Bayesian design and conduct of phase II single-arm clinical trials with binary outcomes: a tutorial

The aim of phase II single-arm clinical trials of a new drug is to determine whether it has sufficient promising activity to warrant its further development. For the last several years Bayesian statistical methods have been proposed and used. Bayesian approaches are ideal for earlier phase trials as they take into account information that accrues during a trial. Predictive probabilities are then updated and so become more accurate as the trial progresses. Suitable priors can act as pseudo samples, which make small sample clinical trials more informative. Thus patients have better chances to receive better treatments. The goal of this paper is to provide a tutorial for statisticians who use Bayesian methods for the first time or investigators who have some statistical background. In addition, real data from three clinical trials are presented as examples to illustrate how to conduct a Bayesian approach for phase II single-arm clinical trials with binary outcomes.

A note on the accuracy of PAC-likelihood inference with microsatellite data

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics. (c) 2006 Elsevier Inc. All rights reserved.

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467-475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters' prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters' prior beliefs. (c) 2006 Elsevier B.V. All rights reserved.

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea Japan land separation. (c) 2005 Elsevier Inc. All rights reserved.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

The expected performance of single nucleotide polymorphism loci in paternity testing

We discuss the utility of single nucleotide polymorphism loci for full trio and mother-unavailable paternity testing cases, in the presence of population substructure and relatedness of putative and actual fathers. We focus primarily on the expected number of loci required to gain specified probabilities of mismatches, and report the expected proportion of paternity indices greater than three threshold values for these loci. (c) 2004 Elsevier Ireland Ltd. All rights reserved.

Evaluation of probabilistic occupancy map people detection for surveillance systems

In this paper, we evaluate the Probabilistic Occupancy Map (POM) pedestrian detection algorithm on the PETS 2009 benchmark dataset. POM is a multi-camera generative detection method, which estimates ground plane occupancy from multiple background subtraction views. Occupancy probabilities are iteratively estimated by fitting a synthetic model of the background subtraction to the binary foreground motion. Furthermore, we test the integration of this algorithm into a larger framework designed for understanding human activities in real environments. We demonstrate accurate detection and localization on the PETS dataset, despite suboptimal calibration and foreground motion segmentation input.

A climate change risk analysis for world ecosystems

We quantify the risks of climate-induced changes in key ecosystem processes during the 21st century by forcing a dynamic global vegetation model with multiple scenarios from 16 climate models and mapping the proportions of model runs showing forest/nonforest shifts or exceedance of natural variability in wildfire frequency and freshwater supply. Our analysis does not assign probabilities to scenarios or weights to models. Instead, we consider distribution of outcomes within three sets of model runs grouped by the amount of global warming they simulate: <2°C (including simulations in which atmospheric composition is held constant, i.e., in which the only climate change is due to greenhouse gases already emitted), 2–3°C, and >3°C. High risk of forest loss is shown for Eurasia, eastern China, Canada, Central America, and Amazonia, with forest extensions into the Arctic and semiarid savannas; more frequent wildfire in Amazonia, the far north, and many semiarid regions; more runoff north of 50°N and in tropical Africa and northwestern South America; and less runoff in West Africa, Central America, southern Europe, and the eastern U.S. Substantially larger areas are affected for global warming >3°C than for <2°C; some features appear only at higher warming levels. A land carbon sink of ≈1 Pg of C per yr is simulated for the late 20th century, but for >3°C this sink converts to a carbon source during the 21st century (implying a positive climate feedback) in 44% of cases. The risks continue increasing over the following 200 years, even with atmospheric composition held constant.

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Relatedness testing in subdivided populations

Assigning probabilities to alleged relationships, given DNA profiles, requires, among other things, calculation of a likelihood ratio (LR). Such calculations usually assume independence of genes: this assumption is not appropriate when the tested individuals share recent ancestry due to population substructure. Adjusted LR formulae, incorporating the coancestry coefficient F(ST), are presented here for various two-person relationships, and the issue of mutations in parentage testing is also addressed.

A two-locus forensic match probability for subdivided populations

A two-locus match probability is presented that incorporates the effects of within-subpopulation inbreeding (consanguinity) in addition to population subdivision. The usual practice of calculating multi-locus match probabilities as the product of single-locus probabilities assumes independence between loci. There are a number of population genetics phenomena that can violate this assumption: in addition to consanguinity, which increases homozygosity at all loci simultaneously, gametic disequilibrium will introduce dependence into DNA profiles. However, in forensics the latter problem is usually addressed in part by the careful choice of unlinked loci. Hence, as is conventional, we assume gametic equilibrium here, and focus instead on between-locus dependence due to consanguinity. The resulting match probability formulae are an extension of existing methods in the literature, and are shown to be more conservative than these methods in the case of double homozygote matches. For two-locus profiles involving one or more heterozygous genotypes, results are similar to, or smaller than, the existing approaches.

