It’s Movember! Review your knowledge of Bayes’ theorem before getting your PSA test.

Background info

There are 3 million in the U.S. currently living with prostate cancer. There are approximately 320 million people in the US today, roughly half of whom will have prostates. Hence, let us take the prevalence of prostate cancer among those who have prostates to be approximately 3 in 160, or just under 2%.

The false positive (type I error) rate is reported at 33% for PSA velocity screening, or as high as 75%. The false negative (type II error) rate is reported as between 10-20%. For the purpose of this analysis, let’s give the PSA test the benefit of the doubt, and attribute to it the lowest type I and type II error rates, namely 33% and 10%.

Skill testing question

If some random person with a prostate from the United States, where the prevalence of prostate cancer is 2%, receives a positive PSA test result, where that test has a false positive rate of 33% and a false negative rate of 10%, what is the chance that this person actually has prostate cancer?

Bayes’ theorem

Recall Bayes’ theorem from your undergraduate Philosophy of Science class. Let us define the hypothesis we’re interested in testing and the evidence we are considering as follows:

P(h): The prior probability that this person has cancer
P(e|¬h): The false positive (type I error) rate
P(¬e|h): The false negative (type II error) rate

P(h) = 3/160
P(e|¬h) = 0.33
P(¬e|h) = 0.10

Given these definitions, the quantity we are interested in calculating is P(h|e), the probability that the person has prostate cancer, given that he returns a positive PSA test result. We can calculate this value using the following formulation of Bayes’ theorem:

P(h|e) = P(h) / [ P(h) + ( P(e|¬h) P(¬h) ) / ( P(e|h) ) ]

From the above probabilities and the laws of probability, we can derive the following missing quantities.

P(¬h) = 1 – 3/160
P(e|h) = 0.90

These can be inserted into the formula above. The answer to the skill-testing question is that there is a 4.95% chance that the randomly selected person in question will have prostate cancer, given a positive PSA test result.

What if we know more about the person in question?

Let’s imagine that the person is not selected at random. Say that this person is a man with a prostate and he is over 60 years old.

According to Zlotta et al, the prevalence of prostate cancer rises to over 40% in men over age 60. If we redo the above calculation with this base rate, P(h) = 0.40, we find that P(h|e) rises to 64.5%.

Take-home messages

  1. Humans are very bad at intuiting probabilities. See Wikipedia for recommended reading on the Base Rate Fallacy.
  2. Having a prostate is neither a necessary nor a sufficient condition for being a man. Just FYI.
  3. Don’t get tested for prostate cancer unless you’re in a higher-risk group, because the base rate of prostate cancer is so low in the general population that if you get a positive result, it’s likely to be a false positive.

The answer to the question

On October 9, inspired by the STREAM research group’s Forecasting Project, I posed a question to the Internet: “Do you know how the election is going to turn out?” I tweeted it at news anchors, MP’s, celebrities, academics, friends and family alike.

I’m very happy with the response! I got 87 predictions, and only 11 of them were what I would consider “spam.” I took those responses and analysed them to see if there were any variables that predicted better success in forecasting the result of the election.

The take-home message is: No. Nobody saw it coming. The polls had the general proportion of the vote pretty much correct, but since polls do not reflect the distribution of voters in individual ridings, the final seat count was very surprising. This may even suggest that the Liberals got the impetus for a majority result from the fact that everyone expected they would only narrowly eke out a victory over the incumbent Tories.

You can view the final report in web format or download it as a PDF.

Aristotle’s Square of Opposition … in Lojban

Here it is: one obscure type of logic expressed in an even more obscure type of logic! You’re welcome!

xusra natfe
kampu ro da poi broda cu brode no da poi broda cu brode
steci da poi broda cu brode da poi broda cu na brode

I wasn’t sure whether to render the O categorical sentence (bottom-right) as {naku ro da poi broda cu brode} or {da poi broda cu na brode}. It has been left as an exercise for the reader to determine whether they are logically equivalent.

Can you predict the outcome of Canada’s 42nd federal election?

The STREAM (Studies of Translation, Ethics and Medicine) research group at McGill University, of which I’m a part, has been working on a project for the last year or so in which we elicit forecasts of clinical trial results from experts in their field. We want to see how well-calibrated clinical trialists are, and to see which members of a team are better or worse at predicting trial outcomes like patient accrual, safety events and efficacy measures.

