Friday, November 10, 2017

What John Snow's Pump Handle Portends for Precision Medicine

John Snow (the physician) traced the 1854 London cholera outbreak to the Broad Street water pump, had the pump handle removed, and saved the day. That's the founding narrative of public health we were taught.

Turns out, the story is more complicated. The pump handle was removed long after the threat of cholera passed from that spot, John Snow had a difficult time convincing people of his theory that cholera was spread by invisible particles borne in water, and London was rocked by Cholera many times in the following decades. Yet, we should remember John Snow for being innovative, and identifying a microbial cause for cholera, an accurate description of how the disease is transmitted.

Cholera rocked London until a bunch of people (including William Farr), pursuing the wrong idea about how cholera spread, acted to protect the population at large by digging out the city streets and putting in an effective sewer system. The sewers of London were designed to cultivate a more productive working class by removing the filth that the city's "better classes" were convinced kept much of their workforce sick, caring for others, or dying before their working years had come to an end. At best, they were part right, in identifying filth. But they were very wrong in their thinking that it was harmful ethers emanating from the filth that was the problem.

Today, the US government has committed a huge sum to the Precision Medicine Initiative, with the goal of recruiting a million Americans into a cohort, and measuring our genes, with the promise of providing individualized medical information to improve the delivery of medical care. The promise is that Precision Medicine will deliver us from the hapless poking and prodding of medical practitioners groping in the dark - to a gleaming future where, after reading our genes, a precisely-guided medication will be identified to provide us with maximal benefit. Turns out, the promise of a gleaming future where we will be known completely and our dis-eases will be readily dispatched is as old as medicine itself (see this great Atlantic post by Nathaniel Comfort).
But perhaps this time, medicine, or particularly Precision Medicine, will deliver on the promise. I would argue, that even if it does deliver miraculous rescues of many people from the clutches of truly horrifying diseases, it will likely have little impact on our health as a population, perhaps even diverting our attention from those interventions most likely to have the greatest beneficial impacts.

John Snow correctly identified the causal mechanism behind the transmission of cholera from one person to another. What he did not do (and I would argue could not do) was use that information to effectively prevent the spread of cholera from one person to another. Imagine, if you will, that he had been able to convince the authorities in London of the water-borne nature of cholera, and that it's spread could be interrupted by the timely removal of pump handles. One can imagine setting up an infrastructure to identify cases of cholera (that already existed, though could have been improved), leading to the deployment of a team of investigators to identify the probable source, and in turn remove pump handles in affected areas. Would this have stopped cholera? Yes, within days, by which time it would likely have spread to dozens of other people. And in London, a hub of global trade, the frequent re-introduction of cholera was virtually guaranteed. Not to mention the hardship on the population of having to travel farther and farther to get their water from an ever-diminishing set of functioning pumps, and whether some of those people were now carrying cholera with them to other parts of the city. John Snow and his pump handle removers would be playing whack-a-mole. They would, over the years, improve their methods and whack the cholera-laden pump handles faster and faster. But it wouldn't do anything to stop cholera from cropping up in the first place.
Installing the sewers, on the other hand, (largely) prevented cholera from being transmitted, even when it was re-introduced to the city.

My analogy then, is to whether the knowledge to be gained from the Precision Medicine Initiative (and the knowledge gained will be vast) will have much impact. The first fruits from precision medicine have been in the area of cancer treatment. Some tremendously impressive gains have been made. I imagine it's likely that many more are coming.

Image result for minority reportBut the promoters of precision medicine also hold out more fantastical ideas. For instance: that we will be better able to assess the risk of future disease. That sounds awesome. If I know I'm at increased risk of heart disease, I can take action - I can eat less red meat, more veggies, exercise more, and so on. But a couple of other things also may happen that should be of great concern. The simplest concern is that people "not" at increased risk of heart disease may think they are wasting their time by doing things to prevent heart disease. Why walk laps at the mall and eat like a bird when I could just eat what I like and spare my knees the agony? But everyone is at risk of heart disease, so what's the great advantage in hair-splitting whether we are 30% likely or 70% likely to die from it?
What about finding out I have an elevated risk of an unpreventable health outcome? Is that knowledge worth knowing? In some cases it may be, but frankly, I'd rather not know if I have a higher risk of Parkinson's or Alzheimer's. It's just one more worry in a life full of worries. I'm glad I didn't waste time worrying about testicular cancer before I got it.
And here's a really scary thought - many of the things we do as individuals to prevent disease are ineffective - either we've got the wrong idea about how the disease works, or we have over-estimated the preventive effect of taking action, or we are taking the right action, but 10 years too late. What then are we doing to people by telling them there is a train coming down the tracks at them, then suggesting they totally change their lives, when those changes may or may not pull them off the tracks - or even worse, put them on more dangerous footing.

