We develop a theory of tubular neighborhoods for the lower strata in manifold stratified spaces with two strata. In these topologically stratified spaces, manifold approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include the classification of neighborhood germs, the construction of exotic stratifications...

In Phase II oncology trials, therapies are increasingly being evaluated for their effectiveness in specific populations of interest. Such targeted trials require designs that allow for stratification based on the participants' molecular characterisation. A targeted design proposed by Jones and Holmgren (JH) Jones CL, Holmgren E: 'An adaptive Simon two-stage design for phase 2 studies of targete...

We propose a jackknife variance estimator for the population average from two, two-phase samples after imputation. The jackknife method has long been used to estimate and reduce bias, but has now become a valuable tool for variance estimation. We apply two different sampling methods, (simple random sampling and stratified random sampling) to derive jackknife variance estimators for the twosampl...

Suppose that for each of a number of subjects, we measure a response y and a vector of covariates x, in order to estimate the parameters β of a regression model which describes the conditional distribution of y given x. If we have sampled directly from the conditional distribution, or even the joint distribution, we can estimate β without knowledge of the distribution of the covariates. In the ...