Statistics in Cancer
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Hierarchical Bayes small‐area estimation with an unknown link function

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Abstract

Area‐level unmatched sampling and linking models have been widely used as a model‐based method for producing reliable estimates of small‐area means. However, one practical difficulty is the specification of a link function. In this paper, we relax the assumption of a known link function by not specifying its form and estimating it from the data. A penalized‐spline method is adopted for estimating the link function, and a hierarchical Bayes method of estimating area means is developed using a Markov chain Monte Carlo method for posterior computations. Results of simulation studies comparing the proposed method with a conventional approach based on a known link function are presented. In addition, the proposed method is applied to data from the Survey of Family Income and Expenditure in Japan and poverty rates in Spanish provinces.

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2005 days ago
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Bayesian Calibration of p‐Values from Fisher's Exact Test

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Summary

p‐Values are commonly transformed to lower bounds on Bayes factors, so‐called minimum Bayes factors. For the linear model, a sample‐size adjusted minimum Bayes factor over the class of g‐priors on the regression coefficients has recently been proposed (Held & Ott, The American Statistician 70(4), 335–341, 2016). Here, we extend this methodology to a logistic regression to obtain a sample‐size adjusted minimum Bayes factor for 2 × 2 contingency tables. We then study the relationship between this minimum Bayes factor and two‐sided p‐values from Fisher's exact test, as well as less conservative alternatives, with a novel parametric regression approach. It turns out that for all p‐values considered, the maximal evidence against the point null hypothesis is inversely related to the sample size. The same qualitative relationship is observed for minimum Bayes factors over the more general class of symmetric prior distributions. For the p‐values from Fisher's exact test, the minimum Bayes factors do on average not tend to the large‐sample bound as the sample size becomes large, but for the less conservative alternatives, the large‐sample behaviour is as expected.

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2005 days ago
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Bayesian non‐parametric survival regression for optimizing precision dosing of intravenous busulfan in allogeneic stem cell transplantation

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Allogeneic stem cell transplantation is now part of standard care for acute leukaemia. To reduce toxicity of the pretransplant conditioning regimen, intravenous busulfan is usually used as a preparative regimen for acute leukaemia patients undergoing allogeneic stem cell transplantation. Systemic busulfan exposure, characterized by the area under the plasma concentration versus time curve, AUC, is strongly associated with clinical outcome. An AUC that is too high is associated with severe toxicities, whereas an AUC that is too low carries increased risks of recurrence of disease and failure to engraft. Consequently, an optimal AUC‐interval needs to be determined for therapeutic use. To address the possibility that busulfan pharmacokinetics and pharmacodynamics vary significantly with patients’ characteristics, we propose a tailored approach to determine optimal covariate‐specific AUC‐intervals. To estimate these personalized AUC‐intervals, we apply a flexible Bayesian non‐parametric regression model based on a dependent Dirichlet process and Gaussian process. Our analyses of a data set of 151 patients identified optimal therapeutic intervals for AUC that varied substantively with age and whether the patient was in complete remission or had active disease at transplant. Extensive simulations to evaluate the dependent Dirichlet process–Gaussian process model in similar settings showed that its performance compares favourably with alternative methods. We provide an R package, DDPGPSurv, that implements the dependent Dirichlet process–Gaussian process model for a broad range of survival regression analyses.

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2005 days ago
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Two steps forward and one step back

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Two steps forward and one step back

Two steps forward and one step back, Published online: 21 December 2018; doi:10.1038/s41571-018-0154-4

Perioperative chemotherapy is the standard of care for localized gastric cancer (GC). In 2018, additional postoperative radiotherapy was found to be ineffective; although, docetaxel was found to be superior to epirubicin in perioperative three-drug chemotherapy regimens. Validated biomarkers are needed for benefit from immunotherapy in advanced-stage GC. Metachronous GC can be prevented by Helicobacter pylori eradication.
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2005 days ago
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