Use Of Informative Priors Research Articles

Surrogacy assessment using principal stratification with multivariate normal and Gaussian copula models.

The validation of intermediate markers as surrogate markers (S) for the true outcome of interest (T) in clinical trials offers the possibility for trials to be run more quickly and cheaply by using the surrogate endpoint in place of the true endpoint. Working within a principal stratification framework, we propose causal quantities to evaluate surrogacy using a Gaussian copula model for an ordinal surrogate and time-to-event final outcome. The methods are applied to data from four colorectal cancer clinical trials, where S is tumor response and T is overall survival. For the Gaussian copula model, a Bayesian estimation strategy is used and, as some parameters are not identifiable from the data, we explore the use of informative priors that are consistent with reasonable assumptions in the surrogate marker setting to aid in estimation. While there is some bias in the estimation of the surrogacy quantities of interest, the estimation procedure does reasonably well at distinguishing between poor and good surrogate markers. Some of the parameters of the proposed model are not identifiable from the data, and therefore, assumptions must be made in order to aid in their estimation. The proposed quantities can be used in combination to provide evidence about the validity of S as a surrogate marker for T.

IDENTIFICATION ISSUES IN LIMITED‐INFORMATION BAYESIAN ANALYSIS OF STRUCTURAL MACROECONOMIC MODELS

SUMMARYThe likelihood of the parameters in structural macroeconomic models typically has non‐identification regions over which it is constant. When sufficiently diffuse priors are used, the posterior piles up in such non‐identification regions. Use of informative priors can lead to the opposite, so both can generate spurious inference. We propose priors/posteriors on the structural parameters that are implied by priors/posteriors on the parameters of an embedding reduced‐form model. An example of such a prior is the Jeffreys prior. We use it to conduct Bayesian limited‐information inference on the new Keynesian Phillips curve with a VAR reduced form for US data. Copyright © 2014 John Wiley & Sons, Ltd.

Bayesian and Frequentist Comparison for Epidemiologists: A Non Mathematical Application on Logistic Regressions

Background: Statistical frequentist techniques are sometimes misinterpreted or misused, while Bayesian techniques seem to present several practical advantages, such as accommodating small sample sizes, unobserved variables along with measurement errors and incorporating information from previous studies. The primary objective of this study was to evaluate the association between waterpipe dependence and chronic obstructive pulmonary disease (COPD), by comparing frequentist and Bayesian methods' results. Methods: It is a multicenter case-control study, comparing a group of COPD patients with a control group. COPD diagnosis was held after clinical and paraclinical testing, while a standardized questionnaire was used to evaluate smoking history. Both frequentist and Bayesian analyses were performed. Results: Although carried out on the same dataset, the results quantitatively differed between the frequentist and Bayesian analysis. Whenever the frequentist results were clear cut such as in case of cigarette smoking association with COPD, performing the MCMC method helped to increase the accuracy of the results, but did not change the direction of hypothesis acceptance, except in doubtful cases. When the frequentist p-value was ≤0.100, such as in case of smoking more than 15 waterpipe-years, the MCMC method improved deciding between the null and alternative hypothesis. Conclusion: The Bayesian approach may have advantages over the frequentist one, particularly in case of a low power of the frequentist analysis, due to low sample size or sparse data; the use of informative priors might be particularly useful in narrowing credible interval and precising the choice between the null and alternative hypothesis. In case of borderline frequentist results, the MCMC method may be more conservative, particularly without priors. However, in case of large sample sizes, using frequentist methods is preferred.

Using informative priors in the estimation of mixtures over time with application to aerosol particle size distributions

The issue of using informative priors for estimation of mixtures at multiple time points is examined. Several different informative priors and an independent prior are compared using samples of actual and simulated aerosol particle size distribution (PSD) data. Measurements of aerosol PSDs refer to the concentration of aerosol particles in terms of their size, which is typically multimodal in nature and collected at frequent time intervals. The use of informative priors is found to better identify component parameters at each time point and more clearly establish patterns in the parameters over time. Some caveats to this finding are discussed.

