Bayesian statistics in oncology: a guide for the clinical investigator

The rise of evidence-based medicine as well as important progress in statistical methods and computational power have led to a second birth of the >200-year-old Bayesian framework. The use of Bayesian techniques, in particular in the design and interpretation of clinical trials, offers several substantial advantages over the classical statistical approach. First, in contrast to classical statistics, Bayesian analysis allows a direct statement regarding the probability that a treatment was beneficial. Second, Bayesian statistics allow the researcher to incorporate any prior information in the analysis of the experimental results. Third, Bayesian methods can efficiently handle complex statistical models, which are suited for advanced clinical trial designs. Finally, Bayesian statistics encourage a thorough consideration and presentation of the assumptions underlying an analysis, which enables the reader to fully appraise the authors' conclusions. Both Bayesian and classical statistics have their respective strengths and limitations and should be viewed as being complementary to each other; we do not attempt to make a head-to-head comparison, as this is beyond the scope of the present review. Rather, the objective of the present article is to provide a nonmathematical, reader-friendly overview of the current practice of Bayesian statistics coupled with numerous intuitive examples from the field of oncology. It is hoped that this educational review will be a useful resource to the oncologist and result in a better understanding of the scope, strengths, and limitations of the Bayesian approach.

A 350 ka record of climate change from Lake El'gygytgyn, Far East Russian Arctic: refining the pattern of climate modes by means of cluster analysis

Abstract. Rock magnetic, biochemical and inorganic records of the sediment cores PG1351 and Lz1024 from Lake El’gygytgyn, Chukotka peninsula, Far East Russian Arctic, were subject to a hierarchical agglomerative cluster analysis in order to refine and extend the pattern of climate modes as defined by Melles et al. (2007). Cluster analysis of the data obtained from both cores yielded similar results, differentiating clearly between the four climate modes warm, peak warm, cold and dry, and cold and moist. In addition, two transitional phases were identified, representing the early stages of a cold phase and slightly colder conditions during a warm phase. The statistical approach can thus be used to resolve gradual changes in the sedimentary units as an indicator of available oxygen in the hypolimnion in greater detail. Based upon cluster analyses on core Lz1024, the published succession of climate modes in core PG1351, covering the last 250 ka, was modified and extended back to 350 ka. Comparison to the marine oxygen isotope (�18O) stack LR04 (Lisiecki and Raymo, 2005) and the summer insolation at 67.5� N, with the extended Lake El’gygytgyn parameter records of magnetic susceptibility (�LF), total organic carbon content (TOC) and the chemical index of alteration (CIA; Minyuk et al., 2007), revealed that all stages back to marine isotope stage (MIS) 10 and most of the substages are clearly reflected in the pattern derived from the cluster analysis.

Design and implementation of a multicriteria medical decision support system for diagnosis and treatment

Health care providers face the problem of trying to make decisions with inadequate information and also with an overload of (often contradictory) information. Physicians often choose treatment long before they know which disease is present. Indeed, uncertainty is intrinsic to the practice of medicine. Decision analysis can help physicians structure and work through a medical decision problem, and can provide reassurance that decisions are rational and consistent with the beliefs and preferences of other physicians and patients. ^ The primary purpose of this research project is to develop the theory, methods, techniques and tools necessary for designing and implementing a system to support solving medical decision problems. A case study involving “abdominal pain” serves as a prototype for implementing the system. The research, however, focuses on a generic class of problems and aims at covering theoretical as well as practical aspects of the system developed. ^ The main contributions of this research are: (1) bridging the gap between the statistical approach and the knowledge-based (expert) approach to medical decision making; (2) linking a collection of methods, techniques and tools together to allow for the design of a medical decision support system, based on a framework that involves the Analytic Network Process (ANP), the generalization of the Analytic Hierarchy Process (AHP) to dependence and feedback, for problems involving diagnosis and treatment; (3) enhancing the representation and manipulation of uncertainty in the ANP framework by incorporating group consensus weights; and (4) developing a computer program to assist in the implementation of the system. ^

