Bootstrapping for penalized spline regression.

We describe and contrast several different bootstrapping procedures for penalized spline smoothers. The bootstrapping procedures considered are variations on existing methods, developed under two different probabilistic frameworks. Under the first framework, penalized spline regression is considered an estimation technique to find an unknown smooth function. The smooth function is represented in a high dimensional spline basis, with spline coefficients estimated in a penalized form. Under the second framework, the unknown function is treated as a realization of a set of random spline coefficients, which are then predicted in a linear mixed model. We describe how bootstrapping methods can be implemented under both frameworks, and we show in theory and through simulations and examples that bootstrapping provides valid inference in both cases. We compare the inference obtained under both frameworks, and conclude that the latter generally produces better results than the former. The bootstrapping ideas are extended to hypothesis testing, where parametric components in a model are tested against nonparametric alternatives.Methods; Framework; Regression; Linear mixed model; Mixed model; Model; Theory; Simulation; Hypothesis testing;

All that glitters is not gold: Relational events models with spurious events

As relational event models are an increasingly popular model for studying relational structures, the reliability of large-scale event data collection becomes more and more important. Automated or human-coded events often suffer from non-negligible false-discovery rates in event identification. And most sensor data are primarily based on actors’ spatial proximity for predefined time windows; hence, the observed events could relate either to a social relationship or random co-location. Both examples imply spurious events that may bias estimates and inference. We propose the Relational Event Model for Spurious Events (REMSE), an extension to existing approaches for interaction data. The model provides a flexible solution for modeling data while controlling for spurious events. Estimation of our model is carried out in an empirical Bayesian approach via data augmentation. Based on a simulation study, we investigate the properties of the estimation procedure. To demonstrate its usefulness in two distinct applications, we employ this model to combat events from the Syrian civil war and student co-location data. Results from the simulation and the applications identify the REMSE as a suitable approach to modeling relational event data in the presence of spurious events

Binary Models for Marginal Independence

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. For the graphical model representation we use bi-directed graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. Finally we consider combining these models with symmetry restrictions

Bayesian Exponential Random Graph Models with Nodal Random Effects

We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011) yields the basis of our modelling algorithm. A central question in network models is the question of model selection and following the Bayesian paradigm we focus on estimating Bayes factors. To do so we develop an approximate but feasible calculation of the Bayes factor which allows one to pursue model selection. Two data examples and a small simulation study illustrate our mixed model approach and the corresponding model selection.Comment: 23 pages, 9 figures, 3 table

Regression spline bivariate probit models: A practical approach to testing for exogeneity

Bivariate probit models can deal with a problem usually known as endogeneity. This issue is likely to arise in observational studies when confounders are unobserved. We are concerned with testing the hypothesis of exogeneity (or absence of endogeneity) when using regression spline recursive and sample selection bivariate probit models. Likelihood ratio and gradient tests are discussed in this context and their empirical properties investigated and compared with those of the Lagrange multiplier and Wald tests through a Monte Carlo study. The tests are illustrated using two datasets in which the hypothesis of exogeneity needs to be tested

Preoperative short-course radiotherapy versus combined radiochemotherapy in locally advanced rectal cancer: a multi-centre prospectively randomised study of the Berlin Cancer Society

BACKGROUND: The additional use of radiotherapy has changed the treatment of locally advanced rectal cancer (LARC) dramatically. But a major achievement has been the development of total mesorectal excision (TME) as a surgical standard and the recognition that the surgeon is the predominant prognostic factor. The benefit of preoperative hypofractionated radiotherapy (SCRT; five fractions each of 5 Gy), initially established by the Swedish Rectal Cancer Trial, has been demonstrated in conjunction with TME by the Dutch Colorectal Cancer Group. The concept of combined neoadjuvant radiochemotherapy (conventional radiation of about 50 Gy with chemotherapy) has not been compared over surgery alone with TME. However, the German Rectal Cancer Study Group recently demonstrated that preoperative radiochemotherapy (RCT) was better than postoperative radiochemotherapy in terms of local control. METHODS: Patients with histological proven rectal cancer staged T2N+ or T3 are randomized to receive either SCRT (25 Gy in five fractions of 5 Gy) plus TME-surgery within 5 days or RCT (50.4 Gy in 28 fractions of 1.8 Gy, continuous infusion 5-fluorouracil) plus TME-surgery 4-6 weeks later. All patients receive adjuvant chemotherapy (12 weeks continuous infusional 5-FU) and are followed up for 5 years. TME-quality is independently documented by the surgeon and the pathologist. Hypothesis of the study is that RCT is superior to SCRT in terms of local recurrence after five years. Secondary endpoints are overall survival, disease-free survival, complete resection rate (R0 resection), rate of sphincter saving resection, acute and late toxicity (radiation related side effects), and quality of life (including long term bowel function). DISCUSSION: Similar long-term survival, local control and late morbidity have been reported for both concepts of preoperative therapy in non-comparative studies. In addition to other ongoing (and recently published) comparative trials we include a larger number of patients for adequate power, apply quality-controlled TME and try to avoid the adjuvant treatment bias by mandatory adjuvant chemotherapy in both groups. Further more, stratification of the initially planned surgical procedure and sphincter-preservation will generate valid evidence whether RCT will allow a less aggressive (sphincter saving) surgical approach

Increased risk of type I errors in cluster randomised trials with small or medium numbers of clusters: a review, reanalysis,and simulation study

Background: Cluster randomised trials (CRTs) are commonly analysed using mixed-effects models or generalised estimating equations (GEEs). However, these analyses do not always perform well with the small number of clusters typical of most CRTs. They can lead to increased risk of a type I error (finding a statistically significant treatment effect when it does not exist) if appropriate corrections are not used. Methods: We conducted a small simulation study to evaluate the impact of using small-sample corrections for mixed-effects models or GEEs in CRTs with a small number of clusters. We then reanalysed data from TRIGGER, a CRT with six clusters, to determine the effect of using an inappropriate analysis method in practice. Finally, we reviewed 100 CRTs previously identified by a search on PubMed in order to assess whether trials were using appropriate methods of analysis. Trials were classified as at risk of an increased type I error rate if they did not report using an analysis method which accounted for clustering, or if they had fewer than 40 clusters and performed an individual-level analysis without reporting the use of an appropriate small-sample correction. Results: Our simulation study found that using mixed-effects models or GEEs without an appropriate correction led to inflated type I error rates, even for as many as 70 clusters. Conversely, using small-sample corrections provided correct type I error rates across all scenarios. Reanalysis of the TRIGGER trial found that inappropriate methods of analysis gave much smaller P values (P ≤ 0.01) than appropriate methods (P = 0.04–0.15). In our review, of the 99 trials that reported the number of clusters, 64 (65 %) were at risk of an increased type I error rate; 14 trials did not report using an analysis method which accounted for clustering, and 50 trials with fewer than 40 clusters performed an individual-level analysis without reporting the use of an appropriate correction. Conclusions: CRTs with a small or medium number of clusters are at risk of an inflated type I error rate unless appropriate analysis methods are used. Investigators should consider using small-sample corrections with mixed-effects models or GEEs to ensure valid results. Abbreviations: CRT, Cluster randomised trial; CI, Confidence interval; GEE, Generalised estimating equations; TRIGGER, Trial in Gastrointestinal Transfusio