<It is only events that matter. No events, no change in p value.
And, conversely, the more events, the better the estimate for the p value. This is why it is short-sighted for companies to keep the intervals between check-ups too long when tracking an event such as progression for which the exact occurring time is unknown so can be set only at check-up time.
As to the p-value remains unchanged during a quiet period, a metaphor that is not exactly correct but useful for thinking about these statistics is that every event is a vote for one arm of the trial or the other. The more votes we get, the more certainty we have in the observation. In a survival analysis, during a period without events, nothing new is learned, therefore the p value does not change. The metaphor is not exactly correct because events have different weights as the trial progresses. They often have more meaning toward the end than at the beginning - the denominators get smaller as Clark would say :).
