arXiv subjects

Tim P. Morris

Publications and source records attributed to Tim P. Morris.

10 recordsLinked to original sources

arXiv2026

Introducing precision-weighted bias as a performance measure to inform the inclusion of adaptive designs in meta-analysis

We propose a novel, intuitive measure of statistical performance: precision-weighted bias. Precision-weighted bias is defined as the unconditional bias of an estimator weighted by the degree of information (precision) it contains. Current guidelines, such as GRADE and CONSORT, often view the potential for increased bias in adaptive designs as a deterrent for the inclusion of such designs in systematic reviews. However, we demonstrate that the bias in a common-effect meta-analysis is approximately equal to the precision-weighted average of the precision-weighted biases of its constituent studies, rather than of their unweighted unconditional biases. Through simulation studies, we show that while adaptive designs may exhibit unweighted bias, they frequently have zero precision-weighted bias. Consequently, including these designs often results in a negligible change to the overall meta-analysis bias. These results suggest that precision-weighted bias is a superior indicator for determining whether to include an adaptive design in a meta-analysis. We recommend that precision-weighted bias be used as a standard complement to unweighted unconditional and conditional bias in simulation studies to support more inclusive and accurate evidence synthesis.

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arXiv2026

How to interpret hazard ratios

The hazard ratio, typically estimated using Cox's famous proportional hazards model, is the most common effect measure used to describe the association or effect of a covariate on a time-to-event outcome. In recent years the hazard ratio has been argued by some to lack a causal interpretation, even in randomised trials, and even if the proportional hazards assumption holds. This is concerning, not least due to the ubiquity of hazard ratios in analyses of time-to-event data. We review these criticisms, describe how we think hazard ratios should be interpreted, and argue that they retain a valid causal interpretation. Nevertheless, alternative measures may be preferable to describe effects of exposures or treatments on time-to-event outcomes.

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arXiv2026

Revealing the Truth: Calculating True Values in Causal Inference Simulation Studies via Gaussian Quadrature

Simulation studies are used to understand the properties of statistical methods. A key luxury in many simulation studies is knowledge of the true value (i.e. the estimand) being targeted. With this oracle knowledge in-hand, the researcher conducting the simulation study can assess across repeated realizations of the data how well a given method recovers the truth. In causal inference simulation studies, the truth is rarely a simple parameter of the statistical model chosen to generate the data. Instead, the estimand is often an average treatment effect, marginalized over the distribution of confounders and/or mediators. Luckily, these variables are often generated from common distributions such as the normal, uniform, exponential, or gamma. For all these distributions, Gaussian quadratures provide efficient and accurate calculation for integrands with integral kernels that stem from known probability density functions. We demonstrate through four applications how to use Gaussian quadrature to accurately and efficiently compute the true causal estimand. We also compare the pros and cons of Gauss-Hermite quadrature to Monte Carlo integration approaches, which we use as benchmarks. Overall, we demonstrate that the Gaussian quadrature is an accurate tool with negligible computation time, yet is underused for calculating the true causal estimands in simulation studies.

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arXiv2024

Rethinking the handling of method failure in comparison studies

Comparison studies in methodological research are intended to compare methods in an evidence-based manner to help data analysts select a suitable method for their application. To provide trustworthy evidence, they must be carefully designed, implemented, and reported, especially given the many decisions made in planning and running. A common challenge in comparison studies is to handle the "failure" of one or more methods to produce a result for some (real or simulated) data sets, such that their performances cannot be measured in those instances. Despite an increasing emphasis on this topic in recent literature (focusing on non-convergence as a common manifestation), there is little guidance on proper handling and interpretation, and reporting of the chosen approach is often neglected. This paper aims to fill this gap and offers practical guidance on handling method failure in comparison studies. After exploring common handlings across various published comparison studies from classical statistics and predictive modeling, we show that the popular approaches of discarding data sets yielding failure (either for all or the failing methods only) and imputing are inappropriate in most cases. We then recommend a different perspective on method failure - viewing it as the result of a complex interplay of several factors rather than just its manifestation. Building on this, we provide recommendations on more adequate handlings of method failure derived from realistic considerations. In particular, we propose considering fallback strategies that directly reflect the behavior of real-world users. Finally, we illustrate our recommendations and the dangers of inadequate handling of method failure through two exemplary comparison studies.

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arXiv2024

Multiple imputation of missing covariates when using the Fine-Gray model

The Fine-Gray model for the subdistribution hazard is commonly used for estimating associations between covariates and competing risks outcomes. When there are missing values in the covariates included in a given model, researchers may wish to multiply impute them. Assuming interest lies in estimating the risk of only one of the competing events, this paper develops a substantive-model-compatible multiple imputation approach that exploits the parallels between the Fine-Gray model and the standard (single-event) Cox model. In the presence of right-censoring, this involves first imputing the potential censoring times for those failing from competing events, and thereafter imputing the missing covariates by leveraging methodology previously developed for the Cox model in the setting without competing risks. In a simulation study, we compared the proposed approach to alternative methods, such as imputing compatibly with cause-specific Cox models. The proposed method performed well (in terms of estimation of both subdistribution log hazard ratios and cumulative incidences) when data were generated assuming proportional subdistribution hazards, and performed satisfactorily when this assumption was not satisfied. The gain in efficiency compared to a complete-case analysis was demonstrated in both the simulation study and in an applied data example on competing outcomes following an allogeneic stem cell transplantation. For individual-specific cumulative incidence estimation, assuming proportionality on the correct scale at the analysis phase appears to be more important than correctly specifying the imputation procedure used to impute the missing covariates.

