[R] Does a survival probability(the probability not experiencing an event) have to be non-increasing?

My question is related to a cox model with time-dependent variable. When I think about it more, I get a little confused about non-increasing assumption for survival probability for an individual. For example, for a time-dependent ,say x, assuming increasing x increases the risk of event.

Re: [R] Does a survival probability(the probability not experiencing an event) have to be non-increasing?

Don't really understand your equations but. If X is the (random variable of) time of event, then the survival S(x) = 1 - Pr( X x ) has to be non increasing since: If t1 t2. then S(t1) - S(t2) = Pr(X t2) - Pr( X t1 ) = Pr( t1 X t2) 0 which means that S(t1) S(t2). But you must not