Individualizing risk individualizes risk
Here I think is the biggest problem, and it's where I come back to John Snow and the individualized approach to prevention. The promise of individualizing our risks - perhaps producing a scorecard with red, orange, yellow and green labels on various potential diseases facing our future selves - this individualization has an insidious impact. It implies that whatever got us to here, we ourselves are responsible for the next step. It localizes prevention to the individual, and as a result, implies we are each responsible in our own way for our health. And re-enforces the notion that others who have befallen ill health may be in some way responsible for it. Especially if we can see that they are lazy, fat, dumb, poorly kept, or even just poor. Sometimes, we just project those qualities upon them. And it takes away from focusing on steps we can take to promote everyone's health. Like sewers. Walkable neighborhoods. Shifting the subsidies for food production that would deliver all of us better options. Fewer handguns. More compassion. More connection.

I can hear some of you shouting that these goals need not be in conflict. I agree, they need not. but I'm arguing that so much of our nation's research budget, and hype about the future, are devoted to diving deeper into our genes, that leaves the rest of us a bit parched.

Friday, October 13, 2017

Me and my Orchid Tumor

The Origin
Back in May, I felt something odd. I was pretty sure it was a tumor, but I also have a touch of hypochondria.
I had felt something odd in the same place a year ago and had it checked out. After a few minutes in the exam room though, the urgent care doc had me convinced not to worry about it. And I didn't.
Until May 18th, when I felt something really and truly odd.
Went back to the same urgent doc. In an even shorter exam, we decided that I needed to get imaging. And fast.

The Work-Up
Within three days, I was being examined by an ultrasound tech. I am grateful she did not remark on what she was seeing. I was fairly certain I had a tumor at that point. I had read enough about it by now to know that a key symptom was the complete absence of pain under circumstances where one should feel it. But, a haze of plausible denial was crucial for getting through the night. And the next day. During these days, I prepared myself, by saying "cancer" out loud a few times.
And I told my boss that bad news might very well be coming. And my parents.

The Diagnosis
Image may contain: 1 person
I waited for the diagnosis. And waited. I checked my health portal a few times a day. No news. A few days later the urgent care doc called. During a work party. That I was hosting.
He delivered the news quickly. Gracefully. And hung up.
There were to be follow-up appointments to confirm the diagnosis, but this is the moment I knew. I had no doubts, no plausible alternatives to cushion me from the inevitable.
I was wounded, as this photo I took moments after hearing the news shows.

At this point, I didn't feel like the tumor was part of me. And I think that's why I didn't think of myself as "having cancer". I had a tumor, a reminder of my embryonic origins, and I wanted it gone.

The Confirmation
No automatic alt text available.I visited the urologist. She wanted it out too. And on June 14th, she delivered a mass that pathology confirmed was a 4.5 centimeter orchid tumor. It's a boy!
I was relieved. It felt great to have it out. And it felt great to have a singular focus in front of me. I had one job, and only one thing on my mind: recovering from being attacked by a very nice woman with a knife.
My parents drove to Worcester to pick me up after surgery, and I developed a nice routine of sleeping, watching TV, and allowing myself to be doted on in the most beautiful place on Earth.

Looking back, I certainly didn't think of myself as a "cancer patient", or a "cancer survivor". I pretty much just focused on the task in front of me - getting back on my feet.
I wasn't really thinking about whether I had cancer, or had had cancer. Or if I should feel affinity with anyone else who had had cancer.
That, and every step of the process since May 18th, I was being fed bits and pieces of information. It was all I could do to keep up with what I had in front of me. And I needed some spare bandwidth to make jokes about it all along the way as well.

