Beta-binomial Research Articles

Quantifying the number of lymph nodes for examination in breast cancer

ObjectiveExamining the correct number of lymph nodes when diagnosing breast cancer invasion is still a problem. This work aimed to develop a qualification model that estimates the possibility of missing nodes and the number of lymph nodes that need to be examined.MethodsBy analyzing lymph node invasion of 303,760 breast cancer samples with primary tumor stage and the number of examined and positive lymph nodes from the Surveillance, Epidemiology and End Results database using a beta-binomial model, the number of nodes that should be examined was quantified in different stages.ResultsIn general, to reduce the possibility of missing positive nodes to less than 10%, 21 lymph nodes should be examined; thus, the current median of dissected nodes (12) is not adequate. The number of nodes needed to be dissected for stages T1, T2, and T3 are 8, 37, and 87, respectively. Currently, the median number of node dissections for these stages were 12, 13, and 14, respectively. The clinical significance of the nodal staging score was validated with survival information.ConclusionCurrently, the number of lymph nodes dissected in breast cancer are excessive for T1 but insufficient for T2 and T3.

SiCloneFit: Bayesian inference of population structure, genotype, and phylogeny of tumor clones from single-cell genome sequencing data.

Accumulation and selection of somatic mutations in a Darwinian framework result in intra-tumor heterogeneity (ITH) that poses significant challenges to the diagnosis and clinical therapy of cancer. Identification of the tumor cell populations (clones) and reconstruction of their evolutionary relationship can elucidate this heterogeneity. Recently developed single-cell DNA sequencing (SCS) technologies promise to resolve ITH to a single-cell level. However, technical errors in SCS data sets, including false-positives (FP) and false-negatives (FN) due to allelic dropout, and cell doublets, significantly complicate these tasks. Here, we propose a nonparametric Bayesian method that reconstructs the clonal populations as clusters of single cells, genotypes of each clone, and the evolutionary relationship between the clones. It employs a tree-structured Chinese restaurant process as the prior on the number and composition of clonal populations. The evolution of the clonal populations is modeled by a clonal phylogeny and a finite-site model of evolution to account for potential mutation recurrence and losses. We probabilistically account for FP and FN errors, and cell doublets are modeled by employing a Beta-binomial distribution. We develop a Gibbs sampling algorithm comprising partial reversible-jump and partial Metropolis-Hastings updates to explore the joint posterior space of all parameters. The performance of our method on synthetic and experimental data sets suggests that joint reconstruction of tumor clones and clonal phylogeny under a finite-site model of evolution leads to more accurate inferences. Our method is the first to enable this joint reconstruction in a fully Bayesian framework, thus providing measures of support of the inferences it makes.

Estimating the Probability of Default for No-Default and Low-Default Portfolios

SummaryThe paper proposes a sequential Bayesian updating approach to estimate default probabilities on rating grade level for no- and low-default portfolios. Bayesian sequential updating enables default probabilities to be obtained also for those rating grades for which no defaults have been observed. The advantage of this approach is that it preserves the rank order of rating grades in the case of no defaults. Rank preservation is not ensured when using an identical prior distribution across all rating grades. We discuss Bayesian sequential updating for the beta–binomial model and a model incorporating the asymptotic single-risk factor model of the Basel Accord. Practical aspects such as incorporating information from external sources and the margin of conservatism are addressed.

108P - Biological difference of tumour mutational burden (TMB) and microsatellite instability (MSI) status in patients (pts) with somatic vs germline BRCA1/2-mutated advanced gastrointestinal (GI) cancers using cell-free DNA (cfDNA) sequencing analysis in the GOZILA study

108P - Biological difference of tumour mutational burden (TMB) and microsatellite instability (MSI) status in patients (pts) with somatic vs germline BRCA1/2-mutated advanced gastrointestinal (GI) cancers using cell-free DNA (cfDNA) sequencing analysis in the GOZILA study

Robustness of statistical methods when measure is affected by ceiling and/or floor effect.

