scholarly journals A decision-theoretic approach to Bayesian clinical trial design and evaluation of robustness to prior-data conflict

Biostatistics ◽  
2020 ◽  
Author(s):  
Silvia Calderazzo ◽  
Manuel Wiesenfarth ◽  
Annette Kopp-Schneider
Keyword(s):  
Prior Information ◽  
Error Rates ◽  
Sensitivity Analyses ◽  
External Information ◽  
Parameter Estimates ◽  
Theoretic Approach ◽  
Proof Of Concept ◽  
Operating Characteristics ◽  
Historical Information ◽  
Integrated Risk

Summary Bayesian clinical trials allow taking advantage of relevant external information through the elicitation of prior distributions, which influence Bayesian posterior parameter estimates and test decisions. However, incorporation of historical information can have harmful consequences on the trial’s frequentist (conditional) operating characteristics in case of inconsistency between prior information and the newly collected data. A compromise between meaningful incorporation of historical information and strict control of frequentist error rates is therefore often sought. Our aim is thus to review and investigate the rationale and consequences of different approaches to relaxing strict frequentist control of error rates from a Bayesian decision-theoretic viewpoint. In particular, we define an integrated risk which incorporates losses arising from testing, estimation, and sampling. A weighted combination of the integrated risk addends arising from testing and estimation allows moving smoothly between these two targets. Furthermore, we explore different possible elicitations of the test error costs, leading to test decisions based either on posterior probabilities, or solely on Bayes factors. Sensitivity analyses are performed following the convention which makes a distinction between the prior of the data-generating process, and the analysis prior adopted to fit the data. Simulation in the case of normal and binomial outcomes and an application to a one-arm proof-of-concept trial, exemplify how such analysis can be conducted to explore sensitivity of the integrated risk, the operating characteristics, and the optimal sample size, to prior-data conflict. Robust analysis prior specifications, which gradually discount potentially conflicting prior information, are also included for comparison. Guidance with respect to cost elicitation, particularly in the context of a Phase II proof-of-concept trial, is provided.

scholarly journals Incorporation of biologic factors for the staging of de novo stage IV breast cancer

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Zhen-Yu He ◽  
Chen-Lu Lian ◽  
Jun Wang ◽  
Jian Lei ◽  
Li Hua ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Risk Score ◽  
Distant Metastasis ◽  
De Novo ◽  
Stage Iv ◽  
Staging System ◽  
Sensitivity Analyses ◽  
Operating Characteristics ◽  
Prognostic Analysis ◽  
Stage Iv Breast Cancer

Abstract This study aimed to investigate the prognostic value of biological factors, including histological grade, estrogen receptor (ER), progesterone receptor (PR), and human epidermal growth factor receptor-2 (HER2) status in de novo stage IV breast cancer. Based on eligibility, patient data deposited between 2010 and 2014 were collected from the surveillance, epidemiology, and end results database. The receiver operating characteristics curve, Kaplan–Meier analysis, and Cox proportional hazard analysis were used for analysis. We included 8725 patients with a median 3-year breast cancer-specific survival (BCSS) of 52.6%. Higher histologic grade, HER2-negative, ER-negative, and PR-negative disease were significantly associated with lower BCSS in the multivariate prognostic analysis. A risk score staging system separated patients into four risk groups. The risk score was assigned according to a point system: 1 point for grade 3, 1 point if hormone receptor-negative, and 1 point if HER2-negative. The 3-year BCSS was 76.3%, 64.5%, 48.5%, and 23.7% in patients with 0, 1, 2, and 3 points, respectively, with a median BCSS of 72, 52, 35, and 16 months, respectively (P < 0.001). The multivariate prognostic analysis showed that the risk score staging system was an independent prognostic factor associated with BCSS. Patients with a higher risk score had a lower BCSS. Sensitivity analyses replicated similar findings after stratification according to tumor stage, nodal stage, the sites of distant metastasis, and the number of distant metastasis. In conclusion, our risk score staging system shows promise for the prognostic stratification of de novo stage IV breast cancer.

