Browsing by Subject "empirical process"

Now showing 1 - 4 of 4
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    Distribution‐free estimation of local growth rates around interval censored anchoring events
    (Wiley, 2019) Chu, Chenghao; Zhang, Ying; Tu, Wanzhu; Biostatistics, School of Public Health
    Biological processes are usually defined on timelines that are anchored by specific events. For example, cancer growth is typically measured by the change in tumor size from the time of oncogenesis. In the absence of such anchoring events, longitudinal assessments of the outcome lose their temporal reference. In this paper, we considered the estimation of local change rates in the outcomes when the anchoring events are interval‐censored. Viewing the subject‐specific anchoring event times as random variables from an unspecified distribution, we proposed a distribution‐free estimation method for the local growth rates around the unobserved anchoring events. We expressed the rate parameters as stochastic functionals of the anchoring time distribution and showed that under mild regularity conditions, consistent and asymptotically normal estimates of the rate parameters could be achieved, with a biom13015-gra-0001 convergence rate. We conducted a carefully designed simulation study to evaluate the finite sample performance of the method. To motivate and illustrate the use of the proposed method, we estimated the skeletal growth rates of male and female adolescents, before and after the unobserved pubertal growth spurt (PGS) times.
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    A nonparametric regression model for panel count data analysis
    (2019) Zhao, Huadong; Zhang, Ying; Zhao, Xingqiu; Yu, Zhangsheng; Biostatistics, School of Public Health
    Panel count data are commonly encountered in analysis of recurrent events where the exact event times are unobserved. To accommodate the potential non-linear covariate effect, we consider a non-parametric regression model for panel count data. The regression B-splines method is used to estimate the regression function and the baseline mean function. The B-splines-based estimation is shown to be consistent and the rate of convergence is obtained. Moreover, the asymptotic normality for a class of smooth functionals of regression splines estimators is established. Numerical studies were carried out to evaluate the finite sample properties. Finally, we applied the proposed method to analyze the non-linear effect of one of interleukin functions with the risk of childhood wheezing.
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    Stochastic functional estimates in longitudinal models with interval‐censored anchoring events
    (Wiley, 2020-09) Chu, Chenghao; Zhang, Ying; Tu, Wanzhu; Biostatistics, School of Public Health
    Timelines of longitudinal studies are often anchored by specific events. In the absence of the fully observed anchoring event times, the study timeline becomes undefined, and the traditional longitudinal analysis loses its temporal reference. In this paper, we considered an analytical situation where the anchoring events are interval censored. We demonstrated that by expressing the regression parameter estimators as stochastic functionals of a plug‐in estimate of the unknown anchoring event time distribution, the standard longitudinal models could be extended to accommodate the situation of less well‐defined timelines. We showed that for a broad class of longitudinal models, the functional parameter estimates are consistent and asymptotically normally distributed with a 𝑛⎯⎯√ convergence rate under mild regularity conditions. Applying the developed theory to linear mixed‐effects models, we further proposed a hybrid computational procedure that combines the strengths of the Fisher's scoring method and the expectation‐expectation (EM) algorithm for model parameter estimation. We conducted a simulation study to validate the asymptotic properties and to assess the finite sample performance of the proposed method. A real data example was used to illustrate the proposed method. The method fills in a gap in the existing longitudinal analysis methodology for data with less well‐defined timelines.
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    Using a monotone single‐index model to stabilize the propensity score in missing data problems and causal inference
    (Wiley, 2019-04) Qin, Jing; Yu, Tao; Li, Pengfei; Liu, Hao; Chen, Baojiang; Biostatistics, School of Public Health
    The augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems. An important component of this method is the propensity score. Popular parametric models for the propensity score include the logistic, probit, and complementary log‐log models. A common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables. To avoid the need to choose a model, we model the propensity score via a semiparametric single‐index model, in which the score is an unknown monotonic nondecreasing function of the given single index. Under this new model, the augmented inverse weighting estimator (AIWE) of the mean of the response is asymptotically linear, semiparametrically efficient, and more robust than existing estimators. Moreover, we have made a surprising observation. The inverse probability weighting and AIWEs based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model. A heuristic explanation of this phenomenon is provided. A real‐data example is used to illustrate the proposed methods.