Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3

This is the final version. Available from NeurIPS 2020 via the DOI in this recordUncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differential Equation (PDE), as is the case in a wide range of engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive Error Model (AEM) is a novel approach, which alleviates this problem by exploiting a hierarchy of models, with increasing complexity and cost, and correcting the inexpensive models on-the-fly. The method has been integrated within the open-source probabilistic programming package PyMC3 and is available in the latest development version. In this paper, the algorithm is presented along with an illustrative example.Turing AI fellowshipEngineering and Physical Sciences Research Council (EPSRC

A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow

In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in porous media flow. We propose a new multilevel Metropolis-Hastings algorithm, and give an abstract, problem dependent theorem on the cost of the new multilevel estimator based on a set of simple, verifiable assumptions. For a typical model problem in subsurface flow, we then provide a detailed analysis of these assumptions and show significant gains over the standard Metropolis-Hastings estimator. Numerical experiments confirm the analysis and demonstrate the effectiveness of the method with consistent reductions of more than an order of magnitude in the cost of the multilevel estimator over the standard Metropolis-Hastings algorithm for tolerances $\varepsilon < 10^{-2}$

A data-centric approach to generative modelling for 3D-printed steel.

The emergence of additive manufacture (AM) for metallic material enables components of near arbitrary complexity to be produced. This has potential to disrupt traditional engineering approaches. However, metallic AM components exhibit greater levels of variation in their geometric and mechanical properties compared to standard components, which is not yet well understood. This uncertainty poses a fundamental barrier to potential users of the material, since extensive post-manufacture testing is currently required to ensure safety standards are met. Taking an interdisciplinary approach that combines probabilistic mechanics and uncertainty quantification, we demonstrate that intrinsic variation in AM steel can be well described by a generative statistical model that enables the quality of a design to be predicted before manufacture. Specifically, the geometric variation in the material can be described by an anisotropic spatial random field with oscillatory covariance structure, and the mechanical behaviour by a stochastic anisotropic elasto-plastic material model. The fitted generative model is validated on a held-out experimental dataset and our results underscore the need to combine both statistical and physics-based modelling in the characterization of new AM steel products

A data-centric approach to generative modelling for 3D-printed steel.

The emergence of additive manufacture (AM) for metallic material enables components of near arbitrary complexity to be produced. This has potential to disrupt traditional engineering approaches. However, metallic AM components exhibit greater levels of variation in their geometric and mechanical properties compared to standard components, which is not yet well understood. This uncertainty poses a fundamental barrier to potential users of the material, since extensive post-manufacture testing is currently required to ensure safety standards are met. Taking an interdisciplinary approach that combines probabilistic mechanics and uncertainty quantification, we demonstrate that intrinsic variation in AM steel can be well described by a generative statistical model that enables the quality of a design to be predicted before manufacture. Specifically, the geometric variation in the material can be described by an anisotropic spatial random field with oscillatory covariance structure, and the mechanical behaviour by a stochastic anisotropic elasto-plastic material model. The fitted generative model is validated on a held-out experimental dataset and our results underscore the need to combine both statistical and physics-based modelling in the characterization of new AM steel products

Adjuvant zoledronic acid reduces fractures in breast cancer patients; an AZURE (BIG 01/04) study

The fracture impact of adjuvant bisphosphonates in breast cancer is not defined with most trials reporting changes in bone mineral density as a surrogate. The AZURE trial (ISRCTN79831382) evaluated the impact of adjuvant zoledronic acid (ZOL) on fractures. The AZURE trial is an academic, multi-centre, randomised phase III study evaluating the addition of ZOL 4 mg to standard therapy (neo/adjuvant chemotherapy and/or endocrine therapy) for 5 years (administered by intravenous (iv) infusion every 3–4 weeks for 6 doses, then 3 monthly × 8 and 6 monthly × 5) in patients with stage II/III early breast cancer. Fracture data collected as part of skeletal-related adverse event reporting were analysed after a median of 84.2 months of follow-up and 966 disease-free survival (DFS) events. We assessed number of fractures, time- to-first fracture and the incidence of fractures before and after disease recurrence. Two hundred forty-four patients reported ≥1 fracture, 140 (8.3%) in the control arm (171 fractures) and 104 (6.2%) in the ZOL arm (120 fractures). Of the 291 fractures reported, 207 fractures occurred in the absence of recurrence (control 111, ZOL 96), 80 after recurrence (control 59, ZOL 21). The 5-year fracture rate was reduced from 5.9% (95%CI 4.8, 7.1%; control) to 3.8% (95%CI 2.9, 4.7%) with ZOL. ZOL significantly increased time-to-first fracture (HR 0.69, 95%CI 0.53–0.90; P = 0.0053) but the majority of fracture prevention benefit occurred after a DFS event (HR 0.3; 95%CI 0.17, 0.53; P < 0.001). Fracture benefits from ZOL were similar across menopausal sub-groups. In conclusion, adjuvant ZOL reduced the risk of clinical fractures, the majority of this protection occurred after disease recurrence

