, do we like doing this ), our pre-selected margin of error is that we would be wrong about rejecting the null hypothesis 5% of the time (our Type 1 error rate)³.

If we fail to show that this calculated probability is <5%, we ‘fail to reject‘ the null hypothesis and conclude that although a difference in effect has not been proven, we can be reasonably comfortable saying that there is in fact no difference in effect.

So Where Are The Gotchas?

If your study isn’t designed or conducted properly (eg: without enough power, inadequate  sample size, improper randomization, loss of subjects to followup, inaccurate measurements, etc.)  you might end up ‘failing to reject’ the null hypothesis whereas if you had taken the necessary precautions, this might not have happened and you would have come to the opposite conclusion. Purely because of random chance (error) effects. Such improper study designs usually dampen any obvious differences in treatment effect in the experiment.

In a non-equivalence study, researchers, whose incentive it is to reject the null hypothesis, are thus forced to make sure that their designs are rigorous.

In an equivalence study, this isn’t the case. Since researchers are motivated to ‘fail to reject’ the null hypothesis from the get go, it becomes an easy trap to conduct a study with all kinds of design flaws and very conveniently come to the conclusion that one has ‘failed to reject’ the null hypothesis!

Hence, it is extremely important, more so in equivalence studies than in non-equivalence studies, to have a critical and alert mind during all phases of the experiment. Interpreting an equivalence study published in a journal is hard, because one needs to know the very guts of everything the research team did!

Even though we have discussed these concepts with drugs as an example, you could apply the same reasoning to many other forms of treatment interventions.

Hope you’ve found this post interesting . Do send in your suggestions, corrections and comments!

Adios for now!

Copyright © Firas MR. All rights reserved.

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1. An alternative hypothesis for such a study is called a ‘two-tailed alternative hypothesis‘. A study that tests for differences in only one direction has an alternative hypothesis that is called a ‘one-tailed alternative hypothesis‘.
2. This situation is a good example of a ‘null’ hypothesis also being a ‘nil’ hypothesis. A null hypothesis is usually a nil hypothesis, but it’s important to realize that this isn’t always the case.
4. Note that we never use the term, ‘accept the null hypothesis’.

A reviewer at the National Institutes of Health evaluates a grant proposal. (Wikipedia)

I managed to read quite a number of interesting books in the last couple of months. Among them, was Scientific Writing: Easy When You Know How by Jennifer Peat et al. Marvelous book and one that I highly recommend. The book has been mainly written for health professionals. It gives you an insider’s view of how the entire peer(expert)-review process in scientific publishing works. There are also interesting nuggets on peer-review outside of medical journals such as conferences, scientific meetings, etc.

The publishing process in a nutshell:

1. Upon submission to a journal, a paper will first go through preliminary screening by special staff who check for typographical errors. Not scientific merit. Did you stick to the word limit? Are the margins, fonts and spaces in accordance with the journal’s ‘instructions to authors‘ policy? If not, the paper will bounce back like rejected email!
2. If it does scrape through, it goes to an editorial committee. Editors in turn run an ambiguous check on the paper’s scientific rigor and impact, whether it appeals to their sensibilities and whether it makes business sense to get it out in their journal. It is then forwarded to external reviewers.
3. Many journals maintain databases of potential external reviewers who are ‘experts’ in their fields, some of whom are on contract for the journal and others who are not. These reviewers have a track record of being active in other journals and meetings. Journals may even rank reviewers based on whether they review papers on time, their general demeanor with authors of papers, etc. Often these chaps are perched in just about every nook and corner of the world. They look at the paper’s strengths and weaknesses in terms of study design, whether the conclusions put forth are in accordance with the reported results, whether the statistics measure up, whether certain areas need clarification, whether some parts should be rephrased or even omitted altogether. Their comments and annotations are then forwarded to the editors and in turn to the authors.
4. Both editors and reviewers often refer to checklists to standardize this process, even if it be somewhat ambiguous. Because different people have different mental cutoffs for ‘clinical significance’ when it comes to reported results, different people will reach different conclusions even if they look at the same ‘statistically significant’ data. When two reviewers differ in what they think about a paper, editors will often request a third reviewer to look at it.
5. After a lot of back and forth communication between authors, editors and reviewers the paper is finally published. The editorial committee is the final arbiter that decides whether or not the paper gets published.
6. This process usually take months, unless there is a good reason.

