Trend surface models in the representation and analysis of time factors in cancer mortality

A method of graphic representation of time factors in cancer mortality is presented, based on different tonalities of grey applied to the surface of the matrix defined by various age-specific rates. It is illustrated using mortality data from cancers of the mouth or pharynx, oesophagus, larynx and lung in Italian and Swiss males. Progressively more complex regression surface equations are defined, on the basis of two independent variables (age and cohort) and a dependent one (each age-specific rate). General patterns of trends were thus identified, showing important similarities in cohort and period effects, but also noticeable differences in time-related factors in mortality from various neoplasms of the upper digestive and respiratory tract. For instance, there were declines in mortality from cancers of the mouth or pharynx in the oldest age groups, whereas rates were appreciably upwards at younger and middle age, particularly in Italy. Likewise, cancers of the oesophagus and, chiefly, of the larynx were substantially increasing, on a cohort basis, in oldest Italian males. Temporal pattern for laryngeal cancer in Italy was similar to that of lung cancer, thus suggesting that (cigarette) smoking has a greater impact on this cancer site as compared with alcohol. However, it is difficult to explain, on this basis alone, the totally diverging pattern for cancer of the larynx (downwards) and of the lung (upwards) observed among older Swiss males. These examples indicate that trend surface models are a useful summary guide to illustrate and understand the general patterns of age, period and cohort effects in cancer mortality.