I don't think it is common to say either higher age or older age. People normally say (in your case):
Or patients of the same age, just like what Max said in the comment above.
But I also think it is grammatically correct to use patients of higher age or of older age (it's just not preferable to use).
Apparently though, based on Google Trends, the phrase older age is more popular than higher age.
Older age is quite popular in the UK, US, Australia, India, Canada and South Africa. Whilst higher age is merely used in the UK, US and India.
Therefore, my conclusion is:
older patients is better to use than patients of older age than patients of higher age.