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Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Frailty models provide a powerful tool to analyze this data, and this book offers different methods based on these models.

This study aimed to propose and compare metrics of accuracy and bias of genomic prediction of breeding values for traits with censored data. Genotypic and censored-phenotypic information were simulated for four traits with QTL heritability and polygenic heritability, respectively: C1: 0.07-0.07, C2: 0.07-0.00, C3: 0.27-0.27, and C4: 0.27-0.00. Genomic breeding values were predicted using the Mixed Cox and Truncated Normal models. The accuracy of the models was estimated based on the Pearson (PC), maximal (MC), and Pearson correlation for censored data (PCC) while the genomic bias was calculated via simple linear regression (SLR) and Tobit (TB). MC and PCC were statistically superior to PC for the trait C3 with 10 and 40% censored information, for 70% censorship, PCC yielded better results than MC and PC. For the other traits, the proposed measures were superior or statistically equal to the PC. The coefficients associated with the marginal effects (TB) presented estimates close to those obtained for the SLR method, while the coefficient related to the latent variable showed almost unchanged pattern with the increase in censorship in most cases. From a statistical point of view, the use of methodologies for censored data should be prioritized, even for low censoring percentages.

This study investigated the effect of a harsh winter climate on the performance of high-speed passenger trains in northern Sweden. Novel approaches based on heterogeneous statistical models were introduced to analyse the train performance to take time-varying risks of train delays into consideration. Specifically, the stratified Cox model and heterogeneous Markov chain model were used to model primary delays and arrival delays, respectively. Our results showed that weather variables including temperature, humidity, snow depth, and ice/snow precipitation have a significant impact on train performance.

We propose a new class of semiparametric estimators for proportional hazards models in the presence of measurement error in the covariates, where the baseline hazard function, the hazard function for the censoring time, and the distribution of the true covariates are considered as unknown infinite dimensional parameters. We estimate the model components by solving estimating equations based on the semiparametric efficient scores under a sequence of restricted models where the logarithm of the hazard functions are approximated by reduced rank regression splines. The proposed estimators are locally efficient in the sense that the estimators are semiparametrically efficient if the distribution of the error-prone covariates is specified correctly and are still consistent and asymptotically normal if the distribution is misspecified. Our simulation studies show that the proposed estimators have smaller biases and variances than competing methods. We further illustrate the new method with a real application in an HIV clinical trial.

Background: COVID-19 pandemic has created many challenges for clinicians. The monitoring trend for laboratory biomarkers is helpful to provide additional information to determine the role of those in the severity status and death outcome. Objective: This article aimed to evaluate the time-varying biomarkers by LOWESS Plot, check the proportional hazard assumption, and use to extended Cox model if it is violated. Methods: In the retrospective study, we evaluated a total of 1641 samples of confirmed patients with COVID-19 from October until March 2021 and referred them to the central hospital of Ayatollah Rohani Hospital affiliated with Babol University of medical sciences, Iran. We measured four biomarkers AST, LDH, NLR, and lymphocyte in over the hospitalization to find out the influence of those on the rate of death of COVID-19 patients. Results: The standard Cox model suggested that all biomarkers were prognostic factors of death (AST: HR=2.89, P<0.001, Lymphocyte: HR=2.60, P=0.004, LDH: HR=2.60, P=0.006, NLR: HR=1.80, P<0.001). The additional evaluation showed that the PH assumption was not met for the NLR biomarker. NLR biomarkers had a significant time-varying effect, and its effect increase over time (HR(t)=exp (0.234+0.261×log(t)), p=0.001). While the main effect of NLR did not show any significant effect on death outcome (HR=1.26, P=0.097). Conclusion: The reversal of results between the Cox PH model and the extended Cox model provides insight into the value of considering time-varying covariates in the analysis, which can lead to misleading results otherwise.

This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location-scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.

We present a new method for post-selection inference for ℓ₁ (lasso)-penalized likelihood models, including generalized regression models. Our approach generalizes the post-selection framework presented in Lee et al. (2013). The method provides P-values and confidence intervals that are asymptotically valid, conditional on the inherent selection done by the lasso. We present applications of this work to (regularized) logistic regression, Cox’s proportional hazards model, and the graphical lasso. We do not provide rigorous proofs here of the claimed results, but rather conceptual and theoretical sketches. Les auteurs présentent une nouvelle méthode d’inférence post-sélection pour les modèles de vraisemblance avec une pénalité ℓ₁(lasso). Leur approche généralise le cadre d’inférence post-sélection de Lee et coll. (2013). Leur méthode génère des p-values et des intervalles de confiance qui sont asymptotiquement valides conditionnellement à la sélection inhérente au lasso. Les auteurs présentent une application de ces résultats à la régression logistique (régularisée), au modèle à risques proportionnels de Cox et au lasso graphique. Ils ne présentent pas de preuves rigoureuses des résultats avanés, mais plutôt une esquisse conceptuelle et théorique.

Background This study is to explore the key genes and signaling transduction pathways related to the survival time of glioblastoma multiforme (GBM) patients. Results Our results not only showed that mutually explored GBM survival time related genes and signaling transduction pathways are closely related to the GBM, but also demonstrated that our innovated constrained optimization algorithm (CoxSisLasso strategy) are better than the classical methods (CoxLasso and CoxSis strategy). Conclusion We analyzed why the CoxSisLasso strategy can outperform the existing classical methods and discuss how to extend this research in the distant future.

Taking the invention patents of the C9 League from 2002 to 2020 as samples, a random survival forest model is established to predict the dynamic time-point of patent transfer cycle. By ranking the variables based on importance, it is found that the countries citing, the non-patent citations and the backward citations have significant impacts on the patent transfer cycle. C-index, Brier score and integrated Brier score are used to measure the discrimination and calibration ability of the four different survival models respectively. It is found that the prediction accuracy of the random survival forest model is higher than that of the Cox proportional risk model, Cox model based on lasso penalty and random forest model. In addition, the survival function and cumulative risk function under the random survival forest are adopted to predict and analyze the individual university patent transfer cycle, which shows that the random survival forest model has good prediction performance and is able to help universities as well as enterprises to identify the patent transfer opportunities effectively, thereby shortening the patent transfer cycle and improving the patent transfer efficiency.