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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 (<inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>2</mn></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>3</mn></msub></semantics></math></inline-formula>) with 1046 patients from four sleep laboratories in Western Romania, including 145 subjects (<inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>1</mn></msub></semantics></math></inline-formula>) with one-night CPAP therapy. Using <inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>1</mn></msub></semantics></math></inline-formula> 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 <inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>2</mn></msub></semantics></math></inline-formula> (OSA-diagnosed) and <inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>3</mn></msub></semantics></math></inline-formula> (control), using the area under the curve. As such, we confirmed the correlation between NC and AHI (<inline-formula><math display="inline"><semantics><mrow><mi>ρ</mi><mo>=</mo><mn>0.35</mn></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.001</mn></mrow></semantics></math></inline-formula>) 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, <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.001</mn></mrow></semantics></math></inline-formula>); 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 <inline-formula><math display="inline"><semantics><mrow><mo>=</mo><mn>41</mn></mrow></semantics></math></inline-formula> cm threshold classified the <inline-formula><math display="inline"><semantics><msub><mi>D</mi><mn>1</mn></msub></semantics></math></inline-formula> 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.