Estimating data transformations in nonlinear mixed effects models.

A routine practice in the analysis of repeated measurement data is to represent individual responses by a mixed effects model on some transformed scale. For example, for pharmacokinetic, growth, and other data, both the response and the regression model are typically transformed to achieve approximate within-individual normality and constant variance on the new scale; however, the choice of transformation is often made subjectively or by default, with adoption of a standard choice such as the log. We propose a mixed effects framework based on the transform-both-sides model, where the transformation is represented by a monotone parametric function and is estimated from the data. For this model, we describe a practical fitting strategy based on approximation of the marginal likelihood. Inference is complicated by the fact that estimation of the transformation requires modification of the usual standard errors for estimators of fixed effects; however, we show that, under conditions relevant to common applications, this complication is asymptotically negligible, allowing straightforward implementation via standard software.

The effect of serial dilution error on calibration inference in immunoassay.

A common practice in immunoassay is the use of sequential dilutions of an initial stock solution of the antigen of interest to obtain standard samples in a desired concentration range. Nonlinear, heteroscedastic regression models are a common framework for analysis, and the usual methods for fitting the model assume that measured responses on the standards are independent. However, the dilution procedure introduces a propagation of random measurement error that may invalidate this assumption. We demonstrate that failure to account for serial dilution error in calibration inference on unknown samples leads to serious inaccuracy of assessments of assay precision such as confidence intervals and precision profiles. Techniques for taking serial dilution error into account based on data from multiple assay runs are discussed and are shown to yield valid calibration inferences.

Estimating the parameters in the Cox model when covariate variables are measured with error.

The Cox proportional hazards model is commonly used to model survival data as a function of covariates. Because of the measuring mechanism or the nature of the environment, covariates are often measured with error and are not directly observable. A naive approach is to use the observed values of the covariates in the Cox model, which usually produces biased estimates of the true association of interest. An alternative strategy is to take into account the error in measurement, which may be carried out for the Cox model in a number of ways. We examine several such approaches and compare and contrast them through several simulation studies. We introduce a likelihood-based approach, which we refer to as the semiparametric method, and show that this method is an appealing alternative. The methods are applied to analyze the relationship between survival and CD4 count in patients with AIDS.

Testing homogeneity of intra-run variance parameters in immunoassay.

A common assumption in the analysis of immunoassay data is a similar pattern of within-run variation across runs of the assays. One makes this assumption without formal investigation of its validity, despite the widely acknowledged fact that accurate understanding of intra-run variation is critical to reliable calibration inference. We propose a simple procedure for a formal test of the assumption of the homogeneity of parameters that characterize intra-run variation based on representation of standard curve data from multiple assay runs by a non-linear mixed effects model. We examine the performance of the procedure and investigate the robustness of calibration inference to incorrect assumptions about the pattern of intra-run variation.

Calibration inference based on multiple runs of an immunoassay.

Several authors have documented the poor performance of usual large-sample, individual calibration confidence intervals based on a single run of an immunoassay. Inaccuracy of these intervals may be attributed to the paucity of information on model parameters available in a single run. Methods for combining information from multiple runs to estimate assay response variance parameters and to refine characterization of the standard curve for the current run via empirical Bayes techniques have been proposed. We investigate formally the utility of these techniques for improving the quality of routine individual calibration inference.

The effect of variance function estimation on nonlinear calibration inference in immunoassay data.

Often with data from immunoassays, the concentration-response relationship is nonlinear and intra-assay response variance is heterogeneous. Estimation of the standard curve is usually based on a nonlinear heteroscedastic regression model for concentration-response, where variance is modeled as a function of mean response and additional variance parameters. This paper discusses calibration inference for immunoassay data which exhibit this nonlinear heteroscedastic mean-variance relationship. An assessment of the effect of variance function estimation in three types of approximate large-sample confidence intervals for unknown concentrations is given by theoretical and empirical investigation and application to two examples. A major finding is that the accuracy of such calibration intervals depends critically on the nature of response variance and the quality with which variance parameters are estimated.