A generalized response surface model with varying relative potency for assessing drug interaction

When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Based on the Loewe additivity reference model, many existing response surface models require constant relative potency and some of them use a single parameter to capture synergy, additivity, or antagonism. However, the assumption of constant relative potency is too restrictive, and these models using a single parameter to capture drug interaction are inadequate to describe the phenomenon when synergy, additivity, and antagonism are interspersed in different regions of drug combinations. We propose a generalized response surface model with a function of doses instead of one single parameter to identify and quantify departure from additivity. The proposed model can incorporate varying relative potencies among multiple drugs as well. Examples and simulations are given to demonstrate that the proposed model is effective in capturing different patterns of drug interaction.     

Resampling-based multiple testing methods with covariate adjustment: application to investigation of antiretroviral drug susceptibility

Summary .   Identifying genetic mutations that cause clinical resistance to antiretroviral drugs requires adjustment for potential confounders, such as the number of active drugs in a HIV-infected patient's regimen other than the one of interest. Motivated by this problem, we investigated resampling-based methods to test equal mean response across multiple groups defined by HIV genotype, after adjustment for covariates. We consider construction of test statistics and their null distributions under two types of model: parametric and semiparametric. The covariate function is explicitly specified in the parametric but not in the semiparametric approach. The parametric approach is more precise when models are correctly specified, but suffer from bias when they are not; the semiparametric approach is more robust to model misspecification, but may be less efficient. To help preserve type I error while also improving power in both approaches, we propose resampling approaches based on matching of observations with similar covariate values. Matching reduces the impact of model misspecification as well as imprecision in estimation. These methods are evaluated via simulation studies and applied to a data set that combines results from a variety of clinical studies of salvage regimens. Our focus is on relating HIV genotype to viral susceptibility to abacavir after adjustment for the number of active antiretroviral drugs (excluding abacavir) in the patient's regimen.     

Semiparametric models for missing covariate and response data in regression models

We consider a class of semiparametric models for the covariate distribution and missing data mechanism for missing covariate and/or response data for general classes of regression models including generalized linear models and generalized linear mixed models. Ignorable and nonignorable missing covariate and/or response data are considered. The proposed semiparametric model can be viewed as a sensitivity analysis for model misspecification of the missing covariate distribution and/or missing data mechanism. The semiparametric model consists of a generalized additive model (GAM) for the covariate distribution and/or missing data mechanism. Penalized regression splines are used to express the GAMs as a generalized linear mixed effects model, in which the variance of the corresponding random effects provides an intuitive index for choosing between the semiparametric and parametric model. Maximum likelihood estimates are then obtained via the EM algorithm. Simulations are given to demonstrate the methodology, and a real data set from a melanoma cancer clinical trial is analyzed using the proposed methods.     

Varying coefficients model with measurement error

Summary .   We propose a semiparametric partially varying coefficient model to study the relationship between serum creatinine concentration and the glomerular filtration rate (GFR) among kidney donors and patients with chronic kidney disease. A regression model is used to relate serum creatinine to GFR and demographic factors in which coefficient of GFR is expressed as a function of age to allow its effect to be age dependent. GFR measurements obtained from the clearance of a radioactively labeled isotope are assumed to be a surrogate for the true GFR, with the relationship between measured and true GFR expressed using an additive error model. We use locally corrected score equations to estimate parameters and coefficient functions, and propose an expected generalized cross-validation (EGCV) method to select the kernel bandwidth. The performance of the proposed methods, which avoid distributional assumptions on the true GFR and residuals, is investigated by simulation. Accounting for measurement error using the proposed model reduced apparent inconsistencies in the relationship between serum creatinine and GFR among different clinical data sets derived from kidney donor and chronic kidney disease source populations.     

Hypothesis testing in semiparametric additive mixed models

We consider testing whether the nonparametric function in a semiparametric additive mixed model is a simple fixed degree polynomial, for example, a simple linear function. This test provides a goodness-of-fit test for checking parametric models against nonparametric models. It is based on the mixed-model representation of the smoothing spline estimator of the nonparametric function and the variance component score test by treating the inverse of the smoothing parameter as an extra variance component. We also consider testing the equivalence of two nonparametric functions in semiparametric additive mixed models for two groups, such as treatment and placebo groups. The proposed tests are applied to data from an epidemiological study and a clinical trial and their performance is evaluated through simulations.     

Two-component mixture cure rate model with spline estimated nonparametric components

Summary In some survival analysis of medical studies, there are often long-term survivors who can be considered as permanently cured. The goals in these studies are to estimate the noncured probability of the whole population and the hazard rate of the susceptible subpopulation. When covariates are present as often happens in practice, to understand covariate effects on the noncured probability and hazard rate is of equal importance. The existing methods are limited to parametric and semiparametric models. We propose a two-component mixture cure rate model with nonparametric forms for both the cure probability and the hazard rate function. Identifiability of the model is guaranteed by an additive assumption that allows no time-covariate interactions in the logarithm of hazard rate. Estimation is carried out by an expectation-maximization algorithm on maximizing a penalized likelihood. For inferential purpose, we apply the Louis formula to obtain point-wise confidence intervals for noncured probability and hazard rate. Asymptotic convergence rates of our function estimates are established. We then evaluate the proposed method by extensive simulations. We analyze the survival data from a melanoma study and find interesting patterns for this study.     

Estimation of population size based on additive hazards models for continuous-time recapture experiments

We use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous-time capture-recapture experiment, and then construct a Horvitz-Thompson-type estimator for the unknown population size. The resulting estimator is consistent and asymptotically normal with an easily estimated variance. Simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed .5. Ignoring covariates would underestimate the population size and the coverage probability is poor. A wildlife example is provided.     

