Social relationships and survival: reading an odds ratio

Step 1 Warm-up recall

From M3.L2 and M4.L1: what does a 95% confidence interval show, and what is publication bias?

Your answer

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Step 2 Learning goal

By the end of this lesson you can:

• state what Holt-Lunstad, Smith and Layton (2010) pooled and found (Foundation);
• convert between probability and odds, and read an odds ratio (Core);
• say what the review does and does not show about cause (Core).

Step 3 A familiar example

Two friends bet on a match. One says the chance their team wins is 50%; the other says the odds are 1 to 1. They are saying the same thing in two different languages. Odds ratios use the second language.

Step 4 Clear explanation

Holt-Lunstad, Smith and Layton (2010) reviewed 148 studies with 308,849 participants. They reported that people with stronger social relationships had a 50% greater likelihood of survival (odds ratio 1.50, 95% confidence interval 1.42 to 1.59). The abstract states that the finding held across follow-up periods, and the authors concluded the influence of social relationships on mortality risk is comparable with well-established risk factors for mortality.

Odds are the chance something happens divided by the chance it does not: odds = p ÷ (1 − p). A probability of 0.2 is odds of 0.2 ÷ 0.8 = 0.25. An odds ratio compares the odds in two groups. An odds ratio of 1.50 means the odds in one group are 1.5 times the odds in the other. It is not the same as 1.5 times the probability, although the two are close when the outcome is rare. Reviewers often describe it as a percentage change in “likelihood”, as the abstract does, which is a loose phrase.

The interval 1.42 to 1.59 lies wholly above 1, so no association is incompatible with the data, and its narrowness shows the estimate is fairly precise, as expected from a very large pooled sample.

What the review shows is a pattern across observational studies. It does not by itself show that adding relationships would extend a given person’s life.

Step 5 Worked example (4 marks)

A study reports an odds ratio of 1.29 for death among socially isolated people.

1. Percentage difference in odds = (1.29 − 1) × 100 = 29%. (1 mark)
2. If the comparison group had a probability of 0.10, the odds are 0.10 ÷ 0.90 = 0.111. (1 mark)
3. Multiply by 1.29: odds 0.143, so probability 0.143 ÷ 1.143 = 0.125. (1 mark)
4. So the probability moves from 10% to about 12.5%, not 12.9%: an odds ratio is not a probability ratio. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• Holt-Lunstad and colleagues (2010): 148 studies, 308,849 participants, odds ratio 1.50 (95% CI 1.42 to 1.59) for survival with stronger social relationships.
• Odds = p ÷ (1 − p); an odds ratio is not a probability ratio.
• A pattern across observational studies is not proof that adding ties extends life.

Step 8 Exit ticket (ungraded)

In one sentence, say what 1.50 does and does not mean.

Your answer

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Step 9 Go further (Extension)

Read the abstract of Holt-Lunstad, Smith and Layton (2010) in PLoS Medicine. Find how many studies were randomised and what the authors say about the limits of their data.