Reliability of operational data from pig herds and performance ratings by veterinarians and pig farmers collected during telephone interviews for the evaluation of a PCV2 piglet vaccination

BackgroundThe aim of the present study was to evaluate the feasibility of using a telephone survey in gaining an understanding of the possible herd and management factors influencing the performance (i.e. safety and efficacy) of a vaccine against porcine circovirus type 2 (PCV2) in a large number of herds and to estimate customers¿ satisfaction.ResultsDatasets from 227 pig herds that currently applied or have applied a PCV2 vaccine were analysed. Since 1-, 2- and 3-site production systems were surveyed, the herds were allocated in one of two subsets, where only applicable variables out of 180 were analysed. Group 1 was comprised of herds with sows, suckling pigs and nursery pigs, whereas herds in Group 2 in all cases kept fattening pigs. Overall 14 variables evaluating the subjective satisfaction with one particular PCV2 vaccine were comingled to an abstract dependent variable for further models, which was characterized by a binary outcome from a cluster analysis: good/excellent satisfaction (green cluster) and moderate satisfaction (red cluster). The other 166 variables comprised information about diagnostics, vaccination, housing, management, were considered as independent variables. In Group 1, herds using the vaccine due to recognised PCV2 related health problems (wasting, mortality or porcine dermatitis and nephropathy syndrome) had a 2.4-fold increased chance (1/OR) of belonging to the green cluster. In the final model for Group 1, the diagnosis of diseases other than PCV2, the reason for vaccine administration being other than PCV2-associated diseases and using a single injection of iron had significant influence on allocating into the green cluster (P¿<¿0.05). In Group 2, only unchanged time or delay of time of vaccination influenced the satisfaction (P¿<¿0.05).ConclusionThe methodology and statistical approach used in this study were feasible to scientifically assess ¿satisfaction¿, and to determine factors influencing farmers¿ and vets¿ opinion about the safety and efficacy of a new vaccine.

Parallel adaptations to nectarivory in parrots, key innovations and the diversification of the Loriinae

Specialization to nectarivory is associated with radiations within different bird groups, including parrots. One of them, the Australasian lories, were shown to be unexpectedly species rich. Their shift to nectarivory may have created an ecological opportunity promoting species proliferation. Several morphological specializations of the feeding tract to nectarivory have been described for parrots. However, they have never been assessed in a quantitative framework considering phylogenetic nonindependence. Using a phylogenetic comparative approach with broad taxon sampling and 15 continuous characters of the digestive tract, we demonstrate that nectarivorous parrots differ in several traits from the remaining parrots. These trait-changes indicate phenotype–environment correlations and parallel evolution, and may reflect adaptations to feed effectively on nectar. Moreover, the diet shift was associated with significant trait shifts at the base of the radiation of the lories, as shown by an alternative statistical approach. Their diet shift might be considered as an evolutionary key innovation which promoted significant non-adaptive lineage diversification through allopatric partitioning of the same new niche. The lack of increased rates of cladogenesis in other nectarivorous parrots indicates that evolutionary innovations need not be associated one-to-one with diversification events.

Continental-Scale Footprint of Balancing and Positive Selection in a Small Rodent (Microtus arvalis)

Genetic adaptation to different environmental conditions is expected to lead to large differences between populations at selected loci, thus providing a signature of positive selection. Whereas balancing selection can maintain polymorphisms over long evolutionary periods and even geographic scale, thus leads to low levels of divergence between populations at selected loci. However, little is known about the relative importance of these two selective forces in shaping genomic diversity, partly due to difficulties in recognizing balancing selection in species showing low levels of differentiation. Here we address this problem by studying genomic diversity in the European common vole (Microtus arvalis) presenting high levels of differentiation between populations (average FST = 0.31). We studied 3,839 Amplified Fragment Length Polymorphism (AFLP) markers genotyped in 444 individuals from 21 populations distributed across the European continent and hence over different environmental conditions. Our statistical approach to detect markers under selection is based on a Bayesian method specifically developed for AFLP markers, which treats AFLPs as a nearly codominant marker system, and therefore has increased power to detect selection. The high number of screened populations allowed us to detect the signature of balancing selection across a large geographic area. We detected 33 markers potentially under balancing selection, hence strong evidence of stabilizing selection in 21 populations across Europe. However, our analyses identified four-times more markers (138) being under positive selection, and geographical patterns suggest that some of these markers are probably associated with alpine regions, which seem to have environmental conditions that favour adaptation. We conclude that despite favourable conditions in this study for the detection of balancing selection, this evolutionary force seems to play a relatively minor role in shaping the genomic diversity of the common vole, which is more influenced by positive selection and neutral processes like drift and demographic history.