Here are some interesting facts that you might not know about scientific journals:

1. Multiple surveys have shown that journals are more likely to publish ‘statistically significant’ findings. This is an important thing to realize. For any scientific study with a Type 1 error rate of 5%, if the null hypothesis was true you would get a statistically significant result 5% of the time. Purely as a result of random chance. But it’s the 5% of studies that report such a ‘statistically significant’ result that are more likely to get published than the remaining 95% of studies that don’t.
2. Most of the scientific literature is biased in favor of content produced in English. Translated works are an extreme minority.
3. The most popular articles in a journal are reviews, editorials, letters, etc. and not research papers. Consequently, journals contain more narrative reviews than genuine research. It’s what keeps them in business.
4. Being published is not necessarily something that is a natural consequence of your scientific caliber or contribution to mankind. It is a very political and arbitrary thing. Maybe the editors or reviewers for the journal are biased against your work. Or it could be that the editors do not think publishing your paper will increase their business, for obscure reasons. Maybe your paper is just too specialized and caters to a minority niche of readers. Editors usually want stuff that sells and increases readership (who by the way, more often care about narrative reviews as mentioned previously), impact factors and profits. Quite similar to newspapers actually. Editors may even decide to publish a paper regardless of what the reviewers think, as long as it makes sense to them to do so!
5. When you submit a paper to a journal for consideration, you immediately transfer whole and sole copyrights to it. You are not permitted to share that paper outside of the research team without prior permission from the editors. Transfer of copyright to journals is pretty common and there are only a minority of fledgling journals out there that give you the luxury of retaining copyrights.
6. Many journals have pre-publication ‘embargoes’. If you have discussed your paper in a scientific conference, meeting, on a random website, with the press … and so on, different journals will have different policies on whether or not such a paper constitutes ‘duplicate’ material. That depends on how many beans you spilled out during such conferences, talks, … etc. and under what circumstances. Did you discuss just the abstract, some random figures and tables or the whole thing? Did you submit the paper before or after such disclosure? Does it constitute a copyright violation? If it’s considered duplicate, it will not be published unless there is a good reason.
7. Transfer of copyright also means that you cannot submit your paper elsewhere or hand out copies of it to colleagues in meetings, conferences, etc. You can’t show off the paper on a website either. As long as the paper is under consideration for publication, you need prior permission from the journal. If the paper is rejected or withdrawn from submission, the copyrights are transferred back to the authors.
8. Different journals will have different time limits on copyright. Some will allow you to maintain a copy on a website or a repository after a number of years have passed. These can rightly be called post-publication ‘embargoes’².
9. Scientific knowledge is thus ultimately controlled by vested interests making it difficult for a free and open society. This has led to calls for reform in peer-reviewed scientific publishing, including the open-access movement. There are two main models in open-access: Open-access journals, that make all peer-reviewed content free to the public. Journals from the Public Library Of Science (PLoS) are a good example. Open-access self-archives are another model. Authors can deposit copies (a.k.a. ‘self-archives’) of pre-prints or post-prints of articles that they have submitted to non-open-access, peer-reviewed journals that agree to such activity. They can then share these self-archives using websites and other tools. However, often self-archives are deposited in repositories which are usually institutional. Such repositories allow free public access not only to peer-reviewed scholarly content, but also non-peer-reviewed content such as theses and other gray literature. OAIster is a good example of a cross-repository search engine¹.
10. In certain cases you may want to submit your research for urgent publishing. Different journals will call these kinds of papers by different names – ‘rapid response’, ‘rapid paper‘ …, etc. Often they do not contain too much detail as to study design or statistical rigor. These papers will be submitted by editors to external reviewers on the condition that they be reviewed within a specified time frame. Once such a paper has been accepted and published, you may not be able to submit an addendum or supplement later as it might be considered ‘duplicate’ material!
11. Following reporting guidelines such as those mentioned at the Equator Network, will improve your chances of being published.
12. Submitting your paper to a specialty journal increases your chances of success. Most papers fulfill a niche and so do most specialty journals.
13. The chances of you being struck by lightning are higher than the chances that your paper will be accepted without modification. Nearly always, editors and reviewers will get back asking you to change your paper in some way.
14. In highly specialized fields, many journals will use the same set of reviewers. If you disagree with a reviewer and choose to withdraw your submission, it will not do you much good to submit to a different journal.
15. Reviewers are usually free to remain anonymous to authors. And some journals will let authors be anonymous to reviewers in the interest of fairness. However, anonymity does not always happen.
16. If you are well known in your field, don’t be surprised if you receive an offer to expert-review a paper from a random journal.
17. Despite how enticing it sounds, reviewers do not make a lot of money from this business!
18. Different journals select editors using different criteria. At the end of the day, it is the business team of a journal that usually decides. A candidate who can improve a journal’s appeal, impact factor and business profits ultimately wins.

Have anything else to share that’s not on the list? Send me your feedback and I’ll put it up here!