Modelling prey consumption and switching by UK grey seals

Abstract Smout, S., Rindorf, A., Hammond, P. S., Harwood, J., and Matthiopoulos, J. Modelling prey consumption and switching by UK grey seals. – ICES Journal of Marine Science, 71: . Grey seals (Halichoerus grypus) are adaptable generalist predators whose diet includes commercial fish species such as cod. Consumption by the seals may reduce the size of some fish stocks or have an adverse effect on stock recovery programmes, especially because predation may trap sparse prey populations in a “predator pit”. To assess the likely impact of such effects, it is important to know how consumption and consequent predation mortality respond to the changing availability of prey. We present a model of grey seal consumption as a function of the availability of multiple prey types [a Multi-Species Functional Response (MSFR)]. We fit this MSFR to data on seal diet and prey availability (based on the overlap between the distributions of predators and prey). Bayesian methodology was employed to account for uncertainties in both dependent and independent variables, improve estimation convergence by the use of informative priors, and allow the estimation of missing data on prey availability. Both hyperbolic (Type 2) and sigmoidal (Type 3) functional response models were fitted to the data and the Type 3 model was clearly favoured during model selection, supporting the conclusion that seal–prey encounter rates change with prey abundance (sometimes referred to as “switching”). This suggests that some prey species may be vulnerable to predator pit effects. The fitted model reproduced contrasts in diet observed between different regions/years and, importantly, added information to the prior distributions of prey abundance in areas where the availability of some prey species (such as sandeels) was not known. This suggests that the diet of predators such as seals could provide information about the abundance and distribution of prey in areas that are not covered by fisheries and research surveys.

A Bayesian model of metapopulation viability, with application to an endangered amphibian

AbstractAimPopulation viability analysis (PVA) is used to quantify the risks faced by species under alternative management regimes. BayesianPVAs allow uncertainty in the parameters of the underlying population model to be easily propagated through to the predictions. We developed a Bayesian stochastic patch occupancy model (SPOM) and used this model to assess the viability of a metapopulation of the growling grass frog (Litoria raniformis) under different urbanization scenarios.LocationMelbourne, Victoria, Australia.MethodsWe fitted a Bayesian model that accounted for imperfect detection to a multiseason occupancy dataset forL. raniformiscollected across northern Melbourne. The probability of extinction was modelled as a function of effective wetland area, aquatic vegetation cover and connectivity, using logistic regression. The probability of colonization was modelled as a function of connectivity alone. We then simulated the dynamics of a metapopulation ofL. raniformissubject to differing levels of urbanization and compensatory wetland creation. Uncertainty was propagated by conducting simulations for 5000 estimates of the parameters of the models for extinction and colonization.ResultsThere was considerable uncertainty in both the probability of quasi‐extinction and the minimum number of occupied wetlands under most urbanization scenarios. Uncertainty around the change in quasi‐extinction risk and minimum metapopulation size increased with increasing habitat loss. For our focal metapopulation, the analysis revealed that significant investment in new wetlands may be required to offset the impacts of urbanization.Main conclusionsBayesian approaches toPVAallow parametric uncertainty to be propagated and considered in management decisions. They also provide means of identifying parameters that represent critical uncertainties, and, through the use of informative priors, can easily assimilate new data to reduce parametric uncertainty. These advantages, and the ready availability of software to run Bayesian analyses, will ensure that Bayesian approaches are used increasingly forPVAs.

Bayesian Approach to Noninferiority Trials for Proportions

Noninferiority trials are unique because they are dependent upon historical information in order to make meaningful interpretation of their results. Hence, a direct application of the Bayesian paradigm in sequential learning becomes apparently useful in the analysis. This paper describes a Bayesian procedure for testing noninferiority in two-arm studies with a binary primary endpoint that allows the incorporation of historical data on an active control via the use of informative priors. In particular, the posteriors of the response in historical trials are assumed as priors for its corresponding parameters in the current trial, where that treatment serves as the active control. The Bayesian procedure includes a fully Bayesian method and two normal approximation methods on the prior and/or on the posterior distributions. Then a common Bayesian decision criterion is used but with two prespecified cutoff levels, one for the approximation methods and the other for the fully Bayesian method, to determine whether the experimental treatment is noninferior to the active control. This criterion is evaluated and compared with the frequentist method using simulation studies in keeping with regulatory framework that new methods must protect type I error and arrive at a similar conclusion with existing standard strategies. Results show that both methods arrive at comparable conclusions of noninferiority when applied to a modified real data set. The advantage of the proposed Bayesian approach lies in its ability to provide posterior probabilities for effect sizes of the experimental treatment over the active control.

