A Semiparametric Approach to Density Estimation

Comparison Of Observation-Based And Model-Based Identification Of Alert Concentrations From Concentration-Expression Data

MOTIVATION

An important goal of concentration-response studies in toxicology is to determine an 'alert' concentration where a critical level of the response variable is exceeded. In a classical observation-based approach, only measured concentrations are considered as potential alert concentrations. Alternatively, a parametric curve is fitted to the data that describes the relationship between concentration and response. For a prespecified effect level, both an absolute estimate of the alert concentration and an estimate of the lowest concentration where the effect level is exceeded significantly are of interest.

RESULTS

In a simulation study for gene expression data, we compared the observation-based and the model-based approach for both absolute and significant exceedance of the prespecified effect level. Results show that, compared to the observation-based approach, the model-based approach overestimates the true alert concentration less often and more frequently leads to a valid estimate, especially for genes with large variance.

AVAILABILITY AND IMPLEMENTATION

The code used for the simulation studies is available via the GitHub repository: https://github.com/FKappenberg/Paper-IdentificationAlertConcentrations.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Subgroup analysis with semiparametric models toward precision medicine

In analyzing clinical trials, one important objective is to classify the patients into treatment-favorable and nonfavorable subgroups. Existing parametric methods are not robust, and the commonly used classification rules ignore the fact that the implications of treatment-favorable and nonfavorable subgroups can be different. To address these issues, we propose a semiparametric model, incorporating both our knowledge and uncertainty about the true model. The Wald statistics is used to test the existence of subgroups, while the Neyman-Pearson rule to classify each subject. Asymptotic properties are derived, simulation studies are conducted to evaluate the performance of the method, and then method is used to analyze a real-world trial data.

A model averaging approach for estimating propensity scores by optimizing balance

Many approaches, including traditional parametric modeling and machine learning techniques, have been proposed to estimate propensity scores. This paper describes a new model averaging approach to propensity score estimation in which parametric and nonparametric estimates are combined to achieve covariate balance. Simulation studies are conducted across different scenarios varying in the degree of interactions and nonlinearities in the treatment model. The results show that, based on inverse probability weighting, the proposed propensity score estimator produces less bias and smaller standard errors than existing approaches. They also show that a model averaging approach with the objective of minimizing the average Kolmogorov–Smirnov statistic leads to the best performing IPW estimator. The proposed approach is also applied to a real data set in evaluating the causal effect of formula or mixed feeding versus exclusive breastfeeding on a child’s body mass index Z-score at age 4. The data analysis shows that formula or mixed feeding is more likely to lead to obesity at age 4, compared to exclusive breastfeeding.

Model averaging for robust assessment of QT prolongation by concentration-response analysis

Assessing the QT prolongation potential of a drug is typically done based on pivotal safety studies called thorough QT studies. Model-based estimation of the drug-induced QT prolongation at the estimated mean maximum drug concentration could increase efficiency over the currently used intersection-union test. However, robustness against model misspecification needs to be guaranteed in pivotal settings. The objective of this work was to develop an efficient, fully prespecified model-based inference method for thorough QT studies, which controls the type I error and provides satisfactory test power. This is achieved by model averaging: The proposed estimator of the concentration-response relationship is a weighted average of a parametric (linear) and a nonparametric (monotonic I-splines) estimator, with weights based on mean integrated square error. The desired properties of the method were confirmed in an extensive simulation study, which demonstrated that the proposed method controlled the type I error adequately, and that its power was higher than the power of the nonparametric method alone. The method can be extended from thorough QT studies to the analysis of QT data from pooled phase I studies.

Improving zero-training brain-computer interfaces by mixing model estimators

OBJECTIVE

Brain-computer interfaces (BCI) based on event-related potentials (ERP) incorporate a decoder to classify recorded brain signals and subsequently select a control signal that drives a computer application. Standard supervised BCI decoders require a tedious calibration procedure prior to every session. Several unsupervised classification methods have been proposed that tune the decoder during actual use and as such omit this calibration. Each of these methods has its own strengths and weaknesses. Our aim is to improve overall accuracy of ERP-based BCIs without calibration.

APPROACH

We consider two approaches for unsupervised classification of ERP signals. Learning from label proportions (LLP) was recently shown to be guaranteed to converge to a supervised decoder when enough data is available. In contrast, the formerly proposed expectation maximization (EM) based decoding for ERP-BCI does not have this guarantee. However, while this decoder has high variance due to random initialization of its parameters, it obtains a higher accuracy faster than LLP when the initialization is good. We introduce a method to optimally combine these two unsupervised decoding methods, letting one method's strengths compensate for the weaknesses of the other and vice versa. The new method is compared to the aforementioned methods in a resimulation of an experiment with a visual speller.

MAIN RESULTS

Analysis of the experimental results shows that the new method exceeds the performance of the previous unsupervised classification approaches in terms of ERP classification accuracy and symbol selection accuracy during the spelling experiment. Furthermore, the method shows less dependency on random initialization of model parameters and is consequently more reliable.

SIGNIFICANCE

Improving the accuracy and subsequent reliability of calibrationless BCIs makes these systems more appealing for frequent use.

Improved estimation of the noncentrality parameter distribution from a large number of t-statistics, with applications to false discovery rate estimation in microarray data analysis

Given a large number of t-statistics, we consider the problem of approximating the distribution of noncentrality parameters (NCPs) by a continuous density. This problem is closely related to the control of false discovery rates (FDR) in massive hypothesis testing applications, e.g., microarray gene expression analysis. Our methodology is similar to, but improves upon, the existing approach by Ruppert, Nettleton, and Hwang (2007, Biometrics, 63, 483-495). We provide parametric, nonparametric, and semiparametric estimators for the distribution of NCPs, as well as estimates of the FDR and local FDR. In the parametric situation, we assume that the NCPs follow a distribution that leads to an analytically available marginal distribution for the test statistics. In the nonparametric situation, we use convex combinations of basis density functions to estimate the density of the NCPs. A sequential quadratic programming procedure is developed to maximize the penalized likelihood. The smoothing parameter is selected with the approximate network information criterion. A semiparametric estimator is also developed to combine both parametric and nonparametric fits. Simulations show that, under a variety of situations, our density estimates are closer to the underlying truth and our FDR estimates are improved compared with alternative methods. Data-based simulations and the analyses of two microarray datasets are used to evaluate the performance in realistic situations.

A semiparametric approach to analysing dose-response data

In the analysis of a quantal dose-response experiment with grouped data, the most commonly used parametric procedure is logistic regression, commonly referred to as 'logit analysis'. The adequacy of the fit by the logistic regression curve is tested using the chi-square lack-of-fit test. If the lack-of-fit test is not significant, then the logistic model is assumed to be adequate and estimation of effective doses and confidence intervals on the effective doses can be made. When the tolerance distribution of the dose-response data is not known and cannot be assumed by the user, one can use non-parametric methods, such as kernel regression or local linear regression, to estimate the dose-response curve, effective doses and confidence intervals. This research proposes another alternative based on semi-parametric regression to analysing quantal dose-response data called model-robust quantal regression (MRQR). MRQR linearly combines the parametric and non-parametric predictions with the use of a mixing parameter. MRQR uses logistic regression as the parametric portion of the model and local linear regression as the non-parametric portion of the model. Our research has shown that the MRQR procedure can improve the fit of the dose-response curve by producing narrower confidence intervals for predictions while providing improved precision of estimates of the effective doses with respect to either logistic or local linear regression results.