Immortal-time bias in older vs younger age groups: a simulation study with application to a population-based cohort of patients with colon cancer

British Journal of Cancer ARTICLE www.nature.com/bjc OPEN Epidemiology Immortal-time bias in older vs younger age groups: a simulation study with application to a population-based cohort of patients with colon cancer Sophie Pilleron 1,2 ✉ , Camille Maringe3, Eva J. A. Morris 1 and Clémence Leyrat 4 1234567890();,: © The Author(s) 2023 BACKGROUND: In observational studies, the risk of immortal-time bias (ITB) increases with the likelihood of early death, itself increasing with age. We investigated how age impacts the magnitude of ITB when estimating the effect of surgery on 1-year overall survival (OS) in patients with Stage IV colon cancer aged 50–74 and 75–84 in England. METHODS: Using simulations, we compared estimates from a time-fixed exposure model to three statistical methods addressing ITB: time-varying exposure, delayed entry and landmark methods. We then estimated the effect of surgery on OS using a population-based cohort of patients from the CORECT-R resource and conducted the analysis using the emulated target trial framework. RESULTS: In simulations, the magnitude of ITB was larger among older patients when their probability of early death increased or treatment was delayed. The bias was corrected using the methods addressing ITB. When applied to CORECT-R data, these methods yielded a smaller effect of surgery than the time-fixed exposure approach but effects were similar in both age groups. CONCLUSION: ITB must be addressed in all longitudinal studies, particularly, when investigating the effect of exposure on an outcome in different groups of people (e.g., age groups) with different distributions of exposure and outcomes. British Journal of Cancer; https://doi.org/10.1038/s41416-023-02187-0 INTRODUCTION Immortal-time bias occurs in longitudinal studies when the exposure is defined based on information available after the start of the participants’ follow-up. This is typically the case when the start of follow-up and treatment initiation do not coincide [1]. In cancer literature, a classic example of ITB is when one wants to estimate the effectiveness of a treatment on survival by comparing survival measures (e.g., median survival, overall survival) from cancer diagnosis between patients who do, and do not, receive it. In practice, treatment is rarely initiated on the day of diagnosis, and therefore, in order to initiate the treatment at some point in time, patients must remain alive at least until the time of the treatment receipt; this period is, therefore, called “immortal time”. By defining the study groups based on the observed treatment assigned later, patients who may have been offered the treatment but died before initiation would contribute to the untreated group and as such inflate the number of deaths in that group. In a hypothetical trial in which patients are randomised to treatment groups at the time of diagnosis, patients who die before treatment initiation would be on average equally represented in both study groups, and the ITB would not be a concern. In non-randomised study design, however, patients in the treated group would have an apparent survival advantage compared to those in the non-treated group, regardless of the efficacy of the treatment studied. Any apparent survival benefit in the treatment group may not, therefore, indicate a benefit of the treatment. Several recent papers in epidemiology from different medical fields (oncology, nephrology, cardiology, etc.) drew attention to this bias [1–5]. However, it seems that this bias is still commonly misunderstood or overlooked in the cancer survival literature. Indeed, ITB was commonly seen in recent literature reviews [6–9]. However, several statistical methods are available to address the issue, including using the treatment as a time-varying exposure, the delayed entry approach or conditioning on a given survival time (landmark time) [4, 10]. Patients aged 75 years or older are underrepresented in randomised clinical trials, and observational studies are often used to study the effectiveness of treatment in terms of survival, with sometimes comparison between older patients and younger patients. Yet, the magnitude of ITB increases with the likelihood of early death, which itself increases as chronological age increases. 1 Nuffield Department of Population Health, University of Oxford, Big Data Institute, Old Road Campus, Oxford OX3 7LF, UK. 2Ageing, Cancer, and Disparities Research Unit, Department of Precision Health, Luxembourg Institute of Health, 1A-B, rue Thomas Edison, 1445 Strassen, Luxembourg. 3Inequalities in Cancer Outcomes Network, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK. 4Department of Medical Statistics, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK. ✉email: Received: 14 March 2022 Revised: 18 January 2023 Accepted: 26 January 2023 S. Pilleron et al. 2 Therefore, the magnitude of the bias may worsen with age. However, to our knowledge, no studies evaluated the impact of age on the magnitude of the ITB in cancer research and assessed the performance of standard and suitable analysis methods to account for this bias. This study, therefore, aims to describe how the magnitude of ITB may differ in relation to age when age modifies the risk of death, the likelihood of receiving the treatment, or both. It also investigates the utility of several analytical techniques to account for this bias in practice. Initially, a simulation study was conducted to empirically illustrate the impact of age on the magnitude of ITB under different scenarios when using a time-fixed exposure statistical approach prone to ITB, and to compare the performance of three alternative methods to account for this bias. Then, these methods were applied to estimate the effect of surgery performed within 6 months of diagnosis on 1-year overall survival in patients diagnosed with Stage IV colon cancer aged 50–74 and separately in those aged 75–84 in England using data from the CORECT-R resource [11]. The problem To estimate the effect of surgery performed within 6 months of diagnosis on the 1-year overall survival probability from cancer diagnosis in those who do, and do not, receive the treatment and by age group one can use the Kaplan–Meier estimator or a Cox regression model by simply including surgery status in the model, that is, whether the patients received surgery in the 6 months following the diagnosis or not. This considers treatment as a timefixed exposure. These methods wrongly assume that surgery occurs at cancer diagnosis whereas in practice, this may not be the case. To illustrate the risk of ITB obtained using standard statistical approaches, we generated simplified data based on our illustrative example, for the estimation of the effect of surgery within 6 months on 1-year overall survival in patients diagnosed with Stage IV colon cancer aged 50–74 (called younger patients hereaf (...truncated)