Asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time

Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood estimators. This paper intends to fill this gap. Specifically, we prove the consistency of the maximum likelihood estimators and derive their asymptotic distributions. The maximum likelihood estimators are shown to be semiparametrically efficient.Comment: Published at http://dx.doi.org/10.1214/009053605000000480 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Variable Selection for Case-Cohort Studies with Failure Time Outcome

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of variable selection using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial likelihood estimator, and show that the proposed variable selection procedure is consistent and has an asymptotic oracle property. Simulation studies compare the finite sample performance of the procedure with Akaike information criterion- and Bayesian information criterion-based tuning parameter selection methods. We make recommendations for use of the procedures in case-cohort studies, and apply them to the Busselton Health Study

Quantile regression models for current status data

Current status data arise frequently in demography, epidemiology, and econometrics where the exact failure time cannot be determined but is only known to have occurred before or after a known observation time. We propose a quantile regression model to analyze current status data, because it does not require distributional assumptions and the coefficients can be interpreted as direct regression effects on the distribution of failure time in the original time scale. Our model assumes that the conditional quantile of failure time is a linear function of covariates. We assume conditional independence between the failure time and observation time. An M-estimator is developed for parameter estimation which is computed using the concave-convex procedure and its confidence intervals are constructed using a subsampling method. Asymptotic properties for the estimator are derived and proven using modern empirical process theory. The small sample performance of the proposed method is demonstrated via simulation studies. Finally, we apply the proposed method to analyze data from the Mayo Clinic Study of Aging

Additive transformation models for clustered failure time data

We propose a class of additive transformation risk models for clustered failure time data. Our models are motivated by the usual additive risk model for independent failure times incorporating a frailty with mean one and constant variability which is a natural generalization of the additive risk model from univariate failure time to multivariate failure time. An estimating equation approach based on the marginal hazards function is proposed. Under the assumption that cluster sizes are completely random, we show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also provide goodness-of-fit test statistics for choosing the transformation. Simulation studies and real data analysis are conducted to examine the finite-sample performance of our estimators

Additive Mixed Effect Model for Clustered Failure Time Data

We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and include a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure

Non-uniform changes in membrane receptors in the rat urinary bladder following outlet obstruction.

The aim of the present study was to investigate the expression and distribution of membrane receptors after bladder outlet obstruction (BOO). Partial bladder outlet obstruction (BOO) was induced in female rats and bladders were harvested after either 10 days or 6 weeks of BOO. The expression of different receptors was surveyed by microarrays and corroborated by immunohistochemistry and western blotting. A microarray experiment identified 10 membrane receptors that were differentially expressed compared to sham-operated rats including both upregulated and downregulated receptors. Four of these were selected for functional experiments on the basis of magnitude of change and relevance to bladder physiology. At 6 weeks of BOO, maximal contraction was reduced for neuromedin B and vasopressin (AVP), consistent with reductions of receptor mRNA levels. Glycine receptor-induced contraction on the other hand was increased and receptor mRNA expression was accordingly upregulated. Maximal relaxation by the β3-adrenergic receptor agonist CL316243 was reduced as was the receptor mRNA level. Immunohistochemistry supported reduced expression of neuromedin B receptors, V1a receptors and β3-adrenergic receptors, but glycine receptor expression appeared unchanged. Western blotting confirmed repression of V1a receptors and induction of glycine receptors in BOO. mRNA for vasopressin was detectable in the bladder, suggesting local AVP production. We conclude that changes in receptor expression following bladder outlet obstruction are non-uniform. Some receptors are upregulated, conferring increased responsiveness to agonist, whereas others are downregulated, leading to decreased agonist-induced responses. This study might help to select pharmacological agents that are effective in modulating lower urinary tract symptoms in BOO

Robust prior-based single image super resolution under multiple Gaussian degradations

Although SISR (Single Image Super Resolution) problem can be effectively solved by deep learning based methods, the training phase often considers single degradation type such as bicubic interpolation or Gaussian blur with fixed variance. These priori hypotheses often fail and lead to reconstruction error in real scenario. In this paper, we propose an end-to-end CNN model RPSRMD to handle SR problem in multiple Gaussian degradations by extracting and using as side information a shared image prior that is consistent in different Gaussian degradations. The shared image prior is generated by an AED network RPGen with a rationally designed loss function that contains two parts: consistency loss and validity loss. These losses supervise the training of AED to guarantee that the image priors of one image with different Gaussian blurs to be very similar. Afterwards we carefully designed a SR network, which is termed as PResNet (Prior based Residual Network) in this paper, to efficiently use the image priors and generate high quality and robust SR images when unknown Gaussian blur is presented. When we applied variant Gaussian blurs to the low resolution images, the experiments prove that our proposed RPSRMD, which includes RPGen and PResNet as two core components, is superior to many state-of-the-art SR methods that were designed and trained to handle multi-degradation

Sample size/power calculation for stratified case-cohort design

The Case-cohort (CC) study design usually has been used for risk factor assessment in epidemiologic studies or disease prevention trials for rare diseases. The sample size/power calculation for the CC design is given in Cai and Zeng [1]. However, the sample size/power calculation for a stratified case-cohort (SCC) design has not been addressed before. This article extends the results of Cai and Zeng [1] to the SCC design. Simulation studies show that the proposed test for the SCC design utilizing small sub-cohort sampling fractions is valid and efficient for situations where the disease rate is low. Furthermore, optimization of sampling in the SCC design is discussed and compared with proportional and balanced sampling techniques. An epidemiological study is provided to illustrate the sample size calculation under the SCC design

Semiparametric additive risks model for interval-censored data

Abstract: Interval-censored event time data often arise in medical and public health studies. In such a setting, the exact time of the event of interest cannot be observed and is only known to fall between two monitoring times. Our interest focuses on the estimation of the effect of risk factors on interval-censored data under the semiparametric additive hazards model. A nonparametric step-function is used to characterize the baseline hazard function. The covariate coefficients are estimated by maximizing the observed likelihood function, and their variances are obtained using the profile likelihood approach. We show that the proposed estimates are consistent and have asymptotic normal distributions. We also show that the estimator obtained for the covariate coefficient is the most efficient estimator. Simulation studies are conducted to assess the performance of the estimate. The method is illustrated through application to a data set from an HIV study