An integrated risk-assessment framework for multiple threats to floodplain values in the Kakadu Region, Australia, under a changing climate

2018 ◽  
Vol 69 (7) ◽  
pp. 1159 ◽  
Author(s):  
P. Bayliss ◽  
C. M. Finlayson ◽  
J. Innes ◽  
A. Norman-López ◽  
R. Bartolo ◽  
...  
Keyword(s):  
Risk Assessment ◽  
At Risk ◽  
Invasive Species ◽  
Freshwater Ecosystems ◽  
Sensitivity Analyses ◽  
Assessment Framework ◽  
Integrated Risk Assessment ◽  
Invasive Species Control ◽  
Integrated Risk ◽  
Time Frames

The internationally important river–floodplains of the Kakadu Region in northern Australia are at risk from invasive species and future sea-level rise–saltwater inundation (SLR–SWI), requiring assessments of multiple cumulative risks over different time frames. An integrated risk-assessment framework was developed to assess threats from feral animals and aquatic weeds at three SLR-scenario time frames (present-day, 2070 and 2100) to natural (magpie goose habitats), cultural (indigenous hunting–fishing sites) and economic (tourism revenue less invasive species control costs) values. Probability density functions (pdfs) were fitted to spatial data to characterise values and threats, and combined with Monte Carlo simulation and sensitivity analyses to account for uncertainties. All risks were integrated in a Bayesian belief network to undertake ‘what if’ management-scenario analyses, and incorporated known ecological interactions and uncertainties. Coastal landscapes and socio-ecological systems in the region will be very different by 2100 as a result of SLR; freshwater ecosystems will transform to marine-dominated ecosystems and cannot be managed back to analogue conditions. In this context, future invasive-species risks will decrease, reflecting substantial loss of freshwater habitats previously at risk and a reduction in the extent of invasive species, highlighting the importance of freshwater refugia for the survival of iconic species.

Applicability of an extant batch respirometric assay in describing dynamics of ammonia and nitrite oxidation in a nitrifying bioreactor

2005 ◽  
Vol 52 (10-11) ◽  
pp. 503-508 ◽  
Author(s):  
K. Chandran ◽  
Z. Hu ◽  
B.F. Smets
Keyword(s):  
Kinetic Parameter ◽  
Sensitivity Analyses ◽  
Continuous Reactor ◽  
Parameter Estimates ◽  
Additional Parameter ◽  
Reactor Performance ◽  
Estimation Techniques ◽  
The Difference ◽  
The Impact ◽  
Best Fit

Several techniques have been proposed for biokinetic estimation of nitrification. Recently, an extant respirometric assay has been presented that yields kinetic parameters for both nitrification steps with minimal physiological change to the microorganisms during the assay. Herein, the ability of biokinetic parameter estimates from the extant respirometric assay to adequately describe concurrently obtained NH4+-N and NO2−-N substrate depletion profiles is evaluated. Based on our results, in general, the substrate depletion profiles resulted in a higher estimate of the maximum specific growth rate coefficient, μmax for both NH4+-N to NO2−-N oxidation and NO2−-N to NO3−-N oxidation compared to estimates from the extant respirograms. The trends in the kinetic parameter estimates from the different biokinetic estimation techniques are paralleled in the nature of substrate depletion profiles obtained from best-fit parameters. Based on a visual inspection, in general, best-fit parameters from optimally designed complete respirograms provided a better description of the substrate depletion profiles than estimates from isolated respirograms. Nevertheless, the sum of the squared errors for the best-fit respirometry based parameters was outside the 95% joint confidence interval computed for the best-fit substrate depletion based parameters. Notwithstanding the difference in kinetic parameter estimates determined in this study, the different biokinetic estimation techniques still are close to estimates reported in literature. Additional parameter identifiability and sensitivity analysis of parameters from substrate depletion assays revealed high precision of parameters and high parameter correlation. Although biokinetic estimation via automated extant respirometry is far more facile than via manual substrate depletion measurements, additional sensitivity analyses are needed to test the impact of differences in the resulting parameter values on continuous reactor performance.

scholarly journals Minimally-modeled search of higher multipole gravitational-wave radiation in compact binary coalescences.