Shifts in microbial communities do not explain the response of grassland ecosystem function to plant functional composition and rainfall change

Ecosystem functioning in grasslands is regulated by a range of biotic and abiotic factors, and the role of microbial communities in regulating ecosystem function has been the subject of much recent scrutiny. However, there are still knowledge gaps regarding the impacts of rainfall and vegetation change upon microbial communities and the implications of these changes for ecosystem functioning. We investigated this issue using data from an experimental mesotrophic grassland study in south-east England, which had been subjected to four years of rainfall and plant functional composition manipulations. Soil respiration, nitrogen and phosphorus stocks were measured, and the abundance and community structure of soil microbes were characterised using quantitative PCR and multiplex-TRFLP analysis, respectively. Bacterial community structure was strongly related to the plant functional composition treatments, but not the rainfall treatment. However, there was a strong effect of both rainfall change and plant functional group upon bacterial abundance. There was also a weak interactive effect of the two treatments upon fungal community structure, although fungal abundance was not affected by either treatment. Next, we used a statistical approach to assess whether treatment effects on ecosystem function were regulated by the microbial community. Our results revealed that ecosystem function was influenced by the experimental treatments, but was not related to associated changes to the microbial community. Overall, these results indicate that changes in fungal and bacterial community structure and abundance play a relatively minor role in determining grassland ecosystem function responses to precipitation and plant functional composition change, and that direct effects on soil physical and chemical properties and upon plant and microbial physiology may play a more important role.

Variance of familial dietary intake

Although many family-based genetic studies have collected dietary data, very few have used the dietary information in published findings. No single solution has been presented or discussed in the literature to deal with the problem of using factor analyses for the analyses of dietary data from several related individuals from a given household. The standard statistical approach of factor analysis cannot be applied to the VIVA LA FAMILIA Study diet data to ascertain dietary patterns since this population consists of three children from each family, thus the dietary patterns of the related children may be correlated and non-independent. Addressing this problem in this project will enable us to describe the dietary patterns in Hispanic families and to explore the relationships between dietary patterns and childhood obesity. ^ In the VIVA LA FAMILIA Study, an overweight child was first identified and then his/her siblings and parents were brought in for data collection which included 24 hour recalls and food frequency questionnaire (FFQ). Dietary intake data were collected using FFQ and 24 hour recalls on 1030 Hispanic children from 319 families. ^ The design of the VIVA LA FAMILIA Study has important and unique statistical considerations since its participants are related to each other, the majority form distinct nuclear families. Thus, the standard approach of factor analysis cannot be applied to these diet data to ascertain dietary patterns. In this project we propose to investigate whether the determinants of the correlation matrix of each family unit will allow us to adjust the original correlation matrix of the dietary intake data prior to ascertaining dietary intake patterns. If these methods are appropriate, then in the future the dietary patterns among related individuals could be assessed by standard orthogonal principal component factor analysis.^

Comparison of Bayesian and frequentist approaches in clinical outcomes between hospitals

