Estimate parametric model from Kaplan Meier CDF

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?

• This only off the top of my head, but I think you could essentially figure out what the raw data was from a given Kaplan Meier curve? So you could "use" the KM curve to fit the parametric model (by first figuring out what the raw data was then fitting the parametric model), which would give you an identical solution to using the raw data. – Cliff AB Sep 2 '15 at 4:45
• @CliffAB I believe you are correct, and that's what I would try to do. However I'm more interested in the pros/cons of fitting from the CDF directly. – Glen Sep 2 '15 at 5:01
• My point is that there is a least an equivalent way to do (i.e. using raw data and KM curves to fit parametric model could lead to the same fit). Clearly, there's terrible ways to do it as well: for example, you could do something really foolish like taking the estimated median and estimated 90th percentile and find the weibull parameters that lead to these same estimates. My point is that without more information about how they will estimate the parameters, we can't assess how good that method is. – Cliff AB Sep 2 '15 at 6:09
• @CliffAB Use the CDF to estimate the parameters via maximum likelihood. – Glen Sep 2 '15 at 16:27