## Frequently Asked Questions

# Events (deaths) at time zero in survival analysis.

FAQ# 1583 Last Modified 15-March-2010

When analyzing survival data, Prism (since version 4) simply ignores any rows with X=0. Our thinking is simple. If alternative treatments begin at time zero, then a death right at the moment treatment begins provides no information to help you decide which of two treatments is better. There is no requirement that X be an integer. If a death occurs half a day into treatment, and X values are tabulated in days, enter 0.5 for that subject.

Some fields (pediatric leukemia is one) do consider events at time zero to be valid. These studies to not simply track death, but track time until recurrence of the disease. But disease cannot recur until it first goes into remission. In the case of some pediatric leukemia trials, the treatment begins 30 days before time zero. Most of the patients are in remission at time zero. Then the patients are followed until death or recurrence of the disease. But what about the subjects who never go into remission? Some investigators consider these to be events at time zero. Some programs, we are told, take into account the events at time zero, so the Kaplan-Meier survival curve starts with survival (at time zero) of less than 100%. If 10% of the patients in one treatment group never went into remission, the survival curve would begin at Y=90% rather than 100%.

We have not changed Prism to account for deaths at time zero for these reasons:

- We have seen no scientific papers, and no text books, that explains what it means to analyze deaths at time zero. It seems far from standard.
- It seems wrong to combine the answers to two very different questions in one survival curve: What fraction of patients go into remission? How long do those in remission stay in remission?
- If we included data with X=0, we are not sure that the results of the survival analysis (median survival times, hazard ratios, P values, etc.) would be meaningful.

The fundamental problem is this: Survival analysis analyses data expressed as the time it takes until an event occurs. Often this event is death. Often it is some other well defined event that can only happen once. But usually the event is defined to be something that could possibly happen to every participant in the trial. With these pediatric leukemia trials, the event is defined to be recurrence of the disease. But, of course, the disease cannot recur unless it first went into remission. So the survival analysis is really being used to track time until the second of two distinct events. That leads to the problem of how to analyze the data from patients who never go into remission (the first event never happens).

We are willing to reconsider our decision to ignore, rather than analyze, survival data entered with X=0. If you think we made the wrong decision, please let us know. Provide references if possible.

There is a simple work around if you really want to analyze your data so deaths at time zero bring down the starting point below 100%, enter some tiny value other than zero. Enter these X values, say, as 0.000001. An alternative is to enter the data with X=0, and then use Prism's transform analysis with this user-defined transform:

X=IF(X=0, 0.000001, X)

In the results of this analysis, all the X=0 values will now be X=0.000001. From that results table, click Analyze and choose Survival analysis.