2.5. Statistical analysis

Statistical analysis was performed using Matlab (version R2016b, MathWorks Inc., Natick, MA). A significance level of 5% was used in all statistical tests, and Benjamini & Hochberg False Discovery Rate (FDR) correction (Benjamini and Hochberg, 1995) was used to correct for multiple comparisons, where applicable. Linear regression was used to investigate the relationship between measured values of VA and imaging parameters. In the linear regression models, VA (measured using the logMAR score) was used as the response variable. The predictor variable of interest was either median FA or median ADC (separate models were used for each), measured in the optic nerves, tracts, or radiations. Patient age, NF1 status and active treatment status (i.e. whether the patient was receiving chemotherapy at the time of imaging) were included as additional predictor variables. Initially, linear regression models were fit using all predictor variables. Backward stepwise regression was then used to determine a final model, in which the least significant terms were progressively removed. After removing each term, an F-test was used to compare the goodness of fit of the reduced/nested model compared to the full model. This process was repeated until the combination of predictors was found which minimised the p-value associated with the F-test. After determining the final linear regression models, a ‘leave-one-out’ analysis was performed to measure prediction accuracy. For this, each patient in turn was excluded from the pool of raw data, and the linear regression model (based on the significant predictors determined above) was fit to the remaining patients. Using this, the difference between the predicted and measured logMAR score for the excluded patient was recorded. After repeating this over all the patients, the root mean square of the prediction error of the final model was recorded.

For the optic nerves, VA in the eye with the highest measureable logMAR score (i.e. the worst measureable eye) was correlated directly against the imaging parameters in the corresponding optic nerve (e.g. if VA was worst in the left eye, this was correlated against median FA or ADC in the left optic nerve). However, the same technique could not be used for the optic tracts and radiations, as, being posterior to the optic chiasm, these receive input from both eyes. Here, mean inter-eye VA was used as the response variable. Median FA or ADC across both optic tracts was the first predictor variable, median FA or ADC across both optic radiations was the second predictor variable, and patient age, NF1 status and active treatment status were included as additional predictors.

Patients for which VA in one eye was too poor to be quantified using a logMAR score were excluded from the linear regression analysis. An additional group-wise analysis was performed in order to include these patients. Group 1 was defined as all patients having VA of ≤ 0.5 logMAR (the WHO defines VA > 0.5 logMAR as part of the criteria for low-vision). Group 2 included all patients with VA > 0.5 logMAR, or with un-measurable VA in one eye. Similar to the linear regression modelling, for the optic nerves, we matched VA in the worst eye to the imaging parameters in the corresponding optic nerve. For the optic tracts and radiations, VA was averaged across both eyes, and imaging parameters were averaged across the left and right optic tracts and radiations.