Linear Transformation Model With Parametric Covariate Transformations

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.

Privileged by rapid increase in available epigenomic data, epigenome‐wide association studies (EWAS) are to make a profound contribution to understand the molecular mechanism of DNA methylation in cognitive aging. Current statistical methods used in EWAS are dominated by models based on multiple assumptions, for example, linear relationship between molecular profiles and phenotype, normal distribution for the methylation data and phenotype. In this study, we applied an assumption‐free method, the generalized correlation coefficient (GCC), and compare it to linear models, namely the linear mixed model and kinship model. We use DNA methylation associated with a cognitive score in 400 and 206 twins as discovery and replication samples respectively. DNA methylation associated with cognitive function using GCC, linear mixed model, and kinship model, identified 65 CpGs (p < 1e‐04) from discovery sample displaying both nonlinear and linear correlations. Replication analysis successfully replicated 9 of these top CpGs. When combining results of GCC and linear models to cover diverse patterns of relationships, we identified genes like KLHDC4, PAPSS2, and MRPS18B as well as pathways including focal adhesion, axon guidance, and some neurological signaling. Genomic region‐based analysis found 15 methylated regions harboring 11 genes, with three verified in gene expression analysis, also the 11 genes were related to top functional clusters including neurohypophyseal hormone and maternal aggressive behaviors. The GCC approach detects valuable methylation sites missed by traditional linear models. A combination of methylation markers from GCC and linear models enriched biological pathways sensible in neurological function that could implicate cognitive performance and cognitive aging.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

The linear transformation model is a semiparametric model which contains the Cox proportional hazards model and the proportional odds model as special cases. Cai et al. (Biometrika 87:867-878, 2000) have proposed an inference procedure for the linear transformation model with correlated censored observations. In this article, we develop formal and graphical model checking techniques for the linear transformation models based on cumulative sums of martingale-type residuals. The proposed method is illustrated with a clinical trial 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.

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.

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

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.

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.

Spline modeling is a mathematically refined modeling tool, that adequately fits complex data, even if they do not fit the traditional mathematical models. It is called the digital clay of the twenty-first century, although, so far, little used in clinical research spline modeling, but this is a matter of time. The usual model for the outcome analysis of clinical trials is the linear or log linear model. However, when the linear model is not significant, or when the data plots suggest nonlinearity, the quadratic and cubic models often produce a better fit. The current chapter shows, that spline modeling can produce curves that even better fit the outcome data of such clinical trials, than these traditional models do. Also, patterns in the data can be detected, that may go unobserved with traditional linear or curvilinear modeling. Spline modeling can adequately assess the relationships between an exposure and outcome variable in a clinical trial. It can detect patterns in a trial that are relevant, but go unobserved with simpler regression models. In clinical research spline modeling has great potential, given the presence of many nonlinear effects in this research field, and given its sophisticated mathematical refinement to fit any nonlinear effect in the most accurate way. Spline modeling should enable to improve making predictions from clinical research for the benefit of health decisions and health care. We hope that this brief introduction to spline modeling will stimulate clinical investigators to start using this wonderful method.

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.

This paper aims to detect the periodic coefficients of a Linear Regression model with Panel Data. Nonparametric locally and asymptotically optimal tests are proposed for testing the null hypothesis of a traditional linear regression model, against an alternative of a Periodic Coefficient Regression model. The Uniform Local Asymptotic Normality (ULAN) property is established for Periodic Linear Regression (PLR) model, to construct Locally asymptotically optimal tests. The rank-based version of the optimal parametric test is provided in particular cases. The performance of the proposed tests is valid with numerical simulations using the Monte Carlo study. Real data was studied for applying the periodic linear regression model which compared to both traditional regression and random coefficient regression 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.

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.

The impact of network connectivity on factor exposures, asset pricing, and portfolio diversification