Missing continuous outcomes under covariate dependent missingness in cluster randomised trials.

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group

Coping with Persistent Pain, Effectiveness Research into Self-management (COPERS): statistical analysis plan for a randomised controlled trial

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated

Target trial emulation: Do antimicrobials or gastrointestinal nutraceuticals prescribed at first presentation for acute diarrhoea cause a better clinical outcome in dogs under primary veterinary care in the UK?

Target trial emulation applies design principles from randomised controlled trials to the analysis of observational data for causal inference and is increasingly used within human epidemiology. Veterinary electronic clinical records represent a potentially valuable source of information to estimate real-world causal effects for companion animal species. This study employed the target trial framework to evaluate the usefulness on veterinary observational data. Acute diarrhoea in dogs was used as a clinical exemplar. Inclusion required dogs aged ≥ 3 months and < 10 years, presenting for veterinary primary care with acute diarrhoea during 2019. Treatment strategies were: 1. antimicrobial prescription compared to no antimicrobial prescription and 2. gastrointestinal nutraceutical prescription compared to no gastrointestinal nutraceutical prescription. The primary outcome was clinical resolution (defined as no revisit with ongoing diarrhoea within 30 days from the date of first presentation). Informed from a directed acyclic graph, data on the following covariates were collected: age, breed, bodyweight, insurance status, comorbidities, vomiting, reduced appetite, haematochezia, pyrexia, duration, additional treatment prescription and veterinary group. Inverse probability of treatment weighting was used to balance covariates between the treatment groups for each of the two target trials. The risk difference (RD) of 0.4% (95% CI -4.5% to 5.3%) was non-significant for clinical resolution in dogs treated with antimicrobials compared with dogs not treated with antimicrobials. The risk difference (RD) of 0.3% (95% CI -4.5% to 5.0%) was non-significant for clinical resolution in dogs treated with gastrointestinal nutraceuticals compared with dogs not treated with gastrointestinal nutraceuticals. This study successfully applied the target trial framework to veterinary observational data. The findings show that antimicrobial or gastrointestinal prescription at first presentation of acute diarrhoea in dogs causes no difference in clinical resolution. The findings support the recommendation for veterinary professionals to limit antimicrobial use for acute diarrhoea in dogs

How to estimate the association between change in a risk factor and a health outcome?

Estimating the effect of a change in a particular risk factor and a chronic disease requires information on the risk factor from two time points; the enrolment and the first follow-up. When using observational data to study the effect of such an exposure (change in risk factor) extra complications arise, namely (i) when is time zero? and (ii) which information on confounders should we account for in this type of analysis? From enrolment or the 1st follow-up? Or from both?. The combination of these questions has proven to be very challenging. Researchers have applied different methodologies with mixed success, because the different choices made when answering these questions induce systematic bias. Here we review these methodologies and highlight the sources of bias in each type of analysis. We discuss the advantages and the limitations of each method ending by making our recommendations on the analysis plan

On the recurrence and robust properties of Lorenz'63 model

Lie-Poisson structure of the Lorenz'63 system gives a physical insight on its dynamical and statistical behavior considering the evolution of the associated Casimir functions. We study the invariant density and other recurrence features of a Markov expanding Lorenz-like map of the interval arising in the analysis of the predictability of the extreme values reached by particular physical observables evolving in time under the Lorenz'63 dynamics with the classical set of parameters. Moreover, we prove the statistical stability of such an invariant measure. This will allow us to further characterize the SRB measure of the system.Comment: 44 pages, 7 figures, revised version accepted for pubblicatio

Importance of patient bed pathways and length of stay differences in predicting COVID-19 hospital bed occupancy in England

BACKGROUND: Predicting bed occupancy for hospitalised patients with COVID-19 requires understanding of length of stay (LoS) in particular bed types. LoS can vary depending on the patient's "bed pathway" - the sequence of transfers of individual patients between bed types during a hospital stay. In this study, we characterise these pathways, and their impact on predicted hospital bed occupancy. METHODS: We obtained data from University College Hospital (UCH) and the ISARIC4C COVID-19 Clinical Information Network (CO-CIN) on hospitalised patients with COVID-19 who required care in general ward or critical care (CC) beds to determine possible bed pathways and LoS. We developed a discrete-time model to examine the implications of using either bed pathways or only average LoS by bed type to forecast bed occupancy. We compared model-predicted bed occupancy to publicly available bed occupancy data on COVID-19 in England between March and August 2020. RESULTS: In both the UCH and CO-CIN datasets, 82% of hospitalised patients with COVID-19 only received care in general ward beds. We identified four other bed pathways, present in both datasets: "Ward, CC, Ward", "Ward, CC", "CC" and "CC, Ward". Mean LoS varied by bed type, pathway, and dataset, between 1.78 and 13.53 days. For UCH, we found that using bed pathways improved the accuracy of bed occupancy predictions, while only using an average LoS for each bed type underestimated true bed occupancy. However, using the CO-CIN LoS dataset we were not able to replicate past data on bed occupancy in England, suggesting regional LoS heterogeneities. CONCLUSIONS: We identified five bed pathways, with substantial variation in LoS by bed type, pathway, and geography. This might be caused by local differences in patient characteristics, clinical care strategies, or resource availability, and suggests that national LoS averages may not be appropriate for local forecasts of bed occupancy for COVID-19. TRIAL REGISTRATION: The ISARIC WHO CCP-UK study ISRCTN66726260 was retrospectively registered on 21/04/2020 and designated an Urgent Public Health Research Study by NIHR