A simulation study investigated how ceiling and floor effect (CFE) affect the performance of Welch's t-test, F-test, Mann-Whitney test, Kruskal-Wallis test, Scheirer-Ray-Hare-test, trimmed t-test, Bayesian t-test, and the "two one-sided tests" equivalence testing procedure. The effect of CFE on the estimate of group difference and on its confidence interval, and on Cohen's d and on its confidence interval was also evaluated. In addition, the parametric methods were applied to data transformed with log or logit function and the performance was evaluated. The notion of essential maximum from abstract measurement theory is used to formally define CFE and the principle of maximum entropy was used to derive probability distributions with essential maximum/minimum. These distributions allow the manipulation of the magnitude of CFE through a parameter. Beta, Gamma, Beta prime and Beta-binomial distributions were obtained in this way with the CFE parameter corresponding to the logarithm of the geometric mean. Wald distribution and ordered logistic regression were also included in the study due to their measure-theoretic connection to CFE, even though these models lack essential minimum/maximum. Performance in two-group, three-group and 2 × 2 factor design scenarios was investigated by fixing the group differences in terms of CFE parameter and by adjusting the base level of CFE. In general, bias and uncertainty increased with CFE. Most problematic were occasional instances of biased inference which became more certain and more biased as the magnitude of CFE increased. The bias affected the estimate of group difference, the estimate of Cohen's d and the decisions of the equivalence testing methods. Statistical methods worked best with transformed data, albeit this depended on the match between the choice of transformation and the type of CFE. Log transform worked well with Gamma and Beta prime distribution while logit transform worked well with Beta distribution. Rank-based tests showed best performance with discrete data, but it was demonstrated that even there a model derived with measurement-theoretic principles may show superior performance. Trimmed t-test showed poor performance. In the factor design, CFE prevented the detection of main effects as well as the detection of interaction. Irrespective of CFE, F-test misidentified main effects and interactions on multiple occasions. Five different constellations of main effect and interactions were investigated for each probability distribution, and weaknesses of each statistical method were identified and reported. As part of the discussion, the use of generalized linear models based on abstract measurement theory is recommended to counter CFE. Furthermore, the necessity of measure validation/calibration studies to obtain the necessary knowledge of CFE to design and select an appropriate statistical tool, is stressed.

Effects of between-batch variability on the type I error rate in biosimilar development

Biological products are known to have some between-batch variation. However, the traditional method to assess biosimilarity does not consider such between-batch variation. Beta-binomial models and linear random effect models are considered in order to incorporate between-batch variation for the binary endpoints and the continuous endpoints, respectively. In this article, emphasis is on the beta-binomial models for the binary endpoint case. For the linear random effect models of the continuous endpoint case, we cite relevant references along with conducting some simulation studies. Overall, we show that the type I error rates are inflated when biosimilarity is evaluated by the traditional method, which ignores between-batch variation.

A Comparison Between a Meta-analytic Approach and Power Prior Approach to Using Historical Control Information in Clinical Trials With Binary Endpoints.

In the process of research and development of a new treatment, clinical trials are conducted to evaluate its safety and efficacy. Key to streamlining the process is to utilize appropriate historical information on an outcome of a control treatment when designing and analyzing a clinical trial. For the use of such historical control information, there exist a meta-analytic approach and power prior approach. In this article, we evaluate their performance with regard to the type I error (TIE) rate and power through a simulation study where we analyze the data on a binary outcome of an experimental treatment and a control treatment from a new small-scale trial, along with the corresponding data of the control treatment from multiple historical trials. The reason is that the difference in the performance between the 2 approaches has not been clear. When historical trials were homogeneous, the power was higher in the power prior approach and the meta-analytic approach using a beta-binomial model with a less noninformative prior than the other approaches. However, when heterogeneous historical trials were mixed, the power was lower, or the TIE rates got inflated. To make use of historical control data, if importance is attached to control of the TIE rate, the meta-analytic approach using a normal-normal hierarchical model may be preferable to the power prior approach, whereas if attached to improvement of the power, this preference be reversed. Anyway, the best approach should be chosen by comparing the operational characteristics of the approaches.

