Additive Rates Model Research Articles

Additive Transformation Models for Recurrent Events

In this article, we propose a class of additive transformation models for recurrent event data, which includes the additive rates model as a special case. The new models offer great flexibility in formulating the effects of covariates on the mean function of recurrent events. Estimating equation approaches are developed for the model parameters, and asymptotic properties of the resulting estimators are established. In addition, a model checking procedure is presented to assess the adequacy of the model. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a bladder cancer study is presented.

A Marginal Additive Rates Model for Recurrent Event Data with a Terminal Event

Recurrent events data with a terminal event often arise in many longitudinal studies. Most of existing models assume multiplicative covariate effects and model the conditional recurrent event rate given survival. In this article, we propose a marginal additive rates model for recurrent events with a terminal event, and develop two procedures for estimating the model parameters. The asymptotic properties of the resulting estimators are established. In addition, some numerical procedures are presented for model checking. The finite-sample behavior of the proposed methods is examined through simulation studies, and an application to a bladder cancer study is also illustrated.

Some stochastic orders of dynamic additive mean residual life model

Sometimes additive hazard rate model becomes more important to study than the celebrated (Cox, 1972) proportional hazard rate model. But the concept of the hazard function is sometimes abstract, in comparison to the concept of mean residual life function. In this paper, we have defined a new model called ‘dynamic additive mean residual life model’ where the covariates are time dependent, and study the closure of this model under different stochastic orders.

Estimation and interpretation of incidence rate difference for recurrent events when the estimation model is misspecified

Recurrent events data are common in experimental and observational studies. It is often of interest to estimate the effect of an intervention on the incidence rate of the recurrent events. The incidence rate difference is a useful measure of intervention effect. A weighted least squares estimator of the incidence rate difference for recurrent events was recently proposed for an additive rate model in which both the baseline incidence rate and the covariate effects were constant over time. In this article, we relax this model assumption and examine the properties of the estimator under the additive and multiplicative rate models assumption in which the baseline incidence rate and covariate effects may vary over time. We show analytically and numerically that the estimator gives an appropriate summary measure of the time-varying covariate effects. In particular, when the underlying covariate effects are additive and time-varying, the estimator consistently estimates the weighted average of the covariate effects over time. When the underlying covariate effects are multiplicative and time-varying, and if there is only one binary covariate indicating the intervention status, the estimator consistently estimates the weighted average of the underlying incidence rate difference between the intervention and control groups over time. We illustrate the method with data from a randomized vaccine trial.

Variable selection in the additive rate model for recurrent event data

In this paper, we investigate the variable selection problem for recurrent event data under the additive rate model. According to the explicit estimator of the regression coefficients of the additive rate model, a loss function is constructed. It has a form similar to the ordinary least squares of a linear regression model up to a constant. We develop variable selection procedures by penalizing the loss function with the adaptive L1 penalty and smoothly clipped absolute derivation penalty, respectively. Under some mild regularity conditions, the oracle properties of both procedures are established. Extensive simulation studies are conducted to examine the performance of our proposed procedures in finite samples. Finally, these methods are applied to the well-known chronic granulomatous disease study.

Semiparametric Transformation Rate Model for Recurrent Event Data

In this article, we propose a class of semiparametric transformation rate models for recurrent event data subject to right-censoring and potentially stopped by a terminating event (e.g., death). These transformation models include both additive rates model and proportional rates model as special cases. Respecting the property that no recurrent events can occur after the terminating event, we model the conditional recurrent event rate given survival. Weighted estimating equations are constructed to estimate the regression coefficients and baseline rate function. In particular, the baseline rate function is approximated by wavelet function. Asymptotic properties of the proposed estimators are derived and a data-dependent criterion is proposed for selecting the most suitable transformation. Simulation studies show that the proposed estimators perform well for practical sample sizes. The proposed methods are used in two real-data examples: a randomized trial of rhDNase and a community trial of Vitamin A.

A semiparametric additive rates model for clustered recurrent event data

Recurrent event data often arises in biomedical studies, and individuals within a cluster might not be independent. We propose a semiparametric additive rates model for clustered recurrent event data, wherein the covariates are assumed to add to the unspecified baseline rate. For the inference on the model parameters, estimating equation approaches are developed, and both large and finite sample properties of the proposed estimators are established.

A class of additive-accelerated means regression models for recurrent event data

In this article, we propose a class of additive-accelerated means regression models for analyzing recurrent event data. The class includes the proportional means model, the additive rates model, the accelerated failure time model, the accelerated rates model and the additive-accelerated rate model as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the model parameters, estimating equation approaches are derived and asymptotic properties of the proposed estimators are established. In addition, a technique is provided for model checking. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is illustrated.

A semiparametric additive rate model for recurrent events with an informative terminal event

We propose a semiparametric additive rate model for modelling recurrent events in the presence of a terminal event. The dependence between recurrent events and terminal event is nonparametric. A general transformation model is used to model the terminal event. We construct an estimating equation for parameter estimation and derive the asymptotic distributions of the proposed estimators. Simulation studies demonstrate that the proposed inference procedure performs well in realistic settings. Application to a medical study is presented.

