Optimal learning under robustness and time-consistency

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed form, with a focus on two specific settings: Ellsberg’s two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied.Accepted manuscrip

Ambiguous volatility and asset pricing in continuous time

This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described

Validation of a contemporary prostate cancer grading system using prostate cancer death as outcome

BACKGROUND: Gleason scoring (GS) has major deficiencies and a novel system of five grade groups (GS⩽6; 3+4; 4+3; 8; ⩾9) has been recently agreed and included in the WHO 2016 classification. Although verified in radical prostatectomies using PSA relapse for outcome, it has not been validated using prostate cancer death as an outcome in biopsy series. There is debate whether an ‘overall' or ‘worst' GS in biopsies series should be used. METHODS: Nine hundred and eighty-eight prostate cancer biopsy cases were identified between 1990 and 2003, and treated conservatively. Diagnosis and grade was assigned to each core as well as an overall grade. Follow-up for prostate cancer death was until 31 December 2012. A log-rank test assessed univariable differences between the five grade groups based on overall and worst grade seen, and using univariable and multivariable Cox proportional hazards. Regression was used to quantify differences in outcome. RESULTS: Using both ‘worst' and ‘overall' GS yielded highly significant results on univariate and multivariate analysis with overall GS slightly but insignificantly outperforming worst GS. There was a strong correlation with the five grade groups and prostate cancer death. CONCLUSIONS: This is the largest conservatively treated prostate cancer cohort with long-term follow-up and contemporary assessment of grade. It validates the formation of five grade groups and suggests that the ‘worst' grade is a valid prognostic measure

Incorporating multiparametric MRI staging and the new histological Grade Group system improves risk-stratified detection of bone metastasis in prostate cancer

$\textbf{BACKGROUND}$: There remains uncertainty on the need for bone staging in men with intermediate-risk prostate cancer. Current guidelines do not use mpMRI-staging information and rely on historic pathology grading. $\textbf{METHODS}$: We investigated the ability of mpMRI and the new Grade Group system to better predict bone metastasis status in a retrospective cohort study of 438 men with prostate cancer undergoing baseline mpMRI and isotope bone scintigraphy (BS). $\textbf{RESULTS}$: Including mpMRI-staging information significantly increased the specificity of bone metastasis detection from 3.0% to 24.2% (P<0.01) and sensitivity from 89.2% to 97.3%. The new Grade Group score demonstrated progressive increase in bone metastasis rates (P<0.001). A novel risk-stratification model combining Grade Groups, PSA and mpMRI staging shows promise in predicting bone metastasis and could potentially reduce BS usage by 22.4%-34.7%. $\textbf{CONCLUSIONS}$: Incorporating the new Grade Group system and mpMRI staging more accurately identified bone metastatic risk and suggests men with Grade Group ⩽2 and/or without radiological T3 disease could safely avoid routine bone staging.We thank research support from the National Institute of Health Research, Cambridge Biomedical Research Centre, Cancer Research UK, Cancer Research UK and the Engineering and Physical Sciences Research Council Imaging Centre in Cambridge and Manchester and the Cambridge Experimental Cancer Medicine Centre

Incidence and mortality of incidental prostate cancer: a Swedish register-based study

In a national register-based study of incidence trends and mortality of incidental prostate cancer in Sweden, we found that a significant proportion (26.6%) of affected men diagnosed died of their disease, which challenges earlier descriptions of incidental prostate cancer as a non-lethal disease

Risk of prostate cancer after isolated high-grade prostatic intraepithelial neoplasia (HGPIN) detected on extended core needle biopsy : a UK hospital experience.

Background High-grade prostatic intraepithelial neoplasia (HGPIN) is a precursor lesion to prostate cancer (CaP). UK-based studies examining the occurrence of isolated HGPIN and subsequent risk of CaP are lacking. Our aim was to assess the occurrence of HGPIN in a regional UK population and to determine whether in a retrievable cohort of such patients that had repeat extended core biopsies, there was an elevated risk of CaP. Methods A retrospective analysis of the pathology database was conducted at our institution (Lancashire Teaching Hospitals NHS Foundation Trust) for prostate biopsies recorded between January 2001 and December 2005 (all extended core biopsies). Those patients with isolated HGPIN on 1st set of biopsies were identified and, their clinical characteristics and pathological findings from subsequent biopsies (if any) were determined. The risk of CaP on subsequent biopsies based on presenting baseline PSA was stratified. Results Of 2,192 biopsied patients, there were 88 cases of isolated HGPIN of which 67 patients underwent one or more repeat biopsies. In this repeat-biopsy group, 28 CaP diagnoses were made. Age at first biopsy (P 20 ng/ml – 87.5%. Conclusion Based on our results, we recommend delaying the 1st repeat biopsy at low PSA range but to have a shorter interval to repeat biopsies at intermediate and higher PSA ranges