Expressions for the Entropy of Basic Discrete Distributions

We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, negative binomial, and hypergeometric distributions. Our results also establish connections between the entropy functions and to the Riemann zeta function and its generalizations.

Global Glomerulosclerosis in Kidney Biopsies With Differing Amounts of Cortex: A Clinical-Pathologic Correlation Study

Rationale & ObjectiveThe number of glomeruli is often used to determine the adequacy of a kidney biopsy (eg, at least 10 glomeruli). It is often assumed that biopsy specimens with limited amounts of cortex are too imprecise for detection of focal pathology.Study DesignClinical-pathologic correlation (cross-sectional).Setting & ParticipantsLiving kidney donors who underwent a needle core biopsy of their kidney at the time of donation.ExposureThe amount of cortex biopsied as determined by either the number of glomeruli or area of cortex on histology.OutcomeThe percentage of globally sclerotic glomeruli, density of interstitial fibrosis foci, and severity of arteriosclerosis were determined.Analytical approachA beta-binomial model assessed how the mean percentage of globally sclerotic glomeruli and patient variability in percentage of globally sclerotic glomeruli differed with the number of glomeruli on the biopsy specimen. Additional models assessed the association of interstitial fibrosis and arteriosclerosis with number of glomeruli.ResultsThere were 2,915 kidney donors studied. Fewer glomeruli on the biopsy specimen associated with higher mean percentage of globally sclerotic glomeruli and higher patient variability in percentage of globally sclerotic glomeruli. Smaller cortical volume on imaging correlated with both less cortex on biopsy and higher percentage of globally sclerotic glomeruli. Based on a statistical simulation, the probability of patient percentage of globally sclerotic glomeruli ≥ 10% if the biopsy percentage of globally sclerotic glomeruli is ≥10% (positive predictive value) was 45% with 1 to 9 glomeruli versus 31% with 10 or more glomeruli; the negative predictive value was 91% versus 98%. Fewer glomeruli also associated with more interstitial fibrosis and arteriosclerosis.LimitationsThe study was limited to living kidney donors. Patient variability in percentage of globally sclerotic glomeruli was based on a statistical model because multiple biopsy specimens per patient were not available.ConclusionsThe amount of cortex on a needle core biopsy is not completely random. Chronic changes from loss of cortex contribute to low amounts of cortex on a kidney biopsy specimen.

How many lymph nodes are enough? Assessing the adequacy of lymph node yield for staging in favorable histology wilms tumor

PurposeCurrent investigational priorities in the treatment of favorable histology Wilms tumor (FHWT) center on accurate staging and risk-stratification. The extent of lymph node (LN) sampling has not been clearly defined; its importance cannot be overstated as it guides adjuvant therapy. The identification of a minimum LN yield to minimize the risk of harboring occult metastatic disease could help development of surgical guidelines. This study focuses on using the beta-binomial distribution to estimate the risk of occult metastatic disease in patients with FHWT. Materials & methodsThe National Cancer Database was queried for patients with unilateral FHWT from 2004 to 2013. Data were used to characterize nodal positivity for patients who underwent surgery and had ≥1 positive LN and ≥2 LNs examined. The probability of missing a positive LN (i.e., false negative) for a given LN yield was calculated using an empirical estimation and the beta-binomial model. Patients were then stratified by tumor size. Results422 patients met study criteria. To limit the chance of missing a positive LN to ≤10%, the empirical estimation and beta-binomial model estimated that 6 and 10 LNs needed to be sampled, respectively. Tumor size did not influence the result. Internal validation showed little variation to maintain a false negative rate ≤ 10%. ConclusionsUsing mathematical modeling, it appears that the desired LN yield in FHWT to reduce the risk of false-negative LN sampling to ≤10% is between 6 and 10. The current analysis represents an objective attempt to determine the desired surgical approach to LN sampling to accurately stage patients with FHWT. Level of evidenceII

MethylSeqDesign: a framework for Methyl-Seq genome-wide power calculation and study design issues

