Asymptotically Optimal Response‐Adaptive Designs for Allocating the Best Treatment: An Overview

Response‐adaptive designs are being used increasingly in applications, and this is especially so in early phase clinical trials. This paper reviews a particular class of response‐adaptive designs that have the property of picking the superior treatment with probability tending to one. This is a desirable property from an ethical point of view in clinical trials. The model underlying such designs is a randomly reinforced urn. This paper provides an overview of results for these designs, starting from the early paper of Durham and Yu (1990) until the recent work by Flournoy, May, Moler and Plo (2010).     

Monitoring risk in a ruin model perturbed by diffusion

We construct a nonparametric sequential test for the ruin probability and a corresponding change-point test in a risk model perturbed by diffusion. Some limiting properties are derived, which extend and improve on recent results of Conti (Stat Prob Lett 72:333–343, 2005) and Jahnke (Diploma thesis, University of Cologne, 2007). It is shown that the monitoring procedures can be designed such that the tests have an asymptotic prescribed false alarm rate (size) α and power 1. Some results from a small simulation study are also presented.     

Cost analysis for different sequential treatment regimens for metastatic renal cell carcinoma in China

Abstract

Purpose: Targeted therapies, including sunitinib, sorafenib, axitinib, and everolimus, have recently become the mainstay for the treatment of metastatic renal cell carcinoma (mRCC). The objective of this study was to estimate the costs of sequential treatment regimens for mRCC and associated adverse events (AEs) from the Chinese payers’ perspective.

Methods: Key inputs included in the calculation were patient population, dosing information, incidence rates and associated costs of Grade 3/4 AEs, treatment costs (including drug discount programs), and patients’ progression-free survival (PFS) as a proxy for length of treatment. To calculate PFS, this study identified pivotal clinical trials and generated a reconstructed individual patient data set from the published Kaplan-Meier survival curves. The median PFS from the pooled estimates were used in the calculation. In the base-case scenario, sunitinib was used as first line and the other three therapies were used as second line. Sensitivity analyses were conducted where (1) sorafenib was used as first line, or (2) a third-line therapy was added to the base-case scenario.

Results: In the base case, the cost per patient per treatment month (PPPM) cost was the lowest for sunitinib?+?axitinib among all sequential regimens (¥14,898) and was the highest for sunitinib?+?sorafenib (¥20,103). If sorafenib is used as first line, everolimus had lower per patient per months (PPPM) cost than axitinib (¥17,046 vs ¥23,337), but also had shorter PFS (13.5 months vs 15 months). Second sensitivity analysis with an additional third-line therapy showed consistent results with the base-case scenario; axitinib as second line was the least costly.

Conclusions: This study demonstrates that, for mRCC sequential treatment, sunitinib followed by axitinib generates the highest cost savings from the Chinese payers’ perspective. Future studies are warranted to examine the cost-effectiveness of various mRCC treatment regimens in Chinese populations.     

A sequential purchasing power parity test for panels of large cross-sections and implications for investors

In this paper we use monthly time series data for not less than 64 countries and a new sequential approach to test for purchasing power parity (PPP). The results are strong in that the evidence in favor of PPP is very weak. In fact, for the US-dollar-based exchange rates the evidence is basically non-existent. In order to eliminate the effect of the base currency, we also apply the sequential PPP test to all pairs of exchange rates, and find similarly weak evidence of PPP. However, for those rates where evidence is found, using a technical trading rule, we find evidence of significant profits. The predictability of the stationary pairs is therefore important for investors.     

Geographical and industrial spillovers in entry decisions across export markets

This article addresses sequential entry decisions in export markets. It focuses on externalities derived from previous export activity in countries close to those for which a potential entry decision is made (geographical spillovers) and externalities derived from previous presence of other firms in the same industry (industrial spillovers). The empirical analysis uses Spanish microdata for the period 2000–2010 in a firm decision model that also integrates country and industry characteristics. The results suggest that these two types of spillovers have a positive effect in explaining entry decisions in new export markets, though both are smaller in magnitude than the effects coming from previous presence in the same specific destination.     

HEDGING BY SEQUENTIAL REGRESSIONS REVISITED

Almost 20 years ago Föllmer and Schweizer (1989) suggested a simple and influential scheme for the computation of hedging strategies in an incomplete market. Their approach of  local  risk minimization results in a sequence of one-period least squares regressions running recursively backward in time. In the meantime, there have been significant developments in the  global  risk minimization theory for semimartingale price processes. In this paper we revisit hedging by sequential regression in the context of global risk minimization, in the light of recent results obtained by Černý and Kallsen (2007) . A number of illustrative numerical examples are given.     

Logrolling Procedure for Multi-Issue Negotiation

In order to better deal with the complexity in multi-issue negotiation, a quantitative method which produces Pareto optimal solutions through jointly improving exchange of issues is proposed. The trade-off process is modelled using logrolling, in which loss in some issues is traded for gain in others, resulting in overall gain for all parties. This mutual gain approach is designed based on the integrative negotiation strategy. The objective of the logrolling method is in negotiation support by providing a structure and systematic analysis for ill-defined multi-issue negotiation problems. This study presents a formal representation of logrolling, the sequential logrolling procedure that is based on the exchange of two issues, and the general properties of the efficient frontier produced by logrolling under a linear preference assumption. The study also includes some discussion on implementation aspects of the logrolling method.     

Recent advances in multiple-objective design strategies

Many experiments have several goals and it is important to incorporate these goals at the onset of the study. Design strategies for accomplishing this task are reviewed with examples from the biological sciences.     

Multivariate multistage methodologies for simultaneous all pairwise comparisons

We consider the problem of constructing simultaneous fixed-width confidence intervals for all pairwise treatment differences μ₁−μ _J , in the presence ofk(≥2) independent populationsN _p (μ₁,Σ), 1≤i≠j≤k. Appropriate purely sequential, accelerated sequential and three-stage sampling strategies have been developed and variousfirst-order asymptotic properties are then derived when Σ _pxp is completely unknown, but positive definite (p.d.). In the two special cases when the largest component variance in Σ is a known multiple of one of the variances or Σ=σ² H where σ(>0) is unknown, butH _pxp is known and p.d., the original multistage sampling strategies are specialized. Under such special circumstances, associatedsecond-order characteristics are then developed. It is to be noted that our present formulation and the methodologies fill important voids in the context of multivariate multiple comparisons which is a challenging area that has not yet been fully explored. Moderate sample performances of the proposed techniques were very encouraging and detailed remarks on these were included in Mukhopadhyay and Aoshima (1997).