Assessing Tuning Parameter Selection Variability in Penalized Regression.

Penalized regression methods that perform simultaneous model selection and estimation are ubiquitous in statistical modeling. The use of such methods is often unavoidable as manual inspection of all possible models quickly becomes intractable when there are more than a handful of predictors. However, automated methods usually fail to incorporate domain-knowledge, exploratory analyses, or other factors that might guide a more interactive model-building approach.

Interactive Q-learning for Quantiles.

A dynamic treatment regime is a sequence of decision rules, each of which recommends treatment based on features of patient medical history such as past treatments and outcomes. Existing methods for estimating optimal dynamic treatment regimes from data optimize the mean of a response variable. However, the mean may not always be the most appropriate summary of performance.

Variable Selection in Kernel Regression Using Measurement Error Selection Likelihoods.

This paper develops a nonparametric shrinkage and selection estimator via the measurement error selection likelihood approach recently proposed by Stefanski, Wu, and White. The Measurement Error Kernel Regression Operator (MEKRO) has the same form as the Nadaraya-Watson kernel estimator, but optimizes a measurement error model selection likelihood to estimate the kernel bandwidths. Much like LASSO or COSSO solution paths, MEKRO results in solution paths depending on a tuning parameter that controls shrinkage and selection via a bound on the harmonic mean of the pseudo-measurement error standard deviations.

iqLearn: Interactive Q-Learning in R.

Chronic illness treatment strategies must adapt to the evolving health status of the patient receiving treatment. Data-driven dynamic treatment regimes can offer guidance for clinicians and intervention scientists on how to treat patients over time in order to bring about the most favorable clinical outcome on average. Methods for estimating optimal dynamic treatment regimes, such as Q-learning, typically require modeling nonsmooth, nonmonotone transformations of data.

Automatic structure recovery for additive models.

We propose an automatic structure recovery method for additive models, based on a backfitting algorithm coupled with local polynomial smoothing, in conjunction with a new kernel-based variable selection strategy. Our method produces estimates of the set of noise predictors, the sets of predictors that contribute polynomially at different degrees up to a specified degree , and the set of predictors that contribute beyond polynomially of degree . We prove consistency of the proposed method, and describe an extension to partially linear models.

Interactive model building for -learning.

Evidence-based rules for optimal treatment allocation are key components in the quest for efficient, effective health care delivery. Q-learning, an approximate dynamic programming algorithm, is a popular method for estimating optimal sequential decision rules from data. Q-learning requires the modeling of nonsmooth, nonmonotone transformations of the data, complicating the search for adequately expressive, yet parsimonious, statistical models.

Moment Adjusted Imputation for Multivariate Measurement Error Data with Applications to Logistic Regression.

In clinical studies, covariates are often measured with error due to biological fluctuations, device error and other sources. Summary statistics and regression models that are based on mismeasured data will differ from the corresponding analysis based on the "true" covariate. Statistical analysis can be adjusted for measurement error, however various methods exhibit a tradeo between convenience and performance.

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood.

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals.

Corrected-loss estimation for quantile regression with covariate measurement errors.

We study estimation in quantile regression when covariates are measured with errors. Existing methods require stringent assumptions, such as spherically symmetric joint distribution of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicate computation. In this paper, we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression.

FSR Methods for Second-Order Regression Models.

Most variable selection techniques focus on first-order linear regression models. Often, interaction and quadratic terms are also of interest, but the number of candidate predictors grows very fast with the number of original predictors, making variable selection more difficult. Forward selection algorithms are thus developed that enforce natural hierarchies in second-order models to control the entry rate of uninformative effects and to equalize the false selection rates from first-order and second-order terms.

Density Estimation with Replicate Heteroscedastic Measurements.

We present a deconvolution estimator for the density function of a random variable from a set of independent replicate measurements. We assume that measurements are made with normally distributed errors having unknown and possibly heterogeneous variances. The estimator generalizes the deconvoluting kernel density estimator of Stefanski and Carroll (1990), with error variances estimated from the replicate observations.

Regression-assisted deconvolution.

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors.

P-Value Precision and Reproducibility.

P-values are useful statistical measures of evidence against a null hypothesis. In contrast to other statistical estimates, however, their sample-to-sample variability is usually not considered or estimated, and therefore not fully appreciated. Via a systematic study of log-scale p-value standard errors, bootstrap prediction bounds, and reproducibility probabilities for future replicate p-values, we show that p-values exhibit surprisingly large variability in typical data situations.

Orthology-based multilevel modeling of differentially expressed mouse and human gene pairs.

There is great interest in finding human genes expressed through pharmaceutical intervention, thus opening a genomic window into benefit and side-effect profiles of a drug. Human insight gained from FDA-required animal experiments has historically been limited, but in the case of gene expression measurements, proposed biological orthologies between mouse and human genes provide a foothold for animal-to-human extrapolation. We have investigated a five-component, multilevel, bivariate normal mixture model that incorporates mouse, as well as human, gene expression data.

Latent-model robustness in joint models for a primary endpoint and a longitudinal process.

Joint modeling of a primary response and a longitudinal process via shared random effects is widely used in many areas of application. Likelihood-based inference on joint models requires model specification of the random effects. Inappropriate model specification of random effects can compromise inference.

Fast FSR variable selection with applications to clinical trials.

A new version of the false selection rate variable selection method of Wu, Boos, and Stefanski (2007, Journal of the American Statistical Association 102, 235-243) is developed that requires no simulation. This version allows the tuning parameter in forward selection to be estimated simply by hand calculation from a summary table of output even for situations where the number of explanatory variables is larger than the sample size. Because of the computational simplicity, the method can be used in permutation tests and inside bagging loops for improved prediction.

A multivariate two-sample mean test for small sample size and missing data.

We develop a new statistic for testing the equality of two multivariate mean vectors. A scaled chi-squared distribution is proposed as an approximating null distribution. Because the test statistic is based on componentwise statistics, it has the advantage over Hotelling's T2 test of being applicable to the case where the dimension of an observation exceeds the number of observations.