In this article, we introduce a long-term survival model in which the number of competing causes of the event of interest follows the zero-modified geometric (ZMG) distribution. Such distribution accommodates equidispersion, underdispersion, and overdispersion and captures deflation or inflation of zeros in the number of lesions or initiated cells after the treatment. The ZMG distribution is also an appropriate alternative for modeling clustered samples when the number of competing causes of the event of interest consists of two subpopulations, one containing only zeros (cure proportion), while in the other (noncure proportion) the number of competing causes of the event of interest follows a geometric distribution. The advantage of this assumption is that we can measure the cure proportion in the initiated cells. Furthermore, the proposed model can yield greater or lower cure proportion than that of the geometric distribution when modeling the number of competing causes. In this article, we present some statistical properties of the proposed model and use the maximum likelihood method to estimate the model parameters. We also conduct a Monte Carlo simulation study to evaluate the performance of the estimators. We present and discuss two applications using real-world medical data to assess the practical usefulness of the proposed model.

A new cure rate model with flexible competing causes with applications to melanoma and transplantation data.

Background The overall risk of reinfection in individuals who have previously had COVID-19 is unknown. To determine if prior SARS-CoV-2 infection (as determined by at least one positive commercial antibody test performed in a laboratory) in healthcare workers confers future immunity to reinfection, we are undertaking a large-scale prospective longitudinal cohort study of healthcare staff across the United Kingdom. Methods Population and Setting: staff members of healthcare organisations working in hospitals in the UK At recruitment, participants will have their serum tested for anti-SARS-CoV-2 at baseline and using these results will be initially allocated to either antibody positive or antibody negative cohorts. Participants will undergo antibody and viral RNA testing at 1-4 weekly intervals throughout the study period, and based on these results may move between cohorts. Any results from testing undertaken for other reasons (e.g. symptoms, contact tracing etc.) or prior to study entry will also be included. Individuals will complete enrolment and fortnightly questionnaires on exposures and symptoms. Follow-up will be for at least 12 months from study entry. Outcome The primary outcome of interest is a reinfection with SARS -CoV-2 during the study period. Secondary outcomes will include incidence and prevalence (both RNA and antibody) of SARS-CoV-2, viral genomics, viral culture, symptom history and antibody/neutralising antibody titres. Conclusion This large study will help us to understand the impact of the presence of antibodies on the risk of reinfection with SARS-CoV-2; the results will have substantial implications in terms of national and international policy, as well as for risk management of contacts of COVID-19 cases. Trial Registration IRAS ID 284460, HRA and Health and Care Research Wales approval granted 22 May 2020.

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SIREN protocol: Impact of detectable anti-SARS-CoV-2 on the subsequent incidence of COVID-19 in 100,000 healthcare workers: do antibody positive healthcare workers have less reinfection than antibody negative healthcare workers?

Introduction Understanding the effectiveness and durability of protection against SARS-CoV-2 infection conferred by previous infection and COVID-19 is essential to inform ongoing management of the pandemic. This study aims to determine whether prior SARS-CoV-2 infection or COVID-19 vaccination in healthcare workers protects against future infection. Methods and analysis This is a prospective cohort study design in staff members working in hospitals in the UK. At enrolment, participants are allocated into cohorts, positive or naïve, dependent on their prior SARS-CoV-2 infection status, as measured by standardised SARS-CoV-2 antibody testing on all baseline serum samples and previous SARS-CoV-2 test results. Participants undergo monthly antibody testing and fortnightly viral RNA testing during follow-up and based on these results may move between cohorts. Any results from testing undertaken for other reasons (eg, symptoms, contact tracing) or prior to study entry will also be captured. Individuals complete enrolment and fortnightly questionnaires on exposures, symptoms and vaccination. Follow-up is 12 months from study entry, with an option to extend follow-up to 24 months. The primary outcome of interest is infection with SARS-CoV-2 after previous SARS-CoV-2 infection or COVID-19 vaccination during the study period. Secondary outcomes include incidence and prevalence (both RNA and antibody) of SARS-CoV-2, viral genomics, viral culture, symptom history and antibody/neutralising antibody titres. Ethics and dissemination The study was approved by the Berkshire Research Ethics Committee, Health Research Authority (IRAS ID 284460, REC reference 20/SC/0230) on 22 May 2020; the vaccine amendment was approved on 12 January 2021. Participants gave informed consent before taking part in the study. Regular reports to national and international expert advisory groups and peer-reviewed publications ensure timely dissemination of findings to inform decision making. Trial registration number ISRCTN11041050.

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Impact of prior SARS-CoV-2 infection and COVID-19 vaccination on the subsequent incidence of COVID-19: a multicentre prospective cohort study among UK healthcare workers – the SIREN (Sarscov2 Immunity & REinfection EvaluatioN) study protocol

Bayesian survival model induced by frailty for lifetime with long‐term survivors

Survival models with a frailty term are presented as an extension of Cox’s proportional hazard model, in which a random effect is introduced in the hazard function in a multiplicative form with the...

Survival models induced by zero-modified power series discrete frailty: Application with a melanoma data set.

Frailty models provide a convenient way of modeling unobserved dependence and heterogeneity in survival data which, if not accounted for duly, would result incorrect inference. Gamma frailty models are commonly used for this purpose, but alternative continuous distributions are possible as well. However, with cure rate being present in survival data, these continuous distributions may not be appropriate since individuals with long-term survival times encompass zero frailty. So, we propose here a flexible probability distribution induced by a discrete frailty, and then present some special discrete probability distributions. We specifically focus on a special hyper-Poisson distribution and then develop the corresponding Bayesian simulation, influence diagnostics and an application to real dataset by means of intensive Markov chain Monte Carlo algorithm. These illustrate the usefulness of the proposed model as well as the inferential results developed here.

Daiane de Souza

Papers

Bayesian cure rate models induced by frailty in survival analysis.