Joint probability framework for the development and validation of a prognostic model for the conditional outcome of quality of life: a retrospective study in historical European cohorts of survivors of head and neck cancer

Background

Conditional outcomes are outcomes defined only under specific circumstances. For example, future quality of life (QoL) can only be ascertained when patients are alive. In prognostic models involving conditional outcomes, a choice must be made on the precise target of prediction: one could target future QoL, given that the individual is still alive (conditional) or target future QoL jointly with the event of being alive (unconditional). We aimed to (1) introduce a probabilistic framework for prognostic models for conditional outcomes, and (2) apply this framework to develop a prognostic model for QoL 3 years after diagnosis in patients with head and neck cancer.

Methods

A joint probability framework was proposed for prognostic model development for a conditional outcome dependent on a post-baseline variable. The framework involved two submodels: one for QoL and one for survival. Joint probability was estimated with conformal estimators using MAPIE with least absolute shrinkage and selection operator (LASSO) regression and XGBoost models. We included patients with head and neck cancer who were alive with no evidence of disease 12 months after diagnosis from the UK-based Head and Neck 5000 cohort (N=3572) and made QoL predictions 3 years after diagnosis. Predictors included clinical and demographic characteristics and longitudinal measurements of QoL. External validation was performed in longitudinal studies led by the University of Mainz (Mainz, Germany) and the Istituto Nazionale dei Tumori (Milan, Italy). A total of 497 patients were used in external validation of the QoL submodel and 281 were used in external validation of the survival submodel. Model performance was evaluated with C-statistics for discrimination, calibration plots, and R2 or mean absolute error (MAE), or both, for overall performance as appropriate.

Findings

Of 3572 patients, 400 (11·2%) were dead by the time of prediction (3 years after diagnosis), whereas 73 (26·0%) of 281 patients were dead in the validation set for the survival submodel. Model performance was assessed for prediction of QoL, both conditionally and jointly with survival. C-statistics ranged from 0·66 to 0·74 in internal validation and 0·60 to 0·80 in external validation. In internal validation, R2 and MAEs ranged from 0·37 to 0·5 and 12·2 to 13·5, respectively, whereas R2 and MAEs ranged from 0.35 to 0.41 and 13.0 to 12.3, respectively, in external validation. The calibration plots showed reasonable calibration in external validation. External performance was weaker for the survival submodel than for the QoL submodel. An application programming interface and dashboard were developed.

Interpretation

Our probabilistic framework for conditional outcomes provides both joint and conditional predictions and thus the flexibility needed to answer different clinical questions. Our model had reasonable performance in external validation and has potential as a tool in long-term follow-up of QoL in patients with head and neck cancer.

Funding

EU’s Horizon 2020 research and innovation programme.