Detecting small-study effects and funnel plot asymmetry in meta-analysis of survival data: A comparison of new and existing tests.

Small-study effects are a common threat in systematic reviews and may indicate publication bias. Their existence is often verified by visual inspection of the funnel plot. Formal tests to assess the presence of funnel plot asymmetry typically estimate the association between the reported effect size and their standard error, the total sample size, or the inverse of the total sample size. In this paper, we demonstrate that the application of these tests may be less appropriate in meta-analysis of survival data, where censoring influences statistical significance of the hazard ratio. We subsequently propose 2 new tests that are based on the total number of observed events and adopt a multiplicative variance component. We compare the performance of the various funnel plot asymmetry tests in an extensive simulation study where we varied the true hazard ratio (0.5 to 1), the number of published trials (N=10 to 100), the degree of censoring within trials (0% to 90%), and the mechanism leading to participant dropout (noninformative versus informative). Results demonstrate that previous well-known tests for detecting funnel plot asymmetry suffer from low power or excessive type-I error rates in meta-analysis of survival data, particularly when trials are affected by participant dropout. Because our novel test (adopting estimates of the asymptotic precision as study weights) yields reasonable power and maintains appropriate type-I error rates, we recommend its use to evaluate funnel plot asymmetry in meta-analysis of survival data. The use of funnel plot asymmetry tests should, however, be avoided when there are few trials available for any meta-analysis

Internal-external cross-validation helped to evaluate the generalizability of prediction models in large clustered datasets

OBJECTIVE: To illustrate how to evaluate the need of complex strategies for developing generalizable prediction models in large clustered datasets. STUDY DESIGN AND SETTING: We developed eight Cox regression models to estimate the risk of heart failure using a large population-level dataset. These models differed in the number of predictors, the functional form of the predictor effects (non-linear effects and interaction) and the estimation method (maximum likelihood and penalization). Internal-external cross-validation was used to evaluate the models' generalizability across the included general practices. RESULTS: Among 871,687 individuals from 225 general practices, 43,987 (5.5%) developed heart failure during a median follow-up time of 5.8 years. For discrimination, the simplest prediction model yielded a good concordance statistic, which was not much improved by adopting complex strategies. Between-practice heterogeneity in discrimination was similar in all models. For calibration, the simplest model performed satisfactorily. Although accounting for non-linear effects and interaction slightly improved the calibration slope, it also led to more heterogeneity in the observed/expected ratio. Similar results were found in a second case study involving patients with stroke. CONCLUSION: In large clustered datasets, prediction model studies may adopt internal-external cross-validation to evaluate the generalizability of competing models, and to identify promising modelling strategies

Missing data is poorly handled and reported in prediction model studies using machine learning: a literature review

OBJECTIVES: Missing data is a common problem during the development, evaluation, and implementation of prediction models. Although machine learning (ML) methods are often said to be capable of circumventing missing data, it is unclear how these methods are used in medical research. We aim to find out if and how well prediction model studies using machine learning report on their handling of missing data. STUDY DESIGN AND SETTING: We systematically searched the literature on published papers between 2018 and 2019 about primary studies developing and/or validating clinical prediction models using any supervised ML methodology across medical fields. From the retrieved studies information about the amount and nature (e.g. missing completely at random, potential reasons for missingness) of missing data and the way they were handled were extracted. RESULTS: We identified 152 machine learning-based clinical prediction model studies. A substantial amount of these 152 papers did not report anything on missing data (n = 56/152). A majority (n = 96/152) reported details on the handling of missing data (e.g., methods used), though many of these (n = 46/96) did not report the amount of the missingness in the data. In these 96 papers the authors only sometimes reported possible reasons for missingness (n = 7/96) and information about missing data mechanisms (n = 8/96). The most common approach for handling missing data was deletion (n = 65/96), mostly via complete-case analysis (CCA) (n = 43/96). Very few studies used multiple imputation (n = 8/96) or built-in mechanisms such as surrogate splits (n = 7/96) that directly address missing data during the development, validation, or implementation of the prediction model. CONCLUSION: Though missing values are highly common in any type of medical research and certainly in the research based on routine healthcare data, a majority of the prediction model studies using machine learning does not report sufficient information on the presence and handling of missing data. Strategies in which patient data are simply omitted are unfortunately the most often used methods, even though it is generally advised against and well known that it likely causes bias and loss of analytical power in prediction model development and in the predictive accuracy estimates. Prediction model researchers should be much more aware of alternative methodologies to address missing data

Developing more generalizable prediction models from pooled studies and large clustered data sets.