Inspired by this, I borrowed some of the code we have been using to get forecasts from clinical trial investigators, and have applied it to the case of Canada’s 42nd federal election, and now I’m asking for you to do your best to predict how many seats each party will get, and who will win in your riding.

Let’s see how well we, as a group, can predict the outcome, and see if there are regional or demographic predictors for who is better or worse at predicting election results. The more people who make predictions, the better the data set I’ll have at the end, so please submit a forecast, and ask your friends!

The link for the forecasting tool is here: http://www.bgcarlisle.com/elxn42/

Just to make it interesting: I will personally buy a beer for the forecaster who gives me the best prediction out of them all.* :)

* If you are younger than 18 years of age, you get a fancy coffee, not a beer. No purchase necessary, only one forecast per person. Forecaster must provide email with the prediction in order for me to contact him/her. In the case of a tie, one lucky beer-receiver will be chosen randomly. Having the beer together with me is conditional on the convenience of both parties (e.g. if you live in Vancouver or something, I’ll just figure out a way to buy you a beer remotely, since I’m in Montreal). You may consult any materials, sources, polls or whatever. This is a test of your prediction ability, not memory, after all. Prediction must be submitted by midnight on October 18, 2015.

Lojban logical connectives illustrated with Venn diagrams

Truth functions for Lojban logical connectives
Truth functions for Lojban logical connectives

For my own reference, I have illustrated the 14 possible truth functions that can be expressed using the A, E, O and U connectives in Lojban, and annotated them with the most appropriate forethought connective to do the job.

In many cases, there are multiple ways to express a single truth function. For example, {gonai broda gi brode} is logically equivalent to {segonai broda gi brode} and {go broda ginai brode} and {sego broda ginai brode}, but despite the fact that they are well-formed Lojban there is literally no reason to ever use those constructions, and ones like {go … ginai …} kind of defeats the purpose of using a forethought connective in the first place. Mutatis mutandis with {ga … gi …} vs {sega … gi …}, etc.

Of course, since there’s 4 regions of the Venn diagram that could be shaded or not, that makes 24=16 possible truth functions. The topmost Venn diagram is the forethought-connected question, not an attempt at the truth function where all the regions are unshaded. So what happened to the remaining two functions? It is not possible, using the regular Lojban connectives, to make a Venn diagram that would be all white or all red. Fortunately, as the CLL says, these are “pretty useless anyway.”

Come to think of it, how would I render those into English? “A or B or both or not A or B?” and “Not A and Not B and not not A or B?” Gross.

For a more legible version, see the attached PDF: Truth functions

Stephen Harper’s “soft on torture” agenda

A longstanding policy of the Conservative government has been reliance on information gathered from, and outright complicity with the torture of human beings. Since we’re deep into an election, and elections are one of the most clear ways that we’re supposed to be keeping our government accountable, let’s have a look back at the Conservative government’s “soft on torture” agenda.

As Man-in-Blue-Suit would say, let’s be clear. I’m not talking about metaphorical torture. I’m talking about purposely imposing literal pain, humiliation and deprivation on actual living human beings in order to elicit information, or to otherwise bring about some political gain. This is serious, and to call it “torture” is not an exaggeration in the slightest. And Stephen Harper has made sure that the Canada is a part of it. To sum up, as Harper said himself, we might not recognise Canada, now that he’s had his way with it.

To start with, this is not a one-off thing. This is a policy that the Cons have crafted over the course of years. Far from being an accident or an oversight, parts of this “soft on torture” policy were implemented in secret, which suggests that they understood the enormity of what they were doing, but they wanted to get away with it anyway.

Contrary to Harper’s patronising dismissals, this is not a conspiracy theory either. This is well-documented by internal government “watchdogs,” military memos, Parliamentary debate and even reports from foreign powers.

The following is not an exhaustive report, but just a convenience sample that I came up with. The earliest article is from the Globe and Mail in 2012, saying that Harper covered up the delivery of prisoners to be tortured more than 5 years prior, and the most recent is the response to the CIA report in December of last year.

Fortunately, Canada is a democracy, and one of the things that we citizens of Canada have is the right—and the responsibility—to hold the government of the day accountable for its actions at the polls.