Information Technology Facilitates Cost-Effectiveness Analysis in Developing Countries

Health information technology offers a powerful tool to monitor the performance of a healthcare system. Advances in computer technology and capacity combined with lower start-up costs will allow developing countries to achieve greater impact when they initiate electronic health information systems. We focused on the integrated health information system that was established in Taiwan in conjunction with the launch of the National Health Insurance (NHI) programme. We used data from that health information system to conduct a cost-effectiveness analysis of chemotherapy use among breast cancer patients. We then used this analysis to discuss what policy makers can learn from this type of analysis. We identified a cohort of patients in the NHI Research Database who had been diagnosed with breast cancer in 2001 and had received chemotherapy following surgical removal of the tumour. We followed these patients for 3 years and conducted a cost-effectiveness analysis from the payer's perspective. Using the net benefit regression approach, we compared the cost effectiveness of the two most commonly prescribed first-line chemotherapy regimens for the treatment of breast cancer in 2001 in Taiwan. The dependent variable of the regression model was the individual-level net benefit, and the independent variables included a binary variable indicating the choice of chemotherapy regimen, the patients' age, co-morbidity, type of surgery, geographic region and type of treatment facility. We employed both frequentist and Bayesian approaches in our net benefit regression analyses. In the Bayesian analysis, we applied non-informative priors to all parameters in the base-case analyses. We then explored the use of informative priors in the sensitivity analysis, using cost-effectiveness data published in the literature to form the prior distributions for the relevant parameters. Over 60% of surgically treated breast cancer patients received either CMF (cyclophosphamide, methotrexate, fluorouracil) or CEF (cyclophosphamide, epirubicin, fluorouracil). A comparison of patient characteristics indicated that patients in the CEF group tended to be younger (47.8 vs 49.1 years; p = 0.016), and were significantly more likely to have undergone a mastectomy (84% vs 76%; p < 0.001) and to have been treated in a teaching hospital (26% vs 13%; p < 0.001). We also observed significant variations in geographic region of the location of facilities between treatment groups. On average, CEF was not cost effective in the treatment of patients with breast cancer in Taiwan, although analyses stratified by geographic region suggested a wide variation across regions. At a societal willingness to pay (WTP) of new Taiwanese dollar ($NT)1 500 000 ($US80 000), the probability that CEF was more cost effective than CMF was 0.0%, 0.0%, 0.0% and 3.9% for the Taipei metropolitan area, and the north, middle and the combined south and east region, respectively; the probability became 0.6%, 0.0%, 1.3% and 54.5%, respectively, at a WTP of $NT5 000 000 ($US270 000). After co-variate adjustments, the probabilities were 0.0%, 0.0%, 0.0% and 0.8%, respectively at a WTP of $NT1 500 000, and were 0.0%, 0.0%, 1.4% and 34.7% at $NT5 000 000. Sensitivity analyses showed that CEF potentially could have been more cost effective than CMF within a reasonable range of societal WTP (i.e. $NT1 000 000-3 000 000 or $US55 000-160 000) had the optimal dosage level for CEF been established for breast cancer patients in Taiwan. A population-based, fully integrated electronic health information system provides useful data to assess the cost effectiveness of competing treatments and interventions in current practice. This research may potentially inform policy makers of modifications that can be instituted to improve the cost effectiveness of a new therapy. However, findings from this study need to be interpreted with caution because the study provided information only on the short-term cost effectiveness (i.e. 3 years) of CEF compared with CMF. It is possible that a future analysis will reach a different conclusion when more years of follow-up data become available.

Handling uncertainty in economic evaluations of patient level data: A review of the use of Bayesian methods to inform health technology assessments

Due to potential advantages (e.g., using all available evidence), Bayesian methods have been proposed to assist healthcare decision making. This review provides a detailed description of how Bayesian methods have been applied to economic evaluations of patient level data. The results serve both as a reference and as a means by which to examine the appropriate application of Bayesian methods to inform decision making. MEDLINE, EMBASE, and Cochrane Economic Evaluation databases were searched to identify studies, published up to November 2007, meeting three inclusion criteria: (i) the study conducted an economic evaluation, (ii) sampling uncertainty was incorporated using Bayesian methods, (iii) the likelihood function was informed by patient level data from a single source. Data were collected on key study characteristics (e.g., prior distribution, likelihood function, presentation of uncertainty). The search identified 366 potentially relevant studies, from which 103 studies underwent full-text review. Sixteen studies met the inclusion criteria. Half of the studies used uninformative priors; most studies incorporated the potential dependence between costs and effects, and presented cost-effectiveness acceptability curves. Results were sensitive to changes in the priors and likelihoods. Limited use of informative priors, among the included studies, gives policy makers little guidance on one of the main benefits of Bayesian methods, the ability to integrate all available evidence to capture the uncertainty inherent in decision making.

