Sankhya. Series B (2008)最新文献

The use of multi-auxiliary variables helps in increasing the precision of the estimators, especially when the population is rare and hidden clustered. In this article, four ratio-cum-product type estimators have been proposed using two auxiliary variables under adaptive cluster sampling (ACS) design. The expressions of the mean square error (MSE) of the proposed ratio-cum-product type estimators have been derived up to the first order of approximation and presented along with their efficiency conditions with respect to the estimators presented in this article. The efficiency of the proposed estimators over similar existing estimators have been assessed on four different populations two of which are of the daily spread of COVID-19 cases. The proposed estimators performed better than the estimators presented in this article on all four populations indicating their wide applicability and precision.

This paper uses the concept of the Mortality Concentration Curve (M-Curve), which plots the cumulative proportion of deaths against the corresponding cumulative proportion of the population (arranged in ascending order of age), and associated measures, to examine mortality experience in India. A feature of the M-curve is that it can be combined with an explicit value judgement (an aversion to early deaths) in order to make welfare-loss comparisons. Empirical comparisons over time, and between regions and genders, are made. Furthermore, in order to provide additional perspective, selective results for the UK and New Zealand are reported. It is also shown how the M-curve concept can be used to separate the contributions to overall mortality of changes over time (or differences between population groups) to the population age distribution and age-specific mortality rates.

We provide a methodology by which an epidemiologist may arrive at an optimal design for a survey whose goal is to estimate the disease burden in a population. For serosurveys with a given budget of C rupees, a specified set of tests with costs, sensitivities, and specificities, we show the existence of optimal designs in four different contexts, including the well known c-optimal design. Usefulness of the results are illustrated via numerical examples. Our results are applicable to a wide range of epidemiological surveys under the assumptions that the estimate's Fisher-information matrix satisfies a uniform positive definite criterion.

The paper intends to serve two objectives. First, it revisits the celebrated Fay-Herriot model, but with homoscedastic known error variance. The motivation comes from an analysis of count data, in the present case, COVID-19 fatality for all counties in Florida. The Poisson model seems appropriate here, as is typical for rare events. An empirical Bayes (EB) approach is taken for estimation. However, unlike the conventional conjugate gamma or the log-normal prior for the Poisson mean, here we make a square root transformation of the original Poisson data, along with square root transformation of the corresponding mean. Proper back transformation is used to infer about the original Poisson means. The square root transformation makes the normal approximation of the transformed data more justifiable with added homoscedasticity. We obtain exact analytical formulas for the bias and mean squared error of the proposed EB estimators. In addition to illustrating our method with the COVID-19 example, we also evaluate performance of our procedure with simulated data as well.

Clinical studies and trials on periodontal disease (PD) generate a large volume of data collected at various tooth locations of a subject. However, they present a number of statistical complexities. When our focus is on understanding the extent of extreme PD progression, standard analysis under a generalized linear mixed model framework with a symmetric (logit) link may be inappropriate, as the binary split (extreme disease versus not) maybe highly skewed. In addition, PD progression is often hypothesized to be spatially-referenced, i.e. proximal teeth may have a similar PD status than those that are distally located. Furthermore, a non-ignorable quantity of missing data is observed, and the missingness is non-random, as it informs the periodontal health status of the subject. In this paper, we address all the above concerns through a shared (spatial) latent factor model, where the latent factor jointly models the extreme binary responses via a generalized extreme value regression, and the non-randomly missing teeth via a probit regression. Our approach is Bayesian, and the inferential framework is powered by within-Gibbs Hamiltonian Monte Carlo techniques. Through simulation studies and application to a real dataset on PD, we demonstrate the potential advantages of our model in terms of model fit, and obtaining precise parameter estimates over alternatives that do not consider the aforementioned complexities.

