Retrospective analysis of sequential dose-finding designs

The continual reassessment method (CRM) is a dose-finding design using a dynamic sequential updating scheme. In common with other dynamic schemes the method estimates a current dose level corresponding to some target percentile for experimentation. The estimate is based on all included subjects. This continual reevaluation is made possible by the use of a simple model. As it stands, neither the CRM, nor any of the other dynamic schemes, allow for the correct estimation of some target percentile, based on retrospective data apart from the exceptional situation in which the simplified model exactly generates the observations. In this article we focus on the very specific issue of retrospective analysis of data generated by some arbitrary mechanism and subsequently analyzed via the continual reassessment method. We show how this can be done consistently. The proposed methodology is not restricted to that particular design and is applicable to any sequential updating scheme in which dose levels are associated with percentiles via model inversion.     

Designs for single- or multiple-agent phase I trials

Phase I trials of cytotoxic agents in oncology are usually dose-finding studies that involve a single cytotoxic agent. Many statistical methods have been proposed for these trials, all of which are based on the assumption of a monotonic dose-toxicity curve. For single-agent trials, this is a valid assumption. In many trials, however, investigators are interested in finding the maximally tolerated dose based on escalating multiple cytotoxic agents. When there are multiple agents, monotonicity of the dose-toxicity curve is not clearly defined. In this article we present a design for phase I trials in which the toxicity probabilities follow a partial order, meaning that there are pairs of treatments for which the ordering of the toxicity probabilities is not known at the start of the trial. We compare the new design to existing methods for simple orders and investigate the properties of the design for two partial orders.     

Continual reassessment method for partial ordering

Summary Much of the statistical methodology underlying the experimental design of phase 1 trials in oncology is intended for studies involving a single cytotoxic agent. The goal of these studies is to estimate the maximally tolerated dose, the highest dose that can be administered with an acceptable level of toxicity. A fundamental assumption of these methods is monotonicity of the dose–toxicity curve. This is a reasonable assumption for single‐agent trials in which the administration of greater doses of the agent can be expected to produce dose‐limiting toxicities in increasing proportions of patients. When studying multiple agents, the assumption may not hold because the ordering of the toxicity probabilities could possibly be unknown for several of the available drug combinations. At the same time, some of the orderings are known and so we describe the whole situation as that of a partial ordering. In this article, we propose a new two‐dimensional dose‐finding method for multiple‐agent trials that simplifies to the continual reassessment method (CRM), introduced by O'Quigley, Pepe, and Fisher (1990, Biometrics 46 , 33–48), when the ordering is fully known. This design enables us to relax the assumption of a monotonic dose–toxicity curve. We compare our approach and some simulation results to a CRM design in which the ordering is known as well as to other suggestions for partial orders.     

SHELL MICROSTRUCTURE OF GASTROPODS FROM LAKE TANGANYIKA,AFRICA: ADAPTATION,CONVERGENT EVOLUTION,AND ESCALATION

Gastropod shells from Lake Tanganyika, with their heavy calcification, coarse noded ribbing, spines, apertural lip thickening and repair scars, resemble marine shells more closely than they resemble other lacustrine shells. This convergence between Tanganyikan and marine gastropod shells, however, is not just superficial. Scanning electron microscope (SEM) studies reveal that the Tanganyikan shells are primarily layers of crossed-lamellar crystal architecture (that is, needle-like aragonite crystals arranged into laths that are packed into sheets such that the aragonite needles of adjacent laths are never parallel). The number of crossed-lamellar layers can vary from one to four between different Tanganyikan gastropod species. In species with two or more crossed-lamellar layers, the orientation of the lamellae is offset by approximately 90° between the different layers. The number of crossed-lamellar layers in the shell wall is positively correlated with shell strength and with predation resistance. Three and four crossed-lamellar layers in the shell wall evolved several times independently within the endemic thiarid gastropod radiation in Lake Tanganyika. Repeated origins of three and four crossed-lamellar layers suggest that they may be specific adaptations by Tanganyikan gastropods to strengthen their shells as a defense against shell-crushing predators.     

Reappraising the early evidence of durophagy and drilling predation in the fossil record: implications for escalation and the Cambrian Explosion

The Cambrian Explosion is arguably the most extreme example of a biological radiation preserved in the fossil record, and studies of Cambrian Lagerstätten have facilitated the exploration of many facets of this key evolutionary event. As predation was a major ecological driver behind the Explosion – particularly the radiation of biomineralising metazoans – the evidence for shell crushing (durophagy), drilling and puncturing predation in the Cambrian (and possibly the Ediacaran) is considered. Examples of durophagous predation on biomineralised taxa other than trilobites are apparently rare, reflecting predator preference, taphonomic and sampling biases, or simply lack of documentation. The oldest known example of durophagy is shell damage on the problematic taxon Mobergella holsti from the early Cambrian (possibly Terreneuvian) of Sweden. Using functional morphology to identify (or perhaps misidentify) durophagous predators is discussed, with emphasis on the toolkit used by Cambrian arthropods, specifically the radiodontan oral cone and the frontal and gnathobasic appendages of various taxa. Records of drill holes and possible puncture holes in Cambrian shells are mostly on brachiopods, but the lack of prey diversity may represent either a true biological signal or a result of various biases. The oldest drilled Cambrian shells occur in a variety of Terreneuvian‐aged taxa, but specimens of the ubiquitous Ediacaran shelly fossil Cloudina also show putative drilling traces. Knowledge on Cambrian shell drillers is sorely lacking and there is little evidence or consensus concerning the taxonomic groups that made the holes, which often leads to the suggestion of an unknown ‘soft bodied driller’. Useful methodologies for deciphering the identities and capabilities of shell drillers are outlined. Evidence for puncture holes in Cambrian shelly taxa is rare. Such holes are more jagged than drill holes and possibly made by a Cambrian ‘puncher’. The Cambrian arthropod Yohoia may have used its frontal appendages in a jack‐knifing manner, similar to Recent stomatopod crustaceans, to strike and puncture shells rapidly. Finally, Cambrian durophagous and shell‐drilling predation is considered in the context of escalation – an evolutionary process that, amongst other scenarios, involves predators (and other ‘enemies’) as the predominant agents of natural selection. The rapid increase in diversity and abundance of biomineralised shells during the early Cambrian is often attributed to escalation: enemies placed selective pressure on prey, forcing phenotypic responses in prey and, by extension, in predator groups over time. Unfortunately, few case studies illustrate long‐term patterns in shelly fossil morphologies that may reflect the influence of predation throughout the Cambrian. More studies on phenotypic change in hard‐shelled lineages are needed to convincingly illustrate escalation and the responses of prey during the Cambrian.     

