The Pseudo-Observation Analysis of Time-To-Event Data. Example from the Danish Diet, Cancer and Health Cohort Illustrating Assumptions, Model Validation and Interpretation of Results

Regression analyses for time-to-event data are commonly performed by Cox regression. Recently, an alternative method, the pseudo-observation method, has been introduced. This method offers new possibilities of analyzing data exploring cumulative risks on both a multiplicative and an additive risk scale, in contrast to the multiplicative Cox regression model for hazard rates. Hence, the pseudo-observation method enables assessment of interaction on an additive scale. However, the pseudo-observation method implies more strict model assumptions regarding entry and censoring but avoids the assumption of proportional hazards (except from combined analyses of several time intervals where assumptions of constant hazard ratios, risk differences and relative risks may be imposed). Only few descriptions of the use of the method are accessible for epidemiologists. In this paper, we present the pseudo-observation method from a user-oriented point of view aiming at facilitating the use of this relatively new analytical tool. Using data from the Diet, Cancer and Health Cohort we give a detailed example of the application of the pseudo-observation method on time-to-event data with delayed entry and right censoring. We discuss model control and suggest analytic strategies when assumptions are not met. The introductory model control in the data example showed that data did not fulfill the assumptions of the pseudo-observation method. This was caused by selection of healthier participants at older baseline ages and a change in the distribution of study participants according to outcome risk during the inclusion period. Both selection effects need to be addressed in any time-to-event analysis and we show how these effects are accounted for in the pseudo-observation analysis. The pseudo-observation method provides us with a statistical tool which makes it possible to analyse cohort data on both multiplicative and additive risk scales including assessment of biological interaction on the risk difference scale. Thus, it might be a relevant choice of method - especially if the focus is to investigate interaction from a public health point of view.