Long-Term Follow-Up of the Intergroup Exemestane Study

Purpose: The Intergroup Exemestane Study, an investigator-led study of 4,724 postmenopausal patients with early breast cancer (clinical trial information: ISRCTN11883920), has previously demonstrated that a switch from adjuvant endocrine therapy after 2 to 3 years of tamoxifen to exemestane was associated with clinically relevant improvements in efficacy. Here, we report the final efficacy analyses of this cohort. Patients and Methods: Patients who remained disease free after 2 to 3 years of adjuvant tamoxifen were randomly assigned to continue tamoxifen or switch to exemestane to complete a total of 5 years of adjuvant endocrine therapy. Given the large number of non–breast cancer–related deaths now reported, breast cancer–free survival (BCFS), with censorship of intercurrent deaths, was the primary survival end point of interest. Analyses focus on patients with estrogen receptor-positive or unknown tumors (n = 4,599). Results: At the time of the data snapshot, median follow-up was 120 months. In the population that was estrogen receptor positive or had unknown estrogen receptor status, 1,111 BCFS events were observed with 508 (22.1%) of 2,294 patients in the exemestane group and 603 (26.2%) of 2,305 patients in the tamoxifen group. The data corresponded to an absolute difference (between exemestane and tamoxifen) at 10 years of 4.0% (95% CI, 1.2% to 6.7%), and the hazard ratio (HR) of 0.81 (95% CI, 0.72 to 0.92) favored exemestane. This difference remained in multivariable analysis that was adjusted for nodal status, prior use of hormone replacement therapy, and prior chemotherapy (HR, 0.80; 95% CI, 0.71 to 0.90; P < .001). A modest improvement in overall survival was seen with exemestane; the absolute difference (between exemestane and tamoxifen) at 10 years in the population that was estrogen receptor positive or had unknown estrogen receptor status was 2.1% (95% CI, −0.5% to 4.6%), and the HR was 0.89 (95% CI, 0.78 to 1.01; P = .08). For the intention-to-treat population, the absolute difference was 1.6% (95% CI, −0.9% to 4.1%); the HR was 0.91 (95% CI, 0.80 to 1.03, P = .15). No statistically significant difference was observed in the proportion of patients who reported a fracture event in the post-treatment period. Conclusion: The Intergroup Exemestane Study and contemporaneous studies have established that a strategy of switching to an aromatase inhibitor after 2 to 3 years of tamoxifen can lead to sustained benefits in terms of reduction of disease recurrence and breast cancer mortality

Current management of treatment-induced bone loss in women with breast cancer treated in the United Kingdom

New therapeutic options in breast cancer have improved survival but consequently increase the relevance of late complications. Ovarian suppression/ablation and aromatase inhibitors (AI) in the adjuvant setting have improved outcome, but have clinically important adverse effects on bone health. However, investigation and management of cancer treatment-induced bone loss (CTIBL) is poorly defined with no national guidance. In 2004, a questionnaire was sent to over 500 breast surgeons and oncologists who treat breast cancer within the United Kingdom. The questionnaire evaluated access to bone densitometry and specialist expertise as well as attitudes to investigation of CTIBL and anticipated changes in the use of AI for postmenopausal early breast cancer. A total of 354 completed questionnaires were received, 47 from clinicians not currently treating breast cancer. Of the 307 evaluable questionnaires, 164 (53%) were from breast surgeons, 112 (36%) from clinical oncologists and 31 (10%) from medical oncologists. Although most respondents recognised that CTIBL was the responsibility of the treating breast team, investigations for CTIBL are limited even though most had adequate access to bone densitometry; 98 (32%) had not requested a DXA scan in the last 6 months and 224 (73%) had requested fewer than five scans. In all, 235 (76%) were not routinely investigating patients on AI for bone loss. A total of 277 (90%) felt that their practice would benefit from national guidelines to manage these patients, and the majority (59%) had little or no confidence in interpreting DXA results and advising on treatment. This questionnaire has highlighted clear deficiencies in management of CTIBL in early breast cancer. The development of national guidelines for the management of these patients and educational initiatives for breast teams are urgently required