Parameterizing age-structured models from a fisheries management perspective

Age-structured models are widely used in fisheries stock assessments and contain two very important parameters that determine the rate and amount of harvest that can be safely taken: the compensation rate in juvenile survival (κ) and the unfished biomass (Bo). These two parameters are often confounded. It is common for relative abundance indices to lack contrast, and the use of informative priors, or fixing at least one of these parameters, is necessary to develop management advice. Providing management advice proceeds by transforming estimates of biological variables such as Boand κ into management variables such as the maximum sustainable yield (C*) and the fishing mortality rate that would achieve this yield (F*). There is no analytical solution for the transformation of Bo, κ to C*, or F* for age-structured models with commonly used stock–recruitment functions and therefore must be done numerically. The opposite transition, however, does have an analytical solution for both the Beverton–Holt and Ricker recruitment models with partial selectivities for all age classes. Use of these analytical solutions allows for age-structured assessment models to be directly parameterized in terms of the management variables C* and F*. The effects of informative priors on C* and F* on the results of the assessment model are completely transparent to management.

Approaches to dimensionality reduction in proteomic biomarker studies

Mass-spectra based proteomic profiles have received widespread attention as potential tools for biomarker discovery and early disease diagnosis. A major data-analytical problem involved is the extremely high dimensionality (i.e. number of features or variables) of proteomic data, in particular when the sample size is small. This article reviews dimensionality reduction methods that have been used in proteomic biomarker studies. It then focuses on the problem of selecting the most appropriate method for a specific task or dataset, and proposes method combination as a potential alternative to single-method selection. Finally, it points out the potential of novel dimension reduction techniques, in particular those that incorporate domain knowledge through the use of informative priors or causal inference.

Ethics of randomised controlled trials – not yet time to give up on equipoise

In this commentary on Fries and Krishnan's argument that 'design bias' undermines the status of equipoise as the ethical justification for randomised controlled trials, it is argued that their argument is analogous to Bayesian arguments for the use of informative priors in trial design, but that this does not undermine the importance of equipoise. In particular, mismatches between the outcomes of interest to industrial sponsors of research and outcomes of interest to patients and clinicians ensure that in many cases industry-sponsored trials can fail to reflect the reasonable equipoise of working clinicians.

How robust are Bayesian posterior inferences based on a Ricker model with regards to measurement errors and prior assumptions about parameters?

We present a Bayesian approach of a Ricker stock-recruitment (S/R) analysis accounting for measurement errors on S/R data. We assess the sensitivity of posterior inferences to (i) the choice of Ricker model parameterizations, with special regards to management-related ones, and (ii) prior parameter distributions. Closed forms for Ricker parameter posterior distributions exist given S/R data known without error. We use this property to develop a procedure based on the Rao–Blackwell formula. This procedure achieves integration of measurement errors by averaging these closed forms over possible S/R data sets sampled from distributions derived from a stochastic model relating field data to the S and R variables. High-quality Bayesian estimates are obtained. The analysis of the influence of different parameterizations and of the priors is made easier. We illustrate our methodological approach by a case study of Atlantic salmon (Salmo salar). Posterior distributions for S and R are computed from a mark–recapture stochastic model. Ignoring measurement errors underestimates parameter uncertainty and overestimates both stock productivity and density dependence. We warn against using management-related parameterizations because it makes the strong prior assumption of long-term sustainability of stocks. Posterior inferences are sensitive to the choice of prior. The use of informative priors as a remedy is discussed.

Implications of Reference Priors for Prior Information and for Sample Size

Abstract Here we use posterior densities based on relative entropy reference priors for two purposes. The first purpose is to identify data implicit in the use of informative priors. We represent an informative prior as the posterior from an experiment with a known likelihood and a reference prior. Minimizing the relative entropy distance between this posterior and the informative prior over choices of data results in a data set that can be regarded as representative of the information in the informative prior. The second implication from reference priors is obtained by replacing the informative prior with a class of densities from which one might wish to make inferences. For each density in this class, one can obtain a data set that minimizes a relative entropy. The maximum of these sample sizes as the inferential density varies over its class can be used as a guess as to how much data is required for the desired inferences. We bound this sample size above and below by other techniques that permit it to ...