Many public health agencies and researchers are interested in comparing hospital outcomes, for example, morbidity, mortality, and hospitalization across areas and hospitals. However, since there is variation of rates in clinical trials among hospitals because of several biases, we are interested in controlling for the bias and assessing real differences in clinical practices. In this study, we compared the variations between hospitals in rates of severe Intraventricular Haemorrhage (IVH) infant using Frequentist statistical approach vs. Bayesian hierarchical model through simulation study. The template data set for simulation study was included the number of severe IVH infants of 24 intensive care units in Australian and New Zealand Neonatal Network from 1995 to 1997 in severe IVH rate in preterm babies. We evaluated the rates of severe IVH for 24 hospitals with two hierarchical models in Bayesian approach comparing their performances with the shrunken rates in Frequentist method. Gamma-Poisson (BGP) and Beta-Binomial (BBB) were introduced into Bayesian model and the shrunken estimator of Gamma-Poisson (FGP) hierarchical model using maximum likelihood method were calculated as Frequentist approach. To simulate data, the total number of infants in each hospital was kept and we analyzed the simulated data for both Bayesian and Frequentist models with two true parameters for severe IVH rate. One was the observed rate and the other was the expected severe IVH rate by adjusting for five predictors variables for the template data. The bias in the rate of severe IVH infant estimated by both models showed that Bayesian models gave less variable estimates than Frequentist model. We also discussed and compared the results from three models to examine the variation in rate of severe IVH by 20th centile rates and avoidable number of severe IVH cases. ^

THE NATURAL AND ORTHOGONAL INTERACTION (NOIA) MODELS FOR QUANTITATIVE TRAITS (QTs) AND COMPLEX DISEASES

My dissertation focuses on developing methods for gene-gene/environment interactions and imprinting effect detections for human complex diseases and quantitative traits. It includes three sections: (1) generalizing the Natural and Orthogonal interaction (NOIA) model for the coding technique originally developed for gene-gene (GxG) interaction and also to reduced models; (2) developing a novel statistical approach that allows for modeling gene-environment (GxE) interactions influencing disease risk, and (3) developing a statistical approach for modeling genetic variants displaying parent-of-origin effects (POEs), such as imprinting. In the past decade, genetic researchers have identified a large number of causal variants for human genetic diseases and traits by single-locus analysis, and interaction has now become a hot topic in the effort to search for the complex network between multiple genes or environmental exposures contributing to the outcome. Epistasis, also known as gene-gene interaction is the departure from additive genetic effects from several genes to a trait, which means that the same alleles of one gene could display different genetic effects under different genetic backgrounds. In this study, we propose to implement the NOIA model for association studies along with interaction for human complex traits and diseases. We compare the performance of the new statistical models we developed and the usual functional model by both simulation study and real data analysis. Both simulation and real data analysis revealed higher power of the NOIA GxG interaction model for detecting both main genetic effects and interaction effects. Through application on a melanoma dataset, we confirmed the previously identified significant regions for melanoma risk at 15q13.1, 16q24.3 and 9p21.3. We also identified potential interactions with these significant regions that contribute to melanoma risk. Based on the NOIA model, we developed a novel statistical approach that allows us to model effects from a genetic factor and binary environmental exposure that are jointly influencing disease risk. Both simulation and real data analyses revealed higher power of the NOIA model for detecting both main genetic effects and interaction effects for both quantitative and binary traits. We also found that estimates of the parameters from logistic regression for binary traits are no longer statistically uncorrelated under the alternative model when there is an association. Applying our novel approach to a lung cancer dataset, we confirmed four SNPs in 5p15 and 15q25 region to be significantly associated with lung cancer risk in Caucasians population: rs2736100, rs402710, rs16969968 and rs8034191. We also validated that rs16969968 and rs8034191 in 15q25 region are significantly interacting with smoking in Caucasian population. Our approach identified the potential interactions of SNP rs2256543 in 6p21 with smoking on contributing to lung cancer risk. Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting affects several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we propose a NOIA framework for a single locus association study that estimates both main allelic effects and POEs. We develop statistical (Stat-POE) and functional (Func-POE) models, and demonstrate conditions for orthogonality of the Stat-POE model. We conducted simulations for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits.

