Recurrence relations for moments of progressively censored order statistics from logistic distribution with applications to inference

In this paper, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a logistic distribution. The use of these relations in a systematic manner allows us to compute all the means, variances and covariances of progressively Type-II right censored order statistics from the logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R₁,…,R_m). The results established here generalize the corresponding results for the usual order statistics due to [Shah, 1966] and [Shah, 1970]. These moments are then utilized to derive best linear unbiased estimators of the location and scale parameters of the logistic distribution. A comparison of these estimators with the maximum likelihood estimations is then made. The best linear unbiased predictors of censored failure times are briefly discussed. Finally, an illustrative example is presented.     

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.     

Statistical approaches for conducting network meta-analysis in drug development

We introduce health technology assessment and evidence synthesis briefly, and then concentrate on the statistical approaches used for conducting network meta-analysis (NMA) in the development and approval of new health technologies. NMA is an extension of standard meta-analysis where indirect as well as direct information is combined and can be seen as similar to the analysis of incomplete-block designs. We illustrate it with an example involving three treatments, using fixed-effects and random-effects models, and using frequentist and Bayesian approaches. As most statisticians in the pharmaceutical industry are familiar with SAS? software for analyzing clinical trials, we provide example code for each of the methods we illustrate. One issue that has been overlooked in the literature is the choice of constraints applied to random effects, and we show how this affects the estimates and standard errors and propose a symmetric set of constraints that is equivalent to most current practice. Finally, we discuss the role of statisticians in planning and carrying out NMAs and the strategy for dealing with important issues such as heterogeneity.     

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.     

Social and semantic coevolution in knowledge networks

Socio-semantic networks involve agents creating and processing information: communities of scientists, software developers, wiki contributors and webloggers are, among others, examples of such knowledge networks. We aim at demonstrating that the dynamics of these communities can be adequately described as the coevolution of a social and a socio-semantic network. More precisely, we will first introduce a theoretical framework based on a social network and a socio-semantic network, i.e. an epistemic network featuring agents, concepts and links between agents and between agents and concepts. Adopting a relevant empirical protocol, we will then describe the joint dynamics of social and socio-semantic structures, at both macroscopic and microscopic scales, emphasizing the remarkable stability of these macroscopic properties in spite of a vivid local, agent-based network dynamics.     

Trajectories of Sexual Risk From Middle Adolescence to Early Adulthood

Developmental trajectories of risky sexual behavior were identified in a multiethnic sample of 1,121 youth drawn from the Children of the National Longitudinal Survey of Youth data set (NLSY79). Group-based trajectory modeling of a composite index of sexual risk taking revealed four sexual risk groups from ages 16 to 22: low risk, decreasing risk, increasing risk, and high risk. The Low Risk group exhibited low levels of risk across the study period. The Decreasing Risk group had high levels of sexual risk in adolescence that declined in early adulthood. The Increasing Risk and High Risk groups showed distinct risk patterns during adolescence but converged in early adulthood. When compared with adolescents in the low-risk group, individuals in the other groups were more likely to be male, had mothers who had an early birth, were less likely to live with both biological parents in early adolescence, had higher risk proneness, and reported more negative peer pressure.