2021 ◽  
Author(s):  
G. Vedovato ◽  
Edoardo Milotti ◽  
Giovanni Andrea Prodi ◽  
Sophie Bini ◽  
Marco Drago ◽  
...  
Keyword(s):  
Wave Radiation ◽  
Full Detail ◽  
Parameter Estimates ◽  
Spectral Features ◽  
Operating Characteristics ◽  
Fast Analysis ◽  
Time Frequency ◽  
Compact Binary ◽  
Frequency Representation ◽  
Novel Method

Abstract As the Advanced LIGO and Advanced Virgo interferometers, soon to be joined by the KAGRA interferometer, increase their sensitivity, they detect an ever-larger number of gravitational waves with a significant presence of higher multipoles in addition to the dominant (2, 2) multipole. These higher multipoles can be detected with different approaches, such as the minimally-modeled burst search methods, and here we discuss one such approach based on the coherent WaveBurst pipeline (cWB). During the inspiral phase the higher multipoles produce chirps whose instantaneous frequency is a multiple of the dominant (2, 2) multipole, and here we describe how cWB can be used to detect these spectral features. The search is performed within suitable regions of the time-frequency representation; their shape is determined by optimizing the Receiver Operating Characteristics. This novel method has already been used in the GW190814 discovery paper (Astrophys. J. Lett. 896 L44) and is very fast and flexible. Here we describe in full detail the procedure used to detect the (3, 3) multipole in GW190814 as well as searches for other higher multipoles during the inspiral phase, and apply it to another event that displays higher multipoles, GW190412, replicating the results obtained with different methods. The procedure described here can be used for the fast analysis of higher multipoles and to support the findings obtained with the model-based Bayesian parameter estimates.

A Kriging Based Fast and Efficient Method for Defect Detection in Massive Pipelines Using Magnetic Flux Leakages

2020 ◽  
Author(s):  
Subrata Mukherjee ◽  
Xuhui Huang ◽  
Lalita Udpa ◽  
Yiming Deng
Keyword(s):  
Magnetic Flux ◽  
Defect Detection ◽  
Synthetic Data ◽  
Cost Effective ◽  
Error Rates ◽  
Lattice Points ◽  
Operating Characteristics ◽  
Wide Range ◽  
Similar Accuracy ◽  
Fast Procedure

Abstract Systems in service continue to degrade with passage of time. Pipelines are among the most common systems that wear away with usage. For public safety it is of utmost importance to monitor pipelines and detect new defects within the pipelines. Magnetic flux leakage (MFL) testing is a widely used nondestructive evaluation (NDE) technique for defect detections within the pipelines, particularly those composed of ferromagnetic materials. Pipeline inspection gauge (PIG) procedure based on line-scans or 2D-scans can collect accurate MFL readings for defect detection. However, in real world applications involving large pipe-sectors such extensive scanning techniques are extremely time consuming and costly. In this paper, we develop a fast and cheap methodology that does not need MFL readings at all the points used in traditional PIG procedures but conducts defect detection with similar accuracy. We consider an under-sampling based scheme that collects MFL at uniformly chosen random scan-points over large lattices instead of extensive PIG scans over all lattice points. Based on readings for the chosen random scan points, we use Kriging to reconstruct MFL readings over the entire pipe-sectors. Thereafter, we use thresholding-based segmentation on the reconstructed data for detecting defective areas. We demonstrate the applicability of our methodology on synthetic data generated using popular finite element models as well as on MFL data collected via laboratory experiments. In these experiments spanning a wide range of defect types, our proposed novel MFL based NDE methodology is witnessed to have operating characteristics within the acceptable threshold of PIG based traditional methods and thus provide an extremely cost-effective, fast procedure with competing error rates that can be successfully used for scanning massive pipeline sectors.

