Penalized likelihood estimation and iterative kalman smoothing for non-gaussian dynamic regression models

Dynamic regression or state space models provide a flexible framework for analyzing non-Gaussian time series and longitudinal data, covering for example models for discrete longitudinal observations. As for non-Gaussian random coefficient models, a direct Bayesian approach leads to numerical integration problems, often intractable for more complicated data sets. Recent Markov chain Monte Carlo methods avoid this by repeated sampling from approximative posterior distributions, but there are still open questions about sampling schemes and convergence. In this article we consider simpler methods of inference based on posterior modes or, equivalently, maximum penalized likelihood estimation. From the latter point of view, the approach can also be interpreted as a nonparametric method for smoothing time-varying coefficients. Efficient smoothing algorithms are obtained by iteration of common linear Kalman filtering and smoothing, in the same way as estimation in generalized linear models with fixed effects can be performed by iteratively weighted least squares estimation. The algorithm can be combined with an EM-type method or cross-validation to estimate unknown hyper- or smoothing parameters. The approach is illustrated by applications to a binary time series and a multicategorical longitudinal data set

Smoothing Hazard Functions and Time-Varying Effects in Discrete Duration and Competing Risks Models

State space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modelling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger data sets. Therefore, based on previous work on filtering and smoothing for multicategorical time series and longitudinal data, our approach uses posterior mode estimation. Thus we have to maximize posterior densities or, equivalently, a penalized likelihood, which enforces smoothness of hazard functions and time-varying effects by a roughness penalty. Dropping the Bayesian smoothness prior and adopting a nonparametric viewpoint, one might also start directly from maximizing this penalized likelihood. We show how Fisher scoring smoothing iterations can be carried out efficiently by iteratively applying linear Kalman filtering and smoothing to a working model. This algorithm can be combined with an EM-type procedure to estimate unknown smoothing- or hyperparameters. The methods are applied to a larger set of unemployment duration data with one and, in a further analysis, multiple terminating events from the German socio-economic panel GSOEP

Hyperparameter Estimation in Exponential Family State Space Models

Data-driven hyperparameter estimation or automatic choice of the smoothing parameter is of great importance, especially in the applications. This article presents and compares three methods for hyperparameter estimation in the framework of exponential family state space models: First, we motivate and derive a formula for an approximative likelihood, and an alternative, yet mathematical equivalent, expression proves to be a generalized version of a proposal in Durbin and Koopman (1992). Second, the EM-type algorithm suggested in Fahrmeir (1992) is restated here for reasons of comparison and third, the idea of cross-validation proposed by Kohn and Ansley (1989) for linear state space models is extended to the present context, in particular for multicategorical and multidimensional responses. Finally, we compare the three methods for hyperparameter estimation by applying each on three real data sets

Estimating Time-Varying Effects of Prognostic Factors for Stomach Cancer Patients within a Dynamic Grouped Cox Model

We describe the identification of prognostic factors in the framework of a completely resected stomach cancer survival-study. For the analysis the dynamic grouped Cox-Model was used allowing for time-varying covariate effects. Therefore the hazard rate might be non-proportional. As estimation concept we applied the posterior mode, computed by iteratively weighted Kalman filtering and smoothing steps. The medical study and questions are described, the statistical method is illustrated, the results are given and interpreted and the method is discussed

Dynamische Modelle zur Ereignisanalyse

Im Rahmen dieser Dissertation werden zeitdiskrete Modelle zur Ereignisanalyse mit dynamischen Effekten vorgestellt, unterteilt nach Ein-Episoden-Ein- Zustands-, Ein-Episoden-Mehr-Zustands- und Mehr-Episoden-Daten. Dabei sind auch Modelle mit nicht proportionalen Hazards zugelassen. Sie sind in Zustandsraumform angegeben. Das Phänomen der Rechtszensierung kann ebenfalls in die Modellierung einbezogen werden. In diesem allgemeinen Modellrahmen wird das Posteriori-Modus-Schätzkonzept zur Bestimmung zeitabhängiger Effekte eingesetzt. Zur numerisch effizienten Schätzung wird der bekannte Kalman Filter und Glätter-Algorithmus zum linear gewichteten Kalman Filter und Glätter modifiziert und dieser wiederum iteriert. Außerdem wird ein neues Schätzverfahren entwickelt und diskutiert, das den Fall einer diffusen beziehungsweise nichtinformativen Start-Priori- Verteilung numerisch stabil und effizient behandet. Insgesamt lassen sich damit Hazardraten und zeitabhängige Kovariableneffekte simultan schätzen bei einem im Vergleich zu anderen Verfahren (z.B. MCMC) geringen zeitlichen und rechnerischen Aufwand

