arXiv subjects

Roger Sewell

Publications and source records attributed to Roger Sewell.

5 recordsLinked to original sources

arXiv2026

A Bayesian Gamma-power-mixture survival regression model: predicting the recurrence of prostate cancer post-prostatectomy

In a dataset of 423 patients who had had radical prostatectomy for localised prostate cancer we estimated the apparent Shannon information (ASI) about time to biochemical recurrence in various subsets of the available pre-op variables using a Bayesian Gamma-power-mixture survival regression model. In all the subsets examined the ASI was positive with posterior probability greater than 0.975 . Using only age and results of pre-operative blood tests (PSA and biomarkers) we achieved 0.232 (0.180 to 0.290) nats ASI (0.335 (0.260 to 0.419) bits) (posterior mean and equitailed 95% posterior confidence intervals). This is more than double the mean posterior ASI previously achieved on the same dataset by a subset of the current authors using a log-skew-Student-mixture model, and is greater than that previous value with posterior probability greater than 0.99 . Additionally using pre- or post-operative Gleason grades, operative findings, clinical stage, and presence or absence of extraprostatic extension or seminal vesicle invasion did not increase the ASI extracted. However removing the blood-based biomarkers and replacing them with either pre-operative Gleason grades or findings available from MRI scanning greatly reduced the available ASI to respectively 0.077 (0.038 to 0.120) and 0.088 (0.045 to 0.132) nats (both less than the values using blood-based biomarkers with posterior probability greater than 0.995). A greedy approach to selection of the best biomarkers gave TGFbeta1, VCAM1, IL6sR, and uPA in descending order of importance from those examined.

stat.AP↗

arXiv2024

Bayesian analysis of biomarker levels can predict time of recurrence of prostate cancer with strictly positive apparent Shannon information against an exponential attrition prior

Shariat et al previously investigated the possibility of predicting from clinical data (including Gleason grade and stage) and preoperative biomarkers, which of any pair of patients would suffer recurrence of prostate cancer first. We wished to establish the extent to which predictions of time of relapse from such a model could be improved upon using Bayesian methods. The same dataset was reanalysed with a Bayesian skew-Student mixture model. Predictions were made of which of any pair of patients would relapse first and of the time of relapse. The benefit of using these biomarkers relative to predictions made without them was measured by the apparent Shannon information, using as prior an exponential attrition model of relapse time independent of input variables. Using half the dataset for training and the other half for testing, predictions of relapse time from the strict Cox model gave $-\infty$ nepers of apparent Shannon information (it predicts that relapse can only occur at times when patients in the training set relapsed). Deliberately smoothed predictions from the Cox model gave -0.001 (-0.131 to +0.120) nepers, while the Bayesian model gave +0.109 (+0.021 to +0.192) nepers (mean, 2.5 to 97.5 centiles), being positive with posterior probability 0.993 and beating the blurred Cox model with posterior probability 0.927. These predictions from the Bayesian model thus outperform those of the Cox model, but the overall yield of predictive information leaves scope for improvement of the range of biomarkers in use. The Bayesian model presented here is the first such model for prostate cancer to consider the variation of relapse hazard with biomarker concentrations to be smooth, as is intuitive. It is also the first to be shown to provide more apparent Shannon information than the Cox model or to be shown to provide positive apparent information relative to an exponential prior.

stat.AP↗

arXiv2024

Assessment of the quality of a prediction

Shannon defined the mutual information between two variables. We illustrate why the true mutual information between a variable and the predictions made by a prediction algorithm is not a suitable measure of prediction quality, but the apparent Shannon mutual information (ASI) is; indeed it is the unique prediction quality measure with either of two very different lists of desirable properties, as previously shown by de Finetti and other authors. However, estimating the uncertainty of the ASI is a difficult problem, because of long and non-symmetric heavy tails to the distribution of the individual values of $j(x,y)=\log\frac{Q_y(x)}{P(x)}$ We propose a Bayesian modelling method for the distribution of $j(x,y)$, from the posterior distribution of which the uncertainty in the ASI can be inferred. This method is based on Dirichlet-based mixtures of skew-Student distributions. We illustrate its use on data from a Bayesian model for prediction of the recurrence time of prostate cancer. We believe that this approach is generally appropriate for most problems, where it is infeasible to derive the explicit distribution of the samples of $j(x,y)$, though the precise modelling parameters may need adjustment to suit particular cases.

math.ST↗

arXiv2023

Methods of self-assessment of confidence for secondary school maths students, and the benefits or otherwise of using such methods

We first consider the method of scoring students' self-assessment of confidence (SAC) used by Foster in [1], and find that with it reporting their true confidence is not the optimal strategy for students. We then identify all continuously differentiable scoring functions that both drive the student towards the optimal strategy of truthful reporting of confidence and satisfy an additional axiom ensuring motivation also to give correct answers to the questions asked. We discuss the relative merits of some of them, and favour splitting marks between a signed mark for correctness or not and a second mark for SAC based on the apparent Shannon information on whether the answer is correct, as the latter also imparts a useful life skill, namely avoiding being overconfident. We then turn to do further Bayesian analysis of the public dataset associated with [1], showing that the effects of incorporating SAC into teaching vary both by school and by quartile of ability in class. Finally we speculate on the potential reasons for this and discuss how future research could identify and avoid some of the causes.

stat.AP↗

arXiv2021

Hypothesis testing and confidence sets: why Bayesian not frequentist, and how to set a prior with a regulatory authority

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker common-sense criteria for solutions to inference problems, all failed by these frequentist methods but satisfied by any admissible method. We note that pseudo-Bayesian methods made by handicapping Bayesian methods to satisfy criteria on type I error rate makes them frequentist not Bayesian in nature. We give five examples showing the differences between Bayesian and frequentist methods; the first requiring little calculus, the second showing in abstract what is wrong with these frequentist methods, the third to illustrate information conservation, the fourth to show that the same problems arise in everyday statistical problems, and the fifth to illustrate how on some real-life inference problems Bayesian methods require less data than fixed sample-size (resp. pseudo-Bayesian) frequentist hypothesis testing by factors exceeding 3000 (resp 300) without recourse to informative priors. To address the issue of different parties with opposing interests reaching agreement on a prior, we illustrate the beneficial effects of a Bayesian "Let the data decide" policy both on results under a wide variety of conditions and on motivation to reach a common prior by consent. We show that in general the frequentist confidence level contains less relevant Shannon information than the Bayesian posterior, and give an example where no deterministic frequentist critical regions give any relevant information even though the Bayesian posterior contains up to the maximum possible amount. In contrast use of the Bayesian prior allows construction of non-deterministic critical regions for which the Bayesian posterior can be recovered from the frequentist confidence.

math.ST↗