Suchergebnisse

This paper provides a test procedure for the problem of testing Bernoulli success probability in the case of costly trials when an inverse sampling is carried out. The proposed test is based on a two population adaptive sampling scheme used in clinical trials. Some exact and asymptotic results related to the test are studied. The proposed procedure is applicable where the alternatives are not too far from the null hypothetical value.

During the last three decades, integer‐valued autoregressive process of order p [or INAR(p)] based on different operators have been proposed as a natural, intuitive and maybe efficient model for integer‐valued time‐series data. However, this literature is surprisingly mute on the usefulness of the standard AR(p) process, which is otherwise meant for continuous‐valued time‐series data. In this paper, we attempt to explore the usefulness of the standard AR(p) model for obtaining coherent forecasting from integer‐valued time series. First, some advantages of this standard Box–Jenkins's type AR(p) process are discussed. We then carry out our some simulation experiments, which show the adequacy of the proposed method over the available alternatives. Our simulation results indicate that even when samples are generated from INAR(p) process, Box–Jenkins's model performs as good as the INAR(p) processes especially with respect to mean forecast. Two real data sets have been employed to study the expediency of the standard AR(p) model for integer‐valued time‐series data.

Adaptive design is a popular concept in several clinical trials, especially in phase III trials. The idea is to allocate treatments to the entering patients according to the state of art of the present data, i.e., to allocate a larger number of patients to the better treatment. The present paper provides a Bayesian formulation of an adaptive allocation design for clinical trials that considers all the continuous responses along with the associated covariates for future allocation. Some Bayesian inferences followed by the allocation are discussed along with a Bayesian prediction for future allocation. The convergence of the allocation probabilities is also discussed along with some related logistics of the design.

Nonparametric two‐sample problems are extremely important for applications in different applied disciplines. We define a general MI based on the φ divergences and use its estimate to propose a new general class of nonparametric two sample tests for continuous distributions. We derive the asymptotic distribution of the estimates of φ‐divergence‐based MI (φDMI) under the assumption of independence in the hybrid setup of one binary and one continuous random variables. Additionally, for finite sample cases, we describe an algorithm for obtaining the bootstrap‐based critical value of our proposed two‐sample test based on the estimated φDMI. We demonstrate through extensive simulations that the proposed class of tests work exceptionally well in many situations and can detect differences where other two‐sample tests fail. Finally, we analyze an application of our proposed tests to assess a solution to information leakage in e‐passport data.

A randomized two‐stage adaptive design is proposed and studied for allocation of patients to treatments and comparison in a phase III clinical trial with survival time as treatment responses. We consider the possibility of several covariates in the design and analysis. Several exact and limiting properties of the design and the follow‐up inference are studied, both numerically and theoretically. The applicability of the proposed methodology is illustrated by using some real data.

Adaptive designs are sometimes used in a phase III clinical trial with the aim, of allocating a larger number of patients to the better treatment. In the present paper, we use some adaptive designs in a two‐treatment two‐period crossover design where the treatment responses are binary. We use some simple designs to choose between the possible treatment combinations AA, AB, BA or BB. The goal is to use the better treatment a larger proportion of times. We calculate the allocation proportions to the possible treatment combinations and their standard deviations. We also study related inferential problems. Related asymptotics are derived. The proposed procedure is compared with some possible competitors. Finally, we use real data to illustrate the applicability of our proposed design.

The problem of finding Effective Sample Size (ESS) in Phase II clinical trials where toxicity and efficacy are the two components of the treatment response vector is considered. In particular, one of the components is assumed to be binary and the other is assumed to be continuous. The case of binary safety and continuous efficacy is studied for different prior distributions under different set up. Theoretical expressions are obtained in various situations. The methods are evaluated and compared by simulation studies. The proposed method is then illustrated by using some real life data on a phase II vaccine trial for Covid‐19.

