Observational versus randomised trial evidence

When observational epidemiological data and randomised controlled trials produce contradictory findings there is a need to explore the reasons. We showed that the relative risks of mortality from coronary heart disease (CHD) for an identical difference in plasma vitamin C (15·7 μmol/L) suggested a strong beneficial effect in the EPIC observational study and weak evidence of possible harm in the Heart Protection randomised controlled trial. These differences seem to us to be contradictory rather than consistent. If the observational findings were always clearly explained by factors for which plasma vitamin C is only a proxy—essentially fruit and vegetable consumption, according to Kay-Tee Khaw and colleagues—then several things are unclear. First, why did Khaw and colleagues not report results with respect to fruit and vegetable consumption or other dietary factors (on which they have data) rather than a proxy variable in their original report? Second, why did mechanisms through which vitamin C could directly affect risk of CHD merit the discussion they received in that article? Finally, why has so much effort been invested in setting up trials to test the antioxidant vitamin hypothesis?

Khaw and colleagues suggest the association between vitamin C and CHD is too strong to be explained by the relatively weak effects of individual confounders. Contrary to their assertion, individually weak risk factors for CHD, operating cumulatively over the life course, can have sufficiently powerful effects to generate strong—but confounded—associations. In the webtable (http://www.image.thelancet.com/extras/04cor6136webtable.pdf) we show exactly how this situation can arise. The predicted odds ratio of CHD if all of the apparent vitamin C effect (contrasting top with bottom quarter of the vitamin C distribution) is due to confounding is shown for each individual risk factor and for all risk factors operating together in the British Women's Heart and Health Study. Khaw and colleagues echo what we wrote when saying that the association between vitamin C and CHD mortality is clearly not explained by any one of these confounding factors. However, if the effects of all confounders are taken into account—and making the not unreasonable assumption that their effects are log-additive—then the predicted odds ratio, comparing the top to bottom quarter of the vitamin C distribution, is 0·60. This effect is strong, consistent with the findings of EPIC and other observational studies, and suggests that such effects could all be explained by confounding by these factors, operating in concert.

Khaw and co-workers' hypothesis that plasma vitamin C is a good marker of fruit and vegetable intake, which protects against CHD, requires some quantitative reasoning. Their data show that plasma vitamin C is only moderately correlated with frequency of fruit intake (independent correlation coefficients of 0·19 and 0·20 for men and women, respectively), green leafy vegetable intake (0·07 and 0·01 for men and women), and other vegetable intakes (0·05 and 0·03). From their published results it is not possible to ascertain the intraclass correlation between total consumption of all fruit and vegetables and vitamin C, but we have assumed that this lies in the region of 0·2 to 0·4 (the latter value is certainly an over-estimate given the correlations reported). This assumption implies that plasma vitamin C substantially under-estimates the true strength of association of fruit and vegetable intake with CHD mortality. We calculate that, taking this regression-dilution effect into account, for a 50 g daily increase in fresh fruit consumption (equivalent to one serving and described by the authors as small and feasible), the hazard ratio of CHD mortality would be 0·10–0·31 for men and 0·06–0·23 for women. These protective effects far out weigh the results that can be achieved by the avoidance of all the major established CHD risk factors. We think that effects of this size are simply implausible, and these implausibly strong associations add weight to our arguments in favour of confounding as underlying the associations.

Finally, as stated in our original article, but not addressed by Khaw and colleagues, it would be illustrative to see if plasma vitamin C concentrations in the EPIC study were associated with violent or external causes of death, as has been previously shown with hormone replacement therapy (HRT). Such lack of specificity of association strongly suggests that plausible associations are indeed due to confounding, as was the case with HRT.