Measuring gametic disequilibrium from multilocus data

We describe a Bayesian approach to analyzing multilocus genotype or haplotype data to assess departures from gametic (linkage) equilibrium. Our approach employs a Markov chain Monte Carlo (MCMC) algorithm to approximate the posterior probability distributions of disequilibrium parameters. The distributions are computed exactly in some simple settings. Among other advantages, posterior distributions can be presented visually, which allows the uncertainties in parameter estimates to be readily assessed. In addition, background knowledge can be incorporated, where available, to improve the precision of inferences. The method is illustrated by application to previously published datasets; implications for multilocus forensic match probabilities and for simple association-based gene mapping are also discussed.

A comparison of extreme European daily precipitation simulated by a global and a regional climate model for present and future climates

The intensity and distribution of daily precipitation is predicted to change under scenarios of increased greenhouse gases (GHGs). In this paper, we analyse the ability of HadCM2, a general circulation model (GCM), and a high-resolution regional climate model (RCM), both developed at the Met Office's Hadley Centre, to simulate extreme daily precipitation by reference to observations. A detailed analysis of daily precipitation is made at two UK grid boxes, where probabilities of reaching daily thresholds in the GCM and RCM are compared with observations. We find that the RCM generally overpredicts probabilities of extreme daily precipitation but that, when the GCM and RCM simulated values are scaled to have the same mean as the observations, the RCM captures the upper-tail distribution more realistically. To compare regional changes in daily precipitation in the GHG-forced period 2080-2100 in the GCM and the RCM, we develop two methods. The first considers the fractional changes in probability of local daily precipitation reaching or exceeding a fixed 15 mm threshold in the anomaly climate compared with the control. The second method uses the upper one-percentile of the control at each point as the threshold. Agreement between the models is better in both seasons with the latter method, which we suggest may be more useful when considering larger scale spatial changes. On average, the probability of precipitation exceeding the 1% threshold increases by a factor of 2.5 (GCM and RCM) in winter and by I .7 (GCM) or 1.3 (RCM) in summer.

Temporal relations of column water vapor and tropical precipitation

Empirical studies using satellite data and radiosondes have shown that precipitation increases with column water vapor (CWV) in the tropics, and that this increase is much steeper above some critical CWV value. Here, eight years of 1-min-resolution microwave radiometer and optical gauge data at Nauru Island are analyzed to better understand the relationships among CWV, column liquid water (CLW), and precipitation at small time scales. CWV is found to have large autocorrelation times compared with CLW and precipitation. Before precipitation events, CWV increases on both a synoptic-scale time period and a subsequent shorter time period consistent with mesoscale convective activity; the latter period is associated with the highest CWV levels. Probabilities of precipitation increase greatly with CWV. Given initial high CWV, this increased probability of precipitation persists at least 10–12 h. Even in periods of high CWV, however, probabilities of initial precipitation in a 5-min period remain low enough that there tends to be a lag before the start of the next precipitation event. This is consistent with precipitation occurring stochastically within environments containing high CWV, with the latter being established by a combination of synoptic-scale and mesoscale forcing.

Ensemble prediction of transitions of the North Atlantic eddy-driven jet

The consistency of ensemble forecasts from three global medium-range prediction systems with the observed transition behaviour of a three-cluster model of the North Atlantic eddy-driven jet is examined. The three clusters consist of a mid jet cluster taken to represent an undisturbed jet and south and north jet clusters representing southward and northward shifts of the jet. The ensemble forecasts span a period of three extended winters (October–February) from October 2007–February 2010. The mean probabilities of transitions between the clusters calculated from the ensemble forecasts are compared with those calculated from a 23-extended-winter climatology taken from the European Centre for Medium-Range Weather Forecasts 40-Year Re-analysis (ERA40) dataset. No evidence of a drift with increasing lead time of the ensemble forecast transition probabilities towards values inconsistent with the 23-extended-winter climatology is found. The ensemble forecasts of transition probabilities are found to have positive Brier Skill at 15 day lead times. It is found that for the three-extended-winter forecast set, probabilistic forecasts initialized in the north jet cluster are generally less skilful than those initialized in the other clusters. This is consistent with the shorter persistence time-scale of the north jet cluster observed in the ERA40 23-extended-winter climatology. Copyright © 2011 Royal Meteorological Society