The Search for Information
Towards the end of my stay in Vermont, I began to read up a bit more on the tumor, mainly to satisfy my parents' curiosity. Early on, I had read up on what clinical trials might be available. And when I saw words like "bleomycin", my stomach sank, and I knew I had to just put it away, and work only with what was right in front of me. To make decisions one at a time, without thinking too hard about them, and definitely without looking back.
Now that I was going back in to the literature, I knew I needed to start out slow. With a review article or two. I found the claim that "the 20-year survival is indistinguishble from 100%" very re-assuring, and I repeated it often, to everyone who would hear me. But I was also reading about "surveillance", "recurrence", and "retroperitoneal lymph nodes". And for the first two weeks back at work, I had no patience for it. Instead, I pulled dozens of articles about seminoma and its management, organized them into folders, and read them. And I remembered everything I read. It was astonishing to me how clearly I could recall exactly what each of the authors had said. I knew where each cohort was located, how many people were in each one, and how the results differed slightly. And how the standards of care for surveillance strategies varied from place to place.
So, by the time I met the oncologist, I knew what I wanted to do, and I had the citations in my head to back my decision up. I was well versed in the arguments for and against each strategy.
I wanted no chemo, and no CT scans. Modestly spaced followup scans for the next 5 years.

The Oncologist
She was not down with my decision. She wanted to follow the US guidelines and do a series of over a dozen CT scans that would produce something like a 2-5% chance of inducing a brand-new tumor. I wanted to do something like the approach endorsed in the UK, Spain, and Norway, countries with much larger cohorts with much better follow-up than in the US (or anywhere else). They do many fewer scans, and over a shorter period. And they do it that way because they have found better survival and fewer side effects than the US approach. I even printed out a schedule to discuss with her. She declined to look at it, and kept repeating the guidelines. I was astonished. I was ready to discuss, to argue if necessary, to listen (if essential). But I was not prepared to find out I had a small role to play in my own care decision. I was furious.
She did agree to run my preference past the 'tumor board'. And I thought, who are they to decide? Can I trust my oncologist to fairly represent my concerns when she resisted hearing them? Can I appeal their decision? But decided in the end I had to stick to what's in front of me.

Midlife - Crisis Preempted
Oh, did I mention that I first met my oncologist on my birthday? My 50th birthday?
Which brings me to how I've been travelling through this experience.
I was not shocked by the diagnosis. I've heard almost everyone else diagnosed with cancer say that they couldn't hear anything else. I was a sponge. I couldn't learn enough. I wanted all the reports, all the lab values, all the articles.
I've often noticed that I've experienced many parts of this process like a road trip. I don't really know what's coming. I've heard some stuff from other people about what's on the road ahead, but there's nothing like seeing it for yourself. I find the anticipation of these new experiences thrilling, even when they are unpleasant in many aspects. And I find myself focused on the new-ness, the unusual-ness, and the quirky unexpected moments of these experiences more than on the pain or the uncertainty. Like when I was getting the ultrasound, I started laughing in the middle of it. I was annoyed by the sound the computer made every time the tech saved a picture. Bzzzt. Bzzzt. Bzzzt. Bzzzt. And I thought, why did they make it sound like a long series of errors? Denied. Denied. Denied. They could have programmed any noise. How about: Ding. Ding. Ding. A small thing would make such a big difference in the experience. And so that made me laugh.

Revising the Decision
Anyway, back to the decision about what to do now that I had no tumor, no sign of any tumor, a small likelihood of ever seeing this cancer again, and a life expectancy "indistiguishable" from someone who had never had a tumor. But somehow, I was still a cancer patient. With a big decision about how to "keep an eye" on things that might crop up in the future. I kept reading, and getting more and more details about recurrence rates, risk factors, short and long term side effects of the various options in front of me.
Image may contain: 1 person, smiling, eyeglasses and indoorAnd then the tumor board ruled. My preference was not an option. I had to choose between getting a long series of CT scans with an unacceptably high level of producing a new (and much less treatable) cancer, or I would have to take chemo. The chemo regimen was carboplatin 7xAUC, taken in two doses, three weeks apart. That chemo regime is one of the "light" ones, it has many possible short term side effects, a low risk of long term debility, and a not inconsequential risk of damaging my heart.
It took me less than a second to decide. I went with chemo. She didn't even have a chance to finish the sentence.

