Purpose in life and risk: reading a relative risk

Step 1 Warm-up recall

From M5.L1: what is the formula for odds, and how does an odds ratio differ from a probability ratio?

Your answer

Private: nothing you type here is sent or stored.

Step 2 Learning goal

By the end of this lesson you can:

• state what Cohen, Bavishi and Rozanski (2016) pooled and found (Foundation);
• read a relative risk and convert it into a percentage change (Core);
• tell relative risk from absolute risk (Core).

Step 3 A familiar example

A shop offers “20% off” on a coffee costing 2 pounds. You save 40 pence. A different shop offers 20% off a car costing 20,000 pounds, and you save 4,000. The same percentage means very different amounts. Risk works the same way.

Step 4 Clear explanation

Cohen, Bavishi and Rozanski (2016) pooled 10 prospective studies with 136,265 participants. After adjustment, a high sense of purpose in life was associated with a pooled relative risk of 0.83 for all-cause mortality (95% confidence interval 0.75 to 0.91) and of 0.83 for cardiovascular events (95% confidence interval 0.75 to 0.92).

Relative risk (RR) is the risk in one group divided by the risk in another. An RR of 0.83 means the risk in the high-purpose group was 83% of the risk in the comparison group: a 17% lower risk, since (1 − 0.83) × 100 = 17. Unlike an odds ratio, a relative risk compares probabilities directly.

Absolute risk is the actual chance. If the comparison group had a 10% risk over the follow-up period, an RR of 0.83 means the high-purpose group had 8.3%: a difference of 1.7 percentage points. The relative figure sounds bigger than the absolute one, and good reports give both.

This is an association across observational studies. Purpose could protect health, but illness could also reduce purpose, and a third factor such as income or social support could affect both, as in M5.L3.

Step 5 Worked example (4 marks)

A study reports RR = 0.75 for a cardiovascular event among people with high purpose. The comparison group’s risk is 8%.

1. Relative reduction = (1 − 0.75) × 100 = 25%. (1 mark)
2. Absolute risk in the high-purpose group = 0.75 × 8% = 6%. (1 mark)
3. Absolute difference = 8 − 6 = 2 percentage points. (1 mark)
4. Fair statement: high purpose was associated with a 25% lower relative risk, about 2 points lower in absolute terms, with cause not established. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• Cohen and colleagues (2016): 10 prospective studies, 136,265 participants; RR 0.83 for mortality and for cardiovascular events.
• Percentage change in risk = (1 − RR) × 100.
• Relative and absolute risk differ; report both.

Step 8 Exit ticket (ungraded)

Write one sentence reporting this finding with both a relative and an absolute figure, using an invented baseline.

Your answer

Private: nothing you type here is sent or stored.

Step 9 Go further (Extension)

Read the abstract of Cohen, Bavishi and Rozanski (2016) in Psychosomatic Medicine. Find how many studies reported on cardiovascular events and what the authors say about limitations.