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Background The StratosPHere 2 trial will evaluate the efficacy of hydroxychloroquine and phenylbutyrate in pulmonary arterial hypertension caused by mutations in BMPR2 by focussing on the novel biomarker and other endpoints including safety. Study design StratosPHere 2 is a three armed, placebo-controlled, phase 2 trial with two strata based on the mutation groups. It is response adaptive where the allocation of treatments follows a Bayesian response-adaptive randomisation algorithm. An expected number of 20 patients will be randomised in each stratum to one of the three arms containing hydroxychloroquine, phenylbutyrate and placebo. The primary outcome is a novel endpoint considering the change in the bone morphogenetic receptor type 2 (BMPR2). Method The final primary analysis on the efficacy of each active treatment against control is assessed using a one-sided nonparametric Wilcoxon test computed on the continuous biomarker data collected up to 8 weeks from the start of treatment. Discussion This manuscript presents the key elements of the StratosPHere 2 implementation and statistical analysis plan. This is submitted to the journal before the first interim analysis to preserve the scientific integrity under a response-adaptive design framework. The StratosPHere 2 trial closely follows published guidelines for the content of Statistical Analysis Plans in clinical trials. Trial registration The ISRCTN Registry ISRCTN10304915 (22/09/2023)

Background Pulmonary arterial hypertension is a life-threatening progressive disorder characterised by high blood pressure (hypertension) in the arteries of the lungs (pulmonary artery). Although treatable, there is no known cure for this rare disorder, and its exact cause is unknown. Mutations in the bone morphogenetic protein receptor type-2 (BMPR2) are the most common genetic cause of familial pulmonary arterial hypertension. This study represents the first-ever trial of treatments aimed at directly rescuing the BMPR2 pathway, repurposing two drugs that have shown promise at restoring levels of BMPR2 signalling: hydroxychloroquine and phenylbutyrate. Methods This three-armed phase II precision medicine study will investigate BMPR2 target engagement and explore the efficacy of two repurposed therapies in pulmonary arterial hypertension patients with BMPR2 mutations. Patients will be stratified based on two BMPR2 mutation classes: missense and haploinsufficient mutations. Eligible subjects will be randomised to one of the three arms (two active therapy arms and a placebo arm, all plus standard of care) following a Bayesian response-adaptive design implemented independently in each stratum and updated in response to a novel panel of primary biomarkers designed to assess biological modification of the disease. Discussion The results of this trial will provide the first randomised evidence of the efficacy of these therapies to rescue BMPR2 function and will efficiently explore the potential for a differential response of these therapies per mutation class to address causes rather than consequences of this rare disease. Trial registration The study has been registered with ISRCTN (ISRCTN10304915, 22/09/2023).

Variability in case severity and in the range of symptoms experienced has been apparent from the earliest months of the COVID-19 pandemic. From a clinical perspective, symptom variability might indicate various routes/mechanisms by which infection leads to disease, with different routes requiring potentially different treatment approaches. For public health and control of transmission, symptoms in community cases were the prompt upon which action such as PCR testing and isolation was taken. However, interpreting symptoms presents challenges, for instance, in balancing the sensitivity and specificity of individual symptoms with the need to maximise case finding, whilst managing demand for limited resources such as testing. For both clinical and transmission control reasons, we require an approach that allows for the possibility of distinct symptom phenotypes, rather than assuming variability along a single dimension. Here we address this problem by bringing together four large and diverse datasets deriving from routine testing, a population-representative household survey and participatory smartphone surveillance in the United Kingdom. Through the use of cutting-edge unsupervised classification techniques from statistics and machine learning, we characterise symptom phenotypes among symptomatic SARS-CoV-2 PCR-positive community cases. We first analyse each dataset in isolation and across age bands, before using methods that allow us to compare multiple datasets. While we observe separation due to the total number of symptoms experienced by cases, we also see a separation of symptoms into gastrointestinal, respiratory and other types, and different symptom co-occurrence patterns at the extremes of age. In this way, we are able to demonstrate the deep structure of symptoms of COVID-19 without usual biases due to study design. This is expected to have implications for the identification and management of community SARS-CoV-2 cases and could be further applied to symptom-based management of other diseases and syndromes.

