Parametric POMDPs for planning in continuous state spaces

This thesis is concerned with planning and acting under uncertainty in partially-observable continuous domains. In particular, it focusses on the problem of mobile robot navigation given a known map. The dominant paradigm for robot localisation is to use Bayesian estimation to maintain a probability distribution over possible robot poses. In contrast, control algorithms often base their decisions on the assumption that a single state, such as the mode of this distribution, is correct. In scenarios involving significant uncertainty, this can lead to serious control errors. It is generally agreed that the reliability of navigation in uncertain environments would be greatly improved by the ability to consider the entire distribution when acting, rather than the single most likely state. The framework adopted in this thesis for modelling navigation problems mathematically is the Partially Observable Markov Decision Process (POMDP). An exact solution to a POMDP problem provides the optimal balance between reward-seeking behaviour and information-seeking behaviour, in the presence of sensor and actuation noise. Unfortunately, previous exact and approximate solution methods have had difficulty scaling to real applications. The contribution of this thesis is the formulation of an approach to planning in the space of continuous parameterised approximations to probability distributions. Theoretical and practical results are presented which show that, when compared with similar methods from the literature, this approach is capable of scaling to larger and more realistic problems. In order to apply the solution algorithm to real-world problems, a number of novel improvements are proposed. Specifically, Monte Carlo methods are employed to estimate distributions over future parameterised beliefs, improving planning accuracy without a loss of efficiency. Conditional independence assumptions are exploited to simplify the problem, reducing computational requirements. Scalability is further increased by focussing computation on likely beliefs, using metric indexing structures for efficient function approximation. Local online planning is incorporated to assist global offline planning, allowing the precision of the latter to be decreased without adversely affecting solution quality. Finally, the algorithm is implemented and demonstrated during real-time control of a mobile robot in a challenging navigation task. We argue that this task is substantially more challenging and realistic than previous problems to which POMDP solution methods have been applied. Results show that POMDP planning, which considers the evolution of the entire probability distribution over robot poses, produces significantly more robust behaviour when compared with a heuristic planner which considers only the most likely states and outcomes

Prognostic variables in low and high risk stage III colon cancers treated in two adjuvant chemotherapy trials

Background: Stratification of patients with stage III colon cancer into low (T1-3N1) and high (T4 and/or N2) risk groups is used to guide the duration of adjuvant chemotherapy. We determined the relative contribution of clinical and molecular features to survival by risk group. Materials & methods: Stage III colon cancer (N = 5337) patients from two adjuvant trials of FOLFOX ± cetuximab [N0147 (Alliance), PETACC-8] were risk grouped, then subgrouped by clinical features and molecular variables [KRAS and BRAF/mismatch repair (MMR) combined variable]. Distributions of disease-free survival (DFS), overall survival (OS), and survival after recurrence (SAR) were estimated. In multivariable Cox models, backward elimination was performed for analysis of candidate predictors of outcomes. Relative contributions of model-selected variables to outcomes by risk group were calculated using χ2. Results: Among low risk tumours, mutant KRAS and male gender were significantly associated with poorer OS multivariately. In high risk tumours, significantly poorer OS was observed for right sidedness and for mutant KRAS and BRAFV600E/pMMR, subgroups. Specifically, BRAFV600E/pMMR (OS: HR = 1.75; 95% CI: 1.36–2.24; Padj<.0001) and right- versus left-sidedness were associated with significantly poorer DFS, OS (HR = 1.56; 95% CI: 1.31–1.83; Padj<.0001), and SAR (HR = 1.64; 95% CI: 1.37–1.95; Padj<.0001). Poor prognosis of mutant KRAS for DFS and OS was similar among risk groups. BRAF/MMR and sidedness were associated with poorer SAR in both low and high risk tumours. Age, gender, and KRAS were the top three relative contributors to DFS and OS among low risk tumours; sidedness ranked first for DFS and OS, and second to BRAF/MMR for SAR among high risk tumours. Conclusion: Sidedness and BRAF/MMR contributed the most to survival outcomes among high risk tumours and should be interpreted in the context of risk group.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Prognostic Value of BRAF and KRAS Mutations in MSI and MSS Stage III Colon Cancer

