Optimum mixture designs for the log-logistic dose–response model with mixture of two similar compounds

The article studies the log-logistic class of dose–response bioassay models in the binomial set-up. The dose is identified by the potency adjusted mixing proportions of two similar compounds. Models for both absence and presence of interaction between the compounds have been considered. The aim is to investigate the D- and D_s-optimal mixture designs for the estimation of the full set of parameters or for the estimation of potency for a best guess of the parameter values. We also indicate how to find the optimal design to estimate the mixing proportions at which the probability of success attains a given value in the absence of the interaction effect.     

Stochastic EM algorithm for generalized exponential cure rate model and an empirical study

In this paper, we consider two well-known parametric long-term survival models, namely, the Bernoulli cure rate model and the promotion time (or Poisson) cure rate model. Assuming the long-term survival probability to depend on a set of risk factors, the main contribution is in the development of the stochastic expectation maximization (SEM) algorithm to determine the maximum likelihood estimates of the model parameters. We carry out a detailed simulation study to demonstrate the performance of the proposed SEM algorithm. For this purpose, we assume the lifetimes due to each competing cause to follow a two-parameter generalized exponential distribution. We also compare the results obtained from the SEM algorithm with those obtained from the well-known expectation maximization (EM) algorithm. Furthermore, we investigate a simplified estimation procedure for both SEM and EM algorithms that allow the objective function to be maximized to split into simpler functions with lower dimensions with respect to model parameters. Moreover, we present examples where the EM algorithm fails to converge but the SEM algorithm still works. For illustrative purposes, we analyze a breast cancer survival data. Finally, we use a graphical method to assess the goodness-of-fit of the model with generalized exponential lifetimes.     

Understanding the effects of siblings on child mortality: evidence from India

Given the intrinsically sequential nature of childbirth, timing of a child’s birth has consequences not only for itself but also for its older and younger siblings. The paper argues that prior spacing and posterior spacing between consecutive siblings are thus important measures of intensity of sibling competition for limited parental resources. While the available estimates of child mortality tend to ignore the endogeneity of sibling composition, we use a correlated recursive model of prior and posterior spacing and child mortality to correct it. There is evidence that uncorrected estimates under-estimate the effects of prior and posterior spacing on child mortality.

A note on the common mean of two normal populations with order restricted variances

Consider the problem of estimating the common mean of two normal populations when the order of the unknown variances is known. In this article we have constructed a simple improved estimator which is better than the usual Graybill-Deal estimator in terms of stochastic domination.