# Survival Analysis - Truncating follow-up period when there are no events after a certain amount of time

Lets say patients in a trial were followed for over 10 years, but there are no events in either treatment or control group after 5 years (the survival curves are flattened after about 5 years). When fitting a cox proportional hazards model, can we truncate the follow-up period to 5 years. I am asking this because I have an important variable that was documented in literature to affect the outcome. In fact, it did with a strong significant result when I restricted the time period to 5 years. However when I analyzed with the entire follow-up period, its significance was lost (no where near the significance level). So my question is will there be any loss of information or power if I truncated my follow-up period to 5 years?

Thank you

A small clarification: Treatment is my main variable of interest. It is still significant with 5 or 10 period follow-up. I have a continuous covariate that is well know to relate to the outcome. When I restricted to 5 years, this covariate is significant but its sinificance was lost when I analyzed the full data set.

• This result seems a little strange. The calculations performed for Cox regression only are done at event times. So if there were no events after 5 years then there should be no difference in the regression results whether you censored all cases at 5 years or didn't. Could you please say more about how you "restricted the time period to 5 years" and post a plot of the survival curves for the 2 groups, with censoring times indicated? – EdM Apr 21 at 15:21

Some distortion of statistical inference will result when you inspect relationships in the data to choose the truncation point. And you are in effect assuming that something magic happens right at 5y, which is unlikely. It is more likely that there is a smooth change in the treated:control hazard ratio over time. You can estimate $$\beta(t)$$, the treatment log hazard ratio, as a function of $$t$$ by making a smoothed scaled Schoenfeld residual plot. This is a computationally quick way to allowing departures from a constant hazard ratio by adding time-dependent covariates to the model.
• Thank you for answering. Please see my edit in posted question. As you suggested I assessed hazards proportionality (using cox.zph in R). The results show that the continuous covariate violated the assumption whereas all other variables including treatment passed the test. So, I used this covariate as a time depending covariate (z*log(t)) using time transfer function tt in my cox model. z is still insignificant but tt(z) is significant. How can I interpret the results? – rftw Apr 21 at 16:25
• What was the result from the global test in the cox.zph output? What is the p-value for the treatment? And show the smooth scaled Schoenfeld residual plot for treatment. When doing time-dependent variates makes sure you are using the special likelihood needed, e.g., by using the R survival package (start,stop) time record setup. – Frank Harrell Apr 21 at 16:43
• The overall global p value incox.zph output is 0.068. The p value for treatment is 0.42 and the p value for the continuous covariate (lets say z) that I am concerned about is 0.043. I am not sure I can use (start, stop) method since all my measurements are baseline values. When I used time transfer function in coxph the p value for z is 0.45 and for tt(z) is 0.01. I will try to post the residual plot as soon as possible. – rftw Apr 21 at 17:30
• You have to use tt in the right context to get the right likelihood function. But the documentation that comes with the survival package will keep you straight. Based on the overall test and the borderline individual p-value I would not worry about non-PH in your case. Note that (start,stop) can be used in all cases if you are changing the impact of a covariate over time (the covariate itself doesn't have to change). – Frank Harrell Apr 21 at 18:53