A Two-Stage Conditional Estimation Procedure for Unrestricted Latent Class Models

1980 ◽  
Vol 5 (2) ◽  
pp. 129-156 ◽  
Author(s):  
George B. Macready ◽  
C. Mitchell Dayton
Keyword(s):  
General Class ◽  
Latent Class ◽  
Estimation Procedure ◽  
Error Rates ◽  
Latent Class Models ◽  
Parameter Estimates ◽  
Probability Models ◽  
Two Stage ◽  
Conditional Estimation ◽  
Class Models

A variety of latent class models has been presented during the last 10 years which are restricted forms of a more general class of probability models. Each of these models involves an a priori dependency structure among a set of dichotomously scored tasks that define latent class response patterns across the tasks. In turn, the probabilities related to these latent class patterns along with a set of “Omission” and “intrusion” error rates for each task are the parameters used in defining models within this general class. One problem in using these models is that the defining parameters for a specific model may not be “identifiable.” To deal with this problem, researchers have considered curtailing the form of the model of interest by placing restrictions on the defining parameters. The purpose of this paper is to describe a two-stage conditional estimation procedure which results in reasonable estimates of specific models even though they may be nonidentifiable. This procedure involves the following stages: (a) establishment of initial parameter estimates and (b) step-wise maximum likelihood solutions for latent class probabilities and classification errors with iteration of this process until stable parameter estimates across successive iterations are obtained.

scholarly journals An atmospheric inversion over the city of Cape Town: sensitivity analyses

2018 ◽  
Author(s):  
Alecia Nickless ◽  
Peter J. Rayner ◽  
Robert J. Scholes ◽  
Francois Engelbrecht ◽  
Birgit Erni
Keyword(s):  
Spatial Distribution ◽  
Correlation Length ◽  
Prior Information ◽  
Fossil Fuel ◽  
Cape Town ◽  
Uncertainty Reduction ◽  
Sensitivity Analyses ◽  
Sensitivity Tests ◽  
Error Correlation ◽  
Biogenic Fluxes

Abstract. We present sixteen different sensitivity tests applied to the Cape Town atmospheric Bayesian inversion analysis from March 2012 until June 2013. The reference inversion made use of a fossil fuel inventory analysis and estimates of biogenic fluxes from CABLE (Community Atmosphere Biosphere Land Exchange model). Changing the prior information product and the assumptions behind the uncertainties in the biogenic fluxes had the largest impact on the inversion results in terms of the spatial distribution of the fluxes, the size of the aggregated fluxes, and the uncertainty reduction achieved. A carbon assessment product of natural carbon fluxes, used in place of CABLE, and the Open-source Data Inventory for Anthropogenic CO2 product, in place of the fossil fuel inventory, resulted in prior estimates that were more positive on average than the reference configuration. The use of different prior flux products to inform separate inversions provided better constraint on the posterior fluxes compared with a single inversion. For the Cape Town inversion we showed that, where our reference inversion had aggregated prior flux estimates that were made more positive by the inversion, suggesting that the CABLE was overestimating the amount of CO2 uptake by the biota, when the alternative prior information was used, fluxes were made more negative by the inversion. As the posterior estimates were tending towards the same point, we could deduce that the best estimate was located somewhere between these two posterior fluxes. We could therefore restrict the best posterior flux estimate to be bounded between the solutions of these separate inversions. The assumed error correlation length for NEE fluxes played a major role in the spatial distribution of the posterior fluxes and in the size of the aggregated flux estimates, where ignoring these correlations led to posterior estimates more similar to the priors compared with the reference inversion. Apart from changing the prior flux products, making changes to the error correlation length in the NEE fluxes resulted in the greatest contribution to variability in the aggregated flux estimates between different inversions. Those cases where the prior information or NEE error correlations were altered resulted in greater variability between the aggregated fluxes of different inversions compared with the uncertainty around the posterior fluxes of the reference inversion. Solving for four separate weekly inversions resulted in similar estimates for the weekly fluxes compared with the single monthly inversion, while reducing computation time by up to 75 %. Solving for a mean weekly flux within a monthly inversion did result in differences in the aggregated fluxes compared with the reference inversion, but these differences were mainly during periods with data gaps. The uncertainty reduction from this inversion was almost double that of the reference inversion (47.2 % versus 25.6 %). Taking advantage of more observations to solve for one flux, such as allowing the inversion to solve for separate slow and fast components of the fossil fuel and NEE fluxes, as well as taking advantage of expected error correlation between fluxes of homogeneous biota, would reduce the uncertainty around the posterior fluxes. The sensitivity tests demonstrate that going one step further and assigning a probability distribution to these parameters, for example in a hierarchical Bayes approach, would lead to more useful estimates of the posterior fluxes and their uncertainties.

