Most Likely Transformations

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a cascade of increasingly complex transformation models that can be estimated, compared and analysed in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable can be set-up and estimated in the same theoretical and computational framework simply by choosing an appropriate transformation function and parameterisation thereof. The ability to evaluate the distribution function directly allows us to estimate models based on the exact likelihood, especially in the presence of random censoring or truncation. For discrete and continuous responses, we establish the asymptotic normality of the proposed estimators. A reference software implementation of maximum likelihood-based estimation for conditional transformation models allowing the same flexibility as the theory developed here was employed to illustrate the wide range of possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics 2017-06-1

Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models

Structured additive regression provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large flexibility of structured additive regression makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive appendix

A generalized additive model approach to time-to-event analysis

This tutorial article demonstrates how time-to-event data can be modelled in a very flexible way by taking advantage of advanced inference methods that have recently been developed for generalized additive mixed models. In particular, we describe the necessary pre-processing steps for transforming such data into a suitable format and show how a variety of effects, including a smooth nonlinear baseline hazard, and potentially nonlinear and nonlinearly time-varying effects, can be estimated and interpreted. We also present useful graphical tools for model evaluation and interpretation of the estimated effects. Throughout, we demonstrate this approach using various application examples. The article is accompanied by a new R-package called pammtools implementing all of the tools described here

Analyzing Competing Risk Data Using the R timereg Package

In this paper we describe flexible competing risks regression models using the comp.risk() function available in the timereg package for R based on Scheike et al. (2008). Regression models are specified for the transition probabilities, that is the cumulative incidence in the competing risks setting. The model contains the Fine and Gray (1999) model as a special case. This can be used to do goodness-of-fit test for the subdistribution hazardsâ proportionality assumption (Scheike and Zhang 2008). The program can also construct confidence bands for predicted cumulative incidence curves. We apply the methods to data on follicular cell lymphoma from Pintilie (2007), where the competing risks are disease relapse and death without relapse. There is important non-proportionality present in the data, and it is demonstrated how one can analyze these data using the flexible regression models.

Very High Dimensional Semiparametric Models

Very high dimensional semiparametric models play a major role in many areas, in particular in signal detection problems when sparse signals or sparse events are hidden among high dimensional noise. Concrete examples are genomic studies in biostatistics or imaging problems. In a broad context all kind of statistical inference and model selection problems were discussed for high dimensional data

Additive and Multiplicative Hazards Regression Models In Competing Risks Analysis: Application To The Canadian Heart Health Survey

Background: In survival analysis, an event whose occurrence influences the occurrence of another event is termed a competing risk event. The Cox hazards model is applicable in standard survival analysis with a single event. To correctly assess covariate effects in competing risks analysis, the Fine & Gray (F-G) subdistribution hazards and the Cox cause-specific hazards models are appropriate. Equally, additive hazards models can be used to examine the covariate effects in a competing risks framework. Objectives: (i) To examine the additive and multiplicative hazards models in the competing risks setting by applying the said models to the Canadian Heart Health Survey data; (ii) To determine the risk factors for cardiovascular disease using the competing risks approach; (iii) To compare the risk factors identified by the additive and multiplicative hazards models in the context of competing risks. Methods: The observational Canadian Heart Health Survey database collected between 1986 and 1995 is the baseline data used in this study. Two competing outcomes, cardiovascular disease (CVD) and non-CVD-related deaths, are analyzed with the Cox cause-specific and the F-G multiplicative hazards models. Similarly, the additive hazards models of Aalen and that of Lin & Ying (L-Y) are modeled for the outcomes using the competing risks approach. Results: There were 13,996 eligible subjects in my data, and 7,071 (50.5%) of them were women. After a median follow-up time of 15 years (interquartile range = 5.52 years), a total of 1,536 deaths were observed, and 549 (35.7%) of these were CVD related deaths. Factors like male gender, old age, and alcohol abstinence significantly increased the risk of CVD mortality in the additive and multiplicative hazards models. Former alcohol users compared to current alcohol users have a 53% (P-value= 0.002) and a 55% (P-value= 0.001) increased risk of CVD mortality in the Cox cause-specific and the F-G models, respectively. In the L-Y additive model, former alcohol users compared to current users increased CVD mortality by adding 16 new cases per 10,000 person-years (P-value = 0.008). Conclusion: The results from my study suggest that covariate effects in the Cox cause-specific and the F-G subdistribution hazards models may be identical in terms of magnitude and direction. The numerical results from the multiplicative and the additive hazards models give different interpretation of the covariate effects, and using both the additive and multiplicative models together would boost understanding of the data

Robust Inference for Univariate Proportional Hazards Frailty Regression Models

We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty. The frailty is assumed to have mean 1 within a known one-parameter family of distributions. Inference is based on a nonparametric likelihood. The behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified. The joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo-value maximizing the asymptotic limit of the likelihood. Appropriately standardized, the estimator converges weakly to a Gaussian process. When the model is correctly specified, the procedure is semiparametric efficient, achieving the semiparametric information bound for all parameter components. It is also proved that the bootstrap gives valid inferences for all parameters, even under misspecification. We demonstrate analytically the importance of the robust inference in several examples. In a randomized clinical trial, a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified. Under certain conditions on the covariates, the ratios of the regression parameters are still identifiable. The practical utility of the procedure is illustrated on a non-Hodgkin's lymphoma dataset.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000053

Exposure, hazard, and survival analysis of diffusion on social networks

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144676/1/sim7658_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144676/2/sim7658.pd

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)