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Your feedback counts:

1. Special thanks to Stevan Harnad of Open Access Archivangelism fame for corrections in the comments. Matt Warren writes in to talk about the NIH’s involvement in open-access. Their Pubmed Central service is worth checking out. ^{[go back]}
2. With regards to ‘embargoes’ and copyrights, Christina Pikas writes in to say that most of this stuff is part of the ‘copyright transfer agreement’, which should always be examined carefully. She also says that many institutions can influence how many rights you have and that if your work was done for a corporation, a corporate lawyer will often help you in the process. Just to add a tiny point, the book that I referred to above mentions that many institutions have policies on copyright and intellectual property (IP) for their departments. Some will allow researchers to hold on to IP rights, while others will take over these IP rights from them. It’s always a good idea to check with your institution or department. ^{[go back]}

Copyright © Firas MR. All rights reserved.

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Cape Lion

It’s been well over a year since I had initially revamped the theme of my blog. At the time, I was mainly interested in improving compatibility with the web browser, Konqueror. The Digg theme worked well for me and I was pretty much happy with it overall. But after a couple of months anything gets boring! One of WordPress’s main strengths is the awesome collection of themes available. Some of these themes trickle down to WordPress’s hosting service, WordPress.com . It’s about time for a brand new theme, don’t you agree ? I now bring to you a completely refreshing look for the blog. Gone is the large image header. The focus is on extreme simplicity and lack of clutter. Even the RSS icon has been done away with completely, leaving only a line of text to click on instead. I’m also sporting a new gravatar – a public domain image that I stumbled upon at Wikimedia Commons and that just absolutely blew me away the first time I saw it. It is a drawing by the Dutch artist Rembrandt Harmenszoon van Rijn of the now extinct Cape Lion (Panthera leo melanochaitus) made circa 1650-52 in Louvre, Paris. I thought, since one of the synonyms of my Arabic name ‘Firas’ (فراس) is ‘Asad’ (اسد) meaning ‘Lion’ in English, it couldn’t get any better!

I hope you like the new look. Do send in your feedback. Polls can be meaningless, with multiple votes. But hey, give it a try!

On a side note, I have now entered exam mode. Yet again! Oh well, just another byproduct of living life as a medic I suppose. My last entry was a little long. I think I’ll be cutting down on writing for a while. Fear not though! If there’s something that can’t wait to be written, you’ll hear about it asap !

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This is an example of a full genome sequencing machine. It is the ABI PRISM 3100 Genetic Analyzer. Sequencers like it completely automate the process of sequencing the entire genome. Yes, even yours! [Courtesy: Wikipedia]

Some Background Before The Tour

Ahoy readers! I’ve had the opportunity to read a number of books recently. Among them, is “Developing Bioinformatics Computer Skills” by Cynthia Gibas and Per Jambeck. I dived into the book straight away, having no basic knowledge at all of what comprises the field of bioinformatics. Actually, it was quite like the first time I started medical college. On our first day, we were handed a tiny handbook on human anatomy, called “Handbook Of General Anatomy” by B D Chaurasia. Until actually opening that book, absolutely no one in the class had any idea of what Medicine truly was. All we had with us were impressions of charismatic white-coats who could, as if by magic, diagnose all kinds of weird things by the mere touch of a hand. Not to mention, legendary tales from the likes of Discovery Channel. Oh yes, our expectations were of epic proportions . As we flipped through the pages of that little book, we were flabbergasted by the sheer volume of information that one had to rote. It had soon become clear to us, what medicine was all about – Physiology is the study of normal body functions akin to physics, Anatomy is the study of the structural organization of the human body a la geography … – and this set us on the path to learning to endure an avalanche of learn-by-rote information for the rest of our lives.

Bioinformatics is shrouded in mystery for most medics. Because, so many of these ideas are completely new. The technologies are new. The data available are new. Before the human genome was sequenced, there was virtually no point of using computers to understand genes and alleles. Most of what needed to be sorted out could be done by hand. But now that we have huge volumes of data, and data that are growing at an exponential rate at that, it makes sense to use computers to connect the dots and frame hypotheses. I guess, bioinformatics is a conundrum to most other people too – whether you are coming from a math background, a computer science background or a biology background – we all have something missing from our repertoire of knowledge and skills.

