We investigate the efficacy of the dual-screening, annual chest X-ray and 4-monthly sputum cytology, for lung cancer detection using the Johns Hopkins Lung Project (JHLP) data. An advanced statistical approach to testing the dependency of dual diagnostic tests, chest X-ray and sputum cytology is applied for lung cancer detection. To achieve this, the screening sensitivities of X-ray only, cytology only, and dual-screening, the overall transition probability, the sojourn time, and the mean lead time were estimated from JHLP data. A derivative-free global optimization method, Particle Swarm Optimization (PSO), was further employed in the procedure to avoid being stuck at a local optimum or the boundary. Our analysis shows that the overall sensitivity of lung cancer screening is 85.34% with chest X-ray of 79.93% and 4-monthly sputum cytology of 26.98%, resulting in a small correlation coefficient of -0.0039, which is not significantly different from zero. As a result, the dual procedure improves the overall screening sensitivity up to ~5% in lung cancer detection.