Checking the linear transformation model for clustered failure time observations

Among several semiparametric models, the Cox proportional hazard model is widely used to assess the association between covariates and the time-to-event when the observed time-to-event is interval-censored. Often, covariates are measured with error. To handle this covariate uncertainty in the Cox proportional hazard model with the interval-censored data, flexible approaches have been proposed. To fill a gap and broaden the scope of statistical applications to analyze time-to-event data with different models, in this paper, a general approach is proposed for fitting the semiparametric linear transformation model to interval-censored data when a covariate is measured with error. The semiparametric linear transformation model is a broad class of models that includes the proportional hazard model and the proportional odds model as special cases. The proposed method relies on a set of estimating equations to estimate the regression parameters and the infinite-dimensional parameter. For handling interval censoring and covariate measurement error, a flexible imputation technique is used. Finite sample performance of the proposed method is judged via simulation studies. Finally, the suggested method is applied to analyze a real data set from an AIDS clinical trial.

While many survival models have been invented, the Cox model and the proportional odds model are among the most popular ones. Both models are special cases of the linear transformation model. The linear transformation model typically assumes a linear function on covariates, which may not reflect the complex relationship between covariates and survival outcomes. Nonlinear functional form can also be specified in the linear transformation model. Nonetheless, the underlying functional form is unknown and mis‐specifying it leads to biased estimates and reduced prediction accuracy of the model. To address this issue, we develop a neural‐network transformation model. Similar to neural networks, the neural‐network transformation model uses its hierarchical structure to learn complex features from simpler ones and is capable of approximating the underlying functional form of covariates. It also inherits advantages from the linear transformation model, making it applicable to both time‐to‐event analyses and recurrent event analyses. Simulations demonstrate that the neural‐network transformation model outperforms the linear transformation model in terms of estimation and prediction accuracy when the covariate effects are nonlinear. The advantage of the new model over the linear transformation model is also illustrated via two real applications.

Linear transformation models, including the proportional hazards model and proportional odds model, under right censoring were discussed by Chen, Jin, and Ying (2002). The asymptotic variance of the estimator they proposed has a closed form and can be obtained easily by plug-in rules, which improves the computational efficiency. We develop an R package TransModel based on Chen's approach. The detailed usage of the package is discussed, and the function is applied to the Veterans' Administration lung cancer data.

Summary form only given, as follows. E to H mode transition is a typical nonlinear problem in an inductive Plasma sources. The mode transition has been explained in terms of power balance. In this presentation, the nonlinear equivalent circuit modeling has been studied. The linear transformer modeling has been used for inductive plasma source. However, linear transformer model can not explain the mode transition. The nonlinear circuit model based on the assumption that induction field is coupled nonlinearly to the plasma. When nonlinear coupling effects included in the linear transformer model, this nonlinear harmonic oscillation problem can be expressed by Duffing equation. The advantage of Duffing equation is hysteresis as well mode transition can be explained.

Optimal estimation of slope vector in high-dimensional linear transformation models

We investigate efficient estimation strategies for partially linear transformation models with time-dependent covariates under interval censoring. The unknown monotone function is approximated using a monotone -spline basis to enable flexible semiparametric modeling, and we develop a computationally efficient nested hybrid EM algorithm that integrates Newton's method with isotonic regression. To support large-sample inference, we propose a straightforward variance-covariance estimation procedure for the regression parameters and introduce a score test to assess the adequacy of the proportional hazards (PH) specification within the broader class of transformation models. The numerical performance of the penalized estimators is examined extensively and compared with both the time-invariant covariate model by Lu et al. and the semiparametric transformation model by Zeng et al. Finally, the proposed methodology is applied to data from the National Alzheimer's Coordinating Center (NACC) to demonstrate its practical utility in a real-world clinical setting.

