In the context of Survival Analysis: When are the covariates for a given patient measured? Are the covariates taken when a datapoint enters the study or at some other time? For example, is a patient's blood pressure taken at his/her entry into the study or do we take it at some other time? Does this depend on the type of study?
 A: A Cox survival model bases it calculations on covariate values for each case still at risk at the time of each event. That means you need covariate values for all cases at early times, maybe not exactly at time = 0 but certainly for the time of the first event. From that perspective you should ideally have continuous measurements of all potentially time-varying covariates throughout the study for all individuals.
As such continuous measurements are impractical, investigators have to use their judgment based on knowledge of the subject matter to decide on the measurement times. For example, if a covariate isn't varying quickly with time a value taken a short while after the formal time = 0 might be used for the value at time = 0. For blood pressure (BP), values might be taken at each follow-up visit; the hidden standard assumption then is that the BP value measured at one visit is constant until the next visit.
Time-varying covariates can be handled well in analysis, but they do pose challenges in terms of predictions from survival models. To predict survival for a new case from a model with time-varying covariates, you somehow have to know all the covariate values for that new case over all time into the future. How can you reasonably expect to know those values? So be very careful with time-varying covariates.
A: It would be ideal to measure all the co-variates at the time the patient enters the study. If you are using something like a proportional hazards model for survival, then the hazard function is assumed separable in time and the covariates, i.e. $h(x,t) = h_0(t) * f(x)$. Now if you are using co-variates like say gender, these are constant and won't change with time. But if your co-variates are also varying with time, e.g. blood pressure, then it's best to measure the blood pressure at a fixed time. However, since in observational studies, this is not always under your control, you can choose a fixed time for each co-variate. For example, the blood pressure could be considered 2 weeks before the time the patient "enters" the study while blood sugar level could be 3 weeks before. But for a given co-variate, it has to be at the same relative time for all patients. Otherwise you might have to treat it as missing data and use some imputation technique.
A: I second dshirodkars answer on this. All variables should be known at the start of your survival period - timepoint 0.
However there are ways to deal with variables that change over the time of observation. For example if you repeatedly measure blood pressure throughout your study. These are called time-dependent or time-varying covariates. There is a great vignette on Cox models that deal with such covariates: https://cran.r-project.org/web/packages/survival/vignettes/timedep.pdf
