Oncology Trial Attrition After Disease Progression

Why Progression-Related Attrition Needs a Sensitivity Model

In an oncology trial, disease progression may be recorded at a visit and followed by withdrawal before the next quality-of-life assessment. The progression record is informative: patients who progress can have a different outcome trajectory from those who do not. But even after accounting for recorded progression and earlier outcomes, withdrawal may depend on the outcome that would have been recorded at the missed visit. A model that assumes otherwise can give an overly optimistic trajectory.

This tutorial uses a hypothetical trial and a quality-of-life score on a 0-to-100 scale, with higher scores indicating better quality of life. The example focuses on one treatment arm to make the missing-outcome model clear; it does not estimate a treatment contrast. The selection model is the Diggle–Kenward model. It represents the joint distribution of outcomes and dropout by specifying an outcome model and a conditional model for dropout.

Let \(Y_{it}\) denote patient \(i\)'s outcome at visit \(t\), and let \(D_{it}=1\) indicate dropout before visit \(t\), among patients still followed at the prior visit. Let \(P_i\) indicate progression recorded by the second visit. A simple outcome component models the distribution of each visit's outcome conditional on earlier outcomes and recorded covariates. A simple dropout component is

where \(\mathbf{H}_{it}\) contains recorded history such as earlier outcomes, progression status, and possibly treatment. The defining feature is that \(Y_{it}\), the outcome at the dropout occasion, appears in the dropout probability. A negative \(\gamma\), for a higher-is-better score, means that lower current scores are associated with higher dropout probability after adjustment for the included history. It does not by itself establish a causal effect of quality of life on withdrawal.

Likelihood and the Missing-Outcome Implication

For a patient who completes visit \(t\), the likelihood contribution includes the outcome density and the probability of remaining in follow-up. For a patient who drops out before that visit, \(Y_{it}\) is not observed. The contribution must therefore integrate over its possible values, weighting each value by both its outcome density and its dropout probability. This is the central selection-model calculation.

Here \(f(y\mid\mathbf{H}_{it})\) is the outcome model conditional on observed history. The model-implied mean among patients with that history who drop out is not generally the ordinary outcome-model mean. It is the density reweighted by dropout probability:

The denominator is the probability of dropout given the history. Dividing by it normalizes the weighted density to integrate to one. If \(\gamma=0\), and there are no other unobserved-outcome terms, dropout is conditionally independent of the current outcome and this conditional mean reduces to the outcome-model mean. If \(\gamma\ne 0\), the two means generally differ. This formula also explains why a dropout model cannot be fitted by simply substituting a made-up value for each missing score: the missing score is integrated out in the likelihood.

The model requires a correctly specified outcome distribution and dropout model for the interpretation to be credible. It also assumes independent patients conditional on modeled covariates, a correctly recorded dropout time and progression history, and a suitable account of the within-patient outcome dependence. In this example, dropout is monotone after the last observed visit. If visits can be missed and later resumed, that intermittent pattern needs an appropriate observation-process model rather than this simple monotone setup.

Fitting and Interpreting a Diggle–Kenward Model

A practical analysis first specifies the outcome model and dropout model, then maximizes their joint observed-data likelihood. For the hypothetical trial, suppose progression status and the week-6 score are included in the history. The dropout probability before week 12 is modeled using week-12 quality of life, even though it is unobserved for dropouts. A fitted model can use the observed completers and the integrated dropout contributions to estimate its parameters. Because the current outcome is missing precisely for dropouts, the dependence parameter \(\gamma\) is not identified from the observed data without modeling restrictions; its estimate is therefore conditional on the chosen parametric model and assumptions.

Assumptions, Diagnostics, and Alternatives

The Diggle–Kenward model is useful when a scientifically plausible explanation is that a patient's current, unobserved outcome helps determine whether the next assessment is missing. Its appeal is also its main limitation: the data do not reveal the missing outcomes, so the dependence between those outcomes and dropout must be supported by assumptions. A single fitted model should not be treated as a definitive correction for attrition.

Before interpreting a fit, check whether the model is numerically and substantively adequate. Review convergence messages, gradients, parameter standard errors, and sensitivity to starting values. Inspect whether the outcome model reproduces the observed means and variability across visits and progression histories. Check the observed dropout rates across recorded histories, and assess whether fitted dropout probabilities are extreme or nearly zero for important histories. Sparse progression strata, little variation in observed outcomes, or few completers can make the dependence parameter unstable. Also verify the pattern coding and visit denominators: the progression-specific week-6 denominator in the example is 18, while the week-12 completer denominator is 22.

A useful comparison is with a pattern-mixture estimate. The pattern-specific approach directly describes observed outcome distributions by missingness pattern, but the missing week-12 mean still requires an identifying restriction, as the worked example made explicit. The selection model instead specifies dropout conditional on current and recorded outcomes, and its missing-group estimate follows from that joint model. Neither framework removes the need for assumptions. The choice of pattern-mixture restriction or selection-model dependence structure should be reported and examined through sensitivity analyses; it should not be hidden behind a single point estimate.

Other failure modes include treating progression as if it were itself dropout, ignoring the time order between progression and withdrawal, and interpreting an association parameter as a causal effect. In this case, progression is an observed history variable; the dropout event occurs later. If progression status is misclassified, omitted from the relevant models, or used to define groups with very few observations, the fitted trajectory may be misleading. If death prevents a quality-of-life measurement, that outcome has a different interpretation from an ordinary missing score and cannot automatically be handled as routine dropout.