Foraminifer counts in core JM01-1199, and review of radiocarbon ages in the Norwegian-Barents Sea-Svalbard margin

We compare six high-resolution Holocene, sediment cores along a S-N transect on the Norwegian-Svalbard continental margin from ca 60°N to 77.4°N, northern North Atlantic. Planktonic foraminifera in the cores were investigated to show the changes in upper surface and subsurface water mass distribution and properties, including summer sea-surface temperatures (SST). The cores are located below the axis of the Norwegian Current and the West Spitsbergen Current, which today transport warm Atlantic Water to the Arctic. Sediment accumulation rates are generally high at all the core sites, allowing for a temporal resolution of 10-102 years. SST is reconstructed using different types of transfer functions, resulting in very similar SST trends, with deviations of no more than +- 1.0/1.5 °C. A transfer function based on the maximum likelihood statistical approach is found to be most relevant. The reconstruction documents an abrupt change in planktonic foraminiferal faunal composition and an associated warming at the Younger Dryas-Preboreal transition. The earliest part of the Holocene was characterized by large temperature variability, including the Preboreal Oscillations and the 8.2 k event. In general, the early Holocene was characterized by SSTs similar to those of today in the south and warmer than today in the north, and a smaller S-N temperature gradient (0.23 °C/°N) compared to the present temperature gradient (0.46 °C/°N). The southern proxy records (60-69°N) were more strongly influenced by slightly cooler subsurface water probably due to the seasonality of the orbital forcing and increased stratification due to freshening. The northern records (72-77.4°N) display a millennial-scale change associated with reduced insolation and a gradual weakening of the North Atlantic thermohaline circulation (THC). The observed northwards amplification of the early Holocene warming is comparable to the pattern of recent global warming and future climate modelling, which predicts greater warming at higher latitudes. The overall trend during mid and late Holocene was a cooling in the north, stable or weak warming in the south, and a maximum S-N SST gradient of ca 0.7 °C/°N at 5000 cal. years BP. Superimposed on this trend were several abrupt temperature shifts. Four of these shifts, dated to 9000-8000, 5500-3000 and 1000 and ~400 cal. years BP, appear to be global, as they correlate with periods of global climate change. In general, there is a good correlation between the northern North Atlantic temperature records and climate records from Norway and Svalbard.

Magnetic properties of Cenozoic MORB and Cretaceous MORB from DSDP and ODP holes

The fact that the natural remanent magnetization (NRM) intensity of mid-oceanic-ridge basalt (MORB) samples shows systematic variations as a function of age has long been recognized: maximum as well as average intensities are generally high for very young samples, falling off rather rapidly to less than half the recent values in samples between 10 and 30 Ma, whereupon they slowly rise in the early Tertiary and Cretaceous to values that approach those of the very young samples. NRM intensities measured in this study follow the same trends as those observed in previous publications. In this study, we take a statistical approach and examine whether this pattern can be explained by variations in one or more of all previously proposed mechanisms: chemical composition of the magnetic minerals, abundance of these magnetization carriers, vectorial superposition of parallel or antiparallel components of magnetization, magnetic grain or domain size patterns, low-temperature oxidation to titanomaghemite, or geomagnetic field behavior. We find that the samples do not show any compositional, petrological, rock-magnetic, or paleomagnetic patterns that can explain the trends. Geomagnetic field intensity is the only effect that cannot be directly tested on the same samples, but it shows a similar pattern as our measured NRM intensities. We therefore conclude that the geomagnetic field strength was, on-average, significantly greater during the Cretaceous than during the Oligocene and Miocene.

Phycoerythrin concentration during POLARSTERN cruises ANT-XXIV/4, ANT-XXV/1, and ANT-XXVI/4

Phycobiliproteins are a family of water-soluble pigment proteins that play an important role as accessory or antenna pigments and absorb in the green part of the light spectrum poorly used by chlorophyll a. The phycoerythrins (PEs) are one of four types of phycobiliproteins that are generally distinguished based on their absorption properties. As PEs are water soluble, they are generally not captured with conventional pigment analysis. Here we present a statistical model based on in situ measurements of three transatlantic cruises which allows us to derive relative PE concentration from standardized hyperspectral underwater radiance measurements (Lu). The model relies on Empirical Orthogonal Function (EOF) analysis of Lu spectra and, subsequently, a Generalized Linear Model with measured PE concentrations as the response variable and EOF loadings as predictor variables. The method is used to predict relative PE concentrations throughout the water column and to calculate integrated PE estimates based on those profiles.