With survival data (censored observations) one can fit a variety of parametric models by modeling the time to failure (i.e. survreg in R). Let's call this method 1.
Another approach (method 2) that I recently saw (and am dubious about), is to use the Kaplan Meier CDF and then estimate the parameters of a parametric model using maximum likelihood from this CDF.
The two methods will produce different results. I think the first method is better than the second, but cannot say exactly why. What are the differences between the two methods? Is the second approach even valid?