Prediction models often yield inaccurate predictions for new individuals. Large data sets from pooled studies or electronic healthcare records may alleviate this with an increased sample size and variability in sample characteristics. However, existing strategies for prediction model development generally do not account for heterogeneity in predictor-outcome associations between different settings and populations. This limits the generalizability of developed models (even from large, combined, clustered data sets) and necessitates local revisions. We aim to develop methodology for producing prediction models that require less tailoring to different settings and populations. We adopt internal-external cross-validation to assess and reduce heterogeneity in models' predictive performance during the development. We propose a predictor selection algorithm that optimizes the (weighted) average performance while minimizing its variability across the hold-out clusters (or studies). Predictors are added iteratively until the estimated generalizability is optimized. We illustrate this by developing a model for predicting the risk of atrial fibrillation and updating an existing one for diagnosing deep vein thrombosis, using individual participant data from 20 cohorts (N = 10 873) and 11 diagnostic studies (N = 10 014), respectively. Meta-analysis of calibration and discrimination performance in each hold-out cluster shows that trade-offs between average and heterogeneity of performance occurred. Our methodology enables the assessment of heterogeneity of prediction model performance during model development in multiple or clustered data sets, thereby informing researchers on predictor selection to improve the generalizability to different settings and populations, and reduce the need for model tailoring. Our methodology has been implemented in the R package metamisc

Transparent reporting of multivariable prediction models developed or validated using clustered data (TRIPOD-Cluster): explanation and elaboration.

The TRIPOD-Cluster (transparent reporting of multivariable prediction models developed or validated using clustered data) statement comprises a 19 item checklist, which aims to improve the reporting of studies developing or validating a prediction model in clustered data, such as individual participant data meta-analyses (clustering by study) and electronic health records (clustering by practice or hospital). This explanation and elaboration document describes the rationale; clarifies the meaning of each item; and discusses why transparent reporting is important, with a view to assessing risk of bias and clinical usefulness of the prediction model. Each checklist item of the TRIPOD-Cluster statement is explained in detail and accompanied by published examples of good reporting. The document also serves as a reference of factors to consider when designing, conducting, and analysing prediction model development or validation studies in clustered data. To aid the editorial process and help peer reviewers and, ultimately, readers and systematic reviewers of prediction model studies, authors are recommended to include a completed checklist in their submission

Internal-external cross-validation helped to evaluate the generalizability of prediction models in large clustered datasets.

OBJECTIVE: To illustrate how to evaluate the need of complex strategies for developing generalizable prediction models in large clustered datasets. STUDY DESIGN AND SETTING: We developed eight Cox regression models to estimate the risk of heart failure using a large population-level dataset. These models differed in the number of predictors, the functional form of the predictor effects (non-linear effects and interaction) and the estimation method (maximum likelihood and penalization). Internal-external cross-validation was used to evaluate the models' generalizability across the included general practices. RESULTS: Among 871,687 individuals from 225 general practices, 43,987 (5.5%) developed heart failure during a median follow-up time of 5.8 years. For discrimination, the simplest prediction model yielded a good concordance statistic, which was not much improved by adopting complex strategies. Between-practice heterogeneity in discrimination was similar in all models. For calibration, the simplest model performed satisfactorily. Although accounting for non-linear effects and interaction slightly improved the calibration slope, it also led to more heterogeneity in the observed/expected ratio. Similar results were found in a second case study involving patients with stroke. CONCLUSION: In large clustered datasets, prediction model studies may adopt internal-external cross-validation to evaluate the generalizability of competing models, and to identify promising modelling strategies

A tutorial on individualized treatment effect prediction from randomized trials with a binary endpoint.

Randomized trials typically estimate average relative treatment effects, but decisions on the benefit of a treatment are possibly better informed by more individualized predictions of the absolute treatment effect. In case of a binary outcome, these predictions of absolute individualized treatment effect require knowledge of the individual's risk without treatment and incorporation of a possibly differential treatment effect (ie, varying with patient characteristics). In this article, we lay out the causal structure of individualized treatment effect in terms of potential outcomes and describe the required assumptions that underlie a causal interpretation of its prediction. Subsequently, we describe regression models and model estimation techniques that can be used to move from average to more individualized treatment effect predictions. We focus mainly on logistic regression-based methods that are both well-known and naturally provide the required probabilistic estimates. We incorporate key components from both causal inference and prediction research to arrive at individualized treatment effect predictions. While the separate components are well known, their successful amalgamation is very much an ongoing field of research. We cut the problem down to its essentials in the setting of a randomized trial, discuss the importance of a clear definition of the estimand of interest, provide insight into the required assumptions, and give guidance with respect to modeling and estimation options. Simulated data illustrate the potential of different modeling options across scenarios that vary both average treatment effect and treatment effect heterogeneity. Two applied examples illustrate individualized treatment effect prediction in randomized trial data