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In this paper, the time dependent carrier-borne epidemic model defined by Weiss in 1965 has been adopted into a Bayesian framework for the estimation of its parameters. A complete methodological structure has been proposed for estimating the relative infection rate and probability of survival of k out of m susceptibles after time t from the start of the epidemic. The methodology has been proposed assuming a single carrier to simplify the study of the behavioral validity of the fitted Bayesian model with respect to time and relative infection rate. Further, the proposed model has been implemented on two real data sets- the typhoid epidemic data from Zermatt in Switzerland and the Covid-19 epidemic data from Kerala in India. Results show that the proposed methodology produces reliable predictions which are consistent with those of the maximum likelihood estimates and with expected epidemiological patterns.

Introduction: Advances in human immunodeficiency virus (HIV) treatment have led to greater survival rates and have brought about a shift in the burden of disease from mortality to morbidity. The main purpose of this study is to estimate the Disability Adjusted Life Years (DALYs) of HIV infected patients associated with different modes of transmission. Methods: Non-parametric Kaplan-Meier estimate has been utilised to develop survival function, and the mean residual life model has been utilised to estimate the life expectancy of patients alive at the end of the study. The impact of factors such as age, sex, hepatitis B and syphilis on life expectancy has also been assessed by fitting a proportional mean residual life model. DALYs have been calculated based on the results of both models. Results: Retrospective time to event data of HIV patients undergoing Antiretroviral Therapy (ART) in Dr Ram Manohar Lohia Hospital, New Delhi, India has been utilised to illustrate the modelling technique. The study suggests that in total, 42300.15 DALYs were lost which includes 39765.10 years of life lost due to premature death and 2535.05 years of life lived with disability. When the covariates were taken into consideration, 47592.14 DALYs were found to have been lost with an average of 17.64 DALYs lost per patient. Conclusion: Our results suggest that the high-risk groups such as homosexuals and parent to child transmission are a major cause of concern, which are in accordance with the existing national policies. Also, we would suggest that gender-based and age-based policies should be incorporated to reduce the burden of disease.

The breeding population of birds are dynamic and are affected by multiple factors including climate and local environmental conditions. However, often to understand such relations requires long-term data modelling. Such long-term population data is either lacking or has data gaps. This study demonstrates the use of Multiple Imputation Chained Equation (MICE) to overcome the problem of missing data population census. This is also the first comprehensive study, modelling the 36-year (1980-2015) long-term breeding population data of a near-threatened bird, Painted Stork, from Keoladeo National Park, India. It tests the effect of local water availability, i.e., water released to the park, and regional rainfall, i.e, climatic condition, on the breeding population using Generalised Additive Model (GAM). Both imputation and observed data series-based GAM models identified the local water availability as the most important factor influencing the breeding population of Painted Stork. More than 80% population decline was observed, despite a slight increase in the rainfall at regional scale, suggesting local hydrological conditions are limiting to the breeding population and not the climate. According to the visual assessment of partial plot of GAM, minimum 200-300 million cubic feet of water is needed each nesting season to ensure sustenance of breeding population. Post-1989, the breeding population was unable to match the long-term mean (~726) except in 1992, 1995, and 1996. The maximum decline was observed between 2000-2009, a decade of frequent droughts. The breeding population was stable until the end of this study, but it was far below the long term mean.

Estimation of Quality Adjusted Life Years (QALYs) is pivotal towards economic evaluation and cost-effectiveness analysis of medical interventions. Most of the methods developed till date for calculating QALYs are based on multi-state structures where fixed utility values are assigned to each disease state and total QALYs are calculated on the basis of total lengths of stay in each state. In this article, we have presented a new proxy approach to define utility as a function of risk factors, which can be used to calculate QALY without defining discrete disease states. Retrospective survival data of HIV/ AIDS patients undergoing treatment at the Antiretroviral Therapy (ART) center of Ram Manohar Lohia hospital in New Delhi has been used to demonstrate implementation of the proposed methodology. Joint modelling, with a mixed effect longitudinal sub-model for CD4 count and a Cox proportional hazard survival sub-model with time dependent covariates, has been used to estimate risks associated with different factors and covariates. Using the proxy utilities, QALYs have been calculated for each individual for their lifetime time horizon, defined as the time since their registration in the ART till death or till their age reach average life expectancy of HIV/ AIDS patients in India. QALY results are consistent with findings of conventional cost-effectiveness studies on ART for HIV/ AIDS patients in India.