It is well-known that mood and pain interact with each other, however individual-level variability in this relationship has been less well quantified than overall associations between low mood and pain. Here, we leverage the possibilities presented by mobile health data, in particular the “Cloudy with a Chance of Pain” study, which collected longitudinal data from the residents of the UK with chronic pain conditions. Participants used an App to record self-reported measures of factors including mood, pain and sleep quality. The richness of these data allows us to perform model-based clustering of the data as a mixture of Markov processes. Through this analysis we discover four endotypes with distinct patterns of co-evolution of mood and pain over time. The differences between endotypes are sufficiently large to play a role in clinical hypothesis generation for personalised treatments of comorbid pain and low mood.

Health is an integral part of human well being, and a holistic perspective on the same involves physical, mental and social factors (World Health Organization et al., 1948). However, “health” itself is a complex concept where many aspects play a role in building a healthy person and meanings of the same can vary across individuals, as per the capability of tackling an illness (Leonardi, 2018). Most of us are aware of physical illness and associated concerns but mental health often gets neglected in the larger discourse on health and wellbeing, and it remains important to remember the adage “no health without mental health” as used used by e.g. Prince et al. (2007) in the context of overall health. Even though recently there has been an increase in awareness towards mental health, the stigma around it continues to exist (Bharadwaj et al., 2017; Gold et al., 2016). Additionally this social stigma around mental health as well as a self-perceived notion of underestimating an issue (Andrade et al., 2014) often leads to lack of treatments. Proper treatments or diagnoses are still unavailable or inaccessible for many individuals (Moreno et al., 2020; Camm-Crosbie et al., 2019; MacDonald et al., 2018). In 2019, the World Health Organisation (WHO) estimated 970 million people in the world to be living with a mental disorder (Organization, 2022). Keeping all of this in mind, it needs to be reiterated that mental ailments are widespread and can affect anyone, just like a physical illness. There are many aspects of this topic that need to be dealt with carefully, but in this thesis, the emphasis has been on finding mental health traits using digital health records and how it can facilitate the process of developing treatments for the same.Mental health can be affected by numerous factors, with examples being: physical health problems, socio-economic conditions, nutrition, genetics, and the environment around us (Kola et al., 2021; Adan et al., 2019; Bhugra et al., 2013; Tew et al., 2012; Rutter, 2005; Morris, 2003; Tsuang, 2000). Even though identifying causes remains an extremely challenging problem, symptoms associated with a decline in mental health can aid diagnoses. It can be found that withdrawal in life, many times shown by lack of motivation, is quite prominent amongst those severely affected by mental affliction and can serve as a vital warning. But, a more comprehensive understanding of mental health requires an interdisciplinary approach (Fried, 2021) which can benefit from insights from various fields including neurology, psychology, sociology, biology etc. and, importantly in the current context, mathematical sciences. The advent of COVID-19 presented a global health crisis which affected lives across the world quite disproportionately (Gibson et al., 2021) and resulted in further widening of inequalities. A rise in mental health problems, as an associated result of worsening physical health or in this case, a physical health calamity, has become a major concern (Vigo et al., 2020) and may have long-term implications (Bourmistrova et al., 2022; Kola et al., 2021). The motivation behind this thesis was to help quantify mental health, model it and see underlying behaviour using mathematical, statistical and computational tools as these would help in comparing and providing better tools for understanding the differences and commonalities in behaviour patterns.While there are pros and cons to the advancement of technology and electronic health (eHealth) (Vitacca et al., 2009), in this context, it has provided us with digital health tools which have facilitated the collection of information on health. Mobile health (mHealth) is potentially revolutionary and opening up doors to opportunities for exploring research in healthcare (Fiordelli et al., 2013). Especially in the sphere of mental health, mhealth helps in overcoming many barriers related to accessibility (Price et al., 2014). Such apps or platforms can be beneficial to those who are unable or are reluctant to be available for an in person appointment, as well as those who want to keep their information completely private or anonymous. This is particularly true in the context of mental health, where many prefer not to be identified while reporting their issues as a result of the stigma attached, although it is difficult to tell if a mHealth based solution or therapy is indeed better than an in-person one (Olff, 2015) but nevertheless, these apps can be useful as they maintain the confidentiality of the patient.

