Purpose: Models relating perimetric sensitivities to ganglion cell numbers have been proposed for combining structural and functional measures from patients with glaucoma. Here we compared seven models for ability to differentiate progressing and stable patients, testing the hypothesis that the model incorporating local spatial scale would have the best performance. Methods: The models were compared for the United Kingdom Glaucoma Treatment Study (UKGTS) data for the right eyes of 489 patients recently diagnosed with glaucoma. The SITA 24‐2 program was utilised for perimetry and Stratus OCT fast scanning protocol for thickness of circumpapillary retinal nerve fibre layer (RNFL). The first analysis defined progression in terms of decline in RNFL thickness. The highest and lowest quintiles (22 subjects per group) were identified for change in thickness of inferior temporal (IT), superior temporal (ST), and global RNFL (μm year$^{−1}$); a two‐way ANOVA was used to look for differences between the models in ability to discriminate the two quintiles. The second analysis defined a ‘progression group’ as those who were flagged by the UKGTS criteria as having progressive loss in perimetric sensitivity, and a ‘no progression’ group as those with rate of change in Mean Deviation (MD) closest to 0 dB year$^{−1}$ (87 subjects per group). The third analysis characterised variability of retinal ganglion cell (RGC) models for the two groups in the second analysis, using the standard deviation of residuals from linear regression of ganglion cell number over time to compute Coefficient of Variation (CoV). Results: The first analysis produced a negative result because the three ANOVAS found no effect of model or interaction of model and group (F$_{6,294}$ < 3.1, $p$ > 0.08). There was an effect of group only for the ANOVA with the ST sector (F$_{6,294}$ = 12.2, $p$ < 0.001). The second analysis also produced a negative result, because ROC areas were in the range 0.69–0.72 for all models. The third analysis found that even when variability in MD was low, the CoV was so large that test‐retest variation could include 100% loss of ganglion cells. Conclusions: Two very different approaches for testing the hypothesis both gave a negative result. For all seven ganglion cell models, rates of ganglion cell loss were highly affected by fluctuations in height of the hill of vision. Methods for reducing effects of between‐visit variability are needed in order to assess progression by relating perimetric sensitivities and ganglion cell numbers.