Joint probability approach for prognostic prediction of conditional outcomes: application to quality of life in head and neck cancer survivors
Authors: Moreira-Soares Mauricio , Fossen Erlend I. F. , Bilbao-Jayo Aritz , Almeida Aitor , Lopez-Perez Laura , Alonso Itziar , Cabrera-Umpierrez Maria Fernanda , Fico Giuseppe , Singer Susanne , Taylor Katherine J. , Ness Andrew , Thomas Steve , Pring Miranda , Licitra Lisa , Cavalieri Stefano , Frigessi Arnoldo , LeBlanc Marissa 
Published: January 2025

Background

Conditional outcomes are outcomes defined only under specific circumstances. For example,futurequality of life can only be ascertained when subjects are alive. In prognostic models involving conditional outcomes, a choice must be made on the precise target of prediction: one could target future quality of life, given that the individual is still alive (conditional) or target future quality of life jointly with the event of being alive (unconditional).We aim to (1) introduce a probabilistic framework for prognostic models for conditional outcomes, and (2) apply this framework to develop a prognostic model for quality of life3 yearsafter diagnosis in head and neck cancer patients.

Methods

A joint probability framework was proposed for prognostic model development for a conditional outcome dependent on a post-baseline variable. Joint probability was estimated with conformal estimators. We included head and neck cancer patients alive with no evidence of disease12 monthsafter diagnosis from the UK-based Head & Neck 5000 cohort (N=3572) and made predictions3 yearsafter diagnosis. Predictors included clinical and demographic characteristics and longitudinal measurements of quality of life. External validation was performed in studies from Italy and Germany.

Findings:

Of 3572 subjects, 400 (11.2%) were deceased by the time of prediction. Model performance was assessed for prediction of quality of life, both conditionally and jointly with survival. C-statistics ranged from 0.66 to 0.80 in internal and external validation, and the calibration curves showed reasonable calibration in external validation. An API 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 quality of life in head and neck cancer patients.

Funding

The EU.

Research in context

Evidence before this study

We searched for “head and neck” AND “quality of life” AND (“prognostic prediction” OR “machine learning” OR “prediction model”) on PubMed for studies published up to September 2024 and found 45 results. The prognostic models developed in the identified publications either excluded subjects who died during follow up or imputed quality of life with 0 for subjects that died during follow up. None of these publications explicitly address the implications of conditioning on survival, which introduces a significant risk of bias and may lead to invalid interpretations. These issues are well known in biostatistics and epidemiology but are often overlooked among machine learning practitioners and data scientists working with health data. Furthermore, recent methodological studies, such as van der Goorbergh et al. 2022, have been raising awareness about the importance of predicting probabilities that are well calibrated and suitable for answering the predictive questions of interest.

Taylor et al. 2019 have shown in a systematic review that health-related quality of life in head and neck cancer survivors can be severely impaired even 10 years after treatment. The scoping review by Alonso et al. 2021 highlights the need for the development of prediction models for supporting quality of life in cancer survivors: from the 67 studies included, 49% conduct parametric tests, 48% used regression models to identify prognostic factors, and only 3% (two studies) applied survival analysis and a non-linear method.

Added value of this study

This study makes an importantmethodological contributionthat can generally be applied to prognostic modeling in patient populations that experience mortality but where survival is not the main target of prediction. to the best of our knowledge, this is the first time that this problem is tackled in the context of clinical prognostic models and successfully addressed with a sound statistical-based approach. In addition, our proposed solution is model agnostic and suitable for modern machine learning applications.

The study makes an importantclinical contributionfor long-term follow up of head and neck cancer patients by developing a joint prognostic model for quality of life and survival. To the best of our knowledge, our model is the first joint model of long-term quality of life and survival in this patient population, with internal and external validation in European longitudinal studies of head and neck cancer patients.

Implications of all the available evidence

The probabilistic framework proposed can impact future development of clinical prediction models, by raising awareness and proposing a solution for a ubiquitous problem in the field. The joint model can be tailored to address different clinical needs, for example to identify patients who are both likely to survive and have low quality of life in the future, or to predict individual patient future quality of life, both conditional or unconditional on survival. The model should be validated further in different countries.