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Population causal effects are often defined as contrasts of average individual-level counterfactual outcomes, comparing different exposure levels. Common examples include causal risk difference and risk ratios. These and most other examples emphasize effects on disease onset, a reflection of the usual epidemiological interest in disease occurrence. Exposure effects on other health characteristics, such as prevalence or conditional risk of a particular disability, can be important as well, but contrasts involving these other measures may often be dismissed as non-causal. For example, an observed prevalence ratio might often viewed as an estimator of a causal incidence ratio and hence subject to bias. In this manuscript, we provide and evaluate a definition of causal effects that generalizes those previously available. A key part of the generalization is that contrasts used in the definition can involve multivariate, counterfactual outcomes, rather than only univariate outcomes. An important consequence of our generalization is that, using it, one can properly define causal effects based on a wide variety of additional measures. Examples include causal prevalence ratios and differences and causal conditional risk ratios and differences. We illustrate how these additional measures can be useful, natural, easily estimated, and of public health importance. Furthermore, we discuss conditions for valid estimation of each type of causal effect, and how improper interpretation or inferences for the wrong target population can be sources of bias.