What is the rationale behind using computation to understand genes? In yore times, all we had were a couple of known genes. We had the tools of Mendelian genetics and linkage analysis to solve most of the genetic mysteries. The human genome project changed that. We are suddenly flooded not only with sequences that we don’t know anything about, but also the gigantic hurdle of finding relationships between them. To give you a sense of the magnitude of numbers we’re talking about here: we could simplify DNA’s 3-D structure and represent the entire genetic code contained in a single polynucleotide strand of the human genome, as a string of letters A, C, G or T each representing a given nucleic acid (base) in a long sequence (like so …..ATCGTTACGTAAAA…..). Since it has been found that this strand is approximately 3 billion bases long, its entire length comes to 3 billion bytes. That’s because each letter A, T, C or G could be thought of as being represented by a single ASCII character. And we all know that an ASCII character is equal to 1 byte of data. Since we are talking about two complementary strands within a molecule of DNA, the amount of information within the genome is 6 billion bytes^§. But human cells are diploid! So the amount of DNA information in the nucleus of a single human cell is 12 billion bytes! That’s 1.2 terabytes of data neatly packed in to the DNA sequence of every cell – we haven’t even begun to talk about the 3-D structure of DNA or the sequence and 3-D structure of RNA and proteins yet!

§ Special thanks to Martijn for bringing this up in the comments: If you really think about it for a moment, bioinformaticians don’t need to store the sequences of both the DNA strands of a genome in a computer, because the sequence of one strand can be derived from the other – they are complementary by definition. If you store 3 billion bytes from one strand, you can easily derive the complementary 3 billion bytes of information on the other strand, provided that the two strands are truly complementary and there aren’t any blips of mismatch mutations between them. Using this concept, you can get away with storing 3 billion bytes and not 6 billion bytes to capture the information in the human genome.

Special thanks also to Dr. Atul Butte ^¥ of Stanford University who dropped by to say that a programmer really doesn’t need a full byte to store a nucleic acid base. A base can be represented by 2 bits (eg. 00 for A, 11 for C, 01 for G and 10 for T). Since 1 byte contains 8 bits, a byte can actually hold 4 bases. Without compression. So 3 billion bases can be held within 750,000,000 bytes. That’s 715 megabytes (1 megabyte = 1048576 bytes), which can easily fit on to an extended-length CD-ROM (not even a DVD). So the entire genetic code from a single polynucleotide strand of the human genome can easily fit on to a single CD-ROM. Since human cells are diploid, with two CD-ROMs – one CD-ROM for each set of chromosomes – you can capture this information for both sets of chromosomes. ^{[go back]}

To compound the issue, we don’t have a taxonomy system in place to describe the sequences we have. When Linnaeus invented his taxonomy system for living things, he used basic morphologic criteria to classify organisms. If it walked like a duck and talked like a duck, it was a duck! But how do you apply this reasoning to genes? You might think, why not classify them by organism? But there’s a more subtle issue here too. Some of these genetic sequences can be classified in to various categories – is this gene a promoter, exon, intron or could it be a sequence that plays a role in growth, death, inflammatory response, and so on. Not only that, many sequences could be found in more than one organism. So how do you solve the problem of classification? Man’s answer to this problem is simple – you don’t!

Here’s how we can get away with that. Simply create a relational database using MySQL, PostgreSQL or what have you and create appropriate links between sequence entries, their functions, etc. Run queries to find relationships and voila, there you have it! This was our first step in developing bioinformatics as a field. Building databases. You can do this with a genetic sequence (a string of letters A for ‘adenine‘, C for ‘cytosine‘, G for ‘guanine‘ and T for ‘thymine‘ …represented like so ATGGCTCCTATGCGGTTAAAATTT….) or with an RNA sequence (a string of letters A for ‘adenine’, C for ‘cytosine, G for ‘guanine’ and U for ‘Uracil‘ like so …AUGGCACCCU…) or even a protein sequence (a string of 20 letters each letter representing one amino acid). By breaking down and simplifying a 3-D structure this way, you can suddenly enhance data storage, retrieval and more importantly, analysis between:

1. Two or more sequences of DNA
2. Two or more sequences of RNA
3. Two or more sequences of Protein

You can even find relationships between:

1. A DNA sequence and an RNA sequence
2. An RNA sequence and a Protein sequence
3. A DNA sequence and a Protein sequence

If you can represent the spatial coordinates of the molecules within a protein 3-D structure as cartesian coordinates (x, y, z), you can even analyze structure not only within a given protein, but also try to predict the best possible 3-D structure for a protein that is hypothetically synthesized by a given DNA or RNA sequence. In fact that is the Holy Grail of bioinformatics today. How to predict protein structure from a DNA sequence? And consequentially, how to manipulate protein structure to suit your needs.

The Tour Begins

Let’s take a tour of what bioinformatics holds for us.

The Ability To Build Relational Databases

We have already discussed this above.

