Rhian M. Daniel

We describe a modular regression framework in which covariate-dependent transformations are composed together and act on probability distributions. This framework is based on group actions of vector spaces, which are computationally convenient families of transformations that are well suited to model building and inference. We quantify covariate contributions to each group action through corresponding linear maps, and these are the only model parameters to be estimated. Algebraic features of group actions-notably, their invariant subsets-are informative about local statistical properties of the regression model. Vector space actions on affine spaces also provide a minimal geometric structure for comparing distributions, with affine transformations characterizing collapsible contrasts. In two substantive data analyses, we illustrate how unconventional models may be expressed as regressions by composition. We exhibit and extend existing nonlinear models for interpolating infant growth curves for individuals, and for producing standard population growth charts. We also use regression by composition to specify and fit a bespoke, mechanistically-motivated binary regression model for antiretroviral therapies in the treatment of HIV.

1. The ICH E9 addendum on estimands and sensitivity analyses lays out a framework for choosing and defining the treatment effect estimand of interest in a clinical trial (ICH 2019). It introduces t...

G-formula is a popular approach for estimating the effects of time-varying treatments or exposures from longitudinal data. G-formula is typically implemented using Monte-Carlo simulation, with non-parametric bootstrapping used for inference. In longitudinal data settings missing data are a common issue, which are often handled using multiple imputation, but it is unclear how G-formula and multiple imputation should be combined. We show how G-formula can be implemented using Bayesian multiple imputation methods for synthetic data, and that by doing so, we can impute missing data and simulate the counterfactuals of interest within a single coherent approach. We describe how this can be achieved using standard multiple imputation software and explore its performance using a simulation study and an application from cystic fibrosis.

The ICH E9 addendum on estimands in clinical trials provides a framework for precisely defining the treatment effect that is to be estimated, but says little about estimation methods. Here, we report analyses of a clinical trial in type 2 diabetes, targeting the effects of randomized treatment, handling rescue treatment and discontinuation of randomized treatment using the so-called hypothetical strategy. We show how this can be estimated using mixed models for repeated measures, multiple imputation, inverse probability of treatment weighting, G-formula, and G-estimation. We describe their assumptions and practical details of their implementation using packages in R. We report the results of these analyses, broadly finding similar estimates and standard errors across the estimators. We discuss various considerations relevant when choosing an estimation approach, including computational time, how to handle missing data, whether to include post intercurrent event data in the analysis, whether and how to adjust for additional time-varying confounders, and whether and how to model different types of intercurrent event data separately.

Introduction Very preterm babies are at risk of poor neurodevelopmental outcomes and death. Intraventricular haemorrhage (IVH) after birth is the most prevalent cause of this. Birth by caesarean section may protect against IVH in very preterm babies, but the evidence is limited. The aim is to identify and obtain the quantitative evidence needed to inform a future definitive clinical trial to determine the optimal mode of delivery in preterm birth. Methods and analysis We will use three broad workstreams (WS) to answer complementary questions. WSs 1 and 2 involve the analysis of routinely recorded national clinical data held in an established research database. In WS1 (October 2023–March 2024), we will use conventional methods to identify what is needed to undertake a trial: the population of interest, areas of equipoise and a plausible range of effect sizes. In WS2 (April 2024–October 2024), using an emulated target trial framework, we will attempt to make inferences about the treatment effect from such a future trial and will identify potential challenges in recruitment and estimate likely ‘intention-to-treat’ versus ‘per-protocol’ profiles; these analyses will also be useful for power calculations for future possible trials. In WS3 (October 2024–March 2025), we will convene a consensus meeting with key stakeholders, supported by a clinical trials unit, to develop a multicentre clinical trial to identify the optimal mode of birth for preterm deliveries. Ethics and dissemination In this study, we will use deidentified data held in the National Neonatal Research Database (NNRD), an established national population database; parents can opt out of their baby’s data being held in the NNRD. HRA/Health and Care Research Wales and National Health Service (NHS) study-specific Research Ethics Committee approval (London—Queen Square Research Ethics Committee) (Ref: 23/LO/0826) ethical approval has been obtained. Key outputs of the PRECIOUS (PREterm Caesarean/vaginal birth and IVH/OUutcomeS) study include the identification of the data, and accordingly of the multidisciplinary team required, to develop, gain funding and complete, a clinical trial to definitively identify the optimal mode of delivery for preterm infants and their mothers.