It is well-known that mood and pain interact with each other, however individual-level variability in this relationship has been less well quantified than overall associations between low mood and pain. Here, we leverage the possibilities presented by mobile health data, in particular the “Cloudy with a Chance of Pain” study, which collected longitudinal data from the residents of the UK with chronic pain conditions. Participants used an App to record self-reported measures of factors including mood, pain and sleep quality. The richness of these data allows us to perform model-based clustering of the data as a mixture of Markov processes. Through this analysis we discover four endotypes with distinct patterns of co-evolution of mood and pain over time. The differences between endotypes are sufficiently large to play a role in clinical hypothesis generation for personalised treatments of comorbid pain and low mood. Author summary Mood and pain are known to interact, and a mobile-phone application recorded information on the variations of mood and pain amongst people in the UK. Using this data, we observed that people have a general tendency of feeling the same mood and pain the next day. Studying further, we were able to separate the people into four groups- three of which were quite different from the general pattern of mood pain. The additional patterns we saw were 1) their mood and pain deteriorating the next day, 2) their mood and pain improving the next day and 3) mood is improving but pain deteriorates the next day. These additional characteristics tell us that there is no definite way that mood and pain are associated for everyone, and personalised treatment to tackle challenges in mood and pain can deliver better results.

It is well-known that mood and pain interact with each other, however individual-level variability in this relationship has been less well quantified than overall associations between low mood and pain. Here, we leverage the possibilities presented by mobile health data, in particular the \"Cloudy with a Chance of Pain\" study, which collected longitudinal data from the residents of the UK with chronic pain conditions. Participants used an App to record self-reported measures of factors including mood, pain and sleep quality. The richness of these data allows us to perform model-based clustering of the data as a mixture of Markov processes. Through this analysis we discover four endotypes with distinct patterns of co-evolution of mood and pain over time. The differences between endotypes are sufficiently large to play a role in clinical hypothesis generation for personalised treatments of comorbid pain and low mood.

Although response-adaptive randomisation (RAR) has gained substantial attention in the literature, it still has limited use in clinical trials. Amongst other reasons, the implementation of RAR in the real world raises important practical questions, often neglected. Motivated by an innovative phase-II stratified RAR trial, this paper addresses two challenges: (1) How to ensure that RAR allocations are both desirable and faithful to target probabilities, even in small samples? and (2) What adaptations to trigger after interim analyses in the presence of missing data? We propose a Mapping strategy that discretises the randomisation probabilities into a vector of allocation ratios, resulting in improved frequentist errors. Under the implementation of Mapping, we analyse the impact of missing data on operating characteristics by examining selected scenarios. Finally, we discuss additional concerns including: pooling data across trial strata, analysing the level of blinding in the trial, and reporting safety results.

Through the use of cutting-edge unsupervised classification techniques from statistics and machine learning, we characterise symptom phenotypes among symptomatic SARS-CoV-2 PCR-positive community cases. We first analyse each dataset in isolation and across age bands, before using methods that allow us to compare multiple datasets. While we observe separation due to the total number of symptoms experienced by cases, we also see a separation of symptoms into gastrointestinal, respiratory and other types, and different symptom co-occurrence patterns at the extremes of age. In this way, we are able to demonstrate the deep structure of symptoms of COVID-19 without usual biases due to study design. This is expected to have implications for the identification and management of community SARS-CoV-2 cases and could be further applied to symptom-based management of other diseases and syndromes.

During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. We illustrate these methods by applying them to the COVID-19 pandemic.