Assessing the inter-patient variability in the area under the concentration curve

In this paper, we check the accuracy of an approximate variance for the area under the concentration curve (AUC). Based on the model function of a random effects model, an analytic expression for the AUC can be obtained. Then an approximate variance for the AUC can be derived after the linearisation of it using the Taylor series expansion. This variance is used in the construction of confidence interval to check the accuracy of the approximation made. We assume that the data on concentration are collected with the advancement of a dose-finding study. Following the allocation of the lowest dose to a cohort of patients, the concentration of drug in the blood samples is measured at the locally D-optimum time points. The successive doses for the cohorts are determined by the popular continual reassessment method. Four PK proles, along with three plausible dose-response scenarios, are investigated through a simulation study. The numerical findings assure the quality of the approximated variance.

ESTIMATION OF SAMPLE SPACING IN STOCHASTIC PROCESSES

Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies.

Estimation of the finite population covariance using calibration

Estimators of the finite population covariance with several systems of weights are considered. New calibrated estimators of the finite population covariance (variance) are derived, using two and three weighting systems that are defined by various calibration equations and loss functions. The expressions of approximate variance for some of these estimators are presented. The estimators derived are compared by simulation. Finally, it is shown how the calibrated estimators of the covariance may be applied in regression estimation of the finite population total.

A family of estimators of population mean using multi-auxiliary variate and post-stratification

This paper suggests a family of estimators of population mean using multiauxiliary variate based on post-stratified sampling and its properties are studied under large sample approximation. Asymptotically optimum estimator in the class is identified alongwith its approximate variance formulae. The proposed class of estimators is also compared with corresponding unstratified class of estimators based on estimated optimum value. At the end, an empirical study has been carried out to support the proposed methodology.

Estimation of a total for rotated sample design using auxiliary information

In this paper we focus on constructions of the total estimator for rotated sampling design. Successive sampling procedure using multi-phase sampling design have been developed. The composite ratio type estimator of the total using auxiliary information and its approximate variance is constructed under simple random sampling design on each phase.

The generalization of ratio-cum product estimator for the arbitrary sample design

The generalization of a dual to ratio-cum-product estimator of the finite population total for the arbitrary sample design is given. The approximate variance is calculated and variance estimator is constructed. Some simulation results are presented for the comparison of ratio-cum-product estimator with some known estimators.