Regression by composition is a new and flexible toolkit for building and understanding statistical models. Focusing here on regression models for a binary outcome conditional on a binary treatment and other covariates, we motivate the need for regression by composition. We do this first by exhibiting—using L’Abbé plots—the families of relationships between untreated and treated conditional outcome risks that emerge from generalized linear models for many different link functions. These are compared with the relationships (between untreated and treated risks) that arise from mechanistic sufficient component cause models, which are first principles causal models for binary outcomes. By considering mechanistic models that allow for non-monotone causal effects and by allowing sufficient causes to be associated, we expand upon similar discussions in the recent literature. We discuss conditions under which commonly used statistical models for binary data, such as logistic regression, arise from mechanistic models where the sufficient causes are associated in a particular way, as well as other situations in which the statistical models arising do not correspond to a generalized linear model but can be naturally expressed as a regression by composition model.

There is uncertainty about outcomes associated with cardiac echogenic foci (CEF) seen at the midtrimester ultrasound scan because of limited population-based follow-up data. This can lead to unnecessary invasive testing and significant parental anxiety. We analysed data from a cohort study, The Welsh Study of Mothers and Babies, to examine whether children with CEF had more adverse outcomes during childhood compared with children without CEF. Children born between 1 January 2009 and 31 December 2011 were followed until 31 January 2018, migration out of Wales, or death. The primary outcome was cardiac hospital admissions, defined a priori by an expert steering group. Secondary outcomes included congenital cardiac anomalies, and hospital admissions for other causes. There was no evidence of an association between isolated CEF and cardiac hospital admissions (hazard ratio 0.87, 95% confidence interval [CI] 0.33–2.25, p value 0.768), or with congenital cardiac anomalies. There was a small increased risk of a respiratory admission with isolated CEF (hazard ratio 1.27, 95% CI 1.04–1.54, p value 0.020). Further research is needed on features of CEF, such as location or number, to fully understand the clinical significance of these findings.

Microbiological data are used as indicators of infection, for diagnosis, and the identification of antimicrobial resistance in trials of antimicrobial stewardship interventions. However, several problems have been identified in a recently conducted systematic review (e.g., inconsistency in reporting and oversimplified outcomes), which motivates the need to understand and improve the use of these data including analysis and reporting. We engaged key stakeholders including statisticians, clinicians from both primary and secondary care, and microbiologists. Discussions included issues identified in the systematic review and questions about the value of using microbiological data in clinical trials, perspectives on current microbiological outcomes reported in trials, and alternative statistical approaches to analyse these data. Various factors (such as unclear sample collection process, dichotomising or categorising complex microbiological data, and unclear methods of handling missing data) were identified that contributed to the low quality of the microbiological outcomes and the analysis of these outcomes in trials. Whilst not all of these factors would be easy to overcome, there is room for improvement and a need to encourage researchers to understand the impact of misusing these data. This paper discusses the experience and challenges of using microbiological outcomes in clinical trials.

Aim: To investigate whether the effect of cystic fibrosis‐related diabetes (CFRD) on the composite outcome of mortality or transplant could act through lung function, pulmonary exacerbations and/or nutritional status.Methods: A retrospective cohort of adult cystic fibrosis (CF) patients who had not been diagnosed with CFRD were identified from the UK Cystic Fibrosis Registry (n = 2750). Rate of death or transplant was compared between patients who did and did not develop CFRD (with insulin use) during follow‐up using Poisson regression, separately by sex. Causal mediation methods were used to investigate whether lung function, pulmonary exacerbations and nutritional status lie on the causal pathway between insulin‐treated CFRD and mortality/transplant.Results: At all ages, the mortality/transplant rate was higher in both men and women diagnosed with CFRD. Pulmonary exacerbations were the strongest mediator of the effect of CFRD on mortality/transplant, with an estimated 15% [95% CI: 7%, 28%] of the effect at 2 years post‐CFRD diagnosis attributed to exacerbations, growing to 24% [95% CI: 9%, 46%] at 4 years post‐diagnosis. Neither lung function nor nutritional status were found to be significant mediators of this effect. Estimates were similar but with wider confidence intervals in a cohort that additionally included people with CFRD but not using insulin.Conclusion: There is evidence that pulmonary exacerbations mediate the effect of CFRD on mortality but, as they are estimated to mediate less than one‐quarter of the total effect, the mechanism through which CFRD influences survival may involve other factors.