Chemo sucks
Image may contain: 1 person, cloud, sky, closeup and outdoorMy first dose of chemo was cool enough. I was back on the road, I had a reason to take myself out of the everyday, and to experience what was happening to my body. I cut my hair short as a ritual to prepare for the chemo. At first, there were no symptoms at all. Over the next few days, I became exquisitely sensitive to sunlight - I got a deep tan in a matter of minutes. I posted updates on social media because I needed to stay in touch. I needed to know for sure people were thinking of me. And I put on a brave face. Thumbs up. But looking back at these photos, I can see I wasn't as upbeat and perky as I felt. I was still able to put in a little bit at work, but that came to a screeching halt with the second dose.

Image may contain: 1 person, outdoorIt is painful to look back at this picture. I swear I was genuinely happy when I took it. I had just showered, and although showering and walking back upstairs afterwards had taken every bit of energy out of me, I felt clean, I had fresh sheets, I could feel the love of so many people flowing through me. And yet, look at that face. I thought I was beaming.

I spent most of the month of August in bed. Most of it sleeping. Some TV, some reading, but mostly just laying in bed resting. My folks were terrific. If this scared them, they didn't show it. We had breakfast every morning. And if I was feeling frisky, we would play a few hands of cards. We had dinner every night. And I shouted questions at Alex Trebek.

But honestly, the fatigue was terrible. For weeks, I couldn't do more than walk downstairs, eat, and I'd be gasping for breath by the time I got back upstairs to bed.
When I got back to work, I could only last about 5 minutes in conversation before my mind would clamp down. My eyes would flow with tears because I couldn't get words to show their faces. I'd have to explain that I needed to be alone.
I couldn't do any programming. I made spelling errors I've never made before. Lots and lots of spelling errors. But it's all part of the road trip. I found myself fascinated by what I could and couldn't do, and how long it took for my brain or my lungs to wave the white flag. The spelling errors were telling me about how my memories are organized, my lungs were a governor. Exhaustion is sweet in its way. It is a clear and unmistakable break. It gives one full permission to stop. Stop and experience the familiar world as alien and new.

I've been back teaching for five weeks now. The first two weeks, it was all I could do to show up and mumble through the slides. Someone in my cancer support group suggested methylphenidate, and the requisite professionals agreed. It makes a huge difference, now I'm back to joking with the students, poking the quiet ones, cruising from one side of the room to the other, fielding questions, re-thinking my approach to teaching the basics: person-time. Randomness. Causation.
I've brought the students right along on this journey with me. They've seen me slouching in the chair, exhausted after an hour but still pushing through. But now they see something very much like my old self.

Very much like.
I feel like a counterfactual me. Almost a mirror image, but more of a quantum-entangled actor on the other side, uncannily diverging from what I would have been.

The road stretches out before us.
Let's roll.

Sunday, June 19, 2016

Guns Don't Solve Problems. Guns Cause Problems.

    A week has passed since the Orlando Massacre. I've spend most of the time since grieving, seeking the comfort of others, and sharing what comfort I can. In the back of my mind has been a battle over how to "respond". Personally, publicly, politically. I'm still at a loss, but here's one partial, tentative response, among the many swirling in my head.
    So many things got "attached" in one way or another to the profound loss Orlando, the Nation, and beyond experienced: gay blood, the presidential race, violence prevention, overpolicing, I could go on.
    Perhaps the thing that most caught my eye was the idea that somehow now that "the gays" were activated, gun control might stand a chance of moving forward in ways it has been slow to in the wake of so many national tragedies. On one hand, I'm perplexed by the idea, but also inspired by the challenge - we've made such huge progress on the "gay agenda", what can we offer?

Levers of Power and Change
    What can "the gays" offer to gun control efforts? I guess I'd start with a basic breakdown of the levers of power and change in this country thatwe've appealed to at one juncture or another in recent years: the executive, legislative, and judiciary branches of government, the press, entertainment, science, and interpersonal relationships.
    It appears that the judiciary is, for the next 3-5 years anyway, unlikely to be of great assistance. The legislature (Federally) is hamstrung, and likely to remain so at least until the 2018 election, and probably beyond. Although some State and local governments have made heroic efforts in recent years, the porous nature of State boundaries put severe limits on what can be accomplished. The Federal executive has done about as much as it can in the face of strident opposition from the other to branches. The press is a strong advocate, and also a strong impediment. More on that later. Science is unlikely to be of great assistance - the basic work demonstrating that possession of a firearm greatly increases one's own risk of death is already well established. In my experience, science itself rarely moves political change. Narratives do what statistics appear to be incapable of. Coming out has been an incredibly powerful method for invoking change, starting at the most atomistic level of power: family and friendship. But frankly, I'm struggling to think of what the corollary in terms of violence reduction through gun control is.

