The editorial [1] on the Holt-Lunstad study [2] raises three data interpretation issues. First, while the editorial emphasizes the failure of previous studies to provide a “precise size of the effect” of social relationships on health outcomes like mortality, it goes on to substantially misdescribe the effect size. The editorial states that the study found that stronger social relationships were associated with a 50% increased chance of survival over the course of the studies, on average.” But the 50% figure is an increase in odds not an increase in risk. In an Editor’s Summary, there is mention that the key figure is an odds ratio of 1.5. But the summary then describes and odds ratio as “the ratio of the chances of an event happening in one group to the chances of the same event happening in the second group.” In fact, the odds ratio is the ratio of the odds for the two groups, not the ratio of the chances for the two groups.

This is an important distinction in a study like that of Holt-Lunstad and colleagues where the average mortality was 29%. In such circumstances, with equal sized groups, a survival odds ratio of 1.5 would be consistent with a mortality rate of .25 (survival rate of .75) for the advantaged group and a mortality rate of .33 (survival rate of .67) for the disadvantaged group. Thus, the advantaged group would be 12% more likely to survive than the disadvantaged group (risk ratio = 1.12 (.75/.67)). And the disadvantaged group would be 32% more likely to die than the advantaged group (risk ratio = 1.32 (.33/.25). Given that the disadvantaged group is likely to be a much smaller than half the total population, the actual figures would differ somewhat. But no scenario would result in anything like a 50% increase in survival.

Second, in noting that the increased mortality risk associated with social isolation is comparable to that associated with smoking, the editors (like Holt-Lunstad et al.) equate effects on mortality with effects on survival. It is true that the disadvantaged group’s increased odds of mortality will equal the advantaged group’s increased odds of survival and hence that one might be able to talk about odds ratios for morality and odds ratios for survival interchangeably or almost interchangeably. But the situation is quite different with regard to differences in the chance of experiencing an outcome. For example, a factor that increases the chance of death from 1% to 2% increases that chance by 100%, while reducing the chance of survival by a little over 1%. Further, overall improvements in health will tend to reduce relative differences in survival while increasing relative differences in mortality.[3-5] Thus, in discussing differences in risks, it is important to distinguish between mortality and survival.

The above, however, should not be read as suggesting that a risk ratio is in fact a useful indicator of an effect size, and I have stated in many places why it is not.[3-6].

Third, assuming that one has a useful indicator of the effect of some health-related factor, such as that discussed in the Solutions sub-page of reference 6,[7] one still should be cautious about relying on such figure for appraising the comparative public health importance of the factor. For one needs to know the sizes of the groups involved. That is, if factors X and Y increase mortality in exactly the same way, the factors could vary substantial in their public health importance if, say, 30% of the population was subject to factor X while only 5% of the population was subject to factor Y. An appraisal of the public health importance of a factor like social isolation would probably most usefully be presented in terms of total lives lost, or useful years lost, in consequence of the factor.

References:

1. The PLoS Medicine Editors (2010) Social Relationships Are Key to Health, and to Health Policy. PLoS Med 7(8): e1000334. doi:10.1371/journal.pmed.1000334: http://www.plosmedicine.o... (Accessed October 22, 2011)

2. Holt-Lunstad J, Smith TB, Layton JB (2010) Social Relationships and Mortality Risk: A Meta-analytic Review. PLoS Med 7(7): e1000316. doi:10.1371/journal.pmed.1000316: http://www.plosmedicine.o... (Accessed October 22, 2011)

3. Scanlan JP (2006) Can we actually measure health disparities? Chance 19(2):47-51: http://www.jpscanlan.com/... (Accessed October 22, 2011)

4. Scanlan JP (2000). Race and mortality. Society 37(2):19-35: http://www.jpscanlan.com/...

5. Mortality and Survival page of jpscanlan.com:
http://jpscanlan.com/mort... (Accessed October 22, 2011)

6. Measuring Health Disparities page of jpscanlan.com: http://jpscanlan.com/meas... (Accessed October 22, 2011)

7. Solutions sub-page of Measuring Health Disparities page of jpscanlan.com:
http://www.jpscanlan.com/... (Accessed October 22, 2011)