This study aimed to compare the ability of narrow-band imaging to detect early and invasive lung cancer with that of conventional pathological analysis and white-light bronchoscopy. We searched the PubMed, EMBASE, Sinomed, and China National Knowledge Infrastructure databases for relevant studies. Meta-disc software was used to perform data analysis, meta-regression analysis, sensitivity analysis, and heterogeneity testing, and STATA software was used to determine if publication bias was present, as well as to calculate the relative risks for the sensitivity and specificity of narrow-band imaging vs those of white-light bronchoscopy for the detection of early and invasive lung cancer. A random-effects model was used to assess the diagnostic efficacy of the above modalities in cases in which a high degree of between-study heterogeneity was noted with respect to their diagnostic efficacies. The database search identified six studies including 578 patients. The pooled sensitivity and specificity of narrow-band imaging were 86% (95% confidence interval: 83-88%) and 81% (95% confidence interval: 77-84%), respectively, and the pooled sensitivity and specificity of white-light bronchoscopy were 70% (95% confidence interval: 66-74%) and 66% (95% confidence interval: 62-70%), respectively. The pooled relative risks for the sensitivity and specificity of narrow-band imaging vs the sensitivity and specificity of white-light bronchoscopy for the detection of early and invasive lung cancer were 1.33 (95% confidence interval: 1.07-1.67) and 1.09 (95% confidence interval: 0.84-1.42), respectively, and sensitivity analysis showed that narrow-band imaging exhibited good diagnostic efficacy with respect to detecting early and invasive lung cancer and that the results of the study were stable. Narrow-band imaging was superior to white light bronchoscopy with respect to detecting early and invasive lung cancer; however, the specificities of the two modalities did not differ significantly.

A new trust-region SQP method for equality constrained optimization is considered. This method avoids using a penalty function or a filter, and yet can be globally convergent to first-order critical points under some reasonable assumptions. Each SQP step is composed of a normal step and a tangential step for which different trust regions are applied in the spirit of Gould and Toint [Math. Program., 122 (2010), pp. 155-196]. Numerical results demonstrate that this new approach is potentially useful. Mathematical subject classification: 65K05, 90C30, 90C55.