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arXiv2022

Phases of methodological research in biostatistics - building the evidence base for new methods

Although the biostatistical scientific literature publishes new methods at a very high rate, many of these developments are not trustworthy enough to be adopted by the scientific community. We propose a framework to think about how a piece of methodological work contributes to the evidence base for a method. Similarly to the well-known phases of clinical research in drug development, we define four phases of methodological research. These four phases cover (I) providing logical reasoning and proofs, (II) providing empirical evidence, first in a narrow target setting, then (III) in an extended range of settings and for various outcomes, accompanied by appropriate application examples, and (IV) investigations that establish a method as sufficiently well-understood to know when it is preferred over others and when it is not. We provide basic definitions of the four phases but acknowledge that more work is needed to facilitate unambiguous classification of studies into phases. Methodological developments that have undergone all four proposed phases are still rare, but we give two examples with references. Our concept rebalances the emphasis to studies in phase III and IV, i.e., carefully planned methods comparison studies and studies that explore the empirical properties of existing methods in a wider range of problems.

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arXiv2021

On the mixed-model analysis of covariance in cluster-randomized trials

In the analyses of cluster-randomized trials, mixed-model analysis of covariance (ANCOVA) is a standard approach for covariate adjustment and handling within-cluster correlations. However, when the normality, linearity, or the random-intercept assumption is violated, the validity and efficiency of the mixed-model ANCOVA estimators for estimating the average treatment effect remain unclear. Under the potential outcomes framework, we prove that the mixed-model ANCOVA estimators for the average treatment effect are consistent and asymptotically normal under arbitrary misspecification of its working model. If the probability of receiving treatment is 0.5 for each cluster, we further show that the model-based variance estimator under mixed-model ANCOVA1 (ANCOVA without treatment-covariate interactions) remains consistent, clarifying that the confidence interval given by standard software is asymptotically valid even under model misspecification. Beyond robustness, we discuss several insights on precision among classical methods for analyzing cluster-randomized trials, including the mixed-model ANCOVA, individual-level ANCOVA, and cluster-level ANCOVA estimators. These insights may inform the choice of methods in practice. Our analytical results and insights are illustrated via simulation studies and analyses of three cluster-randomized trials.

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arXiv2021

Planning a method for covariate adjustment in individually-randomised trials: a practical guide

Background: It has long been advised to account for baseline covariates in the analysis of confirmatory randomised trials, with the main statistical justifications being that this increases power and, when a randomisation scheme balanced covariates, permits a valid estimate of experimental error. There are various methods available to account for covariates but it is not clear how to choose among them. Methods: Taking the perspective of writing a statistical analysis plan, we consider how to choose between the three most promising broad approaches: direct adjustment, standardisation and inverse-probability-of-treatment weighting. Results: The three approaches are similar in being asymptotically efficient, in losing efficiency with mis-specified covariate functions, and in handling designed balance. If a marginal estimand is targeted (for example, a risk difference or survival difference), then direct adjustment should be avoided because it involves fitting non-standard models that are subject to convergence issues. Convergence is most likely with IPTW. Robust standard errors used by IPTW are anti-conservative at small sample sizes. All approaches can use similar methods to handle missing covariate data. With missing outcome data, each method has its own way to estimate a treatment effect in the all-randomised population. We illustrate some issues in a reanalysis of GetTested, a randomised trial designed to assess the effectiveness of an electonic sexually-transmitted-infection testing and results service. Conclusions: No single approach is always best: the choice will depend on the trial context. We encourage trialists to consider all three methods more routinely.

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arXiv2020

INTEREST: INteractive Tool for Exploring REsults from Simulation sTudies

Simulation studies allow us to explore the properties of statistical methods. They provide a powerful tool with a multiplicity of aims; among others: evaluating and comparing new or existing statistical methods, assessing violations of modelling assumptions, helping with the understanding of statistical concepts, and supporting the design of clinical trials. The increased availability of powerful computational tools and usable software has contributed to the rise of simulation studies in the current literature. However, simulation studies involve increasingly complex designs, making it difficult to provide all relevant results clearly. Dissemination of results plays a focal role in simulation studies: it can drive applied analysts to use methods that have been shown to perform well in their settings, guide researchers to develop new methods in a promising direction, and provide insights into less established methods. It is crucial that we can digest relevant results of simulation studies. Therefore, we developed INTEREST: an INteractive Tool for Exploring REsults from Simulation sTudies. The tool has been developed using the Shiny framework in R and is available as a web app or as a standalone package. It requires uploading a tidy format dataset with the results of a simulation study in R, Stata, SAS, SPSS, or comma-separated format. A variety of performance measures are estimated automatically along with Monte Carlo standard errors; results and performance summaries are displayed both in tabular and graphical fashion, with a wide variety of available plots. Consequently, the reader can focus on simulation parameters and estimands of most interest. In conclusion, INTEREST can facilitate the investigation of results from simulation studies and supplement the reporting of results, allowing researchers to share detailed results from their simulations and readers to explore them freely.

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arXiv2017

Multiple imputation in Cox regression when there are time-varying effects of exposures

In Cox regression it is sometimes of interest to study time-varying effects (TVE) of exposures and to test the proportional hazards assumption. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on exposures are common and multiple imputation (MI) is a popular approach to handling this, to avoid the potential bias and loss of efficiency resulting from a 'complete-case' analysis. Two MI methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (White and Royston, Statist. Med. 2009;28:1982-98) and a substantive-model-compatible method (Bartlett et al., SMMR 2015;24:462-87). At present, neither method accommodates TVEs of exposures. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary exposures with missing data, but for continuous exposures the substantive-model-compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE, and gain power to detect TVEs relative to complete-case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. Example R code is provided.

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