Changing the Narrative
     I suspect the way to create the greatest momentum now, which can later be leveraged for policy change, is to work on the narrative of how we tell stories about guns. Guns don't solve problems. Guns cause problems.
    But in the movies and video games, guns are frequently portrayed as solving problems, from a distance, without consequence. Now I love me some violent video games and movies (Reservoir Dogs springs to mind), but to the degree that we don't tell an accurate story about how using guns screws everyone up, we're doing a disservice. We should demand that television and film makers don't turn to guns as a plot device to get rid of a problem to allow the protagonist to progress, but rather every use of a gun should endeavor to show how it makes everyone's life, including the shooter's, much more complicated and less comfortable. That would be a more accurate story.
    Narrative moves opinion more than statistics do. With that in mind, a committed, passionate press should tell more stories about the consequences of firearms use, more about the victims, and also more about what happens to those who carry and fire them. Get into the fears that drive people to carry, and to shoot, get into the legal consequenes, sure; and also the long term psychological consequences of what injuring or killing another human causes. Get the stories of people who used to carry and decided not to any longer - give current firearms owners a path out.

Sunday, January 24, 2016

New Data. New Opportunities.

So, I'm working on a new analysis, and my plan is to describe what I'm doing, why I'm doing it, and what I'm learning along the way, as it happens.

Well, I guess it's not entirely "new", depending on how you count it, I've been working on this for years already.

It's an extension of prior work I've talked about a lot on this blog, the extraordinary finding that gay men are more likely to be in "excellent" health than heterosexual men.

I've looked at this issue in many datasets, and published a paper on it in one particular dataset, the Behavioral Risk Factor Surveillance Survey, where I looked at the self-reported general health of men in same-sex and mixed-sex couples, based on their marital status and household composition.

In that study, I found that about half the general health advantage of men in same-sex couples was explained by the facts that men in same-sex couples were younger on average, better educated, and wealthier. When I looked at some of the specific health characteristics, men in same-sex couples were less likely to be overweight or obese, but more likely to smoke. Taking all the health factors I could into account didn't explain why man in same-sex couples were healthier than men in mixed-sex couples.

But what do I want to do now, in this new analysis? Well, it may yet shift and wiggle from this idea, but I'd like to do a couple of things. First, there's a lot more data to work with now. Instead of having to look at marital status and household composition, we can now look at sexual orientation directly, because a number of states have started to ask people not just who you live with and your marital status, but also whether you think of yourself as heterosexual, gay, lesbian, bisexual, or something else.
Second, because we now have both sexual orientation and marital status, and same-sex couples can get married in a lot more places than when I did the earlier analyses, I can look at single gay, lesbian and bisexual people, bisexual people in same-sex and mised-sex relationships, and a variety of household composition structures.
Third, I'd like to try to fold three different surveys into a single analysis, the BRFSS (which is the largest of the surveys, but the sexual orientation questions are asked in only select states), the National Health Interview Surveys (which are smaller, but comprehensively asked all across the country), and the National Health and Nutrition Examination Surveys (which are smaller still, but have a great deal of depth to them).

There are other ideas I'd like to look at too, like the degree to which heterosexuals would be misidentified as being sexual minorities because they live in same-sex households (like my heterosexual roommate). And what geographic and demographic factors predict that misclassification.
Also on the issue of misclassification, the BRFSS asks interviewers to guess the sex of the person they're on the phone with, and these data give us an estimate of how often they guess wrong.
Another set of issues I could look at with these data are things like basic demographics - Who do gay men and lesbians live with? How many are in relationships? Believe it or not, these basic issues have barely been touched in the academic literature, because data like this has not been available before.

Saturday, December 26, 2015

Coming out as a blood donor

I've been a surreptitious blood donor for 14 years.

It all started after 9/11. I was stricken with grief. The enormity of the tragedy taking place in New York City weighed heavily and I wanted to do something, anything, to help with the recovery.
A few days later, there was a blood drive at school, and I thought long and hard about donating. I desperately wanted to do something useful, but I also knew it would mean lying to do it.
Eventually, I decided that giving blood would be more important than the lie I'd have to tell to give it. It never felt right, lying, and I'm relieved that I won't have to do it ever again.

