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David Oliver: Let’s argue about statistics

BMJ 2016; 355 doi: (Published 21 October 2016) Cite this as: BMJ 2016;355:i5649

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Re: David Oliver: Let’s argue about statistics

Unfortunately it is not only politicians that do not understand statistics. An example.

In a recent Telegraph report around 14 in 1,000 women in their 50s are expected to develop breast cancer, but that rises to 34 in 1000 for women taking the combined pill, the study suggests. The probability of no increase to the individual is 0.98 or a 1 in 50 chance (20 per 1000), but the report continued on to suggest the use of the pill caused a 2-3 times increase in the incidence of breast cancer. Actually this was a relative rate (RR), much valued by the pharmaceutical industry because it makes their drugs look much, much better than they really are. This actually is a very rare case of using odds ratio for an adverse reaction. The most common use of ORs, HRs and RRs is to demonstrate the significance of very small benefits of drugs. Looking at the Telegraph data:

Odds Ratio Confidence Interval Calculation For 2x2 Contingency Table


NO TREAT 986 966 1952

HRT Trt 14 34 48

%age 1.40% 3.40%

Total 1000 1000 2000


Real Increase% = 2.00%

Odds ratio 2.48 = 247.89%

Inflation 0 123.94

95% confidence interval 1.32 to 4.65

Fisher's exact test.

The two-tailed P value equals 0.0050.

The association between rows (groups) and columns (outcomes) is considered to be very statistically significant.

The real increase in risk to the individual patient is (34/1000)-(14/1000) P = 0.02 or 1 in 50,,,,, and the RR is inflated by 124 times.

To Quote from Gigerenzer’s book Risk Savvy: How To Make Good Decisions (p. 165).

After my first CME lecture, a representative of the of the industry approached me: “Very helpful,” he commented, “but we will of course go on using relative risks for advertising benefits.” In advertising parlance it is called astroturfing and agnotology - a powerful PR trick.

Competing interests: No competing interests

30 October 2016
Michael J. Hope CAWDERY
Retired veterinary researcher