We explored the relationship between obstructive sleep apnea (OSA) patients’ anthropometric measures and the CPAP treatment response. To that end, we processed three non-overlapping cohorts (D1, D2, D3) with 1046 patients from four sleep laboratories in Western Romania, including 145 subjects (D1) with one-night CPAP therapy. Using D1 data, we created a CPAP-response network of patients, and found neck circumference (NC) as the most significant qualitative indicator for apnea–hypopnea index (AHI) improvement. We also investigated a quantitative NC cutoff value for OSA screening on cohorts D2 (OSA-diagnosed) and D3 (control), using the area under the curve. As such, we confirmed the correlation between NC and AHI (ρ=0.35, p<0.001) and showed that 71% of diagnosed male subjects had bigger NC values than subjects with no OSA (area under the curve is 0.71, with 95% CI 0.63–0.79, p<0.001); the optimal NC cutoff is 41 cm, with a sensitivity of 0.8099, a specificity of 0.5185, positive predicted value (PPV) = 0.9588, negative predicted value (NPV) = 0.1647, and positive likelihood ratio (LR+) = 1.68. Our NC =41 cm threshold classified the D1 patients’ CPAP responses—measured as the difference in AHI prior to and after the one-night use of CPAP—with a sensitivity of 0.913 and a specificity of 0.859.