Competing risks analysis with missing cause-of-failure-penalized likelihood estimation of cause-specific Cox models

Competing risks models are attractive tools to analyze time-to-event data where several causes of an event are competing. However, a complexity may arise when, for instance, some subjects experience the event of interest but the causes are not known. Assuming that unknown causes of events are missing at random, we developed a novel constrained maximum penalized likelihood method for fitting semi-parametric cause-specific Cox regression models. Here, penalty functions were used to smooth the baseline hazards. An appealing feature of this approach is that all the relevant estimands in competing risks models are estimated including cause-specific hazard ratios, cause-specific baseline hazards, and cumulative incidence functions. Asymptotic results for these estimators were also developed, allowing for direct inferences. The proposed method was compared with some existing methods through a simulation study. A real data example was analyzed using the new method to evaluate the association of age at diagnosis with melanoma-death and non-melanoma-death in patients diagnosed with thin melanoma (tumour thickness ≤1.0  mm). An R function for our proposed method is currently available on GitHub and will be included in the R package "survivalMPL" at CRAN.

Reconstruction of difference in sequential CT studies using penalized likelihood estimation

Characterization of anatomical change and other differences is important in sequential computed tomography (CT) imaging, where a high-fidelity patient-specific prior image is typically present, but is not used, in the reconstruction of subsequent anatomical states. Here, we introduce a penalized likelihood (PL) method called reconstruction of difference (RoD) to directly reconstruct a difference image volume using both the current projection data and the (unregistered) prior image integrated into the forward model for the measurement data. The algorithm utilizes an alternating minimization to find both the registration and reconstruction estimates. This formulation allows direct control over the image properties of the difference image, permitting regularization strategies that inhibit noise and structural differences due to inconsistencies between the prior image and the current data. Additionally, if the change is known to be local, RoD allows local acquisition and reconstruction, as opposed to traditional model-based approaches that require a full support field of view (or other modifications). We compared the performance of RoD to a standard PL algorithm, in simulation studies and using test-bench cone-beam CT data. The performances of local and global RoD approaches were similar, with local RoD providing a significant computational speedup. In comparison across a range of data with differing fidelity, the local RoD approach consistently showed lower error (with respect to a truth image) than PL in both noisy data and sparsely sampled projection scenarios. In a study of the prior image registration performance of RoD, a clinically reasonable capture ranges were demonstrated. Lastly, the registration algorithm had a broad capture range and the error for reconstruction of CT data was 35% and 20% less than filtered back-projection for RoD and PL, respectively. The RoD has potential for delivering high-quality difference images in a range of sequential clinical scenarios including image-guided surgeries and treatments where accurate and quantitative assessments of anatomical change is desired.