In longitudinal studies, outcomes are measured repeatedly over time and it is common that not all the patients will be measured throughout the study. For example patients can be lost to follow-up (monotone missingness) or miss one or more visits (non-monotone missingness); hence there are missing outcomes. In the longitudinal setting, we often assume the missingness is related to the unobserved data, which is non-ignorable. Pattern-mixture models (PMM) analyze the joint distribution of outcome and patterns of missingness in longitudinal data with non-ignorable nonmonotone missingness. Existing methods employ PMM and impute the unobserved outcomes using the distribution of observed outcomes, conditioned on missing patterns. We extend the existing methods using latent class analysis (LCA) and a shared-parameter PMM. The LCA groups patterns of missingness with similar features and the shared-parameter PMM allows a subset of parameters to be different between latent classes when fitting a model. We also propose a method for imputation using distribution of observed data conditioning on latent class. Our model improves existing methods by accommodating data with small sample size. In a simulation study our estimator had smaller mean squared error than existing methods. Our methodology is applied to data from a phase II clinical trial that studies quality of life of patients with prostate cancer receiving radiation therapy.

A nonparametric test labelled 'Rao Spacing-frequencies test' is explored and developed for testing whether two circular samples come from the same population. Its exact distribution and performance relative to comparable tests such as the Wheeler-Watson test and the Dixon test in small samples, are discussed. Although this test statistic is shown to be asymptotically normal, as one would expect, this large sample distribution does not provide satisfactory approximations for small to moderate samples. Exact critical values for small samples are obtained and tables provided here, using combinatorial techniques, and asymptotic critical regions are assessed against these. For moderate sample sizes in-between i.e. when the samples are too large making combinatorial techniques computationally prohibitive but yet asymptotic regions do not provide a good approximation, we provide a simple Monte Carlo procedure that gives very accurate critical values. As is well-known, the large number of usual rank-based tests are not applicable in the context of circular data since the values of such ranks depend on the arbitrary choice of origin and the sense of rotation used (clockwise or anti-clockwise). Tests that are invariant under the group of rotations, depend on the data through the so-called 'spacing frequencies', the frequencies of one sample that fall in between the spacings (or gaps) made by the other. The Wheeler-Watson, Dixon, and the proposed Rao tests are of this form and are explicitly useful for circular data, but they also have the added advantage of being valid and useful for comparing any two samples on the real line. Our study and simulations establish the 'Rao spacing-frequencies test' as a desirable, and indeed preferable test in a wide variety of contexts for comparing two circular samples, and as a viable competitor even for data on the real line. Computational help for implementing any of these tests, is made available online "TwoCircles" R package and is part of this paper.

Social distancing and stay-at-home are among the few measures that are known to be effective in checking the spread of a pandemic such as COVID-19 in a given population. The patterns of dependency between such measures and their effects on disease incidence may vary dynamically and across different populations. We described a new computational framework to measure and compare the temporal relationships between human mobility and new cases of COVID-19 across more than 150 cities of the United States with relatively high incidence of the disease. We used a novel application of Optimal Transport for computing the distance between the normalized patterns induced by bivariate time series for each pair of cities. Thus, we identified 10 clusters of cities with similar temporal dependencies, and computed the Wasserstein barycenter to describe the overall dynamic pattern for each cluster. Finally, we used city-specific socioeconomic covariates to analyze the composition of each cluster.

Magnitude magnetic resonance (MR) images are noise-contaminated measurements of the true signal, and it is important to assess the noise in many applications. A recently introduced approach models the magnitude MR datum at each voxel in terms of a mixture of upto one Rayleigh and an a priori unspecified number of Rice components, all with a common noise parameter. The Expectation-Maximization (EM) algorithm was developed for parameter estimation, with the mixing component membership of each voxel as the missing observation. This paper revisits the EM algorithm by introducing more missing observations into the estimation problem such that the complete (observed and missing parts) dataset can be modeled in terms of a regular exponential family. Both the EM algorithm and variance estimation are then fairly straightforward without any need for potentially unstable numerical optimization methods. Compared to local neighborhood- and wavelet-based noise-parameter estimation methods, the new EM-based approach is seen to perform well not only on simulation datasets but also on physical phantom and clinical imaging data.