Editorial: Recent developments in survival analysis

Survival analysis is one of the oldest statistical disciplines with roots in the 17th and 18th century demography and actuarial science. Thus, both the life-table, the standardised mortality ratio and discussions of competing risks date back to that period (see e.g. Andersen and Keiding1 for a brief account). Later, in the 19th century, parametric (Gompertz-Makeham) models were used for studies of the distribution of human life times. In spite of this long history, survival analysis was not really an integrated part of theoretical statistics in the beginning of the 20th century as illustrated by the rather sceptical papers by Greenwood2 and Westergaard,3 and only in the mid-century were these well-established methods from demography and actuarial science presented to the medical-statistical community.4,5 The classical methods were based on time-grouped data but at this time a new kind of data were emerging in clinical research where smaller samples of patients were studied in clinical trials in chronic diseases. These trials typically produced exact event times, however, with an inevitable presence of right-censoring for patients who were still eventfree at the closing date of the trial. The development initiated a ‘golden half-century for survival analysis’ with three important landmark papers by Kaplan and Meier,6 Cox7 and Aalen.8 The paper by Kaplan and Meier discussed the life-table in continuous time while the Cox paper allowed for inclusion of covariates in regression models for survival data. These two papers are among the most frequently cited of all statistical papers. Aalen’s paper introduced counting processes as a solid mathematical background for inference for survival data. All three landmark papers have inspired much research in the field which is now documented in textbooks on survival analysis with varying levels of mathematical complexity. On that background we felt that it would be timely to review recent developments in survival analysis. This is where the current issue fits in and the idea was to solicit review papers from researchers who have contributed with textbooks in the field. This has resulted in four contributions where, everywhere, younger scientists are on board as co-authors. The Cox model has had a very dominating role in regression analysis of survival data but several regression models with other links between covariates and outcome than proportional hazards have been developed. Cortese, Scheike and Martinussen review this area in the first paper.