Optimal designs for tumor regrowth models

Most growth curves can only be used to model the tumor growth under no intervention. To model the growth curves for treated tumor, both the growth delay due to the treatment and the regrowth of the tumor after the treatment need to be taken into account. In this paper, we consider two tumor regrowth models and determine the locally D- and c-optimal designs for these models. We then show that the locally D- and c-optimal designs are minimally supported. We also consider two equally spaced designs as alternative designs and evaluate their efficiencies.     

On some mixture models based on the Birnbaum-Saunders distribution and associated inference

In this paper, we consider three different mixture models based on the Birnbaum-Saunders (BS) distribution, viz., (1) mixture of two different BS distributions, (2) mixture of a BS distribution and a length-biased version of another BS distribution, and (3) mixture of a BS distribution and its length-biased version. For all these models, we study their characteristics including the shape of their density and hazard rate functions. For the maximum likelihood estimation of the model parameters, we use the EM algorithm. For the purpose of illustration, we analyze two data sets related to enzyme and depressive condition problems. In the case of the enzyme data, it is shown that Model 1 provides the best fit, while for the depressive condition data, it is shown all three models fit well with Model 3 providing the best fit.     

On simultaneous closeness probabilities of order statistics from odd sample sizes to the population median

In this note, we present alternative derivations for the probability that an individual order statistic is closest to the target parameter among all order statistics from a complete random sample. This approach is simpler than the geometric arguments used earlier. We also provide a simple direct proof for the symmetry property of the simultaneous closeness probabilities among order statistics for the estimation of percentiles from a symmetric family. Finally, we offer an alternative simpler proof for the result that sample medians from larger odd sample sizes are Pitman closer to the population median than sample medians from smaller odd sample sizes.     

Unanticipated Educational Consequences of a Positive Parent‐Child Relationship

If today there exists a single transcendent idea about the family‐school connection, it is that a positive parent‐child relationship improves children's chances of succeeding in school. However, using data from the Texas Higher Education Opportunity Project (N = 5,836), we demonstrate that, although positive parent‐child relations are associated with better academic achievement in high school, they also are associated with an increased desire to live at home during college, which in turn decreases students' chances of enrolling in a 4‐year college. Furthermore, we replicated some of these associations using the National Longitudinal Study of Adolescent Health (N = 10,120), demonstrating that positive family dynamics can influence educational outcomes in potentially divergent and unanticipated directions.     

Determinants of Social Expenditure in Sri Lanka

The study examines the determinants of social expenditure in Sri Lanka for the period 1970–2010. The data are from a new data set assembled by the authors. The social spending data are collected from the Central Bank of Sri Lanka on education, health, and also on welfare spending. The study explains the determinants of social spending considering the demand‐side and the supply‐side driving forces and finds that inequality issues have been a major concern of social policy in Sri Lanka. Similarly, this study implies the influence of political behavior to satisfy voters as explained by the fiscal illusion theory. The globalization is not significant for social expenditure as commonly assumed in developed countries. Even the consequences of the self‐interested behavior of bureaucrats are not evident in the Sri Lankan welfare sector.     

Extending the Mann–Whitney–Wilcoxon rank sum test to longitudinal regression analysis

Outliers are commonly observed in psychosocial research, generally resulting in biased estimates when comparing group differences using popular mean-based models such as the analysis of variance model. Rank-based methods such as the popular Mann–Whitney–Wilcoxon (MWW) rank sum test are more effective to address such outliers. However, available methods for inference are limited to cross-sectional data and cannot be applied to longitudinal studies under missing data. In this paper, we propose a generalized MWW test for comparing multiple groups with covariates within a longitudinal data setting, by utilizing the functional response models. Inference is based on a class of U-statistics-based weighted generalized estimating equations, providing consistent and asymptotically normal estimates not only under complete but missing data as well. The proposed approach is illustrated with both real and simulated study data.     

Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence

The Rényi entropy is a generalisation of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g. consistency, asymptotic normality, and Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g. ε-keys in time series databases and distribution identification problems for dependent samples).     

The k-sample problem in a multi-state model and testing transition probability matrices

The choice of multi-state models is natural in analysis of survival data, e.g., when the subjects in a study pass through different states like ‘healthy’, ‘in a state of remission’, ‘relapse’ or ‘dead’ in a health related quality of life study. Competing risks is another common instance of the use of multi-state models. Statistical inference for such event history data can be carried out by assuming a stochastic process model. Under such a setting, comparison of the event history data generated by two different treatments calls for testing equality of the corresponding transition probability matrices. The present paper proposes solution to this class of problems by assuming a non-homogeneous Markov process to describe the transitions among the health states. A class of test statistics are derived for comparison of \(k\) treatments by using a ‘weight process’. This class, in particular, yields generalisations of the log-rank, Gehan, Peto–Peto and Harrington–Fleming tests. For an intrinsic comparison of the treatments, the ‘leave-one-out’ jackknife method is employed for identifying influential observations. The proposed methods are then used to develop the Kolmogorov–Smirnov type supremum tests corresponding to the various extended tests. To demonstrate the usefulness of the test procedures developed, a simulation study was carried out and an application to the Trial V data provided by International Breast Cancer Study Group is discussed.     

Using expected values to simplify decision making under uncertainty

A simulation study examines the impact of a simplification strategy that replaces distributional attribute evaluations with their expected values and uses those expectations in an additive value model. Several alternate simplified forms and approximation approaches are investigated, with results showing that in general the simplified models are able to provide acceptable performance that is fairly robust to a variety of internal and external environmental changes, including changes to the distributional forms of the attribute evaluations, errors in the assessment of the expected values, and problem size. Certain of the simplified models are shown to be highly sensitive to the form of the underlying preference functions, and in particular to extreme non-linearity in these preferences.