Local Sequence Comparison

An example of sequence alignment. Alignment of 27 avian influenza hemagglutinin protein sequences colored by residue conservation (top) and residue properties (bottom) [Courtesy: Wikipedia]

Before we delve in to the idea of sequence comparisons further, let’s take an example from the bioinformatics book I mentioned to understand how sequence comparisons help in the real world. It speaks of a gene-knockout experiment that targets a specific sequence in the fruit fly’s (Drosophila melanogaster) genome. Knocking this sequence out, results in the flies’ progeny being born without eyes. By knocking this gene – called eyeless – out you learn that it somehow plays an important role in eye development in the fruit fly. There’s a similar (but not quite the same) condition in humans called aniridia, in which eyes develop in the usual manner, except for the lack of an iris. Researchers were able to identify the particular gene that causes aniridia and called it aniridia. By inserting the aniridia gene in to an eyeless-knockout Drosophila’s genome, they observed that suddenly its offspring bore eyes! Remarkable isn’t it? Somehow there’s a connection between two genes separated not only by different species, but also by genera and phyla. To discern how each of these genes functions, you proceed by asking if the two sequences could be the same? How similar would they might be exactly? To answer this question you could do an alignment of the two sequences. This is the absolute basic kind of stuff when we do sequence analysis.

Instead of doing it by hand (which could be possible if the sequences being compared were small), you could find the best alignment between these two long sequences using a program such as BLAST. There are a number of ways BLAST can work. Because the two sequences may have only certain regions that fit nicely, with other regions that don’t – called gaps – you can have multiple ways of aligning them side by side. But what you are interested in, is to find the best fit that maximizes how much they overlap with each other (and minimize gaps). Here’s where computer science comes in to play. In order to maximize overlap, you use the concept of ‘dynamic programming‘. It is helpful to understand dynamic programming as an algorithm rather than a program per se (it’s not like you’ll be sitting in front of a computer and programming code if you want to compare eyeless and aniridia; the BLAST program will do the dirty work for you. It uses dynamic programming code that’s built in to it). Amazingly enough, dynamic programming is not something as hi-fi as you might think. It is apparently the same strategy used in many computer spell-checkers! Little did the bioinformaticians who first developed dynamic programming techniques in genetics know, that the concept of dynamic programming was discovered far earlier than them. There are apparently many such cases in bioinformatics where scientists keep reinventing the wheel, purely because it is such an interdisciplinary field! One of the most common algorithms that is a subset of dynamic programming and that is used for aligning specific sequences within a genome is called the Smith-Waterman algorithm. Like dynamic programming, another useful algorithm in bioinformatics is what is called a greedy algorithm. In a greedy algorithm, you are interested in maximizing overlap in each baby-step as you construct the alignment procedure, without consideration to the final overlap. In other words, it doesn’t matter to you how the sequences overlap in the end as long as each step of the way during the alignment process, you maximize overlap. Other concepts in alignment include, using a (substitution) matrix of possible scores when two letters – each in a sequence – overlap and trying to maximize scores using dynamic programming. Common matrices for this purpose are BLOSUM-62, BLOSUM-45 and PAM (Point Accepted Mutation).

So now that we know the basic idea behind sequence alignment, here’s what you can actually do in sequence analysis:

1. Using alignment, find a sequence from a database (eg. GenBank from the NCBI) that maximizes overlap between it and a sequence that isn’t yet in the database. This way, if you discover some new sequence, you can find relationships between it and known sequences. If the sequence in the database is associated with a given protein, you might be able to look for it in your specimen. This is called pairwise alignment.
2. Just as you can compare two sequences and find out if there is a statistically significant association between them or not, you can also compare multiple sequences at once. This is called multiple sequence alignment.
3. If certain regions of two sequences are the same, it can be inferred that they are conserved across species or organisms despite environmental stresses and evolution. A sequence encoding development of the eye is very likely to remain unchanged across multiple species for which sight is an essential function to survive. Here comes another interesting concept – phylogenetic relationships between organisms at a genetic level. Using alignment it is possible to develop phylogenetic trees and phylogenetic networks that link two or more gene sequences and as a consequence find related proteins.
4. Similar to finding evolutionary homology between sequences as above, one could also look for homology between protein structures – motifs – and then conclude that the regions of DNA encoding these proteins have a certain degree of homology.
5. There are tools in sequence analysis that look at features characteristic of known functioning regions of DNA and see if the same features exist in a random sequence. This process is called gene finding. You’re trying to discover functionality in hitherto unknown sequences of DNA. This is important, as the vast majority of genetic code is as far as we know, non-functional random junk. Could there be some region in this vast ocean of randomness that might, just might have an interesting function? Gene finding uses software that looks for tRNA encoding regions, promoter sites, open reading frames, exon-intron splicing regions, … – in short, the whole gamut of what we know is characteristic of functional code – in random junk. Once a statistically significant result is obtained, you’re ready to test this in a lab!
6. A special situation in sequence alignment is whole genome alignment (or global alignment). That is, finding the best fit between entire genomes of different organisms! Despite how arduous this sounds, the underlying ideas are pretty similar to local sequence alignment. One of the most common dynamic programming algorithms used in whole genome alignment is the Needleman–Wunsch algorithm.

