Optimal, minimax, and Bayesian two-stage designs in two-dose phase II clinical trials

Background: For most cytotoxic and biologic anti-cancer agents, the response rate of the drug is commonly assumed to be non-decreasing with an increasing dose. However, an increasing dose does not always result in an appreciable increase in the response rate. This may especially be true at high doses for a biologic agent. Therefore, in a phase II trial the investigators may be interested in testing the anti-tumor activity of a drug at more than one (often two) doses, instead of only at the maximum tolerated dose (MTD). This way, when the lower dose appears equally effective, this dose can be recommended for further confirmatory testing in a phase III trial under potential long-term toxicity and cost considerations. A common approach to designing such a phase II trial has been to use an independent (e.g., Simon's two-stage) design at each dose ignoring the prior knowledge about the ordering of the response probabilities at the different doses. However, failure to account for this ordering constraint in estimating the response probabilities may result in an inefficient design. In this dissertation, we developed extensions of Simon's optimal and minimax two-stage designs, including both frequentist and Bayesian methods, for two doses that assume ordered response rates between doses. ^ Methods: Optimal and minimax two-stage designs are proposed for phase II clinical trials in settings where the true response rates at two dose levels are ordered. We borrow strength between doses using isotonic regression and control the joint and/or marginal error probabilities. Bayesian two-stage designs are also proposed under a stochastic ordering constraint. ^ Results: Compared to Simon's designs, when controlling the power and type I error at the same levels, the proposed frequentist and Bayesian designs reduce the maximum and expected sample sizes. Most of the proposed designs also increase the probability of early termination when the true response rates are poor. ^ Conclusion: Proposed frequentist and Bayesian designs are superior to Simon's designs in terms of operating characteristics (expected sample size and probability of early termination, when the response rates are poor) Thus, the proposed designs lead to more cost-efficient and ethical trials, and may consequently improve and expedite the drug discovery process. The proposed designs may be extended to designs of multiple group trials and drug combination trials.^

Control of the master virulence regulatory gene atxA in Bacillus anthracis

Transcription of the Bacillus anthracis structural genes for the anthrax toxin proteins and biosynthetic operon for capsule are positively regulated by AtxA, a transcription regulator with unique properties. Consistent with the role of atxA in virulence factor expression, a B. anthracis atxA-null mutant is avirulent in a murine model for anthrax. In batch culture, multiple signals impact atxA transcript levels, and the timing and steady state level of atxA expression is critical for optimal toxin and capsule synthesis. Despite the apparent complex control of atxA transcription, only one trans-acting protein, the transition state regulator AbrB, has been demonstrated to directly interact with the atxA promoter. The AbrB-binding site has been described, but additional cis-acting control sequences have not been defined. Using transcriptional lacZ fusions, electrophoretic mobility shift assays, and Western blot analysis, the cis-acting elements and trans-acting factors involved in regulation of atxA in B. anthracis strains containing either both virulence plasmids, pXO1 and pXO2, or only one plasmid, pXO1, were studied. This work demonstrates that atxA transcription from the major start site P1 is dependent upon a consensus sequence for the housekeeping sigma factor SigA, and an A+T-rich upstream element (UP-element) for RNA polymerase (RNAP). In addition, the data show that a trans-acting protein(s) other than AbrB negatively impacts atxA transcription when it binds specifically to a 9-bp palindrome within atxA promoter sequences located downstream of P1. Mutation of the palindrome prevents binding of the trans-acting protein(s) and results in a corresponding increase in AtxA and anthrax toxin production in a strain- and culture-dependent manner. The identity of the trans-acting repressor protein(s) remains elusive; however, phenotypes associated with mutation of the repressor binding site have revealed that the trans-acting repressor protein(s) indirectly controls B. anthracis development. Mutation of the repressor binding site results in misregulation and overexpression of AtxA in conditions conducive for development, leading to a marked sporulation defect that is both atxA- and pXO2-61-dependent. pXO2-61 is homologous to the sensor domain of sporulation sensor histidine kinases and is proposed to titrate an activating signal away from the sporulation phosphorelay when overexpressed by AtxA. These results indicate that AtxA is not only a master virulence regulator, but also a modulator of proper B. anthracis development. Also demonstrated in this work is the impact of the developmental regulators AbrB, Spo0A, and SigH on atxA expression and anthrax toxin production in a genetically incomplete (pXO1+, pXO2-) and genetically complete (pXO1+, pXO2+) strain background. AtxA and anthrax toxin production resulting from deletion of the developmental regulators are strain-dependent suggesting that factors on pXO2 are involved in control of atxA. The only developmental deletion mutant that resulted in a prominent and consistent strain-independent increase in AtxA protein levels was an abrB-null mutant. As a result of increased AtxA levels, there is early and increased production of anthrax toxins in an abrB-null mutant. In addition, the abrB-null mutant exhibited an increase in virulence in a murine model for anthrax. In contrast, virulence of the atxA promoter mutant was unaffected in a murine model for anthrax despite the production of 5-fold more AtxA than the abrB-null mutant. These results imply that AtxA is not the only factor impacting pathogenesis in an abrB-null mutant. Overall, this work highlights the complex regulatory network that governs expression of atxA and provides an additional role for AtxA in B. anthracis development.