Comparing non-hierarchical models: Application to non-linear mixed effects modeling

There is no method available to compare the fit of two non-hierarchical non-linear mixed effects models, although the common practice is to select the model with the lower objective function. Bootstrapping the log-likelihood differences (LLDs) of non-hierarchical models and constructing a bootstrap confidence interval on the LLDs is proposed for comparing the goodness-of-fit of such models. This is illustrated with different parameterizations of clearance models for an anti-infective agent in a longitudinal pharmacokinetic study which are compared. Additive and exponential models of creatinine clearance as a predictor of clearance are used as examples.     

Prediction of the average skin temperature in warm and hot environments

The prediction of the mean skin temperature used for the Required Sweat Rate index was criticised for not being valid in conditions with high radiation and high humidity. Based on a large database provided by 9 institutes, 1999 data points obtained using steady-state conditions, from 1399 experiments and involving 377 male subjects, were used for the development of a new prediction model. The observed mean skin temperatures ranged from 30.7 °C to 38.6 °C. Experimental conditions included air temperatures (T _a) between 20 and 55 °C, mean radiant temperatures (T _r) up to 145 °C, partial vapour pressures (P _a) from 0.2 to 5.3 kPa, air velocities (v _a) between 0.1 and 2 m/s, and metabolic rates (M) from 102 to 620 W. Rectal temperature (T _re) was included in the models to increase the accuracy of prediction. Separate models were derived for nude (clothing insulation, I_cl, ≤0.2 clo, where 1 clo=0.155 m² · °C · W⁻¹, which is equivalent to the thermal insulation of clothing necessary to maintain a resting subject in comfort in a normally ventilated room, air movement=10 cm/s, at a temperature of 21 °C and a humidity of less than 50%) and clothed (0.6 ≤ I_cl ≤ 1.0 clo) subjects using a multiple linear regression technique with re-sampling (non-parametric bootstrap). The following expressions were obtained for nude and clothed subjects, respectively: T _sk=7.19 + 0.064T _a + 0.061T _r + 0.198P _a− 0.348v _a + 0.616T _re and T _sk=12.17 + 0.020T _a + 0.044T _r + 0.194P _a − 0.253v _a + 0.0029M + 0.513T _re. For the nude and clothed subjects, 83.3% and 81.8%, respectively, of the predicted skin temperatures were within the range of ±1 °C of the observed skin temperatures. It is concluded that the proposed models for the prediction of the mean skin temperature are valid for a wide range of warm and hot ambient conditions in steady-state conditions, including those of high radiation and high humidity. Accepted: 7 February 2000     

Empirical Likelihood-Based Confidence Interval of ROC Curves

In this article we propose an empirical likelihood-based confidence interval for receiver operating characteristic curves which are based on a continuous-scale test. The approach is easily understood, simply implemented, and computationally efficient. The results from our simulation studies indicate that the finite-sample numerical performance slightly outperforms the most promising methods published recently. Two real datasets are analyzed by using the proposed method and the existing bootstrap-based method.     

One- and Two-Stage Arrhenius Models for Pharmaceutical Shelf Life Prediction

One of the most challenging aspects of the pharmaceutical development is the demonstration and estimation of chemical stability. It is imperative that pharmaceutical products be stable for two or more years. Long-term stability studies are required to support such shelf life claim at registration. However, during drug development to facilitate formulation and dosage form selection, an accelerated stability study with stressed storage condition is preferred to quickly obtain a good prediction of shelf life under ambient storage conditions. Such a prediction typically uses Arrhenius equation that describes relationship between degradation rate and temperature (and humidity). Existing methods usually rely on the assumption of normality of the errors. In addition, shelf life projection is usually based on confidence band of a regression line. However, the coverage probability of a method is often overlooked or under-reported. In this paper, we introduce two nonparametric bootstrap procedures for shelf life estimation based on accelerated stability testing, and compare them with a one-stage nonlinear Arrhenius prediction model. Our simulation results demonstrate that one-stage nonlinear Arrhenius method has significant lower coverage than nominal levels. Our bootstrap method gave better coverage and led to a shelf life prediction closer to that based on long-term stability data.     

