In this paper, the authors describe fractional polynomials and cubic splines with which to represent smooth dose-response relations in summarizing meta-analytical aggregate data. Use of these two curve-fitting families can help prevent the problems arising from inappropriate linearity assumptions. These methods are illustrated in the problem of estimating the shape of the dose-response curve between alcohol consumption and all-cause mortality risk. The authors considered aggregate data from 29 cohort studies investigating this issue (1966-2000). J-shaped curves with a nadir at approximately 5-7 g/day of alcohol consumption and a last protective dose of 47-60 g/day were consistently obtained from fractional polynomials and cubic splines. The authors conclude that both of the curve-fitting families are useful tools with which to explore dose-response epidemiologic questions by means of meta-analytical approaches, especially when important nonlinearity is anticipated.