Safety of zoledronic acid and incidence of osteonecrosis of the jaw (ONJ) during adjuvant therapy in a randomised phase III trial (AZURE: BIG 01-04) for women with stage II/III breast cancer

The AZURE trial is an ongoing phase III, academic, multi-centre, randomised trial designed to evaluate the role of zoledronic acid (ZOL) in the adjuvant therapy of women with stage II/III breast cancer. Here, we report the safety and tolerability profile of ZOL in this setting. Eligible patients received (neo)adjuvant chemotherapy and/or endocrine therapy and were randomised to receive neither additional treatment nor intravenous ZOL 4 mg. ZOL was administered after each chemotherapy cycle to exploit potential sequence-dependent synergy. ZOL was continued for 60 months post-randomisation (six doses in the first 6 months, eight doses in the following 24 months and five doses in the final 30 months). Serious (SAE) and non-serious adverse event (AE) data generated during the first 36 months on study were analysed for the safety population. 3,360 patients were recruited to the AZURE trial. The safety population comprised 3,340 patients (ZOL 1,665; control 1,675). The addition of ZOL to standard treatment did not significantly impact on chemotherapy delivery. SAE were similar in both treatment arms. No significant safety differences were seen apart from the occurrence of osteonecrosis of the jaw (ONJ) in the ZOL group (11 confirmed cases; 0.7%; 95% confidence interval 0.3–1.1%). ZOL in the adjuvant setting is well tolerated, and can be safely administered in addition to adjuvant therapy including chemotherapy. The adverse events were consistent with the known safety profile of ZOL, with a low incidence of ONJ

Trends in postoperative radiotherapy delay and the effect on survival in breast cancer patients treated with conservation surgery

The adequate timing of adjuvant radiotherapy (RT) in breast cancer has become a subject of increasing interest in recent years. A population-based study was undertaken to determine the influence of demographic and clinical factors on the postoperative RT delay in patients treated with breast-conserving surgery (BCS) and to assess the impact of delay on survival. In total, 7800 breast cancer patients treated with BCS and adjuvant RT between 1986 and 1998 in Yorkshire were included in the study. The median interval between surgery and the start of RT (S-RT interval) was 8 weeks (7 weeks for chemotherapy negative and 11 for chemotherapy positive patients). This interval increased substantially over time from 5 weeks during 1986-1988, irrespective of patients' chemotherapy status, to 10 and 17 weeks among chemotherapy negative and chemotherapy positive patients, respectively, in 1997-1998. The S-RT interval was also significantly influenced by travel time to RT centre, year and at which RT centre patient had the treatment (

The effects of adding zoledronic acid to neoadjuvant chemotherapy on tumour response: exploratory evidence for direct anti-tumour activity in breast cancer

Background: Pre-clinical studies have demonstrated synergistic anti-tumour effects of chemotherapy (CT) and zoledronic acid (ZOL). Within the AZURE trial, designed to determine whether the addition of ZOL to neoadjuvant therapy improves disease outcomes, a subgroup received neoadjuvant CT. We report a retrospective evaluation comparing pathological response in the primary tumour between treatment groups. Methods: In total, 205 patients received neoadjuvant CT±ZOL (CT+ZOL, n=102; CT, n=103). The primary end point was pathologically assessed residual invasive tumour size (RITS) at surgery. Secondary end points were pathological complete response (pCR) rate and axillary nodal involvement. Following review of surgical pathology reports (n=195), outcome differences between groups were assessed adjusting for potential response modifiers. Results: Baseline characteristics and CT treatments were similar. In multivariate analysis, allowing for biological and clinical factors known to influence tumour response, the adjusted mean RITS in CT and CT+ZOL groups were 27.4 and 15.5 mm, respectively, giving a difference in means of 12 mm (95% confidence interval: 3.5–20.4 mm; P=0.006). The pCR rate was 6.9% in the CT group and 11.7% in the CT+ZOL group (P=0.146). There was no difference in axillary nodal involvement (P=0.6315). Conclusion: These data suggest a possible direct anti-tumour effect of ZOL in combination with CT, warranting formal evaluation in prospective studies