Here is how we responded to Referee 1; the changes were incorporated in the published manuscript.

Reviewer #1:

"Although this study is very interesting both from its set-up as from its results, it was performed on a small sample of about 275 patients (each PD and ALS) and 275 control individuals. Based on this one can argue about the power to detect an effect for complex diseases such as PD and ALS. Therefore it would improve the paper if a power calculation would be included in the paper. This power calculation should include a power calculation based on SNPs alone and on SNPs in selected genomic pathways such as axon guidance. These power calculations should also be discussed and compared to the obtained results. The authors should also draw more direct conclusions from these calculations than the current suggestive conclusions stated in the discussion section."

We acknowledge that the samples sizes for the available amyotrophic lateral sclerosis (ALS) and Parkinson’s disease (PD) case-control studies were small. Because we were interested in detecting the large effects of a pathway rather than the small effects of individual SNPs, we believe that the available samples were sufficient in size.

Regarding the main effects of SNPs, we provide in this cover letter a power table that demonstrates that with a pre-specified alpha of 0.05 and a pre-specified power of 0.90, with as few as 269 cases and 267 controls we could detect odds ratios as small as 1.8 in SNPs with population allele frequencies of 0.10 or higher. SNPs with low frequencies or SNPs with only recessive effects would have required larger odds ratios to be significant.

Table 1. Minimum detectable odds ratios using logistic regression models.
Coding Scheme for SNP
Allele Frequency Recessive Dominant Log-additive
.02 85.3 3.1 3.0
.04 23.7 2.4 2.4
.06 12.4 2.2 2.1
.08 8.3 2.0 1.9
.10 6.2 2.0 1.8
.12 5.0 1.9 1.8
.14 4.3 1.9 1.7
.16 3.8 1.8 1.7
.18 3.4 1.8 1.6
.20 3.1 1.8 1.6

Regarding the joint effects of SNPs, our model-building procedure used the subset of SNPs with significant main effects, and we would have thus potentially excluded some rare SNPs or recessive effects due to the small sample size. Our final joint effect models are therefore conservative. About 20% of SNPs that were within axon guidance pathway genes in the ALS dataset had allele frequencies below 0.10. The median allele frequency was 0.23. About 14% of SNPs that were within axon guidance pathway genes in the PD dataset had allele frequencies below 0.10. The median allele frequency was 0.27. Thus, in both analyses, we had reasonable power to capture the majority of SNPs for model-building, though not enough to capture subtle effects of individual SNPs. For our final model of ALS susceptibility, the odds ratio was 1739.73 (95% CI 523.33-5781.32), and for our final model of PD susceptibility, the odds ratio was 391.82 (95% CI 157.94-972.06). These effect sizes were very large. Fewer than 100 subjects in the ALS dataset or the PD dataset would have been required to show significance with these odds ratios. Estimating quantitative traits such as age at onset would require even fewer subjects. For example, the models predicting age at onset of ALS or age at onset of PD had R2 values of about 0.86. The available sample size of about 270 would have allowed us to detect R2 values as low as 0.15, and only about 70 cases would have been required to statistically detect the R2 values of 0.86.

We have added a discussion on statistical power (pages 18-19 of the revised manuscript) based on these calculations. We also recommend studies of the axon guidance pathway in ALS and PD using a higher resolution genomic map of the axon guidance pathway and larger sample sizes, both to refine the final models and to replicate the findings across diverse populations (pages 18-19 of the revised manuscript).

"A point that needs absolute clarification is the control population! No information is available in the paper on the control group. Is this group age, gender and ethnicity matched? How was this control group selected and is disease information (e.g. familial ALS, PD or other neurological disorders,..) available. This information is crucial since a 'wrong' control group can result in false positive p-values due to population stratification, age and gender effects,...especially with the low number of individuals included in the study."

We agree that controls selection and matching are important methodological considerations. The sampling of controls was described in detail by the original genome wide association studies of ALS and PD that provided the data for this study (Schymick et al., Fung et al.; references 19 and 20 in the revised manuscript). The authors of those studies reported that the controls were unrelated to the cases and did not have ALS, PD, or other neurological disorders. Their statistical tests revealed no evidence for population stratification on ethnicity. We now provide information in this paper regarding the sampling methods of those studies (page 5 in the revised manuscript). As described throughout the manuscript, in our study we adjusted the case-control analyses for age and gender. Also, two of the three outcomes that we considered (survival free of ALS or PD, age at onset of ALS or PD) employed data for cases only. It is reassuring that the axon guidance pathway was predictive of outcomes that both included or excluded control subjects in the analyses.