Short story prompt for Lojban enthusiasts: la cizra mensi

Short story prompt: la cizra mensi

The hero of your short story has found a way to summon the Weird Sisters of Macbeth fame to inquire after the future. Worried that the witches will try to trick your hero by giving a prophesy that can be favourably and plausibly read one way, but that also has an alternate, surprising and terrible interpretation that is consistent with the words of the prophesy, your hero finds a way to force the witches to speak in Lojban.

Unfortunately for the hero of your story, a witch’s prophesy can backfire in unexpected ways that still respect the letter of the prophesy itself, even if it’s delivered in a language that’s syntactically unambiguous.

Macbeth 1.3

In the spirit of this short story prompt, I have rendered the first part of Macbeth, act 1 scene 3 into Lojban for your enjoyment. Corrections and suggestions welcome. :)

termafyfe’i 1: [1] .i doi lo mensi do pu zvati ma

termafyfe’i 2 .i lo jai bu’u lo nu catra lo xarju

termafyfe’i 3 .i doi lo mensi do zvati ma

termafyfe’i 1 .i lo fetspe be lo blopre pu cpana be lo galtupcra ku ralte lo narge

[5] gi’e omnomo gi’e omnomo gi’e omnomo .i lu ko dunda fi mi li’u se cusku mi .i lu ko cliva doi lo termafyfe’i li’u lo zargu citka cagna cu se krixa .i lo nakspe be lo se go’i pu klama la .alepos. gi’e bloja’a la .tirxu. .i ku’i ne’i lo julne mi lo te go’i fankla

[10] .ije mi simsa be lo ratcu poi claxu lo rebla ku co’e gi’e co’e gi’e co’e

termafyfe’i 2: .i mi dunda do pa lo brife

termafyfe’i 1 .i do xendo

termafyfe’i 3 .i mi co’e pa lo drata

termafyfe’i 1: [15] .i mi ralte ro da poi drata .i je’a lo blotcana cu bifca’e ro da poi farna be fi lo makfartci pe lo blopre ku’o zi’e poi se djuno .i mi ba simsa be lo sudysrasu bei lo ka sudga ku rincygau

[20] .i lo nu sipna ku ba canai lo donri ku .a lo nicte ku dandu za’e lo galtu dinju canko gacri .i zo’e ba dapma renvi .i ba ca lo tatpi jeftu be li so pi’i so cu jdika lo ka stali .e lo ka pacna .e lo ka gleki

[25] .i zu’u lo bloti to’e pu’i se daspo .i zu’unai lo go’i vilti’a se renro .i ko viska lo se ralte be mi

termafyfe’i 2: .i ko jarco fi mi .i ko jarco fi mi

termafyfe’i 1 .i mi nau ralte lo tamji be fi lo blosazri

[30] poi ca lo nu zdani klama ku bloti janli morsi

[.i ne’i damri]

termafyfe’i 3: .i damri .i damri .ua .i la .makbet. je’a tolcliva

ro da poi termafyfe’i: .i lo cizra mensi noi xance jgari simxu zi’e noi klama be fo lo xamsi .e lo tumla be’o sutra

[35] cu klama fi’o tadji tu’a di’e .i ciroi klama lo tu’a do .i ciroi klama lo tu’a mi .i ciroi ji’a klama .iki’ubo krefu fi li so .i ko smaji .i lo makfa cu bredi

[.i nerkla fa la .makbet. .e la bankos.]

Warboy Nux is Gonzo the Great [Mad Max spoilers]

I saw Mad Max: Fury Road (2015) last week. I wasn’t planning on it, but then I heard that a bunch of Men’s Rights-type dudebros hated it for attempting to undermine the patriarchy or something, so I kinda had to. I didn’t remember it until after the fact when my little sister pointed it out, but the vain cry of “liberal brainwashing” also seems to have been the reason I went to see The Muppets (2011). Apparently the ire of conservative loud-mouths is all it takes to get me to go see a movie. Take note, Hollywood.

Warboy Nux and Gonzo the Great
“Oh what a day! What a lovely day!”

This is not the only parallel I found between Mad Max and The Muppets. Warboy Nux is Gonzo the Great, reimagined as a brainwashed member of a post-apocalyptic automobile cult.

