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.^

Experiment: Growth rates and percentages of normal versus malformed versus incomplete versus incomplete and malformed coccoliths

The coccolithophore Emiliania huxleyi (Lohmann) W. W. Hay et H. Mohler was cultured in natural seawater with the addition of either the microtubule-inhibitor colchicine, the actin-inhibitor cytochalasin B, or the photosynthesis inhibitor 3-(3,4 dichlorophenyl)-1,1-dimethyl-urea (DCMU). Additionally, E. huxleyi was cultured at different light intensities and temperatures. Growth rate was monitored, and coccolith morphology analyzed. While every treatment affected growth rate, the percentage of malformed coccoliths increased with colchicine, cytochalasin B, and at higher than optimal temperature. These results represent the first experimental evidence for the role of microtubules and actin microfilaments in coccolith morphogenesis.

Total nitrogen from solid phase in the Jena Experiment (Block 2 Main Experiment up to 100cm depth, year 2002)

This data set contains measurements of total nitrogen from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Soil sampling and analysis: Stratified soil sampling to a depth of 1m was performed before sowing in April 2002. Three independent samples per plot were taken of all plots in block 2 using a motor-driven soil column cylinder (Cobra, Eijkelkamp, 8.3 cm in diameter). Soil samples were dried at 40°C and segmented to a depth resolution of 5 cm giving 20 depth subsamples per core. All samples were analyzed independently. All soil samples were passed through a sieve with a mesh size of 2 mm. Rarely present visible plant remains were removed using tweezers. Total nitrogen concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany).

Microfossils detected in a block of ancient dense clay coated with a ferromanganese crust, Clarion-Clipperton Province, East Equatorial Pacific

The area in study is characterized by a regional stratigraphic hiatus from Early Miocene to Quaternary. Deposits from Late Eocene to Early Miocene occur on the bottom surface or under a thin sedimentary cover. Ferromanganese nodules, mostly of Oligocene age, formed on surface layers of Tertiary or Quaternary sediments. A detailed micropaleontological study of a block of dense ancient clay coated with a ferromanganese crust was carried out. Composition of found radiolarian and diatomaceous complexes proved that the crust formed in Quaternary on an eroded surface of Late Oligocene clay. In Quaternary Neogene sediments were eroded and washed away by bottom currents. It is likely that the erosion began 0.9-0.7 Ma at the beginning of the "Glacial Pleistocene". The erosion could be initiated by loosening and resuspension of surface sediments resulting from seismic activity generated by strong earthquakes in the Central America subduction zone. The same vibration maintained residual nodules at the seafloor surface. Thus, for the area in study a common reason and a common Quaternary interval for formation of the following features is supposed: a regional stratigraphic hiatus, formation of residual nodule fields, and position of ancient nodules on the surface of Quaternary sediments.

Soil carbon in the Jena Experiment from intensive sampling campaigns (only block 2 Main Experiment up to 1 m depth, year 2007)

This data set contains soil carbon measurements (Organic carbon, inorganic carbon, and total carbon; all measured in dried soil samples) from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Stratified soil sampling to a depth of 1 m was repeated in April 2007 (as had been done before sowing in April 2002). Three independent samples per plot were taken of all plots in block 2 using a motor-driven soil column cylinder (Cobra, Eijkelkamp, 8.3 cm in diameter). Soil samples were dried at 40°C and segmented to a depth resolution of 5 cm giving 20 depth subsamples per core. All samples were analyzed independently. All soil samples were passed through a sieve with a mesh size of 2 mm. Because of much higher proportions of roots in the soil, the samples in 2007 were further sieved to 1 mm according to common root removal methods. No additional mineral particles were removed by this procedure. Total carbon concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s**-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany). We measured inorganic carbon concentration by elemental analysis at 1150°C after removal of organic carbon for 16 h at 450°C in a muffle furnace. Organic carbon concentration was calculated as the difference between both measurements of total and inorganic carbon.

Soil carbon in the Jena Experiment from intensive sampling campaigns (only block 2 Main Experiment up to 1 m depth, year 2002)

This data set contains soil carbon measurements (Organic carbon, inorganic carbon, and total carbon; all measured in dried soil samples) from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Stratified soil sampling to a depth of 1 m was performed before sowing in April 2002. Three independent samples per plot were taken of all plots in block 2 using a motor-driven soil column cylinder (Cobra, Eijkelkamp, 8.3 cm in diameter). Soil samples were dried at 40°C and segmented to a depth resolution of 5 cm giving 20 depth subsamples per core. All samples were analyzed independently. All soil samples were passed through a sieve with a mesh size of 2 mm. Rarely present visible plant remains were removed using tweezers. Total carbon concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s**-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany). We measured inorganic carbon concentration by elemental analysis at 1150°C after removal of organic carbon for 16 h at 450°C in a muffle furnace. Organic carbon concentration was calculated as the difference between both measurements of total and inorganic carbon.

Total nitrogen from solid phase in the Jena Experiment (Block 2 Main Experiment up to 100cm depth, year 2007)

This data set contains measurements of total nitrogen from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Stratified soil sampling to a depth of 1m was repeated in April 2007 (as had been done before sowing in April 2002). Three independent samples per plot were taken of all plots in block 2 using a motor-driven soil column cylinder (Cobra, Eijkelkamp, 8.3 cm in diameter). Soil samples were dried at 40°C and segmented to a depth resolution of 5 cm giving 20 depth subsamples per core. All samples were analyzed independently. All soil samples were passed through a sieve with a mesh size of 2 mm. Because of much higher proportions of roots in the soil, the samples in 2007 were further sieved to 1 mm according to common root removal methods. No additional mineral particles were removed by this procedure. Total nitrogen concentration was analyzed on ball-milled subsamples (time 4 min, frequency 30 s-1) by an elemental analyzer at 1150°C (Elementaranalysator vario Max CN; Elementar Analysensysteme GmbH, Hanau, Germany).

Sampling sites, sampled birds and plants of young larch plantations in Tokachi district, eastern Hokkaido, northern Japan, 2011

Models and data used to describe species-area relationships confound sampling with ecological process as they fail to acknowledge that estimates of species richness arise due to sampling. This compromises our ability to make ecological inferences from and about species-area relationships. We develop and illustrate hierarchical community models of abundance and frequency to estimate species richness. The models we propose separate sampling from ecological processes by explicitly accounting for the fact that sampled patches are seldom completely covered by sampling plots and that individuals present in the sampling plots are imperfectly detected. We propose a multispecies abundance model in which community assembly is treated as the summation of an ensemble of species-level Poisson processes and estimate patch-level species richness as a derived parameter. We use sampling process models appropriate for specific survey methods. We propose a multispecies frequency model that treats the number of plots in which a species occurs as a binomial process. We illustrate these models using data collected in surveys of early-successional bird species and plants in young forest plantation patches. Results indicate that only mature forest plant species deviated from the constant density hypothesis, but the null model suggested that the deviations were too small to alter the form of species-area relationships. Nevertheless, results from simulations clearly show that the aggregate pattern of individual species density-area relationships and occurrence probability-area relationships can alter the form of species-area relationships. The plant community model estimated that only half of the species present in the regional species pool were encountered during the survey. The modeling framework we propose explicitly accounts for sampling processes so that ecological processes can be examined free of sampling artefacts. Our modeling approach is extensible and could be applied to a variety of study designs and allows the inclusion of additional environmental covariates.