Joint Effects of Multiple Risk Factors
Many users of risk assessment, who may be familiar with categorical attribution systems such as the ICD, desire information characterized by additive decomposition. In other words, they would like to know what fraction of the disease burden is related to a particular risk factor or group of risk factors independent of changes in other risk factors. As Mathers and others (2002) discuss, additive decomposition is not generally a property of counterfactual attribution, because many diseases are caused by the interaction of multiple determinants acting simultaneously (Rothman 1976; Rothman and Greenland 1998; Walter 1980; Yerushalmy and Palmer 1959). Indeed, the sum of PAFs for a single disease due to multiple risk factors is theoretically unbounded.
Although epidemiologically unavoidable and conceptually acceptable, the lack of additivity adds to policy complexity and implies the need for great care when interpreting and communicating estimates of PAF and attributable burden. With multiple attribution, a reduction in one risk factor would seem to make other, equally important, risk factors potentially irrelevant from a perspective with limited scope in relation to interpreting quantitative results. It also necessitates the development of methods to quantify the effects of joint counterfactual distributions for multiple risk factors. Estimating the joint effects of multiple distal and proximal risks is particularly important, because many factors act through other intermediate factors (Murray and Lopez 1999; Yerushalmy and Palmer 1959) or in combination with other factors. For example, education, occupation, and income may affect smoking, physical activity, and diet, which are risk factors for cardiovascular diseases, both directly and through further layers of such intermediate factors as BMI, blood pressure, and high cholesterol. Multicausality also means that a range of interventions can be used for disease prevention, with the specific choices determined by factors such as cost, technology availability, infrastructure, and preferences.
In equations 4.1a and 4.1b, RR, P, and P may represent joint relative risks and exposure distributions for multiple risk factors, that is, x may be a vector of risk factors, with RR for each risk factor estimated at the appropriate level of the remaining ones (Eide and Heuch 2001). While such data have been gathered for a small number of risk factor combinations, for example, alcohol and smoking for oral cancer (Rothman and Keller 1972) and some cardiovascular risks (Neaton and Wentworth 1992; Yusuf and others 2004), they are generally rare in epidemiological studies. Alternatively, for n biologically independent and uncorrelated risk factors, the joint PAF is given by equation 4.3 (Miettinen 1974; Walter 1976):
where PAFi shows the PAFs of individual risk factors.
If risk factors are independent and uncorrelated, the proportion of the remaining disease that is attributed to the ith additional risk factor equals PAFi, and hence (1 - PAFi) is not attributable to this factor. Therefore, the second term in the right-hand-side of equation 4.3, that is, the product of all (1 - PAFi) terms, is the fraction of disease not attributable to any of the n risk factors. One minus this term is the fraction attributable to the combined effects of the n risk factors.
Estimating the joint effects of multiple risk factors is, in practice, complex and does not follow the simple, independent, and uncorrelated relationship of equation 4.3 for several reasons. First, some of the effects of the more distal factors, such as physical inactivity, are mediated through intermediate factors. For instance, a proportion of the hazards of physical inactivity is mediated through overweight and obesity, which is itself mediated through elevated blood pressure (figure 4.3). Estimating the joint effects of distal and intermediate factors requires knowledge of independent hazards of the distal ones (versus individual risk factor effects, which are based on total hazard). Second, the hazard due to a risk factor may depend on the presence of other risk factors (Koopman 1981; Rothman and Greenland 1998) (effect modification).1 Third, correlation may exist between exposures to multiple risk factors because they are affected by the same distal factors and policies. For example, under-nutrition, unsafe water and sanitation, and use of solid fuels are more common among poor rural households in developing countries and smokers generally have higher and more harmful patterns of alcohol consumption and worse diets than nonsmokers.
The epidemiological literature refers to the first and second issues as biological interaction and the third issue as statistical interaction (Miettinen 1974; Rothman and Greenland 1998; Rothman, Greenland, and Walker 1980). This distinction is, however, somewhat arbitrary, and the three scenarios may occur simultaneously. For example, zinc deficiency affects mortality from diarrhea directly as well as by reducing growth (first issue) (Brown and others 2002; Zinc Investigators' Collaborative Group 1999), and may also be correlated with underweight, other micronutrient deficiencies, and unsafe water and sanitation (third issue). Similarly, alcohol and smoking may not only be correlated (third issue), but also affect each other's hazard for some diseases (second issue) (Rothman and Keller 1972).
Data Sources for Mediated Effects and Effect Modification
Despite the emphasis on removing or minimizing the effects of confounding in epidemiological research, mediated and stratified hazards have received disproportionately little empirical attention. We therefore reviewed the literature and reanalyzed cohort data to strengthen the empirical basis for considering interactions. The sensitivity of estimates to these assumptions were negligible as described in detail elsewhere (Ezzati, Vander Hoorn, and others 2004; Ezzati and others 2003).
