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Clinical prognostic models help inform decision-making by estimating a patient's risk of experiencing an outcome in the future. The net benefit is increasingly being used to assess the clinical utility of models. By calculating an appropriately weighted average of the true and false positives of a model, the net benefit assesses the value added by a binary decision policy obtained when thresholding a model. Although such 'treat or not' decisions are common, prognostic models are also often used to tailor and personalise the care of patients, which implicitly involves the consideration of multiple interventions at different risk thresholds. We extend the net benefit to consider multiple decision thresholds simultaneously, by taking a weighted area under a rescaled version of the net benefit curve, deriving the continuous net benefit. In addition to the consideration of a continuum of interventions, we also show how the continuous net benefit can be used for populations with a range of optimal thresholds for a single treatment, due to individual variations in expected treatment benefit or harm, highlighting limitations of current proposed methods that calculate the area under the decision curve. We showcase the continuous net benefit through two examples of cardiovascular preventive care, comparing two modelling choices using the continuous net benefit. The continuous net benefit informs researchers of the clinical utility of models during selection, development, and validation, and helps decision makers understand their usefulness, improving their viability towards implementation., Comment: Main text is 17 pages, 3 figures. Supplementary is 9 pages. Submitted to Epidemiology

There are concerns about the fairness of clinical prediction models. 'Fair' models are defined as those for which their performance or predictions are not inappropriately influenced by protected attributes such as ethnicity, gender, or socio-economic status. Researchers have raised concerns that current algorithmic fairness paradigms enforce strict egalitarianism in healthcare, levelling down the performance of models in higher-performing subgroups instead of improving it in lower-performing ones. We propose assessing the fairness of a prediction model by expanding the concept of net benefit, using it to quantify and compare the clinical impact of a model in different subgroups. We use this to explore how a model distributes benefit across a population, its impact on health inequalities, and its role in the achievement of health equity. We show how resource constraints might introduce necessary trade-offs between health equity and other objectives of healthcare systems. We showcase our proposed approach with the development of two clinical prediction models: 1) a prognostic type 2 diabetes model used by clinicians to enrol patients into a preventive care lifestyle intervention programme, and 2) a lung cancer screening algorithm used to allocate diagnostic scans across the population. This approach helps modellers better understand if a model upholds health equity by considering its performance in a clinical and social context., Comment: Main text is 19 pages, with 5 figures. Supplementary is 20 pages. Submitted to Epidemiology

Generalisability and transportability of clinical prediction models (CPMs) refer to their ability to maintain predictive performance when applied to new populations. While CPMs may show good generalisability or transportability to a specific new population, it is rare for a CPM to be developed using methods that prioritise good generalisability or transportability. There is an emerging literature of such techniques; therefore, this scoping review aims to summarise the main methodological approaches, assumptions, advantages, disadvantages and future development of methodology aiding the generalisability/transportability. Relevant articles were systematically searched from MEDLINE, Embase, medRxiv, arxiv databases until September 2023 using a predefined set of search terms. Extracted information included methodology description, assumptions, applied examples, advantages and disadvantages. The searches found 1,761 articles; 172 were retained for full text screening; 18 were finally included. We categorised the methodologies according to whether they were data-driven or knowledge-driven, and whether are specifically tailored for target population. Data-driven approaches range from data augmentation to ensemble methods and density ratio weighting, while knowledge-driven strategies rely on causal methodology. Future research could focus on comparison of such methodologies on simulated and real datasets to identify their strengths specific applicability, as well as synthesising these approaches for enhancing their practical usefulness.

Prediction models are increasingly proposed for guiding treatment decisions, but most fail to address the special role of treatments, leading to inappropriate use. This paper highlights the limitations of using standard prediction models for treatment decision support. We identify `causal blind spots' in three common approaches to handling treatments in prediction modelling: including treatment as a predictor, restricting data based on treatment status and ignoring treatments. When predictions are used to inform treatment decisions, confounders, colliders and mediators, as well as changes in treatment protocols over time may lead to misinformed decision-making. We illustrate potential harmful consequences in several medical applications. We advocate for an extension of guidelines for development, reporting and evaluation of prediction models to ensure that the intended use of the model is matched to an appropriate risk estimand. When prediction models are intended to inform treatment decisions, prediction models should specify upfront the treatment decisions they aim to support and target a prediction estimand in line with that goal. This requires a shift towards developing predictions under the specific treatment options under consideration (`predictions under interventions'). Predictions under interventions need causal reasoning and inference techniques during development and validation. We argue that this will improve the efficacy of prediction models in guiding treatment decisions and prevent potential negative effects on patient outcomes.

