Specificity and sensitivity of bootstrap median regression of joint structure and function glaucoma progression

Abstract

 

Purpose

 

A key question for assessing glaucoma progression is: what is the optimal strategy to separate progressing from stable eyes? The aims of this study were to assess median regression with a bootstrap significance test, taking simple linear regression as landmark, and to compare two different criteria to combine structure and function.

 

Methods

 

Datasets of 220 eyes were simulated with different rates of progression for percent of mean normal mean sensitivity (MS) in a linear scale and for percent mean normal rim area (RA) in mm². Simulations were based on series of 11 visits of 220 real eyes from 150 patients with glaucoma from the Diagnostic Innovations in Glaucoma Study (DIGS) and African Descent and Glaucoma Evaluation Study (ADAGES) studies. For each series of 11 visits, the real linear trend was removed and the first 7 visits subsampled. Sensitivity at α = 5% was estimated for different simulated rates of progression for MS, RA, and two different criteria to combine structure and function; the ALL criterion and the ANY criterion. The theoretical false positive rate was fixed at 5%, and thus an eye was flagged as progressing if p-values for both MS and RA were < 0.224 for the ALL criterion, or if either p-value was < 0.0253 for the ANY criterion.

 

Results

 

The specificity of bootstrap median regression for MS, RA, and the ALL and ANY criteria were 8%, 6%, 4%, and 6%. For simple linear regression specificities were all about 5%. Figure 1 shows sensitivities for all 4 criteria. Bootstrap median regression performed almost as well as simple linear regression in simulations, but flagged fewer eyes as progressing in real data. Although combining structure and function improved sensitivity in simulations, about 35% of eyes with very fast progression (−5% of MS loss per year) were undetected. Table 1 shows the percentage of eyes flagged as progressing with the real dataset.

 

Conclusions

 

Median regression is more robust to heteroskedasticity and other undesirable statistical properties in the data. Yet, it did not perform better than simple linear regression in these simulations. Series of 7 visits are likely insufficient to ensure detection, even in eyes that progress very fast.  

 

Figure 1. Sensitivity of simple linear regression and bootstrap median regression at different simulated progression rates

 

 

Table 1. Number of eyes flagged as progressing with real progression rates