I submitted an article which was rejected due to the improper way of performing the survival analysis. The referee left no other details or explanations other than: "survival analysis on time trends requires more sophisticated ways of censoring."
Has the excess risk of death among smokers been reduced in the last decades?
25.000 smokers in Germany. They were enrolled in the cohort at any time between 1995 and 2014. Each smoker has been matched (at the time of enrollment) to a sex and age matched control from the general population (who did not smoke). I have exact time of death for everyone who died during the whole study period. Those who did not die during follow-up will be censored. The study is powered to examine the excess risk of death among smokers each year from 1995 to 2014.
The aim is to calculate:
- Incidence rates of death for smokers and non smokers each year and examine these trends
- the excess risk of death among smokers, each year (or period of a few consecutive years).
How should the data be analysed? Recall that somebody who is included in 1998 might die in 2015. Is the right approach to use counting process format with start and stop updated for each year?
This is the approach that the referee disliked:
Incidence rates were calculated by means of Poisson regression. We included follow-up time as an offset in the model and included age, sex, smoking status and calendar period (combining two consecutive years) as predictors in the model. Then rates were calculated per 1000 person years using the predict() function of R. The offset (follow-up time) was the persons entire observation time (days) from enrollment.
A Cox model was used to estimate relative risk for smokers each period from the beginning to the end of the study. For simplicity we compared the hazard ratio in the first period with the hazard ratio in the final period.
Issues: - a person (along with his control) might be included in 1998 and thus belong to that calendar group, but suffer an event in 2006. - How should the data be layed out for the analysis of the Poisson and the Cox regression? Counting process for the cox? What is the start and stop time? - How can trends be assessed in this situation?
Some clarifications: Let's say a patient is first observed in 15 of june 1998 and experienced an event december 31 1998, the value for our time variable for this patient is 182.5 out of 730 possible days since time-period consists of 2 subsequent years. The maximum amount of observed time in each time-period is 730 days.
When a patient is observed in one time-period but censored (i.e either experienced and event or dropped out) in another time-period should the amount of days observed be added onto the next time-period or what?
Thus the main problem is the handling of the follow-up time and calendar year (which is used as a categorical variable, consisting of two consecutive years).