Calculating constant hazards in exponential survival distributions

I am trying to do a survival anapysis by fitting exponential model. I was told that I shouldn't just fit my survival data to a exponential model. Instead, I should aim to calculate the hazard fundtion, which is λ in exponential distribution. My data will be like 10 surviving time, for example: 4,4,5,7,7,7,9,9,10,12.

My question is how do I fit the exponential survival distribution and calculate hazard. And what function should I use?

I am new to matlab and I appriciate any help and suggestions.

Answer 1

[Jeff Miller]

The exponential distribution is a one-parameter distribution, so all you can do is estimate that parameter. Once you have that estimate, everything else is also determined, including the hazard function. So you could think of "estimating the parameter" as the same thing as "estimating the hazard function".

For the maximum likelihood estimator of the parameter and a bias-corrected estimator, check Wikipedia

[Yuexun Tian]

Thank you!

I used the following code to estimate the parameter. x is the survival times.

x = [4,4,5,7,7,7,9,9,10,12]'

pd = fitdist(x,'exponential')

pd =

ExponentialDistribution

Exponential distribution

mu = 7.4 [4.33133, 15.4315]

Did I estimate the parameter of exponential model correctly? Does this mean h(t) = 7.4 ?

I appriciate your help!

[Jeff Miller]

Yes, you fit it correctly. Note mean(x) = 7.4.

h(t) = 1 / 7.4, which is the so-called "rate" parameter of the exponential. Sometimes the exponential is described as having this rate parameter and mu=1/rate. It is just conventional whether to use mu or rate as the parameter.

[Yuexun Tian]

Thank you so much!

I think the 'rate' parameter is where I was stucked!

[Jeff Miller]

You are welcome. Please accept the answer if your questions have been resolved.