Introduction. There is currently no guidance on how to assess the calibration of multistate models used for risk prediction. We introduce several techniques that can be used to produce calibration plots for the transition probabilities of a multistate model, before assessing their performance in the presence of non-informative and informative censoring through a simulation. Methods. We studied pseudo-values based on the Aalen-Johansen estimator, binary logistic regression with inverse probability of censoring weights (BLR-IPCW), and multinomial logistic regression with inverse probability of censoring weights (MLR-IPCW). The MLR-IPCW approach results in a calibration scatter plot, providing extra insight about the calibration. We simulated data with varying levels of censoring and evaluated the ability of each method to estimate the calibration curve for a set of predicted transition probabilities. We also developed evaluated the calibration of a model predicting the incidence of cardiovascular disease, type 2 diabetes and chronic kidney disease among a cohort of patients derived from linked primary and secondary healthcare records. Results. The pseudo-value, BLR-IPCW and MLR-IPCW approaches give unbiased estimates of the calibration curves under non-informative censoring. These methods remained unbiased in the presence of informative censoring, unless the mechanism was strongly informative, with bias concentrated in the areas of predicted transition probabilities of low density. Conclusions. We recommend implementing either the pseudo-value or BLR-IPCW approaches to produce a calibration curve, combined with the MLR-IPCW approach to produce a calibration scatter plot, which provides additional information over either of the other methods., Comment: Pre-print for article currently under review

Background: Existing guidelines for handling missing data are generally not consistent with the goals of prediction modelling, where missing data can occur at any stage of the model pipeline. Multiple imputation (MI), often heralded as the gold standard approach, can be challenging to apply in the clinic. Clearly, the outcome cannot be used to impute data at prediction time. Regression imputation (RI) may offer a pragmatic alternative in the prediction context, that is simpler to apply in the clinic. Moreover, the use of missing indicators can handle informative missingness, but it is currently unknown how well they perform within CPMs. Methods: We performed a simulation study where data were generated under various missing data mechanisms to compare the predictive performance of CPMs developed using both imputation methods. We consider deployment scenarios where missing data is permitted/prohibited, and develop models that use/omit the outcome during imputation and include/omit missing indicators. Results: When complete data must be available at deployment, our findings were in line with widely used recommendations; that the outcome should be used to impute development data under MI, yet omitted under RI. When imputation is applied at deployment, omitting the outcome from the imputation at development was preferred. Missing indicators improved model performance in some specific cases, but can be harmful when missingness is dependent on the outcome. Conclusion: We provide evidence that commonly taught principles of handling missing data via MI may not apply to CPMs, particularly when data can be missing at deployment. In such settings, RI and missing indicator methods can (marginally) outperform MI. As shown, the performance of the missing data handling method must be evaluated on a study-by-study basis, and should be based on whether missing data are allowed at deployment., Comment: 42 pages. Submitted to Statistical Methods in Medical Research in October 2021

Observational data in medicine arise as a result of the complex interaction between patients and the healthcare system. The sampling process is often highly irregular and itself constitutes an informative process. When using such data to develop prediction models, this phenomenon is often ignored, leading to sub-optimal performance and generalisability of models when practices evolve. We propose a multi-task recurrent neural network which models three clinical presence dimensions -- namely the longitudinal, the inter-observation and the missingness processes -- in parallel to the survival outcome. On a prediction task using MIMIC III laboratory tests, explicit modelling of these three processes showed improved performance in comparison to state-of-the-art predictive models (C-index at 1 day horizon: 0.878). More importantly, the proposed approach was more robust to change in the clinical presence setting, demonstrated by performance comparison between patients admitted on weekdays and weekends. This analysis demonstrates the importance of studying and leveraging clinical presence to improve performance and create more transportable clinical models.

