I am looking for resources on Cox proportional hazards model with time varying covariates. I'm new to survival analysis so I'm looking for something not overly mathematical. I would also appreciate any information about software implementations that can deal with this problem.
I might be able to give you some tips:
Kleinbaum, Klein: Survival analysis - A Self-Learning text http://www.springer.com/statistics/life+sciences,+medicine+%26+health/book/978-1-4419-6645-2 In my opinion the best book on this matter and it includes time-varying covariates and also how to program the computations in SAS and R.
Also look at: http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-cox-regression.pdf Which is John Fox explanation and he uses R to calculate, which is great.
Second: what type of time-varying covariates do you have? - Multiple observations per individual? - Multiple endpoints per individual?
In general, if you have 1 endpoint of interest and multiple observations per individual, you usually set up the data frame in a format which means that each observation corresponds to one row (therefore one individual may have several rows of data) and you create a start variable and a stop variable, which is simply the start and stop intervals for each observation.
The usual Cox model:
coxph(Surv(survival, event) ~ predictors, data = df)
The time-dependent Cox model (if data is set up as described above):
coxph(Surv(star, stopp, event) ~ predictors, data = df)
A very well written manual can be found here: http://cran.r-project.org/web/packages/survival/vignettes/timedep.pdf
I have one small response which is for time varying predictors in event history analysis in general: when communicating the modeled effects of a time varying predictor, you can present hazard curves and survival curves or cumulative incidence/uptake curves for that predictor for a value with the minimum/maximum observed value in each time period to bracket extremes (even if no subject had the minimum or maximum score across all time periods). And this might be supplemented with curves for $\pm$ 25% or $\pm$ a standard deviation or so of the time-varying predictor held constant across all time periods.