# Informative censoring does not cancel in an unanchored comparison, and adjusting one side can make it worse Ahmad Sofi-Mahmudi 2026-09-23 # Abstract **Background.** When censoring depends on patients’ risk, Kaplan-Meier estimates in each trial are biased. It is often argued that the biases cancel in an indirect comparison. Catalog problem OUT-07 asks when they do. **Methods.** A shared frailty drove both event and censoring hazards, with separate dependence in the source (none or moderate) and the comparator (none, moderate or strong), censoring of 20% or 50%, in unanchored and anchored comparisons: 24 scenarios, 1000 replicates each. Estimand: RMST difference at 24 months (0.62 months unanchored). Methods: Kaplan-Meier, inverse probability of censoring weighting on the source side with a baseline proxy of risk, and a one-sided comparator sensitivity analysis. **Results.** Unanchored, with differing mechanisms the bias ranged from -2.33 to 1.42 months, and the sign of the comparison was wrong in up to 0.973 of analyses. Equal mechanisms nearly cancelled (-0.080 to -0.030). Anchored comparisons were protected in every scenario (-0.202 to 0.219), because both arms of each trial shared its mechanism. Source-side weighting reduced source bias only partly and, where the mechanisms were equal, broke the cancellation (bias -0.080 to -0.515 at 50% censoring). The comparator sensitivity parameter that reproduced the truth lay outside the conventional range 0.5 to 2 in up to 0.703 of analyses. **Conclusion.** Cancellation needs equal mechanisms, which an external or single-arm comparator seldom has. Anchoring protects; adjusting the source alone does not, and a one-sided sensitivity analysis must allow larger departures than usual. # The problem Each Kaplan-Meier RMST ([1](#ref-royston2013)) carries a censoring bias $c$; an unanchored contrast carries $c_S - c_T$ and an anchored one the difference of within-trial differences, in which each trial’s shared mechanism largely cancels. Inverse probability of censoring weighting ([2](#ref-robins2000)) needs the censoring predictors, which exist for the individual-data source and not for an aggregate comparator. # Design Registered protocol: `protocol.md`; ADEMP structure ([3](#ref-morris2019)). Frailty $U \sim N(0, 1)$; event hazard $\lambda e^{0.7U}$ ($\lambda_A = 0.045$, $\lambda_B = 0.05$, $\lambda_C = 0.07$ per month); censoring hazard $\kappa e^{\alpha U}$, $\kappa$ set for the censoring prevalence by 24 months; administrative end at 36; 300 per arm. The source records $W = 0.7U + \text{noise}$. The sensitivity analysis gives censored comparator patients a remaining hazard of $\delta$ times the arm’s crude rate ($\delta = 1$ is independent censoring). # Results
![](figures/fig1-bias.png) Figure 1: Bias of the RMST difference by comparator censoring dependence, for each level of source dependence.
Unanchored bias followed $c_S - c_T$ (Figure 1): positive when only the source censored its high-risk patients, negative when only the comparator did, and roughly twice as large at 50% censoring. With a true difference of 0.62 months, a comparator with strong dependence reversed the comparison in 0.973 of analyses at 50% censoring. Weighting on a proxy correlated 0.7 with the latent risk removed about a third of the source bias. Applied only to the source, it turned a cancelled comparison into a biased one. In the sensitivity analysis the $\delta$ that reproduced the truth had a median of 2.43 with strong comparator dependence, so a range capped at 2 would often not reach it. # What this does not answer No covariate shift between trials, so the population-adjustment layer is absent; time-constant censoring hazards; one sensitivity parameterization; a single baseline proxy stands in for the source’s time-varying censoring predictors. Peer review has not been done. # References
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