Measures of effect based on the sufficient causes model .3. Multivariate analysis

We discuss a method based on the the sufficient causes model for estimating the causal and preventable fractions associated with any number of agents. P-1, the cumulative risk of disease in the exposure category of interest, is given by the function: P-1 = 1 - e (-(i.+i1x1+...+ijxj+...+inxn)t). The presence or absence of sufficient cause j in this exposure category is represented by x(j) (=1,0), and parameter i(j) is the incidence density of completion of sufficient cause j. From i(j), one can derive the risk difference and the causal and preventable fractions associated with sufficient cause j. The main assumptions required for these measures of effect to be unbiased are the constancy of incidence densities i(j) over time, the homogeneity of these densities over subjects, and the independence of occurrence times of sufficient causes within subjects. The estimation of the causal fraction requires all three assumptions. The preventable fraction requires only the homogeneity assumption. The risk difference requires none of these assumptions. This causal model probably applies to very few real situations, but it can serve as an epidemiologically meaningful starting point for the development of models adapted to particular situations whose underlying causal processes are known or can be hypothesized.