Many of the things discussed for sequence analysis of DNA, have equal counterparts for RNA and proteins.

Protein Structure Property Analysis

Say that you have an amino acid sequence for a protein. There’s nothing in the databases that has your sequence. In order to build a 3-D model of this  protein, you’ll need to predict what could be the best possible shape given the constraints of bond angles, electrostatic forces between constituent atoms, etc. There’s a specific technique that warrants mentioning here – the Ramachandran Plot – that takes information on steric hindrance and plots the probabilities for different 3-D structures of an amino acid sequence. With a 3-D model, you could try to predict this protein’s chemical properties (such as pKa, etc.). You could also look for active sites on this protein that are the crucial regions that bind to substrates, based on known structures of active sites from other proteins… and so on.

This figure depicts an unrooted phylogenetic tree for myosin, a superfamily of proteins. [Courtesy: Wikipedia]

Protein Structure Alignment

This is when you try to find the best fit between two protein structures. The idea is very similar to sequence alignment, only this time the algorithms are a bit different. In most cases, the algorithms for this process are computationally intensive and rely on trial and error. You could build phylogenetic trees based on structural evolutionary homology too.

Protein Fingerprint Analysis

This is basically using computational tools to identify relationships between two or more proteins by analyzing their break-down products – their peptide fingerprints. Using protein fragments, it is possible to compare entire cocktails of different proteins. How does the protein mixture from a human retinal cell, compare to a protein mixture from the retinal cell of a mouse? This kind of stuff, is called Proteomics, because you’re comparing the entire protein from an organism to another. You could also analyze protein fragments from different cells within the same organism to see how they might have evolved or developed.

DNA Micro-array Analysis

A DNA microarray is a slide with hundreds of tiny dots on it. Each dot is tagged with a fluorescent marker that glows under UV (or another form of) light, if the cells within that dot produce a given protein. When a given protein is made, it means that a given genetic sequence is being expressed (or transcribed into RNA which in turn is being translated in to protein). By inoculating these dots with the same population of cells and by measuring the amount of light coming from these dots, you could develop a gene expression profile for these cells. You could then study the expression profiles of these cells under different environmental conditions to see how they behave and change.

You could also inoculate different dots with different cell populations and study how their expression profiles differ. Example: normal gastric epithelium vs cancerous gastric epithelium.

Of course you could try looking at all these light emitting dots with your eyes and count manually. If you want to take a shot at it, you might even be able to tell the difference between the different levels of brightness between dots! But why not use computers to do the job for you? There are software tools out there that can quantitatively measure these expression profiles for you.

Primer Design

There are many experiments and indeed diagnostic tests that use an artificially synthesized DNA sequence to serve as an anchor that flanks a specific region of interest in the DNA of a cell, and amplify this region. By amplify – we mean, make multiple copies. These flanking sequences are also called primers. Applications for example include, amplifying DNA material of the HIV virus to better detect presence or absence of HIV in the blood of a patient. The specific name for this kind of test or experiment is called the polymerase chain reaction. There are a number of other applications of primers such as gene cloning, genetic hybridization, etc. Primers ought to be constructed in specific ways that prevent them from forming loops or binding to non-specific sites on cell DNA. How do you find the best candidate for a primer? Of course, computation!

Metabolomics

A fancy word for modeling metabolic pathways and their relationships using computational analyses. How does the glycolytic pathway relate to some random metabolic pathway found in the neurons of the brain? Computational tools help identify potential relationships between all of these different pathways and help you map them. In fact, there are metabolic pathway maps out there on the web that continually get updated to reflect this fascinating area of ongoing research.

I guess that covers a whole lot of what bioinformatics is all about. When it comes to definitions, some people say that bioinformatics is the application part whereas computational biology is the part that mainly deals with the development of algorithms.

Neologisms Galore!