Bisulfite DNA methylation sequencing (Methyl-Seq) becomes one of the most important technologies to study methylation level difference at a genome-wide scale. Due to the complexity and large scale of methyl-Seq data, power calculation and study design method have not been developed. Here, we propose a "MethylSeqDesign" framework for power calculation and study design of Methyl-Seq experiments by utilizing information from pilot data. Differential methylation analysis is based on a beta-binomial model. Power calculation is achieved using mixture model fitting of p-values from pilot data and a parametric bootstrap procedure. To circumvent the issue of existing tens of millions of methylation sites, we focus on the inference of pre-specified targeted regions. The performance of the method was evaluated with simulations. Two real examples are analyzed to illustrate our method. An R package "MethylSeqDesign" to implement this method is publicly available.

Integrating psychosocial care into routine cancer care: A stepped-wedge design cluster randomized controlled trial (SWD-RCT) to evaluate effectiveness of the HuCare Quality Improvement Strategy (HQIS) on health-related quality of life (HRQoL).

6515 Background: Cancer patients (pts) often do not receive evidence-based psychosocial care. We evaluate the effects of an implementation strategy we previously demonstrated feasible, which includes communication skill training for all physicians and nurses; four support visits at the centers by an improvement team to assist staff in identifying obstacles, finding solutions, and strengthening motivation; screening for distress and social needs; individualized pts' education with a referring nurse; use of a question prompt list. Methods: Multicenter incomplete SWD-RCT with 3 clusters of 5 centers each. Consecutive outpatients requiring medical treatment and diagnosed in the previous 2 months were eligible. Primary endpoint: difference of at least one of the 2 domains of HRQoL emotional or social functions, at 3 months from baseline, in pts of the centers that implemented the HQIS vs standard of care (SoC). Secondary endpoints include: patient mood, long-term effect, overall HRQoL. Analyses were performed using a beta-binomial regression model. Results: 762 pts were enrolled. At baseline, 41% showed high anxiety (HADS-A>7), and 88% had at least one psychosocial need. 299 health professionals attended 3-day courses (84% of all clinical staff). 647 pts (85%) were available for analysis. The 315 pts who received HQIS exhibited better quality of life for the emotional domain than those assigned to SOC (OR=1.115, p=0.016). Pts who showed the greatest improvement were the older (OR=1.003, p=0.035), had lower anxiety basal levels (OR=0.853, p<0.001), and social needs were met (OR=1.182, p<0.001). The difference was not significant for the social domain (OR=0.955, p=0.353). The HQIS’s long-term effect was confirmed for the emotional domain at 12 months. No effect on mood (HADS-D) and overall HRQoL was observed. Conclusions: To our knowledge this is the first RCT demonstrating the effectiveness of a psychosocial care implementation strategy on cancer patients’ emotional well-being. Clinical trial information: NCT03008993.

Estimating the Probability of Default for No-Default and Low-Default Portfolios

This article proposes a sequential Bayesian updating approach to estimate default probabilities on rating grade level for no- and low-default portfolios. Bayesian sequential updating allows to obtain default probabilities also for those rating grades for which no defaults have been observed. The advantage of the proposed approach is that it preserves the rank order of rating grades in case of no defaults. Rank-preservation is not ensured when using an identical prior distribution across all rating grades. We discuss Bayesian sequential updating for the beta-binomial model and a model incorporating the asymptotic single risk factor model of the Basel Accord. Practical aspects such as incorporating information from external sources and the margin of conservatism are addressed.

Beta-binomial modeling of CRISPR pooled screen data identifies target genes with greater sensitivity and fewer false negatives.

