arXiv subjects

Gianluca Baio

Publications and source records attributed to Gianluca Baio.

At least 37 records · Page 2Linked to original sources

arXiv2022

Parametric G-computation for Compatible Indirect Treatment Comparisons with Limited Individual Patient Data

Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is based on propensity score weighting, which is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the relevant population to recover a compatible marginal treatment effect. We propose a marginalization method based on parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. The approach views the covariate adjustment regression as a nuisance model and separates its estimation from the evaluation of the marginal treatment effect of interest. The method can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework. A simulation study provides proof-of-principle and benchmarks the method's performance against MAIC and the conventional outcome regression. Parametric G-computation achieves more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yields unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, the marginalized regression-adjusted estimates provide greater precision and accuracy than the conditional estimates produced by the conventional outcome regression, which are systematically biased because the measure of effect is non-collapsible.

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arXiv2022

BCEA: An R Package for Cost-Effectiveness Analysis

We describe in detail how to perform health economic cost-effectiveness analyses (CEA) using the R package $\textbf{BCEA}$ (Bayesian Cost-Effectiveness Analysis). CEA consist of analytic approaches for combining costs and health consequences of intervention(s). These help to understand how much an intervention may cost (per unit of health gained) compared to an alternative intervention, such as a control or status quo. For resource allocation, a decision maker may wish to know if an intervention is cost saving, and if not then how much more would it cost to implement it compared to a less effective intervention. Current guidance for cost-effectiveness analyses advocates the quantification of uncertainties which can be represented by random samples obtained from a probability sensitivity analysis or, more efficiently, a Bayesian model. $\textbf{BCEA}$ can be used to post-process the sampled costs and health impacts to perform advanced analyses producing standardised and highly customisable outputs. We present the features of the package, including its many functions and their practical application. $\textbf{BCEA}$ is valuable for statisticians and practitioners working in the field of health economic modelling wanting to simplify and standardise their workflow, for example in the preparation of dossiers in support of marketing authorisation, or academic and scientific publications.

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arXiv2021

Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review

Large observational data are increasingly available in disciplines such as health, economic and social sciences, where researchers are interested in causal questions rather than prediction. In this paper, we examine the problem of estimating heterogeneous treatment effects using non-parametric regression-based methods, starting from an empirical study aimed at investigating the effect of participation in school meal programs on health indicators. Firstly, we introduce the setup and the issues related to conducting causal inference with observational or non-fully randomized data, and how these issues can be tackled with the help of statistical learning tools. Then, we review and develop a unifying taxonomy of the existing state-of-the-art frameworks that allow for individual treatment effects estimation via non-parametric regression models. After presenting a brief overview on the problem of model selection, we illustrate the performance of some of the methods on three different simulated studies. We conclude by demonstrating the use of some of the methods on an empirical analysis of the school meal program data.

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arXiv2021

Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation

This paper develops a sparsity-inducing version of Bayesian Causal Forests, a recently proposed nonparametric causal regression model that employs Bayesian Additive Regression Trees and is specifically designed to estimate heterogeneous treatment effects using observational data. The sparsity-inducing component we introduce is motivated by empirical studies where not all the available covariates are relevant, leading to different degrees of sparsity underlying the surfaces of interest in the estimation of individual treatment effects. The extended version presented in this work, which we name Shrinkage Bayesian Causal Forest, is equipped with an additional pair of priors allowing the model to adjust the weight of each covariate through the corresponding number of splits in the tree ensemble. These priors improve the model's adaptability to sparse data generating processes and allow to perform fully Bayesian feature shrinkage in a framework for treatment effects estimation, and thus to uncover the moderating factors driving heterogeneity. In addition, the method allows prior knowledge about the relevant confounding covariates and the relative magnitude of their impact on the outcome to be incorporated in the model. We illustrate the performance of our method in simulated studies, in comparison to Bayesian Causal Forest and other state-of-the-art models, to demonstrate how it scales up with an increasing number of covariates and how it handles strongly confounded scenarios. Finally, we also provide an example of application using real-world data.

