Thank you for the help you have offered. In a respect, yes, what I want to put in the model is a covariate that changes over time. Actually, I have used the Cox model with time-dependent variable using PROC PHREG before. After receiving your reply, I revised the theory of the model and found that it does not fully satisfy my expectation. The reasons are as follows. First, using Cox model with time-dependent covariates is not unconditional. Violation of proportional hazards assumption of the covariate(s) is a prerequisite of using the model. Were the assumption not rejected, the Cox proportional hazards model is preferred. In this case, the change of hazard ratio over time cannot be observed. Second, explanatory variables in Cox model with time-dependent covariates are "considered" only once. To make my ideas clearer, let me compare Cox models with ANOVA of longitudinal data. Let us suppose that we are dividing a sample into two groups by their age: senior citizens and youngsters. The variable I am interested in is called "X". By using ANOVA of longitudinal data, data from each and every time point can be considered, eventually reaching conclusion like "the curve of the variable X of the population where the sample was from follows a quadratic pattern", "in the second time point, the level of X is 'statistically different' between senior citizens and youngsters", "the mean of X of the entire population in the first time point is 'statistically different' from that of the entire population in the third time point". However, Cox models with time-dependent variables cannot accommodate levels of X in each and every time point. You can put the baseline level of X when in the model, you can put the level of X when the follow-up terminates in the model, you can put whether X changes a threshold during follow-up (e.g. X rises more than 50% from baseline) in the model, but you cannot put the level of X at baseline, at 1 month after recruitment, at 1 year after recruitment and when the follow-up terminates simultaneously. Moreover, it cannot deduce the pattern of the change in covariates as time passes by, let alone reaching conclusions like "if the level of X rises exponentially, then a patient will have an extra 50% of risk of developing stroke during follow-up, compared to those whose level of X rises in a linear pattern". It may be hard to deduce the pattern of the curve of change, but what I am actually looking for is a model that can put virtually all of the data I collected inside, just like ANOVA of longitudinal data. But since a major defect of ANOVA of longitudinal data is its inability to consider loss of follow-up, which is quite common in time-to-event data; I am looking for a "blend mixture" of methods dealing with longitudinal data (like ANOVA) and methods dealing with time-to-event data (like Cox model). I wonder if that kind of model exists and if there really is one, if I can perform this on SAS. Many thanks!