Error bounds for data-driven models of dynamical systems

This work provides a technique for estimating error bounds about the predictions of data-driven models of dynamical systems. The bootstrap technique is applied to predictions from a set of dynamical system models, rather than from the time-series data, to estimate the reliability (in the form of prediction intervals) for each prediction. The technique is illustrated using human core temperature data, modeled by a hybrid (autoregressive plus first principles) approach. The temperature prediction intervals obtained are in agreement with those from the Camp-Meidell inequality. Moreover, as expected, the prediction intervals increase with the prediction horizon, time-series data variability, and model inaccuracy.     

膳食暴露定量评估模型及其变异性和不确定性研究

目的探讨膳食暴露评估概率性模型及如何量化其变异性和不确定性。方法运用Montecarlo方法量化变异性，运用Bootstrap方法量化不确定性。结果概率性模型比目前应用的点估计模型更合理，Montecarlo方法和Bootstrap方法有效量化了变异性和不确定性。结论建议应用概率性模型进行膳食暴露评估以提高膳食暴露定量评估水平。     

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7-82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.     

Comparison of Parametric and Bootstrap Method in Bioequivalence Test

The estimation of 90% parametric confidence intervals (CIs) of mean AUC and Cmax ratios in bioequivalence (BE) tests are based upon the assumption that formulation effects in log-transformed data are normally distributed. To compare the parametric CIs with those obtained from nonparametric methods we performed repeated estimation of bootstrap-resampled datasets. The AUC and Cmax values from 3 archived datasets were used. BE tests on 1,000 resampled datasets from each archived dataset were performed using SAS (Enterprise Guide Ver.3). Bootstrap nonparametric 90% CIs of formulation effects were then compared with the parametric 90% CIs of the original datasets. The 90% CIs of formulation effects estimated from the 3 archived datasets were slightly different from nonparametric 90% CIs obtained from BE tests on resampled datasets. Histograms and density curves of formulation effects obtained from resampled datasets were similar to those of normal distribution. However, in 2 of 3 resampled log (AUC) datasets, the estimates of formulation effects did not follow the Gaussian distribution. Bias-corrected and accelerated (BCa) CIs, one of the nonparametric CIs of formulation effects, shifted outside the parametric 90% CIs of the archived datasets in these 2 non-normally distributed resampled log (AUC) datasets. Currently, the 80~125% rule based upon the parametric 90% CIs is widely accepted under the assumption of normally distributed formulation effects in log-transformed data. However, nonparametric CIs may be a better choice when data do not follow this assumption.     

Departure from normality in multivariate normative comparison: The Cramér alternative for Hotelling's T

Crawford and Howell (1998) have pointed out that the common practice of z-score inference on cognitive disability is inappropriate if a patient's performance on a task is compared with relatively few typical control individuals. Appropriate univariate and multivariate statistical tests have been proposed for these studies, but these are only valid if the data are Gaussian (normal) distributed. Previous studies have investigated the consequences for Type I error rates of using the univariate test when data are not Gaussian. In this paper we examine the effects of violation of the Gaussian assumption on nominal Type I error rates for the multivariate test. We also consider a new test that has been devised recently, called Cramér's test, as a viable alternative for the multivariate normative comparison. In simulations we show that the new test not only provides a distribution free alternative for existing methods, but also has the advantage that it is substantially more powerful in most common research settings. We demonstrate the use of the new test with an application to two individuals diagnosed with autism.     

清开灵注射液生产过程性能指数研究

为科学评价中药产品质量可靠性和批间一致性,该文以清开灵注射液为研究对象,收集一定时期内清开灵注射液产品质量指标历史数据,将过程性能指数P_p和P_pk应用于中药生产过程能力分析,并采用Bootstrap抽样方法计算过程性能指数置信区间。结果P_pk的估计值和置信区间宽度均低于P_p,表明P_pk用于过程性能分析时灵敏度更高。在考察的生产周期内,以黄芩苷、胆酸、栀子苷和总氮浓度为指标计算的P_pk分别为1.122,2.055,1.564,0.891,即胆酸的过程能力最高,其次为栀子苷和黄芩苷,总氮过程能力较低,提示应加强总氮相关工艺质量管理和控制水平。过程性能分析法可对中药生产过程能力和产品质量一致性进行量化研究,可作为生产过程运行质量的控制手段。