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arXiv2021

Effect modification in anchored indirect treatment comparisons: Comments on "Matching-adjusted indirect comparisons: Application to time-to-event data"

This commentary regards a recent simulation study conducted by Aouni, Gaudel-Dedieu and Sebastien, evaluating the performance of different versions of matching-adjusted indirect comparison (MAIC) in an anchored scenario with a common comparator. The simulation study uses survival outcomes and the Cox proportional hazards regression as the outcome model. It concludes that using the LASSO for variable selection is preferable to balancing a maximal set of covariates. However, there are no treatment effect modifiers in imbalance in the study. The LASSO is more efficient because it selects a subset of the maximal set of covariates but there are no cross-study imbalances in effect modifiers inducing bias. We highlight the following points: (1) in the anchored setting, MAIC is necessary where there are cross-trial imbalances in effect modifiers; (2) the standard indirect comparison provides greater precision and accuracy than MAIC if there are no effect modifiers in imbalance; (3) while the target estimand of the simulation study is a conditional treatment effect, MAIC targets a marginal or population-average treatment effect; (4) in MAIC, variable selection is a problem of low dimensionality and sparsity-inducing methods like the LASSO may be problematic. Finally, data-driven approaches do not obviate the necessity for subject matter knowledge when selecting effect modifiers. R code is provided in the Appendix to replicate the analyses and illustrate our points.

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arXiv2021

Methods for Population Adjustment with Limited Access to Individual Patient Data: A Review and Simulation Study

Population-adjusted indirect comparisons estimate treatment effects when access to individual patient data is limited and there are cross-trial differences in effect modifiers. Popular methods include matching-adjusted indirect comparison (MAIC) and simulated treatment comparison (STC). There is limited formal evaluation of these methods and whether they can be used to accurately compare treatments. Thus, we undertake a comprehensive simulation study to compare standard unadjusted indirect comparisons, MAIC and STC across 162 scenarios. This simulation study assumes that the trials are investigating survival outcomes and measure continuous covariates, with the log hazard ratio as the measure of effect. MAIC yields unbiased treatment effect estimates under no failures of assumptions. The typical usage of STC produces bias because it targets a conditional treatment effect where the target estimand should be a marginal treatment effect. The incompatibility of estimates in the indirect comparison leads to bias as the measure of effect is non-collapsible. Standard indirect comparisons are systematically biased, particularly under stronger covariate imbalance and interaction effects. Standard errors and coverage rates are often valid in MAIC but the robust sandwich variance estimator underestimates variability where effective sample sizes are small. Interval estimates for the standard indirect comparison are too narrow and STC suffers from bias-induced undercoverage. MAIC provides the most accurate estimates and, with lower degrees of covariate overlap, its bias reduction outweighs the loss in effective sample size and precision under no failures of assumptions. An important future objective is the development of an alternative formulation to STC that targets a marginal treatment effect.

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arXiv2020

Conflating marginal and conditional treatment effects: Comments on 'Assessing the performance of population adjustment methods for anchored indirect comparisons: A simulation study'

In this commentary, we highlight the importance of: (1) carefully considering and clarifying whether a marginal or conditional treatment effect is of interest in a population-adjusted indirect treatment comparison; and (2) developing distinct methodologies for estimating the different measures of effect. The appropriateness of each methodology depends on the preferred target of inference.

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arXiv2020

Joint longitudinal models for dealing with missing at random data in trial-based economic evaluations

Health economic evaluations based on patient-level data collected alongside clinical trials~(e.g. health related quality of life and resource use measures) are an important component of the process which informs resource allocation decisions. Almost inevitably, the analysis is complicated by the fact that some individuals drop out from the study, which causes their data to be unobserved at some time point. Current practice performs the evaluation by handling the missing data at the level of aggregated variables (e.g. QALYs), which are obtained by combining the economic data over the duration of the study, and are often conducted under a missing at random (MAR) assumption. However, this approach may lead to incorrect inferences since it ignores the longitudinal nature of the data and may end up discarding a considerable amount of observations from the analysis. We propose the use of joint longitudinal models to extend standard cost-effectiveness analysis methods by taking into account the longitudinal structure and incorporate all available data to improve the estimation of the targeted quantities under MAR. Our approach is compared to popular missingness approaches in trial-based analyses, motivated by an exploratory simulation study, and applied to data from two real case studies.