The simplicity and cost-effectiveness of CRISPR technology have made high-throughput pooled screening approaches accessible to virtually any laboratory. Analyzing the large sequencing data derived from these studies, however, still demands considerable bioinformatics expertise. Various methods have been developed to lessen this requirement, but there are still three tasks for accurate CRISPR screen analysis that involve bioinformatic know-how, if not prowess: designing a proper statistical hypothesis test for robust target identification, developing an accurate mapping algorithm to quantify sgRNA levels, and minimizing the parameters that need to be fine-tuned. To make CRISPR screen analysis more reliable as well as more readily accessible, we have developed a new algorithm, called CRISPRBetaBinomial or CB2. Based on the beta-binomial distribution, which is better suited to sgRNA data, CB2 outperforms the eight most commonly used methods (HiTSelect, MAGeCK, PBNPA, PinAPL-Py, RIGER, RSA, ScreenBEAM, and sgRSEA) in both accurately quantifying sgRNAs and identifying target genes, with greater sensitivity and a much lower false discovery rate. It also accommodates staggered sgRNA sequences. In conjunction with CRISPRcloud, CB2 brings CRISPR screen analysis within reach for a wider community of researchers.

Pitfalls of using the risk ratio in meta-analysis.

For meta‐analysis of studies that report outcomes as binomial proportions, the most popular measure of effect is the odds ratio (OR), usually analyzed as log(OR). Many meta‐analyses use the risk ratio (RR) and its logarithm because of its simpler interpretation. Although log(OR) and log(RR) are both unbounded, use of log(RR) must ensure that estimates are compatible with study‐level event rates in the interval (0, 1). These complications pose a particular challenge for random‐effects models, both in applications and in generating data for simulations. As background, we review the conventional random‐effects model and then binomial generalized linear mixed models (GLMMs) with the logit link function, which do not have these complications. We then focus on log‐binomial models and explore implications of using them; theoretical calculations and simulation show evidence of biases. The main competitors to the binomial GLMMs use the beta‐binomial (BB) distribution, either in BB regression or by maximizing a BB likelihood; a simulation produces mixed results. Two examples and an examination of Cochrane meta‐analyses that used RR suggest bias in the results from the conventional inverse‐variance–weighted approach. Finally, we comment on other measures of effect that have range restrictions, including risk difference, and outline further research.

A Bayesian adaptive marker-stratified design for molecularly targeted agents with customized hierarchical modeling.

It is well known that the treatment effect of a molecularly targeted agent (MTA) may vary dramatically, depending on each patient's biomarker profile. Therefore, for a clinical trial evaluating MTA, it is more reasonable to evaluate its treatment effect within different marker subgroups rather than evaluating the average treatment effect for the overall population. The marker-stratified design (MSD) provides a useful tool to evaluate the subgroup treatment effects of MTAs. Under the Bayesian framework, the beta-binomial model is conventionally used under the MSD to estimate the response rate and test the hypothesis. However, this conventional model ignores the fact that the biomarker used in the MSD is, in general, predictive only for the MTA. The response rates for the standard treatment can be approximately consistent across different subgroups stratified by the biomarker. In this paper, we proposed a Bayesian hierarchical model incorporating this biomarker information into consideration. The proposed model uses a hierarchical prior to borrow strength across different subgroups of patients receiving the standard treatment and, therefore, improve the efficiency of the design. Prior informativeness is determined by solving a "customized" equation reflecting the physician's professional opinion. We developed a Bayesian adaptive design based on the proposed hierarchical model to guide the treatment allocation and test the subgroup treatment effect as well as the predictive marker effect. Simulation studies and a real trial application demonstrate that the proposed design yields desirable operating characteristics and outperforms the existing designs.

A bivariate mixture of negative binomial distributions and its applications

We construct a new bivariate mixture of negative binomial distributions which represents over-dispersed data more efficiently. This is an extension of a univariate mixture of beta and negative binomial distributions. Characteristics of this joint distribution are studied including conditional distributions. Some properties of the correlation coefficient are explored. We demonstrate the applicability of our proposed model by fitting to three real data sets with correlated count data. A comparison is made with some previously used models to show the effectiveness of the new model.

Model to improve specificity for identification of clinically-relevant expanded T cells in peripheral blood.