Additive–multiplicative rates model for recurrent events

Recurrent events are frequently encountered in biomedical studies. Evaluating the covariates effects on the marginal recurrent event rate is of practical interest. There are mainly two types of rate models for the recurrent event data: the multiplicative rates model and the additive rates model. We consider a more flexible additive-multiplicative rates model for analysis of recurrent event data, wherein some covariate effects are additive while others are multiplicative. We formulate estimating equations for estimating the regression parameters. The estimators for these regression parameters are shown to be consistent and asymptotically normally distributed under appropriate regularity conditions. Moreover, the estimator of the baseline mean function is proposed and its large sample properties are investigated. We also conduct simulation studies to evaluate the finite sample behavior of the proposed estimators. A medical study of patients with cystic fibrosis suffered from recurrent pulmonary exacerbations is provided for illustration of the proposed method.

A semiparametric additive rate model for recurrent events with an informative terminal event

A semiparametric additive rate model for recurrent events with an informative terminal event

A semiparametric additive rates model for recurrent event data

Recurrent event data often arise in biomedical studies, with examples including hospitalizations, infections, and treatment failures. In observational studies, it is often of interest to estimate the effects of covariates on the marginal recurrent event rate. The majority of existing rate regression methods assume multiplicative covariate effects. We propose a semiparametric model for the marginal recurrent event rate, wherein the covariates are assumed to add to the unspecified baseline rate. Covariate effects are summarized by rate differences, meaning that the absolute effect on the rate function can be determined from the regression coefficient alone. We describe modifications of the proposed method to accommodate a terminating event (e.g., death). Proposed estimators of the regression parameters and baseline rate are shown to be consistent and asymptotically Gaussian. Simulation studies demonstrate that the asymptotic approximations are accurate in finite samples. The proposed methods are applied to a state-wide kidney transplant data set.

Towards the Reliable Prediction of Time to Flowering in Six Annual Crops. VI. Applications in Crop Improvement

SummaryVariation in time from sowing to flowering (f) was examined for 44 cultivars of soyabean, mungbean, black gram, ricebean, cowpea, chickpea, lentil and barley, when grown in up to 21 diverse environments obtained by making one or more sowings at each of six locations spanning tropical, sub-tropical and temperate climates in Australia. The utility of simple linear models, relating rate of development (l/f) towards flowering to mean photoperiod and temperature prevailing between sowing and flowering, was evaluated. The models were highly efficient, explaining most (86.7%) of the variation observed across species, cultivars and environments. They were particularly efficient in describing responses where cultivars were relatively well-adapted, in agronomic terms, and least efficient where cultivars were exposed to unfavourable temperature and, to a lesser extent, photoperiod. Opportunities for exploiting the models in applied crop improvement include their use in interpretation of G × E interaction, genotypic characterization and selection of parental genotypes, selection of test environments, designing screening procedures, and more efficiently matching genotypes to target environments. The main strengths of these linear, additive rate models in crop improvement are their wide applicability across species and genotypes, their relative simplicity, and the requirement for few genotype-specific response parameters. Their main weakness is their lack of precision in describing responses when plants are exposed to unfavourable photothermal extremes, albeit in circumstances that are sometimes unrealistic for cropping those particular genotypes.Predicciones del tiempo que ha de transcurrir hanta la floración. VI.

Towards the Reliable Prediction of Time to Flowering in Six Annual Crops. V. Chickpea (Cicer arietinum)

SUMMARYFour genotypes of ‘desi’ and two of ‘kabuli’ chickpea (Cicer arietinum) were sown at six locations in Australia on various dates between 1986 and 1988, giving 22 combinations of site and sowing date with diverse photothermal environments. Times from sowing to first flowering (f) varied from 30 to 162 d, mean pre-flowering temperatures from 10.8° to 29.3°C and mean photoperiods from 11.3 to 15.6 h d−1. There was no evidence that any observation had been obtained in photoperiods shorter than the ceiling photoperiod (Pcc) or longer than the critical photoperiod (Pc). This suggests that, in typical agricultural environments, chickpea crops experience photoperiods (P) which should satisfy the condition Pcce < P < Pc. In one ‘kabuli’ and two ‘desi’ genotypes, 1/f was influenced by both temperature and photoperiod. The coefficient of determination (R2) for a linear, additive rate of development model ranged from 0.74 to 0.80, with no significant difference in either temperature sensitivity or photoperiod sensitivity among these three genotypes. In the remaining three genotypes, no significant response to temperature was detected between 10.8° and 29.2°C, so rate of progress to flowering was influenced solely by photoperiod. There was no significant difference in the sensitivity of 1/f to P among these three genotypes. The linear, additive rate model found here to be so satisfactory as a predictive tool for phenology, is also shown to have much wider general application.Predicción del liempo de floración

Modeling Time-Varying Effects of Covariates in Event-History Analysis Using Statistics from the Saturated Hazard Rate Model

This paper presents a method for modeling time-varying effects of categorical covariates in event-history analysis using statistics obtained from the saturated hazard rate model. First, the closed-form solution for the maximum likelihood estimators of pairameters and their variance-covariance matrix for general saturated models of hazard rates are presented. The paper then presents methods that use statistics obtained from the saturated model to conduct (1) a proportionality test of the covariate effect for multiplicative hazard rate models and a linearadditivity test of the covariate effect for additive hazard rate models; (2) a goodness of fit test for various parametric models for time variations in the covariate effects; and (3) a test for ccomparing the relative goodness of fit among alternative parametric models. This paper also discusses the advantages and