This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observe...This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observed on a validation set. A new estimation approach is proposed for estimating the regression function. The authors first estimate the regression function with a kernel smoother based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from the non-validation subsample and the surrogate of response from the full sample. Asymptotic normality of the proposed estimator is derived. The effectiveness of the proposed method is demonstrated via simulations.展开更多
During pre-clinical pharmacokinetic research, it is not easy to gather complete pharmacokinetic data in each animal. In some cases, an animal can only provide a single observation. Under this circumstance, it is not c...During pre-clinical pharmacokinetic research, it is not easy to gather complete pharmacokinetic data in each animal. In some cases, an animal can only provide a single observation. Under this circumstance, it is not clear how to utilize this data to estimate the pharmacokinetic parameters effectively. This study was aimed at comparing a new method to handle such single-observation-per-animal type data with the conventional method in estimating pharmacokinetic parameters. We assumed there were 15 animals within the study receiving a single dose by intravenous injection. Each animal provided one observation point. There were five time points in total, and each time point contained three measurements. The data were simulated with a one-compartment model with first-order elimination. The inter-individual variabilities （ⅡV） were set to 10%, 30% and 50% for both clearance （CL） and apparent volume of distribution （V）. A proportional model was used to describe the residual error, which was also set to 10%, 30% and 50%. Two methods （conventional method and the finite msampling method） to handle with the simulated single-observation-per-animal type data in estimating pharmacokinetic parameters were compared. The conventional method （MI） estimated pharmacokinetic parameters directly with original data, i.e., single-observation-per-animal type data. The finite resampling method （M2） was to expand original data to a new dataset by resampling original data with all kinds of combinations by time. After resampling, each individual in the new dataset contained complete pharmacokinetic data, i.e., in this study, there were 243 （C3^1×C3^1×C3^1×C3^1×C3^1） kinds of possible combinations and each of them was a virtual animal. The study was simulated 100 times by the NONMEM software. According to the results, parameter estimates of CL and V by M2 based on the simulated dataset were closer to their true values, though there was a small difference among different combinations of ⅡVs and the residual errors. In general, M2 was less advantageous over M1 when the residual error increased. It was also influenced by the levels of ⅡV as higher levels of IIV could lead to a decrease in the advantage of M2. However, M2 had no ability to estimate the ⅡV of parameters, nor did M1. The finite resampling method could provide more reliable results compared to the conventional method in estimating pharmacokinetic parameters with single-observation-per-animal type data. Compared to the inter-individual variability, the results of estimation were mainly influenced by the residual error.展开更多
基金This research is supported by the National Natural Science Foundation of the US under Grant No. DMS- 0906482.
文摘This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observed on a validation set. A new estimation approach is proposed for estimating the regression function. The authors first estimate the regression function with a kernel smoother based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from the non-validation subsample and the surrogate of response from the full sample. Asymptotic normality of the proposed estimator is derived. The effectiveness of the proposed method is demonstrated via simulations.
文摘During pre-clinical pharmacokinetic research, it is not easy to gather complete pharmacokinetic data in each animal. In some cases, an animal can only provide a single observation. Under this circumstance, it is not clear how to utilize this data to estimate the pharmacokinetic parameters effectively. This study was aimed at comparing a new method to handle such single-observation-per-animal type data with the conventional method in estimating pharmacokinetic parameters. We assumed there were 15 animals within the study receiving a single dose by intravenous injection. Each animal provided one observation point. There were five time points in total, and each time point contained three measurements. The data were simulated with a one-compartment model with first-order elimination. The inter-individual variabilities （ⅡV） were set to 10%, 30% and 50% for both clearance （CL） and apparent volume of distribution （V）. A proportional model was used to describe the residual error, which was also set to 10%, 30% and 50%. Two methods （conventional method and the finite msampling method） to handle with the simulated single-observation-per-animal type data in estimating pharmacokinetic parameters were compared. The conventional method （MI） estimated pharmacokinetic parameters directly with original data, i.e., single-observation-per-animal type data. The finite resampling method （M2） was to expand original data to a new dataset by resampling original data with all kinds of combinations by time. After resampling, each individual in the new dataset contained complete pharmacokinetic data, i.e., in this study, there were 243 （C3^1×C3^1×C3^1×C3^1×C3^1） kinds of possible combinations and each of them was a virtual animal. The study was simulated 100 times by the NONMEM software. According to the results, parameter estimates of CL and V by M2 based on the simulated dataset were closer to their true values, though there was a small difference among different combinations of ⅡVs and the residual errors. In general, M2 was less advantageous over M1 when the residual error increased. It was also influenced by the levels of ⅡV as higher levels of IIV could lead to a decrease in the advantage of M2. However, M2 had no ability to estimate the ⅡV of parameters, nor did M1. The finite resampling method could provide more reliable results compared to the conventional method in estimating pharmacokinetic parameters with single-observation-per-animal type data. Compared to the inter-individual variability, the results of estimation were mainly influenced by the residual error.