Current methods to quantify T-cell clonal expansion only account for variance due to random sampling from a highly diverse repertoire space. We propose a beta-binomial model to incorporate time-dependent variance into the assessment of differentially abundant T-cell clones, identified by unique T Cell Receptor (TCR) β-chain rearrangements, and show that this model improves specificity for detecting clinically relevant clonal expansion. Using blood samples from ten healthy donors, we modeled the variance of T-cell clones within each subject over time and calibrated the dispersion parameters of the beta distribution to fit this variance. As a validation, we compared pre- versus post-treatment blood samples from urothelial cancer patients treated with atezolizumab, where clonal expansion (quantified by the earlier binomial model) was previously reported to correlate with benefit. The beta-binomial model significantly reduced the false-positive rate for detecting differentially abundant clones over time compared to the earlier binomial method. In the urothelial cancer cohort, the beta-binomial model enriched for tumor infiltrating lymphocytes among the clones detected as expanding in the peripheral blood in response to therapy compared to the binomial model and improved the overall correlation with clinical benefit. Incorporating time-dependent variance into the statistical framework for measuring differentially abundant T-cell clones improves the model's specificity for T-cells that correlate more strongly with the disease and treatment setting of-interest. Reducing background-level clonal expansion, therefore, improves the quality of clonal expansion as a biomarker for assessing the T cell immune response and correlations with clinical measures.

Determinants of bed net use conditional on access in population surveys in Ghana

BackgroundInsecticide-treated nets (ITNs) are one of the most effective and widely available methods for preventing malaria, and there is interest in understanding the complexities of behavioural drivers of non-use among those with access. This analysis evaluated net use behaviour in Ghana by exploring how several household and environmental variables relate to use among Ghanaians with access to a net.MethodsSurvey data from the Ghana 2014 Demographic and Health Survey and the 2016 Malaria Indicator Survey were used to calculate household members’ access to space under a net as well as the proportion of net use conditional on access (NUCA). Geospatial information on cluster location was obtained, as well as average humidex, a measure of how hot it feels, for the month each cluster was surveyed. The relationship between independent variables and net use was assessed via beta-binomial regression models that controlled for spatially correlated random effects using non-Gaussian kriging.ResultsIn both surveys, increasing wealth was associated with decreased net use among those with access in households when compared to the poorest category. In 2014, exposure to messages about bed net use for malaria prevention was associated with increased net use (OR 2.5, 95% CrI 1.5–4.2), as was living in a rural area in both 2014 (OR 2.5, 95% CrI 1.5–4.3) and 2016 (OR 1.6, 95% CrI 1.1–2.3). The number of nets per person was not associated with net use in either survey. Model fit was improved for both surveys by including a spatial random effect for cluster, demonstrating some spatial autocorrelation in the proportion of people using a net. Humidex, electricity in the household and IRS were not associated with NUCA.ConclusionNet use conditional on access is affected by household characteristics and is also spatially-dependent in Ghana. Setting (whether the household was urban or rural) plays a role, with wealthier and more urban households less likely to use nets when they are available. It will likely be necessary in the future to focus on rural settings, urban settings, and wealth status independently, both to better understand predictors of household net use in these areas and to design more targeted interventions to ensure consistent use of vector control interventions that meet specific needs of the population.

Bivariate beta-binomial model using Gaussian copula for bivariate meta-analysis of two binary outcomes with low incidence

In meta-analysis of rare-event outcomes, an additional statistical consideration is necessary due to the occurrence of studies with no event. The traditional approaches of adding a correction factor or omitting these studies are known to result in misleading conclusions. Furthermore, studies involved in the meta-analysis often report results for more than one outcome. Bivariate meta-analysis is known as a promising approach for jointly combining two outcomes whilst incorporating correlations between outcomes. However, there has not been sufficient discussion on a bivariate extension in the context of meta-analysis for rare-event outcomes. We consider a joint synthesis of two binary outcomes with low incidence, and propose a novel bivariate meta-analysis method using copula. The method assumes marginal beta-binomial distributions for the two outcomes, and links these margins by a bivariate copula which identifies an overall dependence structure between outcomes. A simulation study suggested that the method could provide a robust estimation for the incidence of rare events and have potential benefits of bivariate meta-analysis such as an improvement of precision of pooled estimates. We illustrated the method through an application to a meta-analysis of 48 studies that evaluated a potential risk of rosiglitazone on myocardial infection and cardiovascular death.