Predictors of refraction prediction error after cataract surgery: a shared parameter model to account for missing post-operative measurements

Cataract surgery is a common procedure that involves removing the cataractous lens of the eye and implanting a new clear plastic lens, with a goal of improving vision and often changing the refraction of the eye. Unexpected refractive outcomes, or refraction prediction error (PE), may be more likely to occur among patients with certain preexisting ocular conditions. However, longitudinal refractive measurements are often missing after surgery, making it difficult to accurately assess which ocular comorbidities lead to increased PE. Moreover, patients with ideal refractive outcomes in one or both eyes may be less likely to return to the clinic, thus more likely to have missing measurements that are missing not at random (MNAR). Despite this potential complication to data analysis, very few studies evaluating PE address the missing data mechanism and the effect it may have on the results. We propose the application of a shared parameter model to reduce bias in situations of MNAR data and compare this to a linear mixed model that is not able to account for this mechanism. We also conduct a simulation study to better understand the most plausible missing mechanism in our study and to characterize situations in which the shared parameter model may be necessary. Applied to the cataract surgery data, the shared parameter model gives similar results as the linear mixed model, finding that a history of LASIK, PRK, RK, high myopia, hyperopia, astigmatism, or combined surgery lead to increased PE. In addition, the simulations confirm that under certain scenarios, a shared parameter model will greatly reduce bias in situations of MNAR.