I would really appreciate some help on study design. I will present my ideas and if the forum could critique/advise I would be very grateful.

The study compares a new refractive laser eye surgery technique (lets call this Rx2) with the standard treatment (Rx1). It is already known that they perform as well as each other at giving a good visual outcome. However, it is anecdotally recognised that the new treatment (Rx2) initially leaves the patient with poorer vision, at day 1 and likely still at day14 after treatment. Finally, it is also known that pre-existing refraction (eg long or short sightedness) can effect laser refractive surgery outcomes. This is a potentially confounding factor that I would like to attempt to correct for in the study.

The ideal would be a prospective double blind randomised control trial, but this is not possible for me to perform. I am limited in the data available to me. It is anonymised retrospective data from a single laser refractive surgery clinic. Because most people have bilateral procedures I will randomly select only one eye so that one patient = one independent unit of data. Finally there is a manual component to accumulating all the data, it is not all in a spreadsheet so I am also limited in time as to the number of units of data I can collect, realistically 100.

There are over 700 patients who received Rx1

There are 50 patients who received Rx2

Study question:

Does Rx2 have a delayed visual recovery compared with standard Rx1?

Null hypothesis

Best corrected visual acuity (BCVA) at day 14: Rx2 = Rx1

Alternative hypothesis

BCVA at day 14: Rx2 does not equal Rx1

Idea 1

Stratify the groups Rx1 & Rx2 according to the confounding factor (pre-existing refraction) and randomly select 10 from 3 strata for Rx1 & Rx2 then perform an independent t-test on BCVA at day 14.

Idea 2

Use all 50 patients from Rx2 and randomly select 50 from Rx1 and keep my fingers crossed that the refractions have similar descriptive statistics. Then perform independent t-test.

Idea 3

Use all 50 patients from Rx2 and blindly match 50 from Rx1 according to closest refraction. Then perform a paired t-test on the matched pairs.

My instinct is that idea 1 is the best. I am grateful for any advice on whether I am transgressing any obvious statistical rules and suggestions for better approaches within the stated limitations. Thank you!

(I appreciate the data necessarily suffers from convenience bias because I have no access to any other data. Also FYI, the data does follow an approximately normal distribution.)

Cheers,

Dan