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arXiv2020

Dirichlet Process Mixture Models for Regression Discontinuity Designs

The Regression Discontinuity Design (RDD) is a quasi-experimental design that estimates the causal effect of a treatment when its assignment is defined by a threshold value for a continuous assignment variable. The RDD assumes that subjects with measurements within a bandwidth around the threshold belong to a common population, so that the threshold can be seen as a randomising device assigning treatment to those falling just above the threshold and withholding it from those who fall just below. Bandwidth selection represents a compelling decision for the RDD analysis as the results may be highly sensitive to its choice. A number of methods to select the optimal bandwidth, mainly originating from the econometric literature, have been proposed. However, their use in practice is limited. We propose a methodology that, tackling the problem from an applied point of view, consider units' exchangeability, i.e., their similarity with respect to measured covariates, as the main criteria to select subjects for the analysis, irrespectively of their distance from the threshold. We carry out clustering on the sample using a Dirichlet process mixture model to identify balanced and homogeneous clusters. Our proposal exploits the posterior similarity matrix, which contains the pairwise probabilities that two observations are allocated to the same cluster in the MCMC sample. Thus we include in the RDD analysis only those clusters for which we have stronger evidence of exchangeability. We illustrate the validity of our methodology with both a simulated experiment and a motivating example on the effect of statins to lower cholesterol level, using UK primary care data.

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arXiv2019

Computing the Expected Value of Sample Information Efficiently: Expertise and Skills Required for Four Model-Based Methods

Objectives: Value of information (VOI) analyses can help policy-makers make informed decisions about whether to conduct and how to design future studies. Historically, a computationally expensive method to compute the Expected Value of Sample Information (EVSI) restricted the use of VOI to simple decision models and study designs. Recently, four EVSI approximation methods have made such analyses more feasible and accessible. We provide practical recommendations for analysts computing EVSI by evaluating these novel methods. Methods: Members of the Collaborative Network for Value of Information (ConVOI) compared the inputs, analyst's expertise and skills, and software required for four recently developed approximation methods. Information was also collected on the strengths and limitations of each approximation method. Results: All four EVSI methods require a decision-analytic model's probabilistic sensitivity analysis (PSA) output. One of the methods also requires the model to be re-run to obtain new PSA outputs for each EVSI estimation. To compute EVSI, analysts must be familiar with at least one of the following skills: advanced regression modeling, likelihood specification, and Bayesian modeling. All methods have different strengths and limitations, e.g., some methods handle evaluation of study designs with more outcomes more efficiently while others quantify uncertainty in EVSI estimates. All methods are programmed in the statistical language R and two of the methods provide online applications. Conclusion: Our paper helps to inform the choice between four efficient EVSI estimation methods, enabling analysts to assess the methods' strengths and limitations and select the most appropriate EVSI method given their situation and skills.

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arXiv2019

Calculating the Expected Value of Sample Information in Practice: Considerations from Three Case Studies

