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<b>Background</b>: Low-dose computed tomography (LDCT) screening reduces lung cancer mortality; however, the effectiveness of screening programs depends not only on detection, but also on completion of downstream diagnostic pathways following a positive screening result. Refusal of recommended invasive diagnostic procedures represents a critical but understudied form of post-screening attrition. <b>Methods</b>: This retrospective observational study was conducted within an organized multicenter LDCT lung cancer screening program in Vojvodina, Serbia. Consecutive participants screened between September 2020 and October 2025 were included. Positive screening was defined as Lung-RADS 4A, 4B, or 4X. Refusal was defined as the absence of any invasive diagnostic procedure within six months following multidisciplinary team recommendation. Demographic, clinical, smoking-related, and perceptual factors were analyzed. Time to invasive diagnostic procedures was assessed for bronchoscopy and surgical treatment. Multivariable logistic regression was used to identify factors independently associated with refusal. <b>Results</b>: Among 10,261 screened individuals, 479 (4.7%) had positive LDCT findings. Of these, 60 participants (12.5%) refused invasive diagnostic evaluation. In multivariable analysis, multimorbidity (OR 3.45, 95% CI 1.61-7.38), previous malignancy (OR 2.92, 95% CI 1.16-7.35), higher cumulative smoking exposure (OR 1.02 per pack-year, 95% CI 1.00-1.03), and screening center (Subotica vs. Novi Sad: OR 2.40, 95% CI 1.21-4.78) were independently associated with refusal of invasive diagnostic procedures. Greater concern about personal lung cancer risk was associated with a lower likelihood of refusal (OR 0.54, 95% CI 0.29-0.99). Time to bronchoscopy differed significantly across screening centers and screening years, whereas time to surgical treatment was comparable across centers and years. <b>Conclusions</b>: Refusal of invasive diagnostic procedures following positive LDCT screening represents a meaningful implementation challenge influenced by both patient vulnerability and system-level factors. Addressing modifiable barriers through improved risk communication and optimization of post-screening diagnostic pathways may enhance diagnostic continuity and strengthen the real-world effectiveness of lung cancer screening programs.