Reflection on modern methods: trial emulation in the presence of immortal-time bias. Assessing the benefit of major surgery for elderly lung cancer patients using observational data

Abstract

Acquiring real-world evidence is crucial to support health policy, but observational studies are prone to serious biases. An approach was recently proposed to overcome confounding and immortal-time biases within the emulated trial framework. This tutorial provides a step-by-step description of the design and analysis of emulated trials, as well as R and Stata code, to facilitate its use in practice. The steps consist in: (i) specifying the target trial and inclusion criteria; (ii) cloning patients; (iii) defining censoring and survival times; (iv) estimating the weights to account for informative censoring introduced by design; and (v) analysing these data. These steps are illustrated with observational data to assess the benefit of surgery among 70-89-year-old patients diagnosed with early-stage lung cancer. Because of the severe unbalance of the patient characteristics between treatment arms (surgery yes/no), a naïve Kaplan-Meier survival analysis of the initial cohort severely overestimated the benefit of surgery on 1-year survival (22% difference), as did a survival analysis of the cloned dataset when informative censoring was ignored (17% difference). By contrast, the estimated weights adequately removed the covariate imbalance. The weighted analysis still showed evidence of a benefit, though smaller (11% difference), of surgery among older lung cancer patients on 1-year survival. Complementing the CERBOT tool, this tutorial explains how to proceed to conduct emulated trials using observational data in the presence of immortal-time bias. The strength of this approach is its transparency and its principles that are easily understandable by non-specialists.

Keywords: Observational data; elderly; immortal-time bias; inverse-probability-of-censoring weighting; lung cancer; trial emulation.

Figure 1

Graphic description of immortal-time bias and possible corrections. Patients A, B, C, D, E with survival patterns and treatment status as defined in Figure 2.

Figure 2

Definition of the outcome and survival time for each patient in each arm, for both the weight and the analysis models. Patients A–E have records of surgery within the grace period and contribute to the weight models until their time of surgery, with censoring indicators equal to 1 in the control arm as they deviate from the protocol, and equal to 0 in the treated arm as they cannot deviate from the protocol after their record of surgery. For the analysis model in the control arm, these patients are censored at their time of surgery. Patients F–J comply with the control arm’s definition, and as such contribute the full grace period length (180 days, 6 months) to the weight models, with censoring indicators equal to 0 in the control arm as they do not deviate from the protocol, and equal to 1 in the treated arm as they deviate from the protocol. For the analysis model in the treated arm, these patients are censored at 6 months (180 days). Patients K and L contribute to both arms (analysis and weight models) equally as they do not deviate from any of the protocols since their survival times are censored or correspond to the event of interest before we could have assessed their receipt of surgery. Patient M complies with the control arm’s definition and as such contributed the full grace period length (6 months) to the weight models, with event indicators equal to 0 in the control arm as they do not deviate from the protocol, and equal to 1 in the treated arm as they deviate from the protocol. For the analysis model in the treated arm, this patient is censored at 6 months. *Event of interest: death (δ = 1); **event of interest: deviation from protocol (δ_w= 1); ***time in days used as follow-up time in the analysis or weight model; T_X: time to death or time to censoring for patient X; T_XS: time to surgery for patient X.

Figure 3

Contrasting one-year survival curves from different estimation methods.