Giving blood is an important part of my life. I'm humbled by the idea that parting with a pint or two here and there can help others get through the worst day of their lives.
And frankly, selfishly, it feels good to feel 'healthy', that my body has something of value for others. That's not a message that gay men get often enough.

At this point, some of you may be shouting at the screen, wondering how I could be so irresponsible as to endanger the blood supply. I've seen what HIV can do. I've lost friends to it. I've seen what the meds can do. Believe me, I'm under no illusion that HIV is something minor. Sure it's treatable, perhaps even managable at this point, but I could never live with myself if I thought there was even a fraction of a chance I could give HIV to someone through a blood donation.
At the same time, the rule that the blood donation system used is ridiculous - permanent deferment for any man who has had sex with a man since 1978.

So, I had to make up my own rules. I decided to go with six months since last having sex, and then an HIV test just to make sure, before allowing myself to donate.
I guess I have sex so infrequently that waiting six months isn't a big deal. There were even a few opportunities I passed up because my (secret) identity as a blood donor wasn't worth putting on hold.

Speaking of secret identities, it was quite jarring to go back into the closet to give blood. And to stay in the closet about being a blood donor everywhere else. I wanted to ask for the pink gauze to wrap up my arm after the donation, but had to bite my tongue. I had to make sure I wore the t-shirts that they give you inside out, and I couldn't accept as a gift in exchange for donation anything that would visibly associate me with being a donor.

I frequently struggled with who, how and when to "come out" as a donor in the rest of my life. Half of me wanted to come out fully and fight against the injustice of the gay donor ban. Half of my wanted to fly under the radar and help as many people anonymously as I could with my donations. I can't say I ever felt like I made the "right" choice there, often flying a bit close to the sun trying to do both at once.

For those members of my family, my friends, my coworkers, I'm sorry I didn't feel comfortable coming out to you as a blood donor - I hope you won't feel betrayed that I kept this to myself. And of course to the nurses at the dontation centers I've given at, I apologize for lying right to your face.
But to the mucky-mucks at the FDA - screw you. You've made my life uncomfortable and duplicitous and prevented many valuable donations from being received by others.

Gentle readers, I'm curious to hear your thoughts.

Monday, December 15, 2014

Observations on 3-fold interactions

Sorry about how "mathy" this post is. I'm percolating about what to write about gay blood donors, but I need to think on that for another few days.

The last lecture for my epi class was about effect measure modification (interactions). Most people do it completely wrong, they use an interaction term in a statistical model (Y=a +b1X1 + b2X2 + b3X1X2), and then interpret b3 as though it's telling you something interesting. It isn't (except in extremely unusual circumstances).
What you really want to know is the degree to which being exposed to X1 and X2 produces more disease than you'd expect if all you know was the effect of X1 in the absence of X2 and the effect of X2 in the absence of X1.
Or, in mathy terms, let Rij be the rate of disease when X1=i and X2=j
We want to know whether (R11-R00), The difference that both make when working together, is greater or less than (R01-R00) + (R10-R00), the difference each makes in the absence of the other.

I'm going to skip right to the three-factor effect measure modification - here the idea is whether:
(R111-R000), the effect of all three together,
is comparable to the effect of each of the three in isolation:
(R100-R000) + (R010-R000) + (R001-R000).

First implication: In order to make that assessment, your study needs people with none of the exposures, all of the exposures, and at most one of the exposures. It does not need anyone with two of the exposures, so including any such subjects would be inefficient. That's bizarre.

Second implication: The fact that those people with two exposures are irrelevant actually points to the fact that there could be four quantities of interest: First, the one comparing each of the three in isolation to the effect of all three together, and then three iterations of comparing one in isolation with the other two in combination, i.e.
(R110-R000) + (R001-R000)
or (R101-R000) + (R010-R000)
or (R011-R000) + (R100-R000)
So, there are actually four interaction terms to compare to the joint effect: (R111-R000).

Third implication: I love how the math and the concepts circle around and inform one another. In this case, the fact that there is one comparison to make when there are two exposures, but four to make when there are three, suggests to me that our brains are not well suited to thinking about the issue of three factor interactions, and the whole idea should ideally not be attempted at all.

