Reply to Leah Bensimon, Samy Suissa, and Laurent Azoulay's letter to the editor re: Daniel E. Spratt, Chi Zhang, Zachary S. Zumsteg, Xin Pei, Zhigang Zhang, Michael J. Zelefsky. metformin and prostate cancer: reduced development of castration-resistant disease and prostate cancer mortality. Eur Urol 2013;63:709-16.

We appreciate the thoughtful comments made by Bensimon and colleagues. The concern they raise regarding the method of our analysis [1] is related to what has been termed immortal time bias. Immortal time refers to a period of time that, if included in one’s analyses, falsely implies that no event can occur during that time period (hence, it is immortal because, by definition, no event can occur during this time period). As shown in Figure 1a, including immortal time alters a study’s follow-up time, assumes that no events can occur during the immortal time period, and ultimately leads to selection bias and misclassification bias [2]. To better appreciate the potential importance of immortal time bias and how it may be applicable to a statistical analysis, we present an example that has been published previously regardingwhether Oscarwinners live longer than non-Oscar winners [3]. The original findings reported that Oscar winners live almost 4 yr longer than their non–Oscarwinning counterparts! The authors conducted the analysis using the start of follow-up as birth, the intervention as winning anOscar, and the event of interest as death (Fig. 1b). However, what may not be apparent at first is that one must live long enough towin anOscar to be ‘‘eligible’’ for inclusion in the analysis. The bias is introduced by using follow-up starting at birth rather than at the time of Oscar nomination. The time period between birth and Oscar nomination, by definition, is immortal time in that it assumes no events (deaths) could occur during this period (hence, making this time immortal). Yet, many actors may die before they are eligible to win an Oscar, and this poses a bias for the study. In a similar vein, Bensimon et al. claim that our ‘‘results are likely due to immortal time bias.’’ This is because a subset of our cohort began the intervention (metformin) after the start of follow-up (radiotherapy [RT] treatment), and this subset had the potential to be affected by immortal time bias [1]. For example, if we defined metformin use as only those who started metformin at 10 yr posttreatment and made the claim that patients on metformin live longer than non–metformin-using patients, our analysis would be subjected to an extreme immortal time bias. We are well aware of this concern, but we do not believe immortal time bias is a significant issue for the analysis we performed, for several reasons. First, only 18% of our population was not on metformin at the initiation of RT, as stated in themethods section of our paper. Second, only 8% of thepatients initiatedmetformin after 3 yrposttreatment, and thus >92% of the cohort was exposed for a significant duration of follow-up (as stated in the paper, the median duration of metformin use was 58.2 mo [interquartile range: 38–88 mo]). This is visually represented in Figure 1c. Consequently, it is unclear that immortal time bias plays as significant a role in our study as Bensimon et al. believe it does. We nevertheless agree with Bensimon et al. that when one wants to remove any concerns about an immortal time bias, a time-dependent adjustment analysis should be performed. So, as suggested, we took them up on their challenge. We performed a reanalysis of the entire data set that would ultimately determine whether the effect of immortal time bias was a confounder in our analysis, which concluded that the use of metformin was associated with a superior clinical outcome. When we reanalyzed our data correcting for time dependency in multivariate analysis, our initial results were maintained: Diabetic patients taking metformin continued to have significantly better prostate-specific antigen recurrence-free survival (hazard ratio [HR]: 1.69; p = 0.03), distant metastasis (HR: 3.27; p = 0.001), and overall survival (HR: 1.90; p = 0.01) compared with diabetic patients not usingmetformin. TheHRs are slightly lower, and the p values remain significant but larger due to the adjustment of using the time-dependent covariate. Bensimon et al. also criticized Figure 3 in our study [1] as being ‘‘affected by immortal time bias.’’ This issue is more complex. First, their letter wrongly regarded these curves as Kaplan-Meier curves. They are actually cumulative incidence curves due to competing risks. Second, the events captured by the curves were due to prostate cancer, and there existed deaths due to other causes thatwere not depicted in Figure 3 (considered as a competing risk in the analysis of prostate cancer–specific mortality [PCSM]). Third, although 18% of patients were not initially on metformin at time of RT, the EU RO P E AN URO LOGY 6 4 ( 2 0 1 3 ) e 2 9 – e 3 0