Relative risk and odds ratio regression.

Consider a cohort of nearly 20,000 residents of Hiroshima and Nagasaki who have undergone biennial clinical examinations for the past 20 years under the auspices of the Radiation Effects Research Foundation. Suppose that one would like to use a series of blood pressure measurements on an individual to assess the risk of a subsequent cardiovascular disease event. This type of assessment is complicated by a number of features: the "risk factors" of interest are evolving over time, risk factor data may be missing, there may be many other "confound­ ing" factors, and endpoint events may be censored due to competing risks or dropout. During the past 15 years a vast biostatistical literature has developed on the regression analysis of "failure" time data. This literature is relevant to a range of problems in medicine and public health as well as in other areas. For example "failure time" may refer to time-to-relapse in a clinical trial, or to the age of disease diagnosis in an epidemiologic cohort study or in a disease prevention trial. Often interest will center on the dependence of failure rate on individual characteristics, exposures, or treatment assignments, which are collectively referred to here as "covariates." In the above example the covariates may include the sequence of preceding blood pressure readings, along with such control factors as age at cohort selection and sex. Relative risk regression models express the ratio of instantaneous failure rates (i.e. hazard rates) as a function of covariates. A chief accomplishment of the literature alluded to above is the demonstration that such relative risks, or more generally relative