A comparison of two frameworks for multi-state modelling, applied to outcomes after hospital admissions with COVID-19.

We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using 'cure-rate' models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events.

Changes in in-hospital mortality in the first wave of COVID-19: a multicentre prospective observational cohort study using the WHO Clinical Characterisation Protocol UK.

BACKGROUND: Mortality rates in hospitalised patients with COVID-19 in the UK appeared to decline during the first wave of the pandemic. We aimed to quantify potential drivers of this change and identify groups of patients who remain at high risk of dying in hospital. METHODS: In this multicentre prospective observational cohort study, the International Severe Acute Respiratory and Emerging Infections Consortium WHO Clinical Characterisation Protocol UK recruited a prospective cohort of patients with COVID-19 admitted to 247 acute hospitals in England, Scotland, and Wales during the first wave of the pandemic (between March 9 and Aug 2, 2020). We included all patients aged 18 years and older with clinical signs and symptoms of COVID-19 or confirmed COVID-19 (by RT-PCR test) from assumed community-acquired infection. We did a three-way decomposition mediation analysis using natural effects models to explore associations between week of admission and in-hospital mortality, adjusting for confounders (demographics, comorbidities, and severity of illness) and quantifying potential mediators (level of respiratory support and steroid treatment). The primary outcome was weekly in-hospital mortality at 28 days, defined as the proportion of patients who had died within 28 days of admission of all patients admitted in the observed week, and it was assessed in all patients with an outcome. This study is registered with the ISRCTN Registry, ISRCTN66726260. FINDINGS: Between March 9, and Aug 2, 2020, we recruited 80 713 patients, of whom 63 972 were eligible and included in the study. Unadjusted weekly in-hospital mortality declined from 32·3% (95% CI 31·8-32·7) in March 9 to April 26, 2020, to 16·4% (15·0-17·8) in June 15 to Aug 2, 2020. Reductions in mortality were observed in all age groups, in all ethnic groups, for both sexes, and in patients with and without comorbidities. After adjustment, there was a 32% reduction in the risk of mortality per 7-week period (odds ratio [OR] 0·68 [95% CI 0·65-0·71]). The higher proportions of patients with severe disease and comorbidities earlier in the first wave (March and April) than in June and July accounted for 10·2% of this reduction. The use of respiratory support changed during the first wave, with gradually increased use of non-invasive ventilation over the first wave. Changes in respiratory support and use of steroids accounted for 22·2%, OR 0·95 (0·94-0·95) of the reduction in in-hospital mortality. INTERPRETATION: The reduction in in-hospital mortality in patients with COVID-19 during the first wave in the UK was partly accounted for by changes in the case-mix and illness severity. A significant reduction in in-hospital mortality was associated with differences in respiratory support and critical care use, which could partly reflect accrual of clinical knowledge. The remaining improvement in in-hospital mortality is not explained by these factors, and could be associated with changes in community behaviour, inoculum dose, and hospital capacity strain. FUNDING: National Institute for Health Research and the Medical Research Council.

Optimal individualized decision rules from a multi-arm trial: A comparison of methods and an application to tailoring inter-donation intervals among blood donors in the UK.

There is a growing interest in precision medicine where individual heterogeneity is incorporated into decision-making and treatments are tailored to individuals to provide better healthcare. One important aspect of precision medicine is the estimation of the optimal individualized treatment rule (ITR) that optimizes the expected outcome. Most methods developed for this purpose are restricted to the setting with two treatments, while clinical studies with more than two treatments are common in practice. In this work, we summarize methods to estimate the optimal ITR in the multi-arm setting and compare their performance in large-scale clinical trials via simulation studies. We then illustrate their utilities with a case study using the data from the INTERVAL trial, which randomly assigned over 20,000 male blood donors from England to one of the three inter-donation intervals (12-week, 10-week, and eight-week) over two years. We estimate the optimal individualized donation strategies under three different objectives. Our findings are fairly consistent across five different approaches that are applied: when we target the maximization of the total units of blood collected, almost all donors are assigned to the eight-week inter-donation interval, whereas if we aim at minimizing the low hemoglobin deferral rates, almost all donors are assigned to donate every 12 weeks. However, when the goal is to maximize the utility score that "discounts" the total units of blood collected by the incidences of low hemoglobin deferrals, we observe some heterogeneity in the optimal inter-donation interval across donors and the optimal donor assignment strategy is highly dependent on the trade-off parameter in the utility function.

Two-part models with stochastic processes for modelling longitudinal semicontinuous data: Computationally efficient inference and modelling the overall marginal mean.

Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice, the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus, non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence, maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.

A corrected formulation for marginal inference derived from two-part mixed models for longitudinal semi-continuous data.

For semi-continuous data which are a mixture of true zeros and continuously distributed positive values, the use of two-part mixed models provides a convenient modelling framework. However, deriving population-averaged (marginal) effects from such models is not always straightforward. Su et al. presented a model that provided convenient estimation of marginal effects for the logistic component of the two-part model but the specification of marginal effects for the continuous part of the model presented in that paper was based on an incorrect formulation. We present a corrected formulation and additionally explore the use of the two-part model for inferences on the overall marginal mean, which may be of more practical relevance in our application and more generally.

A likelihood-based two-part marginal model for longitudinal semicontinuous data.

Two-part models are an attractive approach for analysing longitudinal semicontinuous data consisting of a mixture of true zeros and continuously distributed positive values. When the population-averaged (marginal) covariate effects are of interest, two-part models that provide straightforward interpretation of the marginal effects are desirable. Presently, the only available approaches for fitting two-part marginal models to longitudinal semicontinuous data are computationally difficult to implement. Therefore, there exists a need to develop two-part marginal models that can be easily implemented in practice. We propose a fully likelihood-based two-part marginal model that satisfies this need by using the bridge distribution for the random effect in the binary part of an underlying two-part mixed model; and its maximum likelihood estimation can be routinely implemented via standard statistical software such as the SAS NLMIXED procedure. We illustrate the usage of this new model by investigating the marginal effects of pre-specified genetic markers on physical functioning, as measured by the Health Assessment Questionnaire, in a cohort of psoriatic arthritis patients from the University of Toronto Psoriatic Arthritis Clinic. An added benefit of our proposed marginal model when compared to a two-part mixed model is the robustness in regression parameter estimation when departure from the true random effects structure occurs. This is demonstrated through simulation.

Re-weighted inference about hepatitis C virus-infected communities when analysing diagnosed patients referred to liver clinics.

To project national hepatitis C virus (HCV) burden, unbiased estimation of HCV progression to liver cirrhosis is required for the whole community of HCV-infected individuals. However, widely varying estimates of progression rates to cirrhosis have been produced. This disparity is partly associated with the statistical methods applied, but is mainly due to the differing types of study cohort. We use an inverse probability weighted estimation method to recover the true parameters for the (Weibull regression) model that determines the incubation period from infection to cirrhosis for the community of HCV-infected individuals, when there is cirrhosis-related recruitment bias to the studied cohort. We apply the method to simulated data for a liver clinic which attracts patients from a community of 1000 HCV-infected individuals under different event-biased referral patterns. We investigate how well the method performs in recovering the true community parameters, and then apply it to Edinburgh Royal Infirmary's liver clinic series. The results obtained are compared to those from a Weibull survival analysis which ignores the selection bias.