Like Nux, it would not be out of character for Gonzo to stand on a moving vehicle, throw an exploding spear at something and cry “Witness me!” as he performs a stunt that is very likely to kill him. Gonzo and Nux are both creatures of the extreme. This is why we like them. They are interesting because their characters feel things so deeply, and the storytellers, in both cases, know that the way to highlight this depth of feeling is by making them care—and care strongly—about things that seem absolutely strange to us.

While Gonzo is less likely to be actively trying to hurt someone with his antics, even Nux seems to be less motivated by malice than by a heartfelt (albeit misguided) desire to live a life that is remarkable and meaningful. These characters both have an exterior of explosions, chrome and spectacle, and it takes barely a scratch to reveal an interior of adorable, sometimes-pathetic, but utterly non-ironic, earnest longing. In The Muppet Movie (1979), the most touching moment is Gonzo’s I’m going to go back there someday. If you’re going to cry during The Muppet Movie, this is when it will happen.1 Nux’s whispered “Witness me” in his final few seconds is similarly and unexpectedly emotional. Nux gets a finale that’s as climactic as he could have ever dreamed of. And most heart-wrenching, after an earlier failure in the eyes of his god, he expresses his redemption among his new friends in the language of the cult he came from.

I think that’s what’s so great about Nux and Gonzo: They feel, believe and act in extreme ways. They don’t do things by half-measures and they don’t try to hide their passions under a layer of irony or sarcasm. This makes them very vulnerable, and this is what makes them great.


1 Recommended reading on the subject of Gonzo the Great: Joey Comeau’s Lockpick Pornography.

Gotcha! This is why piracy happens

Stata

This summer, I took a two-week long course on systematic reviews and meta-analytic techniques for which there was some required software, in this case, Stata. As a McGill student, I was encouraged to buy the student version, which was about $50 for “Stata Small.” Not bad. I’ve paid more for textbooks. So I got out my credit card, bought the license, installed it on my computer, and ran the very first example command of the course. I immediately got a string of red letter error text.

The error message was telling me that my license did not allow me enough variables to complete the command. I checked the license, and it said I was allowed 120 variables. I checked the “Variable manager” in Stata, and I had only assigned 11 variables. (I checked the variable limit beforehand in fact, and made sure that none of the data sets that we’d be working with had more than 120 variables. None of them came close to that limit.)

So I emailed Stata technical support. It turns out that the meta-analysis package for Stata creates “hidden variables.” Lots of them, apparently. So many that the software cannot accomplish the most basic commands. Then they tried to up-sell me to “Stata SE.” For $100 more, they said, they would send me a license for Stata that would allow me to run the meta-analysis package—for realsies this time.

I asked for a refund and decided that if I really needed Stata, I would use the copy that’s installed on the lab computers. (Now I’m just using the meta package in R, which does everything Stata does, just with a bit more effort.)

For the record: I am perfectly fine with paying for good software. I am not okay with a one-time purchase turning me into a money-pump. I thought that the “small” student license would work. All their documentation suggested it would. If I had upgraded to “Stata SE,” would that have actually met my needs, or would they have forced me to upgrade again later, after I’d already made Stata a part of my workflow?

It probably would have been okay, but the “gotcha” after the fact soured me on the prospect of sending them more money, and provided all the incentive I need to find a way to not use Stata.

iTunes

A few years ago, I bought a number of pieces of classical music through the iTunes Store. I shopped around, compared different performances, and found recordings that I really liked. This was back when the iTunes store had DRM on their music.

I’ve recently switched to Linux, and now much of the music that I legally bought and paid for can’t be read by my computer. Apple does have a solution for me, of course! For about $25, I can subscribe to a service of theirs that will allow me to download a DRM-free version of the music that I already paid for.

This is why I won’t even consider buying television programmes through the iTunes Store: It’s not that I think that I will want to re-watch the shows over and over and I’m afraid of DRM screwing that up for me. It’s because I’ve had some nasty surprises from iTunes in the past, and I can borrow the DVD’s from the Public Library for free.

For the record: I do not mind paying for digital content. But I won’t send you money if I think there’s a “gotcha” coming after the fact.

I’m really trying my best

People who produce good software or music should be compensated for their work. I don’t mind pulling out my wallet to help make that happen. But I don’t want to feel like I’m being tricked, especially if I’m actually making an effort in good faith to actually pay for something.

Since DRM is almost always fairly easily circumvented, it only punishes those who pay for digital content. And this is why I’m sympathetic to those who pirate software, music, TV shows, etc.