Three Different Learning Curves Have an Independent Impact on Perioperative Outcomes After Robotic Partial Nephrectomy: A Comparative Analysis

Background Robot-assisted partial nephrectomy (RAPN) has become widely accepted, but its different underlying types of learning curves have not been comparatively analyzed to date. This study aimed to determine and compare the impact that the learning curve of the department, the console surgeon, and the bedside assistant as well as patient-related factors has on the perioperative outcomes of RAPN. Methods The study retrospectively analyzed 500 consecutive transperitoneal RAPNs (2007–2018) performed in a tertiary referral center by 7 surgeons and 37 bedside assistants. Patient characteristics and surgical data were obtained. Experience (EXP) was defined as the current number of RAPNs performed by the department, the surgeon, and the assistant. As the primary outcome, the impact of EXP and patient-related factors on perioperative outcomes were analyzed and compared. As the secondary outcome, a cutoff between “experienced” and “inexperienced” was defined. Correlation and regression analysis, receiver operating characteristic curve analysis, Fisher’s exact test, and the Mann–Whitney U test were performed, with p values lower than 0.05 denoting significance. Results The EXP of the department, the surgeon, and the assistant each has a major influence on perioperative outcome in RAPN irrespective of patient-related factors. Perioperative outcomes improve significantly with EXP greater than 100 for the department, EXP greater than 35 for the surgeon, and EXP greater than 15 for the assistant. Conclusions The perioperative results of RAPN are influenced by three different types of learning curves including those for the surgical department, the console surgeon, and the assistant. The influence of the bedside assistant clearly has been underestimated to date because it has a significant impact on the perioperative outcomes of RAPN

Open versus robot-assisted partial nephrectomy: A longitudinal comparison of 880 patients over 10 years

Background Most comparisons between robot‐assisted partial nephrectomy (RAPN) and open partial nephrectomy (OPN) indicate the superiority of RAPN, but the learning curve is often not considered. Methods All consecutive partial nephrectomies from the very first RAPN at a single tertiary referral centre (n = 818, 500 RAPN vs. 313 OPN) were retrospectively analyzed. Complications, success rates and surgical outcomes were compared. Inequalities between cohorts and the inherent learning curve were controlled by subgroup comparisons, regression analyses, and propensity score matching. Results Overall, RAPN had fewer complications, less blood loss, and shorter length of stay. However, an inherent learning curve caused higher complications for the first 4 years. Thereafter, perioperative outcomes clearly favoured RAPN, even for more complex tumours. Conclusions In one of the largest monocentric cohorts over more than 10 years, RAPN was found to be superior to OPN. However, not all advantages of RAPN are immediate because a learning curve must be passed

Robot-assisted versus open radical cystectomy: A cohort study on perioperative outcomes accounting for stage selection bias and surgical experience

Background Most comparisons of robot-assisted (RARC) versus open radical cystectomy (ORC) for urothelial carcinoma do not factor the inherent stage selection bias or surgical experience. Methods We compared the perioperative outcomes of 229 RARC and 335 ORC at a single tertiary referral centre with propensity score matching and multiple regression models, when controlling for tumour and patient characteristics, surgeon's experience and type of urinary diversion. Results RARC had less major complications (19.8% vs. 34.1%) and ICU admissions (6.6% vs. 19.8%), with lower blood loss (400 vs. 500 ml) and transfusion rates. The operating time was longer (336 vs. 286 min), but decreased with surgeon's experience. RARC had less positive surgical margins (3% vs. 8.4%) and a higher lymph node count (14 vs. 11). Conclusions In this large single centre series comparing RARC with ORC controlling for stage selection bias and surgical experience, RARC proved significantly better outcomes, especially with intracorporeal urinary diversion