Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients.

In many applications, comparing the q-quantiles of several normal populations are more advantageous than comparing their means. In this paper, we consider the problem of constructing simultaneous confidence intervals (SCIs) for quantile differences of several heterogeneous normal distributions. To the best of our knowledge, this problem remains unsolved. We propose a novel method for constructing a set of SCI. We propose two new sets of SCI by using the proposed technique and discuss two classic and two simulation-based SCIs. We show that the proposed classic SCIs are conservative for all population parameters configuration. We also show that the simulation-based SCIs have correct coverage probability asymptotically. We then compare these six sets of SCI in terms of average volume and coverage probability via an extensive simulation study. Results show that one of the proposed classic SCI can be recommended. Finally, the proposed methods are illustrated by a real example that is a vitamin D study on colorectal cancer patients.

Confidence intervals for the ratio of two independent Poisson rates: Parametric bootstrap, modified asymptotic, and approximate-estimate approaches.

We propose four confidence intervals for the ratio of two independent Poisson rates. We apply a parametric bootstrap approach, two modified asymptotic results, and we propose an ad-hoc approximate-estimate method to construct confidence intervals. We justify the correctness of the proposed methods asymptotically in the case of non-rare events (when the Poisson rates are large). We also compare the proposed confidence intervals with some recommended ones in the case of rare events (when the Poisson rates are small) via an extensive simulation study. The results show that the proposed modified asymptotic and the approximate-estimate confidence intervals perform reasonably well in terms of coverage probability and average length.

Optimization of an extracellular zinc-metalloprotease (SVP2) expression in Escherichia coli BL21 (DE3) using response surface methodology.

In this work, SVP2 from Salinivibrio proteolyticus strain AF-2004, a zinc metalloprotease with suitable biotechnological applications, was cloned for expression at high levels in Escherichia coli with the intention of changing culture conditions to generate a stable extracellular enzyme extract. The complete ORF of SVP2 gene was heterologously expressed in E. coli BL21 (DE3) by using pQE-80L expression vector system. In initial step, the effect of seven factors include: incubation temperature, peptone and yeast extract concentration, cell density (OD600) before induction, inducer (IPTG) concentration, induction time, and Ca(2+) ion concentrations on extracellular recombinant SVP2 expression and stability were investigated. The primary results revealed that the IPTG concentration, Ca(2+) ion concentration and induction time are the most important effectors on protease secretion by recombinant E. coli BL21. Central composite design experiment in the following showed that the maximum protease activity (522 U/ml) was achieved in 0.0089 mM IPTG for 24h at 30 °C, an OD600 of 2, 0.5% of peptone and yeast extract, and a Ca(2+) ion concentration of 1.3 mM. The results exhibited that the minimum level of IPTG concentration along with high cell density and medium level of Ca(2+) with prolonged induction time provided the best culture condition for maximum extracellular production of heterologous protease SVP2 in E. coli expression system.