Reporting Censoring Assumptions and Corrections

Why Censoring Must Be Reported Precisely

A censoring adjustment can only be assessed if readers can tell what was censored, why it was censored, and which assumptions connected the observed records to the target quantity. Saying only that “censoring was handled with weights” leaves out the key information: the censoring definition, the follow-up window, the variables in the censoring model, and whether the resulting weights were credible. Reporting these elements is part of the statistical argument for an estimate, not an administrative detail.

In time-to-event data, let \(T^*\) denote the event time that would be observed with complete follow-up, and let \(C\) denote the censoring time. The observed time is \(T=\min(T^*,C)\), and \(\Delta=I(T^*\leq C)\) indicates whether the event was observed before censoring. In competing-risks data, an observed event of a different cause is an outcome, not censoring. Likewise, a transition to another observed state is not loss to follow-up merely because it prevents a later transition of interest. The censoring definition must match the estimand and the event process under study.

The independence assumption is not automatically unconditional. A common formulation is \(T^* \perp C\mid Z\), where \(Z\) includes sufficient measured baseline covariates; with time-varying information, the condition must be formulated using the observed history available before each time. The assumption is not verified simply because censoring rates look similar across groups. It is a substantive claim that, after conditioning on the stated information, censoring does not selectively remove subjects with different future event prospects.

Define the Censoring Process and Follow-Up

A report should specify the event or state being followed, the time origin, the event-time rule, and the censoring rule. State the administrative study end date or maximum follow-up, how loss to follow-up was identified, and how withdrawal, transfer, database closure, or other censoring reasons were classified. If censoring reasons are combined, say so; if they are modeled separately, explain the categories. Report whether death or another competing event was treated as an outcome or as censoring, and justify that choice for the estimand.

Follow-up completeness should be described with a denominator and a time reference. Useful summaries include numbers at risk at selected times, counts with the target event, competing events, losses to follow-up, and those still event-free at the administrative end. A single percentage “followed” can conceal important timing: losing 10% early may affect estimation more than losing 10% near the end. Where appropriate, report the distribution of observed follow-up, with a clear method and a statement that it summarizes observation time rather than event-free survival.

State the Assumptions Before Reporting Corrections

For inverse probability of censoring weighting (IPCW), define \(G(t\mid H)=P(C\geq t\mid H)\), the conditional probability of remaining uncensored through time \(t\), given the specified covariate or observed history \(H\). A typical unstabilized weight for a record observed through \(t\) is \(1/G(t\mid H)\). The correction relies on a correctly specified censoring model, conditional independent censoring given \(H\), and positivity: \(G(t\mid H)>0\) for histories represented in the target population over the time range of interest. State the target population and time horizon for which those conditions are being invoked.

A short justification explains why the weight is used. Let \(Y(t)\) be a complete-follow-up contribution to the target quantity at time \(t\), and suppose censoring is conditionally independent of that contribution given \(H\). If \(G(t\mid H)>0\), then

The second equality follows because conditional independence gives \(P(C\geq t\mid Y(t),H)=P(C\geq t\mid H)=G(t\mid H)\). Thus, among subjects still observed at \(t\), inverse probabilities can recover the complete-follow-up contribution in expectation. If independence fails after conditioning on the recorded history, or if the model gives a probability near zero, this argument does not justify the correction. It also does not guarantee that a finite-sample estimate is stable.

Report the censoring model in enough detail to assess its plausibility: the time scale; the model family and functional forms; baseline and time-varying covariates; how histories were updated; how censoring times and tied event times were handled; and any interactions or stratification. Distinguish predictors used in the censoring model from variables used in the outcome model. For stabilized weights, give the numerator and denominator definitions; for truncated weights, state the truncation rule and the proportion affected. Report how uncertainty was calculated, including whether estimation of the censoring model and any clustering were accounted for.

Diagnose the Weights and Their Consequences

Weight reporting should include more than a minimum and maximum. Summarize the distribution using measures such as selected quantiles, the maximum, and the proportion above a prespecified threshold. Check positivity by examining estimated censoring probabilities across relevant covariate histories and over time. Assess balance or other implications of weighting as appropriate, and identify whether a small number of observations dominate the weighted estimate. Report effective sample size as a diagnostic, not as a replacement for the original sample size:

A low effective sample size relative to the number of weighted observations signals concentration of influence. It does not by itself prove bias, nor does a large value establish that the censoring model or independence assumption is correct.

Diagnostics that suggest trouble include estimated uncensoring probabilities approaching zero, very large or highly skewed weights, markedly reduced effective sample size, poor weighted balance, and estimates that change sharply when a few observations are removed or weights are truncated. These findings should be reported even when a correction is retained. Truncation can reduce variance or influence, but it changes the estimator and does not repair a lack of support or make informative censoring ignorable.

Sensitivity Analyses and Alternative Approaches

Conditional independent censoring is generally not testable from observed data alone. Sensitivity analysis should therefore make the departure being considered explicit. Report the parameter or scenario varied, its scale and rationale, the estimator under each scenario, and how conclusions change. Depending on the analysis, scenarios may represent higher or lower event risk among censored participants, a different dependence between censoring and latent event times, or bounds under specified restrictions. The sensitivity range is not a confidence interval: it describes variation across assumptions, whereas a confidence interval quantifies sampling uncertainty under a given analysis and assumptions.

The main alternatives answer different practical needs. An unweighted complete-case analysis discards incomplete follow-up and may target a selected population or be biased if completeness is associated with outcome. A standard survival or cumulative-incidence estimator can accommodate right censoring under its own independent-censoring conditions; it does not remove the need to state those conditions. IPCW can address measured predictors of censoring when the model, conditional independence, and positivity assumptions are credible, but it can be unstable. Outcome-model approaches may adjust for measured prognostic variables, while augmented approaches combine outcome and censoring models; neither eliminates the need to assess assumptions and support. State which approach was used and why it matches the estimand rather than presenting the methods as interchangeable.

Limitations should be specific. A well-fitting censoring model cannot rule out dependence on unmeasured prognostic factors. Large weights may make estimates imprecise and sensitive to model choices. Truncation introduces a bias-variance trade-off, and sensitivity analyses depend on the plausibility and range of their scenarios. A transparent report separates these limitations from statistical uncertainty and avoids interpreting a stable point estimate as proof that censoring was noninformative.

A Practical Reporting Sequence

Common Reporting Mistakes

• Calling every non-target event censoring. In competing-risks analysis, a competing event is observed and must be classified as an outcome for the relevant estimand.
• Reporting “independent censoring” without qualification. State what history or covariates are conditioned upon and why they are sufficient for the analysis; do not present an untestable assumption as a diagnostic finding.
• Giving only a weight maximum. Include distributional summaries, positivity checks, and measures of concentration such as effective sample size.
• Describing truncation as a cure. Truncation limits extreme values but does not restore missing support or guarantee unbiasedness.
• Calling scenario variation a confidence interval. Sensitivity analyses vary assumptions; confidence intervals quantify sampling uncertainty conditional on a specified analysis.