Background and Aims: The methods with which prediction models are usually developed mean that neither the parameters nor the predictions should be interpreted causally. However, when prediction models are used to support decision making, there is often a need for predicting outcomes under hypothetical interventions. We aimed to identify published methods for developing and validating prediction models that enable risk estimation of outcomes under hypothetical interventions, utilizing causal inference: their main methodological approaches, underlying assumptions, targeted estimands, and potential pitfalls and challenges with using the method, and unresolved methodological challenges. Methods: We systematically reviewed literature published by December 2019, considering papers in the health domain that used causal considerations to enable prediction models to be used for predictions under hypothetical interventions. Results: We identified 4919 papers through database searches and a further 115 papers through manual searches, of which 13 were selected for inclusion, from both the statistical and the machine learning literature. Most of the identified methods for causal inference from observational data were based on marginal structural models and g-estimation. Conclusions: There exist two broad methodological approaches for allowing prediction under hypothetical intervention into clinical prediction models: 1) enriching prediction models derived from observational studies with estimated causal effects from clinical trials and meta-analyses; and 2) estimating prediction models and causal effects directly from observational data. These methods require extending to dynamic treatment regimes, and consideration of multiple interventions to operationalise a clinical decision support system. Techniques for validating 'causal prediction models' are still in their infancy.

Clinical prediction models (CPMs) are used to predict clinically relevant outcomes or events. Typically, prognostic CPMs are derived to predict the risk of a single future outcome. However, with rising emphasis on the prediction of multi-morbidity, there is growing need for CPMs to simultaneously predict risks for each of multiple future outcomes. A common approach to multi-outcome risk prediction is to derive a CPM for each outcome separately, then multiply the predicted risks. This approach is only valid if the outcomes are conditionally independent given the covariates, and it fails to exploit the potential relationships between the outcomes. This paper outlines several approaches that could be used to develop prognostic CPMs for multiple outcomes. We consider four methods, ranging in complexity and assumed conditional independence assumptions: namely, probabilistic classifier chain, multinomial logistic regression, multivariate logistic regression, and a Bayesian probit model. These are compared with methods that rely on conditional independence: separate univariate CPMs and stacked regression. Employing a simulation study and real-world example via the MIMIC-III database, we illustrate that CPMs for joint risk prediction of multiple outcomes should only be derived using methods that model the residual correlation between outcomes. In such a situation, our results suggest that probabilistic classification chains, multinomial logistic regression or the Bayesian probit model are all appropriate choices. We call into question the development of CPMs for each outcome in isolation when multiple correlated or structurally related outcomes are of interest and recommend more holistic risk prediction., Comment: 34 pages, 2 tables and 5 figures

Background: In view of the growth of published papers, there is an increasing need for studies that summarise scientific research. An increasingly common review is a 'Methodology scoping review', which provides a summary of existing analytical methods, techniques and software, proposed or applied in research articles, which address an analytical problem or further an analytical approach. However, guidelines for their design, implementation and reporting are limited. Methods: Drawing on the experiences of the authors, which were consolidated through a series of face-to-face workshops, we summarise the challenges inherent in conducting a methodology scoping review and offer suggestions of best practice to promote future guideline development. Results: We identified three challenges of conducting a methodology scoping review. First, identification of search terms; one cannot usually define the search terms a priori and the language used for a particular method can vary across the literature. Second, the scope of the review requires careful consideration since new methodology is often not described (in full) within abstracts. Third, many new methods are motivated by a specific clinical question, where the methodology may only be documented in supplementary materials. We formulated several recommendations that build upon existing review guidelines. These recommendations ranged from an iterative approach to defining search terms through to screening and data extraction processes. Conclusion: Although methodology scoping reviews are an important aspect of research, there is currently a lack of guidelines to standardise their design, implementation and reporting. We recommend a wider discussion on this topic., Comment: 22 pages, 2 tables

The objective is to assess the extent of variation of data quality and completeness of electronic health records and impact on the robustness of risk predictions of incident cardiovascular disease (CVD) using a risk prediction tool that is based on routinely collected data (QRISK3). The study design is a longitudinal cohort study with a setting of 392 general practices (including 3.6 million patients) linked to hospital admission data. Variation in data quality was assessed using Saez stability metrics quantifying outlyingness of each practice. Statistical frailty models evaluated whether accuracy of QRISK3 predictions on individual predictions and effects of overall risk factors (linear predictor) varied between practices. There was substantial heterogeneity between practices in CVD incidence unaccounted for by QRISK3. In the lowest quintile of statistical frailty, a QRISK3 predicted risk of 10% for female was in a range between 7.1% and 9.0% when incorporating practice variability into the statistical frailty models; for the highest quintile, this was 10.9%-16.4%. Data quality (using Saez metrics) and completeness were comparable across different levels of statistical frailty. For example, recording of missing information on ethnicity was 55.7%, 62.7%, 57.8%, 64.8% and 62.1% for practices from lowest to highest quintiles of statistical frailty respectively. The effects of risk factors did not vary between practices with little statistical variation of beta coefficients. In conclusion, the considerable unmeasured heterogeneity in CVD incidence between practices was not explained by variations in data quality or effects of risk factors. QRISK3 risk prediction should be supplemented with clinical judgement and evidence of additional risk factors., Comment: 2 tables 4 figures in the main manuscript, 1 table 3 figure in appendix. Online published in IJMI, license CC-BY-NC-ND