But hmmm, what happens when we go to four....
(R1111-R0000) would be the joint effect of all four.
The single factors adding up would be:
(R1000-R0000) + (R0100-R0000)  + (R0010-R0000) + (R0001-R0000)
Three together + one more would be:
(R1110-R0000) + (R0001-R0000)
(R1101-R0000) + (R0010-R0000)
(R1011-R0000) + (R0100-R0000)
(R0111-R0000) + (R1000-R0000)
Two together plus each of the other two alone would be:
(R1100-R0000) + (R0010-R0000)  + (R0001-R0000)
(R1010-R0000) + (R0100-R0000)  + (R0001-R0000)
(R1001-R0000) + (R0100-R0000)  + (R0010-R0000)
(R0110-R0000) + (R1000-R0000)  + (R0001-R0000)
(R0101-R0000) + (R1000-R0000)  + (R0010-R0000)
(R0011-R0000) + (R1000-R0000)  + (R0100-R0000)
And then two together plus the other two together would be:
(R1100-R0000) + (R0011-R0000)
(R1010-R0000) + (R0101-R0000)
(R1001-R0000) + (R0110-R0000)

Ai! 14 terms to keep in mind simultaneously.

Sunday, February 2, 2014

Interpreting interaction terms

I've had the great privilege of developing a class on social epidemiology this semester, and it's been a lot of fun so far. A ton of work, but fun.
There's a problem that keep cropping up though. A bunch of the articles I've picked out for my class to read have botched the interpretation of interaction terms. Even well-established leaders in the field of social epi routinely botch interpreting their interaction terms.

It may sound like arcane statistical mumbo jumbo, but interpreting interaction terms is really important in the following context. Let's say I want to see whether X causes more or less disease (Y) in group A or group B. That's a classic setting for an interaction term.

You could make B the reference group and model it as:
Y = a + b1X + b2A + b3A*X
Or you could make A the reference group and model it as:
Y = a+ b1X + b2B + b3B*X
You should get the same interpretation either way.
You do when you interpret things correctly.
A lot of people interpret b1 as being the effect of X in the referent group (it is), and b3 as being the effect of X in the comparison group. Sometimes it is, but usually that's not the case.

Here's some real data. Let's say we were looking for the effect of state tax revenues per capita on mortality among Blacks vs. Whites in the 10 most populous states. (full disclosure, I started out with income inequality, but the data didn't look good. I figured state tax revenues per capita are probably a good indicator of redistributive potential)

Age-adjusted mortality in the populous states with the highest tax revenues (CA, MI, NY, NC, PA) was 776.9 per 100,000 Whites per year, and 985.2 per 100,000 Blacks per year.
Age-adjusted mortality in the populous states with the lowest tax revenues (FL, GA, IL, OH, TX) was 806.4 per 1000,000 Whites per year, and 1,026.0 per 100,000 Blacks per year.

Let's make White the reference group, as is standard practice. Then, let's do the standard logistic model.

Mortality = -4.85761 + 0.037268*low tax base + 0.237533*Black + 0.0033101*low tax base*Black

According to the flawed interpretation, the effect of having a low tax base among Whites is exp(0.037268) = 1.038, or a 3.8% increase in mortality in low tax base states, and the effect among Blacks is exp(0.0033101) = 1.003, or a 0.3% increase in mortality in low tax base states, so sloppy interpretation would lead you to think that living in a low tax base state has more impact on Whites than it does on Blacks.

But what happens when you switch the reference group to Blacks?

Mortality = -4.62008 + 0.040578*low tax base -0.23753*White - 0.0033101*low tax base*White

Using the flawed approach, we would get that the effect of having a low tax base among Blacks is exp(0.040578) = 1.041, or a 4.1% increase in mortality in low tax base states, and the effect among Whites is exp(-0.0033101) = 0.997, or a 0.3% decrease in mortality in low tax base states, so the sloppy interpretation suggests that living in a low tax base state increases mortality more for Blacks than Whites, and might even be beneficial for Whites (laying aside for the moment the very important issue of the role of stochastic error in the measures).

What's the real answer? Well it's right there when we look at the two models next to each other. Whites in a low tax base state have a 3.8% increase in mortality, but Blacks have a 4.1% increase in mortality. Not much difference, but the effect appears to be slightly stronger among Blacks than Whites. There is a way to get both the 3.8% and the 4.1% from only one model, but that's a bit more complicated than I want to get into in a blog post...