With the death toll from a recent killer heat wave in India up over 2,500, making it India’s 2nd-deadliest heat wave on record and the world’s 7th-deadliest, I can’t help but think how much more common this is becoming. Russia 2010 with over 55,000 casualties, the 2003 European heat wave killing over 70,000, are still fresh in our memories. One wonders how many more such “memories” lie ahead.



Meanwhile, a recent paper (Gasparrini et al. 2015) looked in depth at the relationship between temperature and mortality. It found many interesting things, and also drew some conclusions I don’t necessariliy agree or disagree with. More than that, it led some (not the authors) to conclude that when it comes to the threat of deadly heat waves due to global warming, “don’t worry, be happy.” The abstract states:



… More temperature-attributable deaths were caused by cold (7·29%, 7·02–7·49) than by heat (0·42%, 0·39–0·44). Extreme cold and hot temperatures were responsible for 0·86% (0·84–0·87) of total mortality. Interpretation Most of the temperature-related mortality burden was attributable to the contribution of cold. The effect of days of extreme temperature was substantially less than that attributable to milder but non-optimum weather. This evidence has important implications for the planning of public-health interventions to minimise the health consequences of adverse temperatures, and for predictions of future effect in climate-change scenarios.



Yet considerable research has drawn a different conclusion. In another recent paper by Kinney et al., the abstract states:



… Comparing across cities,we found that excess winter mortality did not depend on seasonal temperature range, and was no lower in warmer vs. colder cities, suggesting that temperature is not a key driver of winter excess mortality. Using regression models within monthly strata, we found that variability in daily mortality within cities was not strongly influenced by winter temperature. Finally we found that inadequate control for seasonality in analyses of the effects of cold temperatures led to spuriously large assumed cold effects, and erroneous attribution of winter mortality to cold temperatures. Our findings suggest that reductions in cold-related mortality under warming climate may be much smaller than some have assumed. This should be of interest to researchers and policy makers concerned with projecting future health effects of climate change and developing relevant adaptation strategies.



The essence of such research is this: study daily data of temperature and mortality from a large number of locations. Find what relationships exist between the two, allowing for the fact that the effect of temperature on human health (and therefore mortality) can last longer than the temperature itself, so it’s desirable to allow for lagged effects of temperature on death rates.

One of the (many) locations studied in Gasparrini et al., and one for which the authors kindly include the data (as well as computer code) in their supplemental information, is that for London, England (part of the England-and-Wales data in the supplemental info). Their result for that location is summarized in this graph:

The colored line (blue to the left, for cold, red on the right for hot) shows the relative risk, which is their estimate of the risk of death due to the given temperature relative to the “minimum” risk. In this case they define “minimum mortality temperature” as the temperature with minimum risk according to their model; for London they get about 19 deg.C. The model they use to produce that estimate allows for the effect of temperature, not just on the day it occurs, but its lagged effect up to 21 days.

I get very similar results just by averaging the number of deaths per day by temperature (well, fitting a smooth curve to be precise):

Although similar in shape, my numbers (for the relative risk) are generally less than theirs. That’s because I’m only showing the immediate (i.e., same-day) risk, not their longer-term estimate which includes lagged effects.

Which raises an interesting issue. If we look at the time series of the daily number of deaths, we note at least two features:

First and foremost, there is a very strong annual cycle. Second, there’s a steady decline over the years which is strong enough that it’s plain to see even without removing the annual cycle. I expect the decline is due to improved public health policies and the advancement of medical science, but I don’t really know.

As for the seasonal cycle, the annual wintertime spike is sometimes quite pronounced. I expect it’s due to peak rates of disease, perhaps the height of the flu season in London.

I’ll refer to it as the “flu season” in what follows, mainly as a convenient label since I don’t know whether or not it’s a valid description.

What Gasparrini et al. have shown without doubt is that the seasonal cycle of mortality is correlated with the seasonal cycle of temperature. They even make a case for causation by allowing both temperature effects and a generic seasonal cycle in their model. But in my opinion, with so many lags stretching as far back as they allow, there’s too much freedom for the temperature cycle to mimic a generic seasonal cycle. There’s such strong colinearity between temperature and seasons, it’s difficult to separate their effects. In fact that seems to be the point of Kinney et al.

We can do with the mortality data from Gasparrini et al. what we so often do with temperature, and compute its difference from the usual value for that time of year to define mortality anomaly. We’ll even call it “excess deaths” to borrow terminology from others. We’ll simultaneously fit a straight line and remove that too, so we can see what’s happening besides the seasonal cycle and the long-term decline:

There are some strong deviations, both spikes (higher-than-seasonal) and dips (lower-than-seasonal) in excess deaths. Two of the tallest spikes are unusually lethal flu seasons, but the tallest of all concides with the 2003 European heat wave. Many of the strongest dips are unusually non-lethal flu seasons. If we plot excess deaths against temperature, we get this (I’ve simply added 150 to the excess death figures, so they won’t overlay the histogram of temperatures):

That’s quite a different picture. By removing the seasonal cycle of mortality, we have of course removed any temperature effect which is purely due to its seasonal cycle. This enables us to focus on the “prompt” (within a few days at most) effect of extreme temperature. Having done so, we see that the effect is stronger for extreme heat than for extreme cold.

There is still the issue of the “flu season.” Note that for the year 2000 and before many of the flu seasons are extreme, but after 2000 they’re not. Furthermore, the severity of the flu season has much weaker correlation with temperature than one might expect; some of the deadliest flu seasons correspond with cold winter seasons, others do not. And, there’s the distinct possibility that the severity of a flu season has more to do with public health policies and the effectiveness of vaccines than with temperature.

A very interesting perspective emerges if we split the data into two pieces to analyze separately: first, up to mid-2000 to include the severe flu seasons; second, after mid-2000 to study data untainted by those. Here’s what we get for the first section of data, up to 2000.5:

When we isolate (and therefore focus on) the years with more extreme flu seasons, suddenly cold looks more like a killer than hot (but even that conclusion comes with statistical caveats).

However — here’s how things look after 2000.5:

There’s no sign at all of any excess mortality due to cold temperatures. As for hot spells, the effect is not only present, it’s quite pronounced.

So, what’s the bottom line? In my opinion, the issue under dispute (whether the seasonal changes in mortality are because of, or just correlated with, seasonal temperature variations) isn’t yet settled. But one issue is beyond doubt: extreme heat kills. The clearest factor, it seems to me, is that global warming will bring about extreme heat we haven’t yet seen the likes of. All the available evidence points to the deadly nature of extreme heat waves, and the severity we expect to face in the future will have a much more pronounced effect on mortality than any reduction of wintertime cold, by virtue of its unprecedented extremity.