Background: The prognostic value of BRAF and KRAS mutations within microsatellite-unstable (MSI) and microsatellite-stable (MSS) subgroups of resected colon carcinoma patients remains controversial. We examined this question in prospectively collected biospecimens from stage III colon cancer with separate analysis of MSI and MSS tumors from patients receiving adjuvant FOLFOX +/- cetuximab in two adjuvant therapy trials. Methods: Three groups were defined: BRAF Mutant, KRAS Mutant, and double wild-type. The analytic strategy involved estimation of study-specific effects, assessment of homogeneity of results, and then analysis of pooled data as no differences in patient outcome were found between treatment arms in both trials. Associations of mutations with patient outcome were analyzed, and multivariable models were adjusted for treatment and relevant factors. Results: Four thousand four hundred eleven tumors were evaluable for BRAF and KRAS mutations and mismatch repair status; 3934 were MSS and 477 were MSI. In MSS patients, all BRAF V600E mutations (hazard ratio [HR] = 1.54, 95% confidence interval [CI] = 1.23 to 1.92, P <. 001), KRAS codon 12 alterations, and p.G13D mutations (HR = 1.60, 95% CI = 1.40 to 1.83, P <. 001) were associated with shorter time to recurrence (TTR) and shorter survival after relapse (SAR; HR = 3.02, 95% CI = 2.32 to 3.93, P <. 001, and HR = 1.20, 95% CI = 1.01 to 1.44, P = .04, respectively). Overall survival (OS) in MSS patients was poorer for BRAF-mutant patients (HR = 2.01, 95% CI = 1.56 to 2.57, P <. 001) and KRAS-mutant patients (HR = 1.62, 95% CI = 1.38 to 1.91, P <. 001) vs wild-type. No prognostic role of KRAS or BRAF mutations was seen in MSI patients. Furthermore, no interaction was found between treatment arm (with or without cetuximab) and KRAS and BRAF mutations for TTR or OS in MSS patients. Conclusions: In a pooled analysis of resected stage III colon cancer patients receiving adjuvant FOLFOX, BRAF or KRAS mutations are independently associated with shorter TTR, SAR, and OS in patients with MSS, but not MSI, tumors. Future clinical trials in the adjuvant setting should consider these mutations as important stratification factors.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Role of deficient DNA mismatch repair status in patients with stage III colon cancer treated with FOLFOX adjuvant chemotherapy a pooled analysis from 2 randomized clinical trials

IMPORTANCE The prognostic impact of DNA mismatch repair (MMR) status in stage III colon cancer patients receiving FOLFOX (folinic acid, fluorouracil, and oxaliplatin) adjuvant chemotherapy remains controversial. OBJECTIVE To determine the association of MMR status with disease-free survival (DFS) in patients with stage III colon cancer treated with FOLFOX. DESIGN, SETTING, AND PARTICIPANTS The evaluated biomarkers for MMR status were determined from prospectively collected tumor blocks from patients treated with FOLFOX in 2 open-label, phase 3 randomized clinical trials: NCCTG N0147 and PETACC8. The studies were conducted in general community practices, private practices, and institutional practices in the United States and Europe. All participants had stage III colon adenocarcinoma. They were enrolled in NCCTG N0147 from February 2004 to November 2009 and in PETACC8 from December 2005 to November 2009. INTERVENTIONS Patients in the clinical trials were randomly assigned to receive 6 months of chemotherapy with FOLFOX or FOLFOX plus cetuximab. Only those patients treated with FOLFOX alone were included in the present study. MAIN OUTCOMES AND MEASURES Association of MMR status with DFS was analyzed using a stratified Cox proportional hazards model. Multivariable models were adjusted for age, sex, tumor grade, pT/pN stage, tumor location, ECOG (Eastern Cooperative Oncology Group) performance status, and BRAF V600E mutational status. RESULTS Among 2636 patients with stage III colon cancer treated with FOLFOX, MMR status was available for 2501. Of these, 252 (10.1%) showed deficient MMR status (dMMR; 134 women, 118 men; median age, 59 years), while 2249 (89.9%) showed proficient MMR status (pMMR; 1020 women, 1229 men; median age, 59 years). The 3-year DFS rates in the dMMR and pMMR groups were 75.6% and 74.4%, respectively. By multivariate analysis, patients with dMMR phenotype had significantly longer DFS than those with pMMR (adjusted hazard ratio, 0.73; 95% CI, 0.54-0.97; P = .03). CONCLUSIONS AND RELEVANCE The deficient MMR phenotype remains a favorable prognostic factor in patients with stage III colon cancer receiving FOLFOX adjuvant chemotherapy.SCOPUS: ar.jinfo:eu-repo/semantics/publishe