AbstractIn this article, we consider the problem of change‐point analysis for the count time series data through an integer‐valued autoregressive process of order 1 (INAR(1)) with time‐varying covariates. These types of features we observe in many real‐life scenarios especially in the COVID‐19 data sets, where the number of active cases over time starts falling and then again increases. In order to capture those features, we use Poisson INAR(1) process with a time‐varying smoothing covariate. By using such model, we can model both the components in the active cases at time‐point t namely, (i) number of nonrecovery cases from the previous time‐point and (ii) number of new cases at time‐point t. We study some theoretical properties of the proposed model along with forecasting. Some simulation studies are performed to study the effectiveness of the proposed method. Finally, we analyze two COVID‐19 data sets and compare our proposed model with another PINAR(1) process which has time‐varying covariate but no change‐point, to demonstrate the overall performance of our proposed model.

Background India has made substantial progress in improving child survival over the past few decades, but a comprehensive understanding of child mortality trends at disaggregated geographical levels is not available. We present a detailed analysis of subnational trends of child mortality to inform efforts aimed at meeting the India National Health Policy (NHP) and Sustainable Development Goal (SDG) targets for child mortality. Methods We assessed the under-5 mortality rate (U5MR) and neonatal mortality rate (NMR) from 2000 to 2017 in 5 × 5 km grids across India, and for the districts and states of India, using all accessible data from various sources including surveys with subnational geographical information. The 31 states and groups of union territories were categorised into three groups using their Socio-demographic Index (SDI) level, calculated as part of the Global Burden of Diseases, Injuries, and Risk Factors Study on the basis of per-capita income, mean education, and total fertility rate in women younger than 25 years. Inequality between districts within the states was assessed using the coefficient of variation. We projected U5MR and NMR for the states and districts up to 2025 and 2030 on the basis of the trends from 2000 to 2017 and compared these projections with the NHP 2025 and SDG 2030 targets for U5MR (23 deaths and 25 deaths per 1000 livebirths, respectively) and NMR (16 deaths and 12 deaths per 1000 livebirths, respectively). We assessed the causes of child death and the contribution of risk factors to child deaths at the state level. Findings U5MR in India decreased from 83·1 (95% uncertainty interval [UI] 76·7–90·1) in 2000 to 42·4 (36·5–50·0) per 1000 livebirths in 2017, and NMR from 38·0 (34·2–41·6) to 23·5 (20·1–27·8) per 1000 livebirths. U5MR varied 5·7 times between the states of India and 10·5 times between the 723 districts of India in 2017, whereas NMR varied 4·5 times and 8·0 times, respectively. In the low SDI states, 275 (88%) districts had a U5MR of 40 or more per 1000 livebirths and 291 (93%) districts had an NMR of 20 or more per 1000 livebirths in 2017. The annual rate of change from 2010 to 2017 varied among the districts from a 9·02% (95% UI 6·30–11·63) reduction to no significant change for U5MR and from an 8·05% (95% UI 5·34–10·74) reduction to no significant change for NMR. Inequality between districts within the states increased from 2000 to 2017 in 23 of the 31 states for U5MR and in 24 states for NMR, with the largest increases in Odisha and Assam among the low SDI states. If the trends observed up to 2017 were to continue, India would meet the SDG 2030 U5MR target but not the SDG 2030 NMR target or either of the NHP 2025 targets. To reach the SDG 2030 targets individually, 246 (34%) districts for U5MR and 430 (59%) districts for NMR would need a higher rate of improvement than they had up to 2017. For all major causes of under-5 death in India, the death rate decreased between 2000 and 2017, with the highest decline for infectious diseases, intermediate decline for neonatal disorders, and the smallest decline for congenital birth defects, although the magnitude of decline varied widely between the states. Child and maternal malnutrition was the predominant risk factor, to which 68·2% (65·8–70·7) of under-5 deaths and 83·0% (80·6–85·0) of neonatal deaths in India could be attributed in 2017; 10·8% (9·1–12·4) of under-5 deaths could be attributed to unsafe water and sanitation and 8·8% (7·0–10·3) to air pollution. Interpretation India has made gains in child survival, but there are substantial variations between the states in the magnitude and rate of decline in mortality, and even higher variations between the districts of India. Inequality between districts within states has increased for the majority of the states. The district-level trends presented here can provide crucial guidance for targeted efforts needed in India to reduce child mortality to meet the Indian and global child survival targets. District-level mortality trends along with state-level trends in causes of under-5 and neonatal death and the risk factors in this Article provide a comprehensive reference for further planning of child mortality reduction in India.