As you can see, some fancy new words have come into existence as a result of all this frenzied activity:

• Genomics: Strictly speaking, the study of entire genomes of organisms/cells. In bioinformatics, this term is applied to any studies on DNA.
• Transcriptomics: Strictly speaking, the study of entire transcriptomes (the RNA complement of DNA) of organisms/cells. In bioinformatics, this term is applied to any studies on RNA.
• Proteomics: Strictly speaking, the study of entire proteins made by organisms/cells. In bioinformatics, this term is applied to any studies on proteins. Structural biology is a special branch of proteomics that explores the 3-D structure of proteins.
• Metabolomics: The study of entire metabolic pathways in organisms/cells. In bioinformatics, this term is applied to any studies on metabolic pathways and their inter-relationships.

Real World Impact

So what can all of this theoretical ‘data-dredging’ give us anyway? Short answer – hypotheses. Once you have a theoretical hypothesis for something you can test it in the lab. Without forming intelligent hypotheses, humanity might very well take centuries to experiment with every possible permutation or combination of data that has been amassed so far and mind you, which continues to grow as we speak!

Thanks to bioinformatics, we are now discovering genetic relationships between different diseases that were hitherto considered completely unrelated – such as diabetes mellitus and rheumatoid arthritis! Scientists like Dr. Atul Butte ^{[go back]} and his team are trying to reclassify all known diseases using all of the data that we’ve been able to gather from Genomics. Soon, the days of the traditional International Classification of Diseases (ICD) might be gone. We might some day have a genetic ICD!

Sequencing of individual human genomes (technology for this already exists and many commercial entities out there will happily sequence your genome for a fee) could help in detecting or predicting disease susceptibility.

Proteins could be substituted between organisms (a la pig and human insulin) and better yet, completely manipulated to suit an objective – such as drug delivery or effectiveness. Knowing a DNA sequence, would give you enough information to predict protein structure and function, giving you yet another tool in diagnosis.

And the list of possibilities is endless!

Bioinformatics, is thus man’s attempt to making biology and medicine a predictive science .

Further Reading

I haven’t had the chance to read any other books on bioinformatics, what with exams just a couple of months away. Having read, “Developing Bioinformatics Computer Skills“, and found it a little too dense especially in the last couple of chapters, I would only recommend it as an introductory text to someone who already has some knowledge of computer algorithms. Because different algorithms have different caveats and statistical gotchas, it makes sense to have a sound understanding of what each of these algorithms do. Although the authors have done a pretty decent job in describing the essentials, the explanations of the algorithms and how they really function are a bit complicated for the average biologist. It’s difficult for me to recommend a book that I might not have read, but here are two I’m considering worth exploring in the future:

Understanding Bioinformatics by Marketa Zvelebil and Jeremy Baum

Introduction to Bioinformatics: A Theoretical And Practical Approach by Stephen Krawetz and David Womble

As books to refresh my knowledge of molecular biology and genetics I’m considering the following:

Molecular Biology Of The Cell by Bruce Alberts et al

Molecular Biology Of The Gene by none other than James D Watson himself et al (Of ‘Watson & Crick‘ model of DNA fame)

Let me know if you have any other suggested readings in the comments¹.

There are also a number of excellent Opencourseware lectures on bioinformatics out on the web (example: at AcademicEarth.org. For beginners though, I suggest Dr. Daniel Lopresti’s (Lehigh University) fantastic high level introduction to the field here. Also don’t forget to check out “A Short Course On Synthetic Genomics” by George Church and Craig Venter on Edge.org for a fascinating overview of what might lie ahead in the future! In the race to sequence the human genome, Craig Venter headed the main private company that posed competition to the NIH’s project. His group of researchers ultimately developed a much faster way to sequence the genome than had previously been imagined - the shotgun sequencing method.

Hope you’ve enjoyed this high level tour. Do send in your thoughts, suggestions and corrections!

UPDATE 1: Check out Dr. Eric Lander‘s (one of the stalwarts behind the Human Genome Project) excellent lecture at The Royal Society from 2005 called Beyond the Human Genome Project – Medicine in the 21st Century that tries to gives you the big picture on this topic.

UPDATE 2: Also check out NEJM’s special review on Genomics called Genomics — An Updated Primer.

Copyright © Firas MR. All rights reserved.

–

Your feedback counts:

1. Dr. Atul Butte ^¥ suggests checking out some of the excellent material at NCBI’s Bookshelf. ^{[go back]}

Readability grades for this post:

Flesch reading ease score: 57.4
Automated readability index: 10.8
Flesch-Kincaid grade level: 9.7
Coleman-Liau index: 11.5
Gunning fog index: 13.4
SMOG index: 12.2

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The Monty Hall Paradox

One of the 3 doors hides a car. The other two hide a goat each. In search of a new car, the player picks a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player pick door 2 instead of door 1. Is there an advantage if the the player decides to switch? (Courtesy: Wikipedia)

Hola amigos! Yes, I’m back! It’s been eons and I’m sure many of you may have been wondering why I was MIA. Let’s just say it was academia as usual.