Modeling Biodegradation of Subsurface Oil in Sand Beaches Polluted with Oil

2014 ◽  
Vol 2014 (1) ◽  
pp. 1113-1125
Author(s):  
Xiaolong Geng ◽  
Michel C. Boufadel
Keyword(s):  
Microbial Biomass ◽  
Galvanized Steel ◽  
Sensitivity Analyses ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Zone Model ◽  
Residual Oil ◽  
Monod Kinetics ◽  
Microbial Biomass Nitrogen ◽  
Total N

ABSTRACT In April 2010, the explosion of the Deepwater Horizon (DWH) drilling platform led to the release of nearly 4.9 million barrels of crude oil into the Gulf of Mexico. The oil was brought to the supratidal zone of beaches (landward of the high tide line) by waves during storms, and was buried during subsequent storms. The objective of this paper is to investigate the biodegradation of subsurface oil in a tidally influenced sand beach located at Bon Secour National Wildlife Refuge and polluted by the DWH oil spill. Two transects were installed perpendicular to the shoreline within the supratidal zone of the beach. One transect had four galvanized steel piezometer wells to measure the water level. The other transect had four stainless steel multiport sampling wells that were used to collect pore water samples below the beach surface. The samples were analyzed for dissolved oxygen (DO), nitrogen, and redox conditions. Sediment samples were also collected at different depths to measure residual oil concentrations and microbial biomass. As the biodegradation of hydrocarbons was of interest, a biological model based on Monod kinetics was developed and coupled to the transport model MARUN, which is a two dimensional (vertical slice) finite element model for water flow and solute transport in tidally influenced beaches. The resulting coupled model, BIOMARUN, was used to simulate the biodegradation of total n-alkanes and polycyclic aromatic hydrocarbons (PAHs) trapped as residual oil in the unsaturated zone. Model parameter estimates were constrained by published Monod kinetics parameters. The field measurements, such as the concentrations of the oil, microbial biomass, nitrogen, and DO, were used as inputs for the simulations. The biodegradation of alkanes and PAHs was predicted in the simulation, and sensitivity analyses were conducted to assess the effect of the model parameters on the modeling results. Simulation results indicated that n-alkanes and PAHs would be biodegraded by 80% after 2 ± 0.5 years and 3.5 ± 0.5 years, respectively.

A MIXTURE MODEL FOR PAYMENTS AND PAYMENT NUMBERS IN CLAIMS RESERVING

2016 ◽  
Vol 48 (1) ◽  
pp. 25-53 ◽  
Author(s):  
Patrizia Gigante ◽  
Liviana Picech ◽  
Luciano Sigalotti
Keyword(s):  
Random Effects ◽  
Linear Models ◽  
External Information ◽  
Parameter Estimates ◽  
Prediction Errors ◽  
Poisson Regression Model ◽  
External Data ◽  
Fixed And Random Effects ◽  
Likelihood Approach ◽  
The Impact

AbstractWe consider a Tweedie's compound Poisson regression model with fixed and random effects, to describe the payment numbers and the incremental payments, jointly, in claims reserving. The parameter estimates are obtained within the framework of hierarchical generalized linear models, by applying the h-likelihood approach. Regression structures are allowed for the means and also for the dispersions. Predictions and prediction errors of the claims reserves are evaluated. Through the parameters of the distributions of the random effects, some external information (e.g. a development pattern of industry wide-data) can be incorporated into the model. A numerical example shows the impact of external data on the reserve and prediction error evaluations.

scholarly journals Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

2013 ◽  
Vol 17 (12) ◽  
pp. 4995-5011 ◽  
Author(s):  
Y. Sun ◽  
Z. Hou ◽  
M. Huang ◽  
F. Tian ◽  
L. Ruby Leung
Keyword(s):  
Inverse Modeling ◽  
Bayesian Model Averaging ◽  
Surface Flux ◽  
Sensitivity Analyses ◽  
Soil Conditions ◽  
Bayesian Inversion ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Community Land Model

Abstract. This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

Sign in / Sign up

Export Citation Format

Share Document