On the estimation of the effect of weight change on a health outcome using observational data, by utlilising the target trial emulation framework

Background/Objectives: When studying the effect of weight change between two time points on a health outcome using observational data, two main problems arise initially (i) ‘when is time zero?’ and (ii) ‘which confounders should we account for?’ From the baseline date or the 1st follow-up (when the weight change can be measured)? Different methods have been previously used in the literature that carry different sources of bias and hence produce different results. Methods: We utilised the target trial emulation framework and considered weight change as a hypothetical intervention. First, we used a simplified example from a hypothetical randomised trial where no modelling is required. Then we simulated data from an observational study where modelling is needed. We demonstrate the problems of each of these methods and suggest a strategy. Interventions: weight loss/gain vs maintenance. Results: The recommended method defines time-zero at enrolment, but adjustment for confounders (or exclusion of individuals based on levels of confounders) should be performed both at enrolment and the 1st follow-up. Conclusions: The implementation of our suggested method [adjusting for (or excluding based on) confounders measured both at baseline and the 1st follow-up] can help researchers attenuate bias by avoiding some common pitfalls. Other methods that have been widely used in the past to estimate the effect of weight change on a health outcome are more biased. However, two issues remain (i) the exposure is not well-defined as there are different ways of changing weight (however we tried to reduce this problem by excluding individuals who develop a chronic disease); and (ii) immortal time bias, which may be small if the time to first follow up is short

The effect of a one-year vigorous physical activity intervention on fitness, cognitive performance and mental health in young adolescents: the Fit to Study cluster randomised controlled trial.

BackgroundPhysical activity (PA) may positively stimulate the brain, cognition and mental health during adolescence, a period of dynamic neurobiological development. High-intensity interval training (HIIT) or vigorous PA interventions are time-efficient, scalable and can be easily implemented in existing school curricula, yet their effects on cognitive, academic and mental health outcomes are unclear. The primary aim of the Fit to Study trial was to investigate whether a pragmatic and scalable HIIT-style VPA intervention delivered during school physical education (PE) could improve attainment in maths. The primary outcome has previously been reported and was null. Here, we report the effect of the intervention on prespecified secondary outcomes, including cardiorespiratory fitness, cognitive performance, and mental health in young adolescents.MethodsThe Fit to Study cluster randomised controlled trial included Year 8 pupils (n = 18,261, aged 12-13) from 104 secondary state schools in South/Mid-England. Schools were randomised into an intervention condition (n = 52), in which PE teachers delivered an additional 10 min of VPA per PE lesson for one academic year (2017-2018), or into a "PE as usual" control condition. Secondary outcomes included assessments of cardiorespiratory fitness (20-m shuttle run), cognitive performance (executive functions, relational memory and processing speed) and mental health (Strength and Difficulties Questionnaire and self-esteem measures). The primary intention-to-treat (ITT) analysis used linear models and structural equation models with cluster-robust standard errors to test for intervention effects. A complier-average causal effect (CACE) was estimated using a two-stage least squares procedure.ResultsThe HIIT-style VPA intervention did not significantly improve cardiorespiratory fitness, cognitive performance (executive functions, relational memory or processed speed), or mental health (all p > 0.05). Subgroup analyses showed no significant moderation of intervention effects by sex, socioeconomic status or baseline fitness levels. Changes in cardiorespiratory fitness were not significantly related to changes in cognitive or mental health outcomes. The trial was marked by high drop-out and low intervention compliance. Findings from the CACE analysis were in line with those from the ITT analysis.ConclusionThe one-academic year HIIT-style VPA intervention delivered during regular school PE did not significantly improve fitness, cognitive performance or mental health, but these findings should be interpreted with caution given low implementation fidelity and high drop-out. Well-controlled, large-scale, school-based trials that examine the effectiveness of HIIT-style interventions to enhance cognitive and mental health outcomes are warranted.Trial registrationISRCTN registry, 15,730,512 . Trial protocol and analysis plan for primary outcome prospectively registered on 30th March 2017. ClinicalTrials.gov , NCT03286725 . Secondary measures (focus of current manuscript) retrospectively registered on 18 September 2017