Joint Hazards of Cardiovascular Disease Risk Factors.
Epidemiological studies of the effects of overweight and obesity, physical inactivity, and low fruit and vegetable intake on cardiovascular diseases have illustrated some attenuation of the effects after adjustment for intermediate factors such as blood pressure or cholesterol (Berlin and Colditz 1990; Blair, Cheng, and Holder 2001; Eaton 1992; Gaziano and others 1995; Jarrett, Shipley, and Rose 1982; Jousilahti and others 1999; Khaw and Barrett-Connor 1987; Liu and others 2000, 2001; Manson and others 1990, 2002; Rosengren, Wedel, and Wilhelmsen 1999; Tate, Manfreda, and Cuddy 1998). This attenuation confirms that some of the hazard of the more distal factors is mediated through the intermediate ones (figure 4.3). The extent of attenuation has varied from study to study, but has consistently been less than half of the excess risk of the distal factors. We used an estimate of 50 percent as the proportion of the excess risk from these risk factors mediated through intermediate factors that are themselves among the selected risks. To include effect modification, we used deviations from the multiplicative model of 10 percent for ischemic heart disease and 30 percent for ischemic stroke based on existing studies, both submultiplicative (Eastern Stroke and Coronary Heart Disease Collaborative Research Group 1998; Neaton and Wentworth 1992).
Joint Hazards of Smoking and Other Risk Factors.
Liu and others (1998, figures 4 and 6) find that in China, the relative risks of mortality from lung and other cancers, respiratory diseases, and vascular diseases are approximately constant in different cities where mortality rates for these diseases among nonsmokers varied by a factor of 4 to 10. Studies that stratified hazards of smoking on serum cholesterol have confirmed this finding (Jee and others 1999).
Joint Hazards of Childhood Undernutrition for Infectious Diseases.
Zinc affects growth in children (Brown and others 2002), and some of its effects on infectious diseases may be mediated through reducing growth. Because no published source for such mediated effects existed, data from some of the available zinc trials were reanalyzed (Zinc Investigators' Collaborative Group 1999). We used an upper bound of 50 percent on the proportion of zinc deficiency risk mediated through underweight.
Investigators have found that vitamin A deficiency, which affects some of the same diseases as underweight and zinc deficiency, does not change the hazard size for the other two risk factors based on stratified results from clinical trials and recent reviews of the literature on micronutrient deficiencies (Christian and West 1998; Ramakrishnan, Latham, and Abel 1995; Ramakrishnan and Martorell 1998; West and others 1991).
Joint Hazards of Undernutrition and Environmental Risk Factors in Childhood Diseases.
Anthropometric (growth) indicators of childhood nutrition, such as weight-for-age, are aggregate measures of multiple factors that include nutrition and previous infection (Pelletier, Frongillo, and Habicht 1993; Scrimshaw, Taylor, and Gordon 1968; UNICEF 1990). Therefore, some of the risks from indoor smoke from household use of solid fuels and unsafe water, sanitation, and hygiene, which result in lower respiratory infections and diarrhea respectively, may be mediated through underweight. In a review of the literature, Briend (1990) concludes that attempts to disentangle direct and mediated contributions, especially over the long periods needed to affect population-level anthropometry, have not established diarrhea as a significant cause of underweight. Other works, however, have found evidence that infection, especially diarrhea, could reduce growth and increase the prevalence of underweight (Black 1991; Guerrant and others 1992; Lutter and others 1989, 1992; Martorell, Habicht and others 1975; Martorell, Yarbrough, and others 1975; Stephensen 1999). To account for potential mediated effects, we considered an upper bound of 50 percent on the proportion of the excess risks from indoor smoke from household use of solid fuels and unsafe water, sanitation, and hygiene mediated through underweight in regions where underweight was present.
Risk Factor Correlation
To estimate the joint effects of risk factors with a continuous exposure variable, for instance, blood pressure and cholesterol, each integral in the PAF relationship may be replaced with where subscripts 1 and 2 denote the two risk factors and P is the joint distribution of the two exposures. If joint RR were a linear function of exposure levels (x1 and x2), then correlation between the two risk factors would not affect total hazard. Because individual RRs are nonlinear functions of exposure, for example, in a Cox proportional hazard model, and joint RRs are the product of such nonlinear terms, positive correlation between risk factors would, in general, imply a larger PAF than zero correlation,2 which in turn would be larger than negative correlation. Similarly, for categorical risk factors, positive correlation would in general result in a larger PAF (see also Greenland 1984). For the range of exposures and relative risks in the CRA, this secondary effect of risk factor correlation would be considerably smaller than the joint attributable fraction, as described in detail elsewhere (Ezzati and others 2003).