Proportional hazards models for average data for groups

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Abstract
In ecological studies it is sometimes tempting to apply statistical models derived from longitudinal studies of individuals to cross-sectional data which may be available only in aggregate form for groups of individuals. This paper examines the assumptions and approximations that are made when average data for groups are used with predictive equations derived for individuals, in particular for the proportional hazards model. It is shown that this method underestimates age-specific hazard functions but that if ratios of hazard functions are used to compare groups then the approach is valid provided that certain plausible conditions hold. A numerical example is given about trends in heart disease mortality in Australia. Group data are available on risk factor levels and mortality. A proportional hazards model derived from the Framingham study is used to estimate the effects on mortality which may be attributed to risk factor changes and the effects attributable to other factors such as improved medical treatment. The interpretation of the results is discussed.