Let P, and P 2 be two probability measures on the same space and let 4> be the generalized Radon-Nikodyrn derivative of P 2 with respect to Pl' If Cis a continuous convex function of a real variable such that the Pl-expectation (generalized as in Section 3) of C(4)) provides a reasonable coefficient of the Pcdispersion of 4>, then this expectation has basic properties which it is natural to demand of a coefficient of divergence of P 2 from Pl' A general class of coefficients of divergence is generated in this way and it is shown that various available measures of divergence, distance, discriminatory information, etc., are members of this class.

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Several population-based studies have examined the prevalence and trends of the American Heart Association's ideal cardiovascular health (CVH) metrics as well as its association with cardiovascular disease (CVD)-related morbidity and mortality and with non-CVD outcomes. However, no efforts have been made to aggregate these studies. Accordingly, we conducted a systematic review to synthesize available data on the distribution and outcomes associated with ideal CVH metrics in both US and non-US populations. We conducted a systematic search of relevant studies in the MEDLINE and CINAHL databases, as well as the Cochrane Register of Controlled Trials (CENTRAL). Search terms used included "life's simple 7", "AHA 2020" and "ideal cardiovascular health". We included articles published in English Language from January 1, 2010, to July 31, 2015. Of the 14 US cohorts, the prevalence of 6 to 7 ideal CVH metrics ranged from as low as 0.5% in a population of African Americans to 12% in workers in a South Florida health care organization. Outside the United States, the lowest prevalence was found in an Iranian study (0.3%) and the highest was found in a large Chinese corporation (15%). All 6 mortality studies reported a graded inverse association between the increasing number of ideal CVH metrics and the all-cause and CVD-related mortality risk. A similar relationship between ideal CVH metrics and incident cardiovascular events was found in 12 of 13 studies. Finally, an increasing number of ideal CVH metrics was associated with a lower prevalence and incidence of non-CVD outcomes such as cancer, depression, and cognitive impairment. The distribution of ideal CVH metrics in US and non-US populations is similar, with low proportions of persons achieving 6 or more ideal CVH metrics. Considering the strong association of CVH metrics with both CVD and non-CVD outcomes, a coordinated global effort for improving CVH should be considered a priority.

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