In the absence of sufficient testing capacity for COVID-19, a substantial number of infecteds are expected to remain undetected, and hence, are not quarantined. This, in turn, defeats the whole purpose of non-medical containment measures, like quarantine, lockdown, travel ban, physical distancingetc., by keeping the average reproduction rate above 1. To stress upon the importance of extensive random testing for breaking the chains of transmissions, we have formulated a detailed framework for carrying out cost-effectiveness analysis (CEA) of extensive random testing in comparison to targeted testing (the existing testing policy followed by most countries). This framework can be easily extended for CEA of any other non-medical or even medical interventions for containing epidemics.We have developed a new version of the basic susceptible-infected-removed (SIR) compartmental model, called the susceptible-infected (quarantined/ free) - recovered-deceased [SI(Q/F)RD] model, to incorporate the impact of undetected cases on the transmission dynamics of the epidemic. Further, we have presented a Dirichlet-Beta state-space formulation of the SI(Q/F)RD model for the estimation of its parameters using posterior realizations from Gibbs sampling procedure. As an application, the proposed methodology is implemented to forecast the COVID-19 transmission in California and Florida, and further carry out CEA of extensive random testing over targeted testing.HighlightsEstimated values of excess deaths associated with COVID-19 are used to account for underreporting, and for calibrating data to obtain actual counts of cases.A new flexible version of SIR compartmental model, called SI(Q/F)RD, is introduced to facilitate in the CEA exercise.Dirichlet-Beta state-space formulation of the SI(Q/F)RD model is used to predict the transmission dynamics of the epidemic.CEA is conducted in terms of outcome (reduction in infections and deaths) and total cost of tests.Proposed methodology is applied on the data of California and Florida.

Estimation of Quality Adjusted Life Years (QALYs) is pivotal towards cost-effectiveness analysis (CEA) of medical interventions. Most of the CEA studies employ multi-state decision analytic modelling approach, where fixed utility values are assigned to each disease state and total QALYs are calculated on the basis of total lengths of stay in each state.In this paper, we have formulated a new approach to CEA by defining utility as a function of a longitudinal covariate which is significantly associated with disease progression. Association parameter between the longitudinal covariate and survival times is estimated through joint modelling of the longitudinal linear mixed effects model and the Weibull accelerated failure time survival model. Metropolis-Hastings algorithm and Monte Carlo integration are used to predict expected survival times of each censored case using the joint model. Fitted longitudinal model is further used to project values of the longitudinal covariate at all time points for each patient. Utility values calculated using these projected covariate values are used to evaluate QALYs for each patient.Retrospective survival data of HIV/ AIDS patients undergoing treatment at the Antiretroviral Therapy centre of Ram Manohar Lohia hospital in New Delhi is used to demonstrate the implementation of the proposed methodology. A simulation exercise is also carried out to gauge the predictive capability of the joint model in projecting the values of the longitudinal covariate.The proposed dynamic approach to calculate QALY provides a promising alternative to the popular multi-state decision analytic modelling approach, especially when the standard utility values for different stages of the concerned disease are not available.

ObjectivesOur primary objective is to predict the dynamics of COVID-19 epidemic in India while adjusting for the effects of various progressively implemented containment measures. Apart from forecasting the major turning points and parameters associated with the epidemic, we intend to provide an epidemiological assessment of the impact of these containment measures in India.MethodsWe propose a method based on time-series SIR model to estimate time-dependent modifiers for transmission rate of the infection. These modifiers are used in state-space SIR model to estimate reproduction numberR0, expected total incidence, and to forecast the daily prevalence till the end of the epidemic. We consider four different scenarios, two based on current developments and two based on hypothetical situations for the purpose of comparison.ResultsAssuming gradual relaxation in lockdown post 17 May 2020, we expect the prevalence of infecteds to cross 9 million, with at least 1 million severe cases, around the end of October 2020. For the same case, estimates ofR0for the phases no-intervention, partial-lockdown and lockdown are 4.46 (7.1), 1.47 (2.33), and 0.817 (1.29) respectively, assuming 14-day (24-day) infectious period.ConclusionsEstimated modifiers give consistent estimates of unadjustedR0across different scenarios, demonstrating precision. Results corroborate the effectiveness of lockdown measures in substantially reducingR0. Also, predictions are highly sensitive towards estimate of infectious period.