In this study, a novel model for the analysis and optimisation of numerical and experimental chemical kinetics is developed. Concentration–time profiles of non-diffusive chemical kinetic processes and flame speed profiles of fuel–oxidiser mixtures can be described by certain characteristic points, so that relations between the coordinates of these points and the input parameters of chemical kinetic models become almost linear. This linear transformation model simplifies the analysis of chemical kinetic models, hence creating a robust global sensitivity analysis and allowing quick optimisation and reduction of these models. Firstly, in this study the model is extensively validated by the optimisation of a syngas combustion model with a large data set of imitated ignition experiments. The optimisation with the linear transformation model is quick and accurate, revealing the potential for decreasing the numerical costs of the optimisation process by at least one order of magnitude compared to established methods. Additionally, the optimisation on this data set demonstrates the capability of predicting reaction rate coefficients more accurately than by currently known confidence intervals. In a first application, methane combustion models are optimised with a small experimental set consisting of OH(A) and CH(A) concentration profiles from shock tube ignition experiments, species profiles from flow reactor experiments and laminar flame speeds. With the optimised models, especially the predictability for the flame speeds of mixtures of hydrogen, carbon monoxide and methane can be increased compared to established models. With the analysis of the optimised models, new information on the low pressure reaction coefficient of the fall-off reaction H+CH3(+M)⟺CH4(+M) is determined. In addition, the optimised combustion model is quickly and efficiently reduced to validate a new rapid reduction scheme for chemical kinetic models.

ABSTRACTThis paper discusses regression analysis of clustered interval-censored failure time data, which often occur in medical follow-up studies among other areas. For such data, sometimes the failure time may be related to the cluster size, the number of subjects within each cluster or we have informative cluster sizes. For the problem, we present a within-cluster resampling method for the situation where the failure time of interest can be described by a class of linear transformation models. In addition to the establishment of the asymptotic properties of the proposed estimators of regression parameters, an extensive simulation study is conducted for the assessment of the finite sample properties of the proposed method and suggests that it works well in practical situations. An application to the example that motivated this study is also provided.

Dynamic prediction of the risk of a clinical event using longitudinally measured biomarkers or other prognostic information is important in clinical practice. We propose a new class of landmark survival models. The model takes the form of a linear transformation model, but allows all the model parameters to vary with the landmark time. This model includes many published landmark prediction models as special cases. We propose a unified local linear estimation framework to estimate time-varying model parameters. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. We apply the methodology to a dataset from the African American Study of Kidney Disease and Hypertension and predict individual patient's risk of an adverse clinical event.

Robust feature screening for elliptical copula regression model

We take a semiparametric approach in fitting a linear transformation model to a right censored data when predictive variables are subject to measurement errors. We construct consistent estimating equations when repeated measurements of a surrogate of the unobserved true predictor are available. The proposed approach applies under minimal assumptions on the distributions of the true covariate or the measurement errors. We derive the asymptotic properties of the estimator and illustrate the characteristics of the estimator in finite sample performance via simulation studies. We apply the method to analyze an AIDS clinical trial data set that motivated the work.

Case-cohort analysis with semiparametric transformation models

In statistical analysis, when the value of a random variable is only known to be between two bounds, we say that this random variable is interval censored. This complicated censoring pattern is a common problem in research fields such as clinical trials or actuarial studies and raises challenges for statistical analysis. In this paper, we focus on regression analysis of case 2 interval-censored data. We first briefly review existing regression methods and an estimation approach under the class of linear transformation models developed by Zhang et al. We then propose a method for survival probability prediction via generalized estimating equations. We also consider a graphical model checking technique and a model selection tool. Some theoretical properties are established and the performance of our procedures is evaluated and illustrated by numerical studies including a real-life data analysis.

SUMMARY We consider the problem of estimating the regression coefficients in a competing risks model, where the relationship between the cause-specific hazard for the cause of interest and covariates is described using linear transformation models and when cause of failure is missing at random for a subset of individuals. Using the theory of Robins et al. (1994) for missing data problems and the approach of Chen et al. (2002) for estimating regression coefficients for linear transformation models, we derive augmented inverse probability weighted complete-case estimators for the regression coefficients that are doubly robust. Simulations demonstrate the relevance of the theory in finite samples.

The traditional linear transformation model assumes a linear relationship between the transformed response and the covariates. However, in real data, this linear relationship may be violated. We propose a linear transformation model that allows parametric covariate transformations to recover the linearity. Although the proposed generalization may seem rather simple, the inferential issues are quite challenging due to loss of identifiability under the null of no effects of transformed covariates. This article develops tests for such hypotheses. We establish rigorous inferences for parameters and the unspecified transformation function when the transformed covariates have nonzero effects. The estimates and tests perform well in simulation studies using a realistic sample size. We also develop goodness-of-fit tests for the transformation and R 2 for model comparison. GAGurine data are used to illustrate the practical utility of the proposed methods.