Objectives: Clinical prediction models (CPMs) can inform decision-making concerning treatment initiation. Here, one requires predicted risks assuming that no treatment is given. This is challenging since CPMs are often derived in datasets where patients receive treatment; moreover, treatment can commence post-baseline - treatment drop-ins. This study presents a novel approach of using marginal structural models (MSMs) to adjust for treatment drop-in. Study Design and Setting: We illustrate the use of MSMs in the CPM framework through simulation studies, representing randomised controlled trials and observational data. The simulations include a binary treatment and a covariate, each recorded at two timepoints and having a prognostic effect on a binary outcome. The bias in predicted risk was examined in a model ignoring treatment, a model fitted on treatment na\"ive patients (at baseline), a model including baseline treatment, and the MSM. Results: In all simulation scenarios, all models except the MSM under-estimated the risk of outcome given absence of treatment. Consequently, CPMs that do not acknowledge treatment drop-in can lead to under-allocation of treatment. Conclusion: When developing CPMs to predict treatment-na\"ive risk, authors should consider using MSMs to adjust for treatment drop-in. MSMs also allow estimation of individual treatment effects.

When using mixture models it may be the case that the modeller has a-priori beliefs or desires about what the components of the mixture should represent. For example, if a mixture of normal densities is to be fitted to some data, it may be desirable for components to focus on capturing differences in location rather than scale. We introduce a framework called proximity penalty priors (PPPs) that allows this preference to be made explicit in the prior information. The approach is scale-free and imposes minimal restrictions on the posterior; in particular no arbitrary thresholds need to be set. We show the theoretical validity of the approach, and demonstrate the effects of using PPPs on posterior distributions with simulated and real data., Comment: 14 pages, 6 figures

In genetics it is often of interest to discover single nucleotide polymorphisms (SNPs) that are directly related to a disease, rather than just being associated with it. Few methods exist, however, addressing this so-called `true sparsity recovery' issue. In a thorough simulation study, we show that for moderate or low correlation between predictors, lasso-based methods perform well at true sparsity recovery, despite not being specifically designed for this purpose. For large correlations, however, more specialised methods are needed. Stability selection and direct effect testing perform well in all situations, including when the correlation is large., Comment: 19 pages, 6 figures

We introduce new methods of analysing time to event data via extended versions of the proportional hazards and accelerated failure time (AFT) models. In many time to event studies, the time of first observation is arbitrary, in the sense that no risk modifying event occurs. This is particularly common in epidemiological studies. We show formally that, in these situations, it is not sensible to take the first observation as the time origin, either in AFT or proportional hazards type models. Instead, we advocate using age of the subject as the time scale. We account for the fact that baseline observations may be made at different ages in different patients via a two stage procedure. First, we marginally regress any potentially age-varying covariates against age, retaining the residuals. These residuals are then used as covariates in the fitting of either an AFT model or a proportional hazards model. We call the procedures residual accelerated failure time (RAFT) regression and residual proportional hazards (RPH) regression respectively. We compare standard AFT with RAFT, and demonstrate superior predictive ability of RAFT in real examples. In epidemiology, this has real implications in terms of risk communication to both patients and policy makers.

We develop a simulation tool to support policy-decisions about healthcare for chronic diseases in defined populations. Incident disease-cases are generated in-silico from an age-sex characterised general population using standard epidemiological approaches. A novel disease-treatment model then simulates continuous life courses for each patient using discrete event simulation. Ideally, the discrete event simulation model would be inferred from complete longitudinal healthcare data via a likelihood or Bayesian approach. Such data is seldom available for relevant populations, therefore an innovative approach to evidence synthesis is required. We propose a novel entropy-based approach to fit survival densities. This method provides a fully flexible way to incorporate the available information, which can be derived from arbitrary sources. Discrete event simulation then takes place on the fitted model using a competing hazards framework. The output is then used to help evaluate the potential impacts of policy options for a given population., Comment: 24 pages, 13 figures, 11 tables