Whereas a propensity score summarizes the way potential risk factors differ between users of alternative treatments to be compared, a disease risk score characterizes the relationship of risk factors with the study outcome. Summary measures of disease risk play a prominent role in guidelines for drug use and the evaluation of possible effect measure modification of new treatments or new indications for established therapies. For example, 5-year risk of invasive breast cancer estimated from the Gail model critically influences use of selective estrogen receptor modulators for risk reduction.^{9,10} Similarly, guidelines for the use of statins in the primary prevention of cardiovascular disease incorporate the Framingham risk score as a key determinant of treatment eligibility.^{11} Other summary measures of disease severity that often direct treatments include the APACHE II score in intensive care patients,^{12} the NIH stroke scale,^{13} and the Glasgow coma scale.^{14} Strengths of these scales include their applicability in different populations and time periods.

When summary evidence suggests the value of a treatment in a target population, a disease risk score provides an important axis for evaluation of possibly varying effects, and for characterization of subgroup-specific absolute treatment effects. For example, in consideration of the use of statins for primary prevention, treatment guidelines require specific information on risks and benefits within categories of absolute disease risk.^{15}

Although disease risk scores with pre-specified weights are a useful tool for confounder adjustment in studies of treatment effectiveness and safety, they are seldom sufficient to completely control for potential confounding. In the use of administrative data, the predictive ability of available comorbidity scores such as those developed by Charlson et al.^{16} and Elixhauser et al.^{17} can be enhanced through estimation of weights for their components within the study population of interest.^{18,19} However, these risk scores are generally considered to be only one component of a strategy to control confounding, rather than a self-sufficient approach. Even when total mortality is the study endpoint, administrative datasets generally contain additional determinants of death that are not included in available scores. A wider view of such potential determinants is generally required for adequate confounder adjustment, compared with the perspective provided by construction of a parsimonious comorbidity index. As in the construction of a propensity score,^{20} the disease risk score should err on the side of inclusion of variables that show even a modest association with the outcome.

The notion that a study-specific disease risk score alone can control confounding and aid in causal inference has a substantial history. Peters^{21} and Belson^{22} proposed a two-step approach for confounder adjustment with the first-stage development of a model to predict the outcome among the unexposed, followed by adjustment for the predicted outcome in a comparison between the exposed and unexposed. Cochran^{23} described the conditions under which this Peters-Belson approach is preferable to multivariable adjustment for causal inference. In particular, this approach has theoretical advantages in the presence of effect-measure modification across the dimension of outcome risk in the unexposed, and has extensive applications in economics and health-services research.^{24}

In considering the value of alternative summary confounder scores to reveal potential problems with a multivariable analysis of the effects of an exposure, Miettinen recommended the use of a form of disease risk score.^{25} Specifically, in the setting of a case-control study, he recommended inclusion of the exposure status and all potential confounding variables in a multivariate model to predict the study outcome. Then each subject’s predicted risk was obtained by setting the exposure status to zero, and stratified analysis was used to evaluate the relationship of the exposure and outcome.

An important theoretical development in understanding the disease risk score is an appreciation of its balancing properties as described by Hansen, which parallels the balancing property of the propensity score.^{26} Specifically, with a properly developed propensity score PS(X) to summarize the way a vector of covariates X predicts treatment assignment, Rosenbaum and Rubin showed that if sufficiently large groups of exposed and unexposed subjects with the same value of PS(X) are identified, these two groups will have the same distributions of all components of X.^{27,28} This implies that stratification or matching on the propensity score can yield a better exposed/unexposed balance of these measured covariates than would be obtained by randomized treatment assignment.^{29}

In parallel, a well-formed disease risk score DR(X) has the property that the potential outcome if untreated is independent of covariates X, given DR(X). Note that this is a balance of disease risks, as distinct from the balance of treatment propensities provided by the propensity score. This prognostic balance can only be evaluated in the untreated. Further, as Hansen points out, its evaluation in the untreated subjects within a population including treated and untreated subjects requires an assumption: that the potential outcome if untreated is independent of the actual treatment assignment given X.^{26} This is an assumption of no unmeasured confounders outside X. summarizes the aspects of study design that can influence the relative utility of disease risk scores and propensity scores.

| **Table 1**Study design features that influence the value or feasibility of disease risk scores (DRS) or propensity scores (PS) |