Voters deserve better actuaries

Bragg is promoting his actuarial analysis of McCain and Obama again:

McCain would be the oldest president to begin a first term in office. By the end of a second term, Jan. 20, 2017, he would have a 24.44 percent chance of dying, compared with 5.76 percent for Obama, the firm estimates.

As far as I can tell, those numbers seriously understate the difference in the candidates' respective longevity prospects.

Let's start from the average mortality, given only the candidates' age and sex. McCain is 72 years and 32 days old and he will be 80 years and 144 days old on January 20, 2017. Using Social Security's life tables, his probability of dying before the end of his second term is 32.2%. Barack Obama is 47 years and 57 days old; his probability of dying by the same day, which in his case is age 55 years and 169 days, is 4.3%.

(Non-geeks may skip this paragraph: I used the 1940 cohort table for McCain and 1960 cohort table for Obama. Those are the closest to their birth years. Those choices favor McCain by the amount of mortality improvement from his 1936 cohort to the 1940 cohort. The difference is hardly negligible: using the 1930 cohort, we'd get 34.7% for the same ages, and linear interpolation yields approximately 33.2%, so the result I used is biased in McCain's favor by about 1 percentage point. Similarly, using 1960 cohort mortality for Obama introduces a slight - although almost negligible in this case - bias against Obama. One further geek note: I derived all survival probabilities by linear interpolation between nearest integer-year ages. That is more than accurate enough for the purpose of this analysis.)

Of course, there is more information available about the candidates, and Bragg lists some factors used:

He classified the Democrat as a smoker with minor upper respiratory problems, probably linked to his smoking. Obama announced in February that he was trying to quit smoking again, with the aid of nicotine gum.

"We don't consider you a nonsmoker until you stay quit for 12 months," said Brooks.

In the spring, the Obama campaign released a letter from the candidate's doctor declaring him to be in excellent health. He had very good cholesterol levels, his EKG was normal, his pulse was 60 beats per minute, and his blood pressure was an outstanding 90 over 60. Obama also exercises regularly.

But Obama has a family history of cancer. His mother died of ovarian cancer and his maternal grandfather died of prostate cancer. Obama's PSA screening test for prostate cancer showed no sign of abnormalities.

For the Republican, Brooks took into account a history of skin cancer, degenerative arthritis from his Vietnam war injuries, moderately high cholesterol, mild vertigo and that McCain is a former smoker who quit in 1980.

McCain allowed reporters to review eight years of medical records, more than 1,000 pages. They show that he is cancer-free, has a strong heart and is generally in good health. As a three-time melanoma survivor, his biggest health worry is a recurrence of that cancer. But he is closely watched by his dermatologist, and any future melanoma should be caught in time to be treated successfully. McCain maintains a healthy weight and blood pressure, and takes medication for his cholesterol.

That is hardly an unbiased account, and the statement that "McCain allowed reporters to review eight years of medical records" is, at best, barely true. In any case, the factors mentioned in the article should be worse news for McCain than for Obama.

Let's start with smoking. It is true that Obama wouldn't qualify for non-smoker rates if he applied for a life insurance policy today, but life insurance underwriting imposes rather crude discrete categories by necessity. (Verification is costly and the potential for cheating is high; for example, someone who smokes two packs a day could claim to smoke one pack a week.) This individualized analysis can do much better than that. Obama's quitting has not been entirely successful, but he is clearly closer to a former smoker than to a current one. McCain stopped smoking years ago, but he used to smoke two packs a day for 25 years. So they have a similar smoking history and quit at a similar age. By itself, this factor would make each of them more likely to die than an average man of their age. The effect is probably greater for Obama mainly because fewer men of his age are smokers, so average mortality for his cohort is based on a higher percentage of non-smokers. I would be curious to see what factors Bragg applied to account for smoking history.

(Another note for wonks: Insurers generally charge smokers double or even higher rates than nonsmokers, and that is soundly based on experience, but those factors apply to a baseline of the insured population, i.e., to the people who have passed other underwriting hurdles. For example, by the Society of Actuaries' 90-95 Basic Select tables, a male smoker of Obama's age would have about 3.5% chance of dying in the next 8 years, which is better than the average from the Social Security tables. Similarly, a smoker of McCain's age would have 23% chance of dying in the next 8 years, again better than in the SSA tables. Another thing to keep in mind is that, in insurance underwriting, smoking also serves as a proxy to other risky behavior, which means that not all of the excess mortality of smokers is caused by smoking.)

The candidates' fitness balances their smoking history. Both candidates seem to have healthy hearts, and Obama's pulse and blood pressure cited by Bragg are impressive. Obama is thin and McCain's weight is normal. They both seem significantly more fit than average men of their respective ages. Fitness-related mortality patterns are far less well known than smoking-related ones, but my guess would be that both candidates make up in fitness about as much as they lose from smoking history. Additionally, both are married and have (as far as we know) healthy spouses, which also improves their longevity prospects. Not to mention that both have access to best available health care.

So far, very similar adjustments to age/sex baseline apply to both candidates, but the rest is all bad news for McCain. Melanoma is a serious type of cancer, prone to metastasizing that is hard to detect and treat. It is true that McCain has been free of symptoms for 8 years and that it improves his prognosis, but the fact that he's had 4 episodes of melanoma, and that the last one was over 2 mm deep, raise additional concerns. For lesions like his last one, 5-year survival rate is 63-79% and 10-year 51-64%. He has survived for 8 years, so the greatest risk is behind him, but he is not out of the woods:

“With melanoma, a patient is never completely clear,” said Dr. Shapiro, the N.Y.U. expert.

If melanomas do recur, standard treatment options are limited for many to surgery and a difficult form of chemotherapy. The chances of long-term survival diminish.

Precise estimates aren't available, but it is hard to see how McCain's chance of dying from this one cause alone would be less than 10% over the next 8 years.

Another issue for McCain is the long-term effects of maltreatment by the Vietcong. Five and a half years of injuries, torture and malnutrition certainly have health consequences. Quantifying the effect is difficult, but that's not a good reason to ignore it altogether.

In summary, there is little reason to think that Obama's probability of dying in the next 8 years exceeds that of an average man of his age - 4.3 percent. In fact, it is probably less than 3.5 percent, the number based on life insurance policy experience. On the other hand, I don't see how McCain's probability of dying in the same period would be much less than one-third. In other words, McCain is at least 9 times as likely to die in office as Obama. Bragg tells us it is not quite 4.5 times. Unless he publishes more details about the calculation and the assumptions, I can't see how his results could be justified.

UPDATE: It is probably wrong to focus on survival to the end of second term. Incumbency is an advantage in an election, but we don't elect a President for 8 years, and we would (hopefully) have updated health information before the next election. Going back to the baseline (Social Security tables), a man of McCain's age has 15.4% chance of dying before January 20, 2013, and a man of Obama's age has 2.0% chance of dying in the same period. By the way, the shorter the period we look at, the more significant a factor McCain's cancer is, because the probability of recurrence goes down the longer he's already survived.