Likelihood theory for the graph Ornstein-Uhlenbeck process

We consider the problem of modelling restricted interactions between continuously-observed time series as given by a known static graph (or network) structure. For this purpose, we define a parametric multivariate Graph Ornstein-Uhlenbeck (GrOU) process driven by a general Lévy process to study the momentum and network effects amongst nodes, effects that quantify the impact of a node on itself and that of its neighbours, respectively. We derive the maximum likelihood estimators (MLEs) and their usual properties (existence, uniqueness and efficiency) along with their asymptotic normality and consistency. Additionally, an Adaptive Lasso approach, or a penalised likelihood scheme, infers both the graph structure along with the GrOU parameters concurrently and is shown to satisfy similar properties. Finally, we show that the asymptotic theory extends to the case when stochastic volatility modulation of the driving Lévy process is considered.

Impact of Q.Clear reconstruction algorithm on the interpretation of PET/CT images in patients with lymphoma

Background. Q.Clear is a new Bayesian penalised-likelihood PET reconstruction algorithm. It has been documented that Q.Clear increases SUVmax values of different malignant lesions. Purpose. As SUVmax values are crucial for interpretation of PET/CT images in patients with lymphoma, particularly when early and final response to treatment is evaluated, aim of the study was to systematically analyze the impact of the use of Q.Clear on interpretation of PET/CT in patients with lymphoma. Methods. 280 18F-FDG PET/CT scans in patients with lymphoma performed for staging (sPET), for early treatment response (iPET), after the end of treatment (ePET) and when a lymphoma relapse was suspected (rPET) were retrospectively analyzed. Scans separately reconstructed with two algorithms: Q.Clear and OSEM were compared. Results. The lymphoma stage was concordantly diagnosed in 69/70 patients with both algorithms in sPET. Discordant assessment of Deauville score (p < 0.001) was found in 11 cases (15.7%) of 70 iPET scans and in 11 cases of 70 ePET scans. An upgrade from negative to positive scan by Q.Clear resulted in case of 3 (4.3%) iPET scans and 7 (10.0%) ePET scans that resulted in alteration of management. Results of all 70 r-PET scans were concordant. SUVmax values of the target lymphoma lesions measured with Q.Clear were higher than with OSEM in 88.8% scans. Conclusion. Although the Q.Clear algorithm may alter interpretation of PET/CT only in a small proportion of patients, we recommend to use standard OSEM reconstruction for assessment of treatment response.

Impact of Q.Clear reconstruction algorithm on the interpretation of PET/CT images in patients with lymphoma

Background Q.Clear is a new Bayesian penalised-likelihood PET reconstruction algorithm. It has been documented that Q.Clear increases SUVmax values of different malignant lesions. Purpose. As SUVmax values are crucial for interpretation of PET/CT images in patients with lymphoma, particularly when early and final response to treatment is evaluated, aim of the study was to systematically analyze the impact of the use of Q.Clear on interpretation of PET/CT in patients with lymphoma. Methods 280 18 F-FDG PET/CT scans in patients with lymphoma performed for staging (sPET), for early treatment response (iPET), after the end of treatment (ePET) and when a lymphoma relapse was suspected (rPET) were retrospectively analyzed. Scans separately reconstructed with two algorithms: Q.Clear and OSEM were compared. Results The lymphoma stage was concordantly diagnosed in 69/70 patients with both algorithms in sPET. Discordant assessment of Deauville score (p<0.001) was found in 11 cases (15.7%) of 70 iPET scans and in 11 cases of 70 ePET scans. An upgrade from negative to positive scan by Q.Clear resulted in case of 3 (4.3%) iPET scans and 7 (10.0%) ePET scans that resulted in alteration of management. Results of all 70 r-PET scans were concordant. SUVmax values of the target lymphoma lesions measured with Q.Clear were higher than with OSEM in 88.8% scans. Conclusion Although the Q.Clear algorithm may alter interpretation of PET/CT only in a small proportion of patients, we recommend to use standard OSEM reconstruction for assessment of treatment response.

Ordered subset expectation maximisation vs Bayesian penalised likelihood reconstruction algorithm in 18F-PSMA-1007 PET/CT

Background The aim of the study was to compare widely used ordered subset expectation maximisation (OSEM) algorithm with a new Bayesian penalised likelihood (BPL) Q.Clear algorithm in 18F-PSMA-1007 PET/CT. Methods We retrospectively assessed 25 18F-PSMA-1007 PET/CT scans with both OSEM and Q.Clear reconstructions available. Each scan was independently reported by two physicians both in OSEM and Q.Clear. SUVmax, SUVmean and tumour-to-background ratio (TBR) of each lesion were measured. Reports were also compared for their final conclusions and the number and localisation of lesions. Results In both reconstructions the same 87 lesions were reported. Mean SUVmax, SUVmean and TBR were higher for Q.Clear than OSEM (7.01 vs 6.53 [p = 0.052], 4.16 vs 3.84 [p = 0.036] and 20.2 vs 16.8 [p < 0.00001], respectively). Small lesions (< 10 mm) had statistically significant higher SUVmax, SUVmean and TBR in Q.Clear than OSEM (5.37 vs 4.79 [p = 0.032], 3.08 vs 2.70 [p = 0.04] and 15.5 vs 12.5 [p = 0.00214], respectively). For lesions ≥ 10 mm, no significant differences were observed. Findings with higher tracer avidity (SUVmax ≥ 5) tended to have higher SUVmax, SUVmean and TBR values in Q.Clear (11.6 vs 10.3 [p = 0.00278], 7.0 vs 6.7 [p = 0.077] and 33.9 vs 26.7 [p < 0.00001, respectively). Mean background uptake did not differ significantly between Q.Clear and OSEM (0.42 vs 0.39, p = 0.07). Conclusions In 18F-PSMA-1007 PET/CT, Q.Clear SUVs and TBR tend to be higher (regardless of lesion localisation), especially for small and highly avid lesions. Increase in SUVs is also higher for lesions with high tracer uptake. Still, Q.Clear does not affect 18F-PSMA-1007 PET/CT specificity and sensitivity.

Combining multiple data sources in species distribution models while accounting for spatial dependence and overfitting with combined penalised likelihood maximisation

SummaryThe increase in availability of species data sets means that approaches to species distribution modelling that incorporate multiple data sets are in greater demand. Recent methodological developments in this area have led to combined likelihood approaches, in which a log-likelihood comprised of the sum of the log-likelihood components of each data source is maximised. Often, these approaches make use of at least one presence-only data set and use the log-likelihood of an inhomogeneous Poisson point process model in the combined likelihood construction. While these advancements have been shown to improve predictive performance, they do not currently address challenges in presence-only modelling such as checking and correcting for violations of the independence assumption of a Poisson point process model or more general challenges in species distribution modelling such as overfitting.In this paper, we present an extension of the combined likelihood frame-work which accommodates alternative presence-only likelihoods in the presence of spatial dependence as well as lasso-type penalties to account for potential overfitting. We compare the proposed combined penalised likelihood approach to the standard combined likelihood approach via simulation and apply the method to modelling the distribution of the Eurasian lynx in the Jura Mountains in eastern France.The simulations show that the proposed combined penalised likelihood approach has better predictive performance than the standard approach when spatial dependence is present in the data. The lynx analysis shows that the predicted maps vary significantly between the model fitted with the proposed combined penalised approach accounting for spatial dependence and the model fitted with the standard combined likelihood.This work highlights the benefits of careful consideration of the presence-only components of the combined likelihood formulation, and allows greater flexibility and ability to accommodate real datasets.