Reply to Hamada et al.

We thank Hamada et al. for their interest in our study [1] and their valuable comments. Hamada et al. commented that according to our findings a greater time-to-progression (TTP) and first-line chemotherapy were associated with significantly longer patency of self-expanding metal stents. However, our multivariate analysis, using the Cox proportional hazards model (and not Kaplan–Meier analysis) showed that a longer TTP and first-line chemotherapy were protective factors against restenosis (not patency). Kaplan–Meier analysis is a statistical method for estimating survival distribution and this was presented in the legends of Figures 2 and 3 in our article [1]. We included the Kaplan–Meier plots to provide readers with an alternative way to understand our data, but our conclusions were based on the Cox proportional hazards model.

Hamada et al. suggested that cumulative incidence functions of stent dysfunction should be estimated and compared using competing risk analysis. Death before stent dysfunction would be considered a competing risk event for stent dysfunction. We agree that competing risk analysis is a more detailed method than the Kaplan–Meier estimate for comparing cumulative incidence functions of long-term clinical gastrointestinal stent outcomes. We therefore reanalyzed our data using this method to compare cumulative incidence functions of the long-term outcomes (cumulative restenosis rates). First, we considered migration as a competing risk event. Patients without stent dysfunction were censored regardless of death at the end of the follow-up period. Comparisons of patients grouped according to the TTP (long versus short) showed that the curves for the two groups differed significantly (P < 0.001). Similarly, comparisons of patients grouped according to therapy (first-line versus salvage) also revealed significantly different curves (P = 0.024). Second, we considered migration or death as competing risk events. Patients without stent dysfunction were censored if they were alive at the end of the follow-up period. We found that the cumulative incidence curves did not differ significantly (long TTP versus short TTP, P = 0.320; first-line therapy versus salvage therapy, P = 0.164), but the curves were similar to the plots that considered only migration as a competing risk event.

Hamada et al. also suggested using a competing risk regression model instead of the Cox proportional hazards model, because migration and restenosis are potential competing risk events for each other. We agree with this suggestion. When we used the Cox proportional hazards model, a long TTP (adjusted hazard ratio [aHR] = 0.29, 95 % confidence interval [CI] 0.13 – 0.67, P = 0.04) and first-line chemotherapy (aHR = 0.45, 95 %CI 0.22 – 0.93, P = 0.030) were found to be protective factors against restenosis in the multivariate analysis. When we analyzed the data using migration as a competing risk, the HR associated with longer TTP was 0.30 (95 %CI 0.14 – 0.63, P = 0.001), and the HR associated with first-line chemotherapy was 0.46 (95 %CI 0.24 – 0.89, P = 0.022). In the multivariate analysis, the aHR associated with a long TTP was 0.31 (95 %CI 0.15 – 0.64, P = 0.002), and the aHR associated with first-line chemotherapy was 0.51 (95 %CI 0.26 – 1.00, p = 0.051).

Hamada et al. also suggested including only baseline characteristics in the Cox proportional hazards model, using the landmark method when response to chemotherapy or TTP was analyzed. Anderson et al. recommend using the landmark method to analyze survival according to tumor response [2]. Statistical methods such as the landmark method can be used to minimize bias due to the guarantee time for responders [2]. A frequently used method for analyzing survival according to response involves dividing patients into two groups according to whether or not they ever achieved a response. However, the length of survival may influence the assignment of patients to the responder or non-responder group. To be classified as a responder, the patient must survive at least until the first response evaluation, but this guarantee time is not required for the non-responder group. The landmark method selects a fixed time after initiation of therapy as a landmark for the analysis. Only those patients who are still included in the study at this landmark time are categorized as responders or non-responders [2]. However, we excluded patients in whom tumor response could not be evaluated due to death or other reasons described in the Methods section of our article. Therefore we believe that we avoided guarantee-time bias in our study.

Based on the results of the competing risk analysis we conclude that a longer TTP and first-line chemotherapy were meaningful protective factors against restenosis after pyloric stent placement.

• References

• 1 Kim CG, Park SR, Choi IJ et al. Effect of chemotherapy on the outcome of self-expandable metallic stents in gastric cancer patients with malignant outlet obstruction. Endoscopy 2012; 44: 807-812
• 2 Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor response. J Clin Oncol 1983; 1: 710-719