Immortal time bias and reverse causality in retrospective analysis: Comment on “effect of cumulative bortezomib dose on survival in multiple myeloma patients receiving bortezomib–melphalan–prednisone in the phase III <scp>VISTA</scp> study”
Authors: Pei‐Ying Hsieh, Chia‐Jen Liu, Chung‐Jen Teng
Journal: American Journal of Hematology (2015)

To the Editor: We read with interest "Effect of cumulative bortezomib dose on survival in multiple myeloma patients receiving bortezomib–melphalan–prednisone in the phase III VISTA study" 1. Mateos et al. reported a retrospective post hoc analysis by using data from a randomized phase III trial, VISTA 2, which showed improved outcomes of patients with newly diagnosed myeloma who were ineligible for high-dose therapy by adding bortezomib to melphalan–prednisone. Furthermore, Mateos et al. found that the transplant-ineligible myeloma patients who received a cumulative bortezomib dose of more than the median (39 mg/m2) had better overall survival (OS). This study provides new evidence that an increased cumulative bortezomib dose could improve OS in transplant-ineligible untreated myeloma patients. However, according to protocol, patients had to survive at least 151 days to have a cumulative bortezomib dose of 39 mg/m2. If the data was analyzed by using a log-rank test or time-independent Cox proportional hazards model, it would be likely that an "immortal time bias" could interfere with these results 3-6. "Immortal time" implies to a time interval during the follow-up period in which death cannot occur because of exposure definition. For instance, mortality "cannot" occur in the first five months of follow-up in the patients who had received at least 30 doses of protocol bortezomib. In conventional survival analysis using the likelihood ratio or log-rank tests, the immortal time bias can confer a spurious survival advantage to patients with a higher cumulative dose. The authors further performed a landmark analysis of OS that was conducted at 180 days post-randomization that might be unable to avoid this bias. In contrast, the results should be analyzed by using time-dependent analysis 3, 6, such as Cox regression with the cumulative dose of bortezomib as a time-dependent covariate. Furthermore, the planned dose of bortezomib in the VISTA trial was 67.6 mg/m2 2. Patients who had a cumulative bortezomib dose of less than 39 mg/m2 had higher probability of serious adverse effects and disease progression, both of which were correlated to death. Obviously, patients who had better response to bortezomib can live longer and have a chance to receive more doses of bortezomib. Reverse causality means that Y might exert a causal effect on X, in addition to the effects of X on Y 7. In this study, a longer OS might also offer a causal effect on higher cumulative dose of bortezomib, which could not be solved by a 180-day landmark or time-dependent analysis. We believe that the best way to evaluate the effect of cumulative dose of bortezomib on survival of multiple myeloma patients is a randomized controlled study while the cut-off value of the cumulative dose was best determined by receiver operating characteristic curve analysis. Pei-Ying Hsieh,1 Chia-Jen Liu,2,3,4 and Chung-Jen Teng1,2,3* 1Division of Oncology and Hematology, Department of Medicine, Far Eastern Memorial Hospital, New Taipei City, Taiwan; 2School of Medicine, National Yang-Ming University, Taipei, Taiwan; 3Institute of Public Health, National Yang-Ming University, Taipei, Taiwan; 4Division of Hematology and Oncology, Department of Medicine, Taipei Veterans General Hospital, Taipei, Taiwan