Increased risk of type I errors in cluster randomised trials with small or medium numbers of clusters: a review, reanalysis,and simulation study

Background: Cluster randomised trials (CRTs) are commonly analysed using mixed-effects models or generalised estimating equations (GEEs). However, these analyses do not always perform well with the small number of clusters typical of most CRTs. They can lead to increased risk of a type I error (finding a statistically significant treatment effect when it does not exist) if appropriate corrections are not used. Methods: We conducted a small simulation study to evaluate the impact of using small-sample corrections for mixed-effects models or GEEs in CRTs with a small number of clusters. We then reanalysed data from TRIGGER, a CRT with six clusters, to determine the effect of using an inappropriate analysis method in practice. Finally, we reviewed 100 CRTs previously identified by a search on PubMed in order to assess whether trials were using appropriate methods of analysis. Trials were classified as at risk of an increased type I error rate if they did not report using an analysis method which accounted for clustering, or if they had fewer than 40 clusters and performed an individual-level analysis without reporting the use of an appropriate small-sample correction. Results: Our simulation study found that using mixed-effects models or GEEs without an appropriate correction led to inflated type I error rates, even for as many as 70 clusters. Conversely, using small-sample corrections provided correct type I error rates across all scenarios. Reanalysis of the TRIGGER trial found that inappropriate methods of analysis gave much smaller P values (P ≤ 0.01) than appropriate methods (P = 0.04–0.15). In our review, of the 99 trials that reported the number of clusters, 64 (65 %) were at risk of an increased type I error rate; 14 trials did not report using an analysis method which accounted for clustering, and 50 trials with fewer than 40 clusters performed an individual-level analysis without reporting the use of an appropriate correction. Conclusions: CRTs with a small or medium number of clusters are at risk of an inflated type I error rate unless appropriate analysis methods are used. Investigators should consider using small-sample corrections with mixed-effects models or GEEs to ensure valid results. Abbreviations: CRT, Cluster randomised trial; CI, Confidence interval; GEE, Generalised estimating equations; TRIGGER, Trial in Gastrointestinal Transfusio

Living risk prediction algorithm (QCOVID) for risk of hospital admission and mortality from coronavirus 19 in adults: national derivation and validation cohort study.

OBJECTIVE: To derive and validate a risk prediction algorithm to estimate hospital admission and mortality outcomes from coronavirus disease 2019 (covid-19) in adults. DESIGN: Population based cohort study. SETTING AND PARTICIPANTS: QResearch database, comprising 1205 general practices in England with linkage to covid-19 test results, Hospital Episode Statistics, and death registry data. 6.08 million adults aged 19-100 years were included in the derivation dataset and 2.17 million in the validation dataset. The derivation and first validation cohort period was 24 January 2020 to 30 April 2020. The second temporal validation cohort covered the period 1 May 2020 to 30 June 2020. MAIN OUTCOME MEASURES: The primary outcome was time to death from covid-19, defined as death due to confirmed or suspected covid-19 as per the death certification or death occurring in a person with confirmed severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in the period 24 January to 30 April 2020. The secondary outcome was time to hospital admission with confirmed SARS-CoV-2 infection. Models were fitted in the derivation cohort to derive risk equations using a range of predictor variables. Performance, including measures of discrimination and calibration, was evaluated in each validation time period. RESULTS: 4384 deaths from covid-19 occurred in the derivation cohort during follow-up and 1722 in the first validation cohort period and 621 in the second validation cohort period. The final risk algorithms included age, ethnicity, deprivation, body mass index, and a range of comorbidities. The algorithm had good calibration in the first validation cohort. For deaths from covid-19 in men, it explained 73.1% (95% confidence interval 71.9% to 74.3%) of the variation in time to death (R2); the D statistic was 3.37 (95% confidence interval 3.27 to 3.47), and Harrell's C was 0.928 (0.919 to 0.938). Similar results were obtained for women, for both outcomes, and in both time periods. In the top 5% of patients with the highest predicted risks of death, the sensitivity for identifying deaths within 97 days was 75.7%. People in the top 20% of predicted risk of death accounted for 94% of all deaths from covid-19. CONCLUSION: The QCOVID population based risk algorithm performed well, showing very high levels of discrimination for deaths and hospital admissions due to covid-19. The absolute risks presented, however, will change over time in line with the prevailing SARS-C0V-2 infection rate and the extent of social distancing measures in place, so they should be interpreted with caution. The model can be recalibrated for different time periods, however, and has the potential to be dynamically updated as the pandemic evolves