Investing efficiently in future research to improve policy decisions is an important goal. Expected Value of Sample Information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of a range of different studies. Estimating EVSI with the standard nested Monte Carlo algorithm has a notoriously high computational burden, especially when using a complex decision model or when optimizing over study sample sizes and designs. Therefore, a number of more efficient EVSI approximation methods have been developed. However, these approximation methods have not been compared and therefore their relative advantages and disadvantages are not clear. A consortium of EVSI researchers, including the developers of several approximation methods, compared four EVSI methods using three previously published health economic models. The examples were chosen to represent a range of real-world contexts, including situations with multiple study outcomes, missing data, and data from an observational rather than a randomized study. The computational speed and accuracy of each method were compared, and the relative advantages and implementation challenges of the methods were highlighted. In each example, the approximation methods took minutes or hours to achieve reasonably accurate EVSI estimates, whereas the traditional Monte Carlo method took weeks. Specific methods are particularly suited to problems where we wish to compare multiple proposed sample sizes, when the proposed sample size is large, or when the health economic model is computationally expensive. All the evaluated methods gave estimates similar to those given by traditional Monte Carlo, suggesting that EVSI can now be efficiently computed with confidence in realistic examples.

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arXiv2018

A dynamic Bayesian Markov model for health economic evaluations of interventions in infectious disease

Background. Health economic evaluations of interventions against infectious diseases are commonly based on the predictions of ordinary differential equation (ODE) systems or Markov models (MMs). Standard MMs are static, whereas ODE systems are usually dynamic and account for herd immunity which is crucial to prevent overestimation of infection prevalence. Complex ODE systems including probabilistic model parameters are computationally intensive. Thus, mainly ODE-based models including deterministic parameters are presented in the literature. These do not account for parameter uncertainty. As a consequence, probabilistic sensitivity analysis (PSA), a crucial component of health economic evaluations, cannot be conducted straightforwardly. Methods. We present a dynamic MM under a Bayesian framework. We extend a static MM by incorporating the force of infection into the state allocation algorithm. The corresponding output is based on dynamic changes in prevalence and thus accounts for herd immunity. In contrast to deterministic ODE-based models, PSA can be conducted straightforwardly. We introduce a case study of a fictional sexually transmitted infection and compare our dynamic Bayesian MM to a deterministic and a Bayesian ODE system. The models are calibrated to time series data. Results. By means of the case study, we show that our methodology produces outcome which is comparable to the "gold standard" of the Bayesian ODE system. Conclusions. In contrast to ODE systems in the literature, the setting of the dynamic MM is probabilistic at manageable computational effort (including calibration). The run time of the Bayesian ODE system is 44 times longer.

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arXiv2018

Modeling outcomes of soccer matches

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalized version of it, while the posterior densities of the parameters of the hierarchical Poisson log-linear model are approximated using integrated nested Laplace approximations. The prediction performance of the various modeling approaches is assessed using a novel, context-specific framework for temporal validation that is found to deliver accurate estimates of the test error. The direct modeling of outcomes via the various Bradley-Terry extensions and the modeling of match scores using the hierarchical Poisson log-linear model demonstrate similar behavior in terms of predictive performance.

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arXiv2018

A Bayesian Parametric Approach to Handle Missing Longitudinal Outcome Data in Trial-Based Health Economic Evaluations

Trial-based economic evaluations are typically performed on cross-sectional variables, derived from the responses for only the completers in the study, using methods that ignore the complexities of utility and cost data (e.g. skewness and spikes). We present an alternative and more efficient Bayesian parametric approach to handle missing longitudinal outcomes in economic evaluations, while accounting for the complexities of the data. We specify a flexible parametric model for the observed data and partially identify the distribution of the missing data with partial identifying restrictions and sensitivity parameters. We explore alternative nonignorable scenarios through different priors for the sensitivity parameters, calibrated on the observed data. Our approach is motivated by, and applied to, data from a trial assessing the cost-effectiveness of a new treatment for intellectual disability and challenging behaviour.