This post is unique as it’s probably the first where I’ve actually learned something from contributors and feedback. A very critical audience and pure awesome discussion. The main thrust was going to be an analysis of the question, “If you had to pick an answer in an MCQ randomly, does changing your answer alter the probabilities to success?” and it was my hope to use decision trees to attack the question. I first learned about decision trees and decision analysis in Dr. Harvey Motulsky’s great book, “Intuitive Biostatistics“. I do highly recommend his book. As I pondered over the question, I drew a decision tree that I extrapolated from his book. Thanks to initial feedback from BrownSandokan (my venerable computer scientist friend from yore ) and Dr. Motulsky himself, who was so kind as to write back to just a random reader, it turned out that my diagram was wrong and so was the original analysis. The problem with the original tree (that I’m going to maintain for other readers to see and reflect on here) was that the tree in the book is specifically for a math (or rather logic) problem called the Monty Hall Paradox. You can read more about it here. As you can see, the Monty Hall Paradox is a special kind of unequal conditional probability problem, in which knowing something for sure, influences the probabilities of your guesstimates. It’s a very interesting problem, and has bewildered thousands of people, me included. When it was originally circulated in a popular magazine,  “nearly 1000 PhDs” (cf. Wikipedia) wrote back to say that the solution put forth was wrong, prompting numerous psychoanalytical studies to understand human behavior. A decision tree for such a problem is conceptually different from a decision tree for our question and so my original analysis was incorrect.

So what the heck are decision trees anyway? They are basically conceptual tools that help you make the right decisions given a couple of known probabilities. You draw a line to represent a decision, and explicitly label it with a corresponding probability. To find the final probability for a number of decisions (or lines) in sequence, you multiply or add their individual probabilities. It takes skill and a critical mind to build a correct tree, as I learned. But once you have a tree in front of you, its easier to see the whole picture.

Let’s just ignore decision trees completely for the moment and think in the usual sense. How good an idea is it to change an answer on an MCQ exam such as the USMLE? The Kaplan lecture notes will tell you that your chances of being correct are better off if you don’t. Let’s analyze this. If every question has 1 correct option and 4 incorrect options (the total number of options being 5), then any single try on a random choice gives you a probability of 20% for the correct choice and 80% for the incorrect choice. The odds are higher that on any given attempt, you’ll get the answer wrong. If your choice was correct the first time, it still doesn’t change these basic odds. You are still likely to pick the incorrect choice 80% of the time. Borrowing from the concept of “regression towards the mean” (repeated measurements of something, yield values closer to said thing’s mean), we can apply the same reasoning to this problem. Since the outcomes in question are categorical (binomial to be exact), the measure of central tendency used is the Mode (defined as the most commonly or frequently occurring thing in a series). In a categorical series – cat, dog, dog, dog, cat – the mode is ‘dog’. Since the Mode in this case happens to be the category “incorrect”, if you pick a random answer and repeat this multiple times, you are more likely to pick an incorrect answer! See, it all make sense ! It’s not voodoo after all !

Coming back to decision analysis, just as there’s a way to prove the solution to the Monty Hall Paradox using decision trees, there’s also a way to prove our point on the MCQ problem using decision trees. While I study to polish my understanding of decision trees, building them for either of these problems will be a work in progress. And when I’ve figured it all out, I’ll put them up here. A decision tree for the Monty Hall Paradox can be accessed here.

To end this post, I’m going to complicate our main question a little bit and leave it out in the void. What if on your initial attempt you have no idea which of the answers is correct or incorrect but on your second attempt, your mind suddenly focuses on a structure flaw in one or more of the options? Assuming that an option with a structure flaw can’t be correct, wouldn’t this be akin to Monty showing the goat? One possible structure flaw, could be an option that doesn’t make grammatical sense when combined with the stem of the question. Does that mean you should switch? Leave your comments below!

Hope you’ve found this post interesting. Adios for now!

Copyright © Firas MR. All rights reserved.

Readability grades for this post:

Flesch reading ease score:  72.4
Automated readability index: 7.8
Flesch-Kincaid grade level: 7.3
Coleman-Liau index: 8.5
Gunning fog index: 11.4
SMOG index: 10.7

Readings:

Intuitive Biostatistics, by Harvey Motulsky

The Monty Hall Problem: The Remarkable Story Of Math’s Most Contentious Brain Teaser, by Jason Rosenhouse

usmle, decisionanalysis, decisiontree, examination, examinationtechnique, “examination technique”, “decision analysis”, “decision tree’, montyhallproblem, “monty hall problem”

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