Analyzing the impact of depth of response on survival in patients with metastatic non-small-cell lung cancer
Authors: S. Weber, M. Wolkewitz, M. Schumacher
Journal: Annals of Oncology (2017)

We read with great interest the article by McCoach et al. [1.McCoach C.E. Blumenthal G.M. Zhang L. et al.Exploratory analysis of the association of depth of response and survival in patients with metastatic non-small-cell lung cancer treated with a targeted therapy or immunotherapy.Ann Oncol. 2017; 28: 2707-2714Abstract Full Text Full Text PDF Scopus (41) Google Scholar] investigating the association of depth of response (DepOR) with survival in patients with metastatic non-small-cell lung cancer. The authors found that good response (such as maximal tumor shrinkage of 76%–100%) was associated with longer progression-free survival (PFS) and overall survival (OS) compared with non-responders, estimated by a very low hazard ratio (HR) of 0.03. We believe that these results are prone to survival bias. Already in 1983 and re-emphasized in 2008, Anderson et al. [2.Anderson J.R. Cain K.C. Gelber R.D. Analysis of survival by tumor response and other comparisons of time-to-event by outcome variables.JCO. 2008; 26: 3913-3915Crossref PubMed Scopus (161) Google Scholar] discussed the statistical challenges of analyzing survival by tumor response. Anderson et al. [2.Anderson J.R. Cain K.C. Gelber R.D. Analysis of survival by tumor response and other comparisons of time-to-event by outcome variables.JCO. 2008; 26: 3913-3915Crossref PubMed Scopus (161) Google Scholar] pointed out that a bias occurs when patients are categorized into good and bad responder groups at baseline and then survival in these groups is compared. This approach is biased because in order to obtain a good response individuals have to survive long enough to belong to the good responder group. On the other hand, there is no condition on survival for the non-responders. This bias is called time-dependent bias or immortal time bias, as described by van Walraven et al. [3.van Walraven C. Davis D. Forster A.J. Wells G.A. Time-dependent bias was common in survival analyses published in leading clinical journals.J Clin Epidemiol. 2004; 57: 672-682Abstract Full Text Full Text PDF PubMed Scopus (229) Google Scholar] and Gill et al. [4.Gill B.S. Flickinger J.C. Beriwal S. Caveat for immortal time bias in adjuvant therapy–related population-based analyses.JCO. 2015; 33: 2931Crossref PubMed Scopus (6) Google Scholar]. The analysis of McCoach et al. [1.McCoach C.E. Blumenthal G.M. Zhang L. et al.Exploratory analysis of the association of depth of response and survival in patients with metastatic non-small-cell lung cancer treated with a targeted therapy or immunotherapy.Ann Oncol. 2017; 28: 2707-2714Abstract Full Text Full Text PDF Scopus (41) Google Scholar] is prone to immortal time bias, because DepOR develops over time, but patients were categorized based on DepOR into responder groups using the maximal tumor shrinkage. Hence, DepOR is considered as being already known at baseline. However, a good tumor response of 75%–100% shrinkage usually takes a couple of months to develop. There are methodological papers addressing the presence of time-dependent bias and its impact, such as van Walraven et al. [3.van Walraven C. Davis D. Forster A.J. Wells G.A. Time-dependent bias was common in survival analyses published in leading clinical journals.J Clin Epidemiol. 2004; 57: 672-682Abstract Full Text Full Text PDF PubMed Scopus (229) Google Scholar] and Beyersmann et al. [5.Beyersmann J. Gastmeier P. Wolkewitz M. Schumacher M. An easy mathematical proof showed that time-dependent bias inevitably leads to biased effect estimation.J Clin Epidemiol. 2008; 61: 1216-1221Abstract Full Text Full Text PDF PubMed Scopus (120) Google Scholar]. Beyersmann et al. [5.Beyersmann J. Gastmeier P. Wolkewitz M. Schumacher M. An easy mathematical proof showed that time-dependent bias inevitably leads to biased effect estimation.J Clin Epidemiol. 2008; 61: 1216-1221Abstract Full Text Full Text PDF PubMed Scopus (120) Google Scholar] delivered an easy mathematical proof showing that in the presence of time-dependent bias the HRs are always smaller than they actually are. Consider the results of McCoach et al. in more detail: the Kaplan–Meier curves for PFS show no events during the first 5–6 months for the good responder group. This is not surprising as most of the patients have not had a tumor shrinkage of more than 75% within the first 6 months whereas all events occurred during the first 6 months in the non-responder group. This reflects the time dependency of response and results in an extremely low HR. However, with the results of Beyersmann et al. [5.Beyersmann J. Gastmeier P. Wolkewitz M. Schumacher M. An easy mathematical proof showed that time-dependent bias inevitably leads to biased effect estimation.J Clin Epidemiol. 2008; 61: 1216-1221Abstract Full Text Full Text PDF PubMed Scopus (120) Google Scholar] we can show that the HR is closer to 1. There are appropriate approaches for the investigation of treatment response and survival. Treatment response can be considered as a time-dependent covariate or a landmark approach can be carried out [2.Anderson J.R. Cain K.C. Gelber R.D. Analysis of survival by tumor response and other comparisons of time-to-event by outcome variables.JCO. 2008; 26: 3913-3915Crossref PubMed Scopus (161) Google Scholar]. Ignoring time dependency leads to seriously biased results and therefore to wrong conclusions. This is a crucial topic and the time dependency of treatment response needs to be taken into account when investigating the association with survival. We hope that our letter leads to a better awareness of the immortal time bias and hence improves investigations. This work has been funded by the German Research Foundation (Deutsche Forschungsgemeinschaft) (grant No WO 1746/1-1); MW received this funding.