Author’s response to reviews Title: Factors associated with Developing a Fear of Falling in Subjects with Primary Open-angle Glaucoma Authors:

Inclusion of regression models, eg. "The optimal regression model for patients' baseline fear of falling (+) = -7.0 + 0.062 x age + 0.58 x female 0.088 x mTDIP + 0.87 x number of previous fall" in the abstract results are hard to interpret the results should be expressed in a way that has meaning even to a reader who has not read the whole paper. Thank you very much indeed. The abstract has been corrected. Methods: The fear of falling measure is quite simplistic as outlined above there are much more appropriate measures available. Thank you for this comment. We do agree and have expanded the limitations section to emphasize this concern. (page 16, line 265-266, page 17, line 267-271) Similarly, the measure of falls asks "How many times did you fall in the last year?" and "Have you experienced any injurious falls in the last year?" There is no definition of what constitutes a fall and the use of a single question to determine the number of falls is not considered the standard (as outlined by Hauer et al (2006) in their systematic review of definitions of falls) We now discuss this in the limitation section, thank you. (page 17, line 268-271) Why weren't falls rates and visual function measures also collected at the subsequent visits along with the fear of falling question it seems unlikely that visual fields would not have been tested at the follow-up visits. We tested visual fields at the follow-up visits. Results: Why did 50 patients drop out from the study over the 3 year follow-up? These patients did not appear in the outpatient clinic. We could not obtain any information about these drop-outs. This is a limitation that we now discuss in the manuscript. (page 17, line 274275) It would be good to get ranges as well as men values for the various parameters described at baseline. Thank you very much. We added these to Table 1 and 2. The falls rates at baseline seems very low general population studies of older adults are around 30%, whereas for this group it is only 6%. The age range of our study subject was 40 to 85 years; the average age was much younger than previous papers. Another possible reason is that falling risk among older adults varies by racial/ethnic groups. We now discuss the low rate and possible reasons in the manuscript. (page 17, line 275-282, page 18, line 283-284) The statistical analysis is unclear there is a lot of complex modelling for predicting the outcome of fear of falling which is based on one simple question. Model selection with AICc is an established method to assess the importance of variables, when the number of investigated variables is large. We chose AICc model selection method, because the degrees of freedom in a multivariate logistic regression model decreases with a large number of (i.e., redundant) variables. In evaluating the effect of each variable, it is therefore recommended to use model selection methods to improve the model fit by removing redundant variable, rather than using multiple logistic regression with all variables (Tibshirani RJ, Taylor J. Degrees of freedom in lasso problems. Ann Stat. 2012;40:1198–232. Mallows C. Some comments on Cp. Technometrics. 1973;15: 661–675.). How was the optimal model determined from the 2 raised to the power 13 combinations? Thank you very much for this comment. We chose the optimal model from all possible combinations of included variables using the AICc statistics. In this case, there were 13 variables, so a model with the smallest AICc was identified from all 213 candidate models, as described in Method (Page 11 Line 185).