Contrasting levels of β-diversity and underlying phylogenetic trends indicate different paths to chemical diversity in highland and lowland willow species

Diverse specialised metabolites contributed to the success of vascular plants in colonising most terrestrial habitats. Understanding how distinct aspects of chemical diversity arise through heterogeneous environmental pressures can help us understand the effects of abiotic and biotic stress on plant evolution and community assembly. We examined highland and lowland willow species within a phylogenetic framework to test for trends in their chemical α-diversity (richness) and β-diversity (variation among species sympatric in elevation). We show that differences in chemistry among willows growing at different elevations occur mainly through shifts in chemical β-diversity and due to convergence or divergence among species sharing their elevation level. We also detect contrasting phylogenetic trends in concentration and α-diversity of metabolites in highland and lowland willow species. The resulting elevational patterns contribute to the chemical diversity of willows and suggest that variable selective pressure across ecological gradients may, more generally, underpin complex changes in plant chemistry.     

Escalation of aggressive vocal signals: a sequential playback study

Rival conspecifics often produce stereotyped sequences of signals as agonistic interactions escalate. Successive signals in sequence are thought to convey increasingly pronounced levels of aggressive motivation. Here, we propose and test a model of aggressive escalation in black-throated blue warblers, presenting subjects with two sequential and increasingly elevated levels of threat. From a speaker outside the territorial boundary, we initiated an interaction (low-threat level), and from a second speaker inside the territory, accompanied by a taxidermic mount, we subsequently simulated a territorial intrusion (escalated threat level). Our two main predictions were that signalling behaviours in response to low-threat boundary playback would predict signalling responses to the escalated within-territory threat, and that these latter signalling behaviours would in turn reliably predict attack. We find clear support for both predictions: (i) specific song types (type II songs) produced early in the simulated interaction, in response to boundary playback, predicted later use of low-amplitude ‘soft’ song, in response to within-territory playback; and (ii) soft song, in turn, predicted attack of the mount. Unexpectedly, use of the early-stage signal (type II song) itself did not predict attack, despite its apparent role in aggressive escalation. This raises the intriguing question of whether type II song can actually be considered a reliable aggressive signal. Overall, our results provide new empirical insights into how songbirds may use progressive vocal signalling to convey increasing levels of threat.     

Determining a maximum-tolerated schedule of a cytotoxic agent

Most phase I clinical trials are designed to determine a maximum-tolerated dose (MTD) for one initial administration or treatment course of a cytotoxic experimental agent. Toxicity usually is defined as the indicator of whether one or more particular adverse events occur within a short time period from the start of therapy. However, physicians often administer an agent to the patient repeatedly and monitor long-term toxicity due to cumulative effects. We propose a new method for such settings. It is based on the time to toxicity rather than a binary outcome, and the goal is to determine a maximum-tolerated schedule (MTS) rather than a conventional MTD. The model and method account for a patient's entire sequence of administrations, with the overall hazard of toxicity modeled as the sum of a sequence of hazards, each associated with one administration. Data monitoring and decision making are done continuously throughout the trial. We illustrate the method with an allogeneic bone marrow transplantation (BMT) trial to determine how long a recombinant human growth factor can be administered as prophylaxis for acute graft-versus-host disease (aGVHD), and we present a simulation study in the context of this trial.     

Is dose escalation achievable for esophageal carcinoma?

Aim

To investigate the feasibility of dose escalation using rapid arc (RA) and Helical Tomotherapy (HT) for patients with upper, middle and distal esophageal carcinomas, even for large tumor volumes.

Background

In esophageal cancer, for patients with exclusive radio-chemotherapy, local disease control remains poor. Planning study with dose escalation was done for two sophisticated modulated radiotherapy techniques: Rapid arc against Tomotherapy.

Materials and methods

Six patients treated with a RA simultaneous integrated boost (SIB) of 60 Gy were re-planned for RA and HT techniques with a SIB dose escalated to 70 Gy. Dose volume histogram statistics, conformity indices and homogeneity indices were analyzed. For a given set of normal tissue constraints, the capability of each treatment modality to increase the GTV dose to 70 Gy was investigated.

Results

Either HT or VMAT may be used to escalate the dose delivered in esophageal tumors while maintaining the spinal cord, lung and heart doses within tolerance. Adequate target coverage was achieved by both techniques. Typically, HT achieved better lung sparing and PTV coverage than did RA.

Conclusions

Dose escalation for esophageal cancer becomes clinically feasible with the use of RA and HT. This promising result could be explored in a carefully controlled clinical study which considered normal tissue complications and tumor control as endpoints.