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arXiv2018

Calculating the Expected Value of Sample Information using Efficient Nested Monte Carlo: A Tutorial

Objective: The Expected Value of Sample Information (EVSI) quantifies the economic benefit of reducing uncertainty in a health economic model by collecting additional information. This has the potential to improve the allocation of research budgets. Despite this, practical EVSI evaluations are limited, partly due to the computational cost of estimating this value using the "gold-standard" nested simulation methods. Recently, however, Heath et al developed an estimation procedure that reduces the number of simulations required for this "gold-standard" calculation. Up to this point, this new method has been presented in purely technical terms. Study Design: This study presents the practical application of this new method to aid its implementation. We use a worked example to illustrate the key steps of the EVSI estimation procedure before discussing its optimal implementation using a practical health economic model. Methods: The worked example is based on a three parameter linear health economic model. The more realistic model evaluates the cost-effectiveness of a new chemotherapy treatment which aims to reduce the number of side effects experienced by patients. We use a Markov Model structure to evaluate the health economic profile of experiencing side effects. Results: This EVSI estimation method offers accurate estimation within a feasible computation time, seconds compared to days, even for more complex model structures. The EVSI estimation is more accurate if a greater number of nested samples are used, even for a fixed computational cost. Conclusions: This new method reduces the computational cost of estimating the EVSI by nested simulation.

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arXiv2018

Estimating the Expected Value of Sample Information across Different Sample Sizes using Moment Matching and Non-Linear Regression

Background: The Expected Value of Sample Information (EVSI) determines the economic value of any future study with a specific design aimed at reducing uncertainty in a health economic model. This has potential as a tool for trial design; the cost and value of different designs could be compared to find the trial with the greatest net benefit. However, despite recent developments, EVSI analysis can be slow especially when optimising over a large number of different designs. Methods: This paper develops a method to reduce the computation time required to calculate the EVSI across different sample sizes. Our method extends the moment matching approach to EVSI estimation to optimise over different sample sizes for the underlying trial with a similar computational cost to a single EVSI estimate. This extension calculates posterior variances across the alternative sample sizes and then uses Bayesian non-linear regression to calculate the EVSI. Results: A health economic model developed to assess the cost-effectiveness of interventions for chronic pain demonstrates that this EVSI calculation method is fast and accurate for realistic models. This example also highlights how different trial designs can be compared using the EVSI. Conclusion: The proposed estimation method is fast and accurate when calculating the EVSI across different sample sizes. This will allow researchers to realise the potential of using the EVSI to determine an economically optimal trial design for reducing uncertainty in health economic models. Limitations: Our method relies on some additional simulation, which can be expensive in models with very large computational cost.

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arXiv2018

A Full Bayesian Model to Handle Structural Ones and Missingness in Economic Evaluations from Individual-Level Data

Economic evaluations from individual-level data are an important component of the process of technology appraisal, with a view to informing resource allocation decisions. A critical problem in these analyses is that both effectiveness and cost data typically present some complexity (e.g. non normality, spikes and missingness) that should be addressed using appropriate methods. However, in routine analyses, simple standardised approaches are typically used, possibly leading to biased inferences. We present a general Bayesian framework that can handle the complexity. We show the benefits of using our approach with a motivating example, the MenSS trial, for which there are spikes at one in the effectiveness and missingness in both outcomes. We contrast a set of increasingly complex models and perform sensitivity analysis to assess the robustness of the conclusions to a range of plausible missingness assumptions. This paper highlights the importance of adopting a comprehensive modelling approach to economic evaluations and the strategic advantages of building these complex models within a Bayesian framework.

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arXiv2017

Efficient Monte Carlo Estimation of the Expected Value of Sample Information using Moment Matching

The Expected Value of Sample Information (EVSI) is used to calculate the economic value of a new research strategy. While this value would be important to both researchers and funders, there are very few practical applications of the EVSI. In the main, this is due to computational difficulties associated with calculating the EVSI in practical health economic models using nested simulations. We present an approximation method for the EVSI that is based on estimating the distribution of the posterior mean of the incremental net benefit across all the possible future samples, known as the distribution of the preposterior mean. Specifically, we suggest that this distribution is estimated using moment matching coupled with simulations that are available for probabilistic sensitivity analysis, which is typically mandatory in health economic evaluation. We demonstrate that this method is successful using an example that has previously been applied to other EVSI approximation methods. We then conclude by discussing how our method fits in with other recent additions to the literature that detail approximation methods for the EVSI.

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