Model checking in regression via dimension reduction

Lack-of-fit checking for parametric and semiparametric modelsis essential in reducing misspecification. The efficiency ofmost existing model-checking methods drops rapidly as the dimensionof the covariates increases. We propose to check a model byprojecting the fitted residuals along a direction that adaptsto the systematic departure of the residuals from the desiredpattern. Consistency of the method is proved for parametricand semiparametric regression models. A bootstrap implementationis also discussed. Simulation comparisons with several existingmethods are made, suggesting that the proposed methods are moreefficient than the existing methods when the dimension increases.Air pollution data from Chicago are used to illustrate the procedure.     

Structured additive regression for categorical space-time data: a mixed model approach

Motivated by a space-time study on forest health with damage state of trees as the response, we propose a general class of structured additive regression models for categorical responses, allowing for a flexible semiparametric predictor. Nonlinear effects of continuous covariates, time trends, and interactions between continuous covariates are modeled by penalized splines. Spatial effects can be estimated based on Markov random fields, Gaussian random fields, or two-dimensional penalized splines. We present our approach from a Bayesian perspective, with inference based on a categorical linear mixed model representation. The resulting empirical Bayes method is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are estimated using (approximate) restricted maximum likelihood. In simulation studies we investigate the performance of different choices for the spatial effect, compare the empirical Bayes approach to competing methodology, and study the bias of mixed model estimates. As an application we analyze data from the forest health survey.     

Mining significant substructure pairs for interpreting polypharmacology in drug-target network

A current key feature in drug-target network is that drugs often bind to multiple targets, known as polypharmacology or drug promiscuity. Recent literature has indicated that relatively small fragments in both drugs and targets are crucial in forming polypharmacology. We hypothesize that principles behind polypharmacology are embedded in paired fragments in molecular graphs and amino acid sequences of drug-target interactions. We developed a fast, scalable algorithm for mining significantly co-occurring subgraph-subsequence pairs from drug-target interactions. A noteworthy feature of our approach is to capture significant paired patterns of subgraph-subsequence, while patterns of either drugs or targets only have been considered in the literature so far. Significant substructure pairs allow the grouping of drug-target interactions into clusters, covering approximately 75% of interactions containing approved drugs. These clusters were highly exclusive to each other, being statistically significant and logically implying that each cluster corresponds to a distinguished type of polypharmacology. These exclusive clusters cannot be easily obtained by using either drug or target information only but are naturally found by highlighting significant substructure pairs in drug-target interactions. These results confirm the effectiveness of our method for interpreting polypharmacology in drug-target network.     

"Smooth" semiparametric regression analysis for arbitrarily censored time-to-event data

Summary .   A general framework for regression analysis of time-to-event data subject to arbitrary patterns of censoring is proposed. The approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models, such as the baseline hazard function in the proportional hazards model, have densities satisfying mild "smoothness" conditions. Densities are approximated by a truncated series expansion that, for fixed degree of truncation, results in a "parametric" representation, which makes likelihood-based inference coupled with adaptive choice of the degree of truncation, and hence flexibility of the model, computationally and conceptually straightforward with data subject to any pattern of censoring. The formulation allows popular models, such as the proportional hazards, proportional odds, and accelerated failure time models, to be placed in a common framework; provides a principled basis for choosing among them; and renders useful extensions of the models straightforward. The utility and performance of the methods are demonstrated via simulations and by application to data from time-to-event studies.     

Correlating the Structure and Activity of Y. pestis Ail in a Bacterial Cell Envelope

Understanding microbe-host interactions at the molecular level is a major goal of fundamental biology and therapeutic drug development. Structural biology strives to capture biomolecular structures in action, but the samples are often highly simplified versions of the complex native environment. Here, we present an Escherichia coli model system that allows us to probe the structure and function of Ail, the major surface protein of the deadly pathogen Yersinia pestis. We show that cell surface expression of Ail produces Y. pestis virulence phenotypes in E. coli, including resistance to human serum, cosedimentation of human vitronectin, and pellicle formation. Moreover, isolated bacterial cell envelopes, encompassing inner and outer membranes, yield high-resolution solid-state NMR spectra that reflect the structure of Ail and reveal Ail sites that are sensitive to the bacterial membrane environment and involved in the interactions with human serum components. The data capture the structure and function of Ail in a bacterial outer membrane and set the stage for probing its interactions with the complex milieu of immune response proteins present in human serum.     

Analysis of covariance with incomplete data via semiparametric model transformations

We propose a method for fitting semiparametric models such as the proportional hazards (PH), additive risks (AR), and proportional odds (PO) models. Each of these semiparametric models implies that some transformation of the conditional cumulative hazard function (at each t) depends linearly on the covariates. The proposed method is based on nonparametric estimation of the conditional cumulative hazard function, forming a weighted average over a range of t-values, and subsequent use of least squares to estimate the parameters suggested by each model. An approximation to the optimal weight function is given. This allows semiparametric models to be fitted even in incomplete data cases where the partial likelihood fails (e.g., left censoring, right truncation). However, the main advantage of this method rests in the fact that neither the interpretation of the parameters nor the validity of the analysis depend on the appropriateness of the PH or any of the other semiparametric models. In fact, we propose an integrated method for data analysis where the role of the various semiparametric models is to suggest the best fitting transformation. A single continuous covariate and several categorical covariates (factors) are allowed. Simulation studies indicate that the test statistics and confidence intervals have good small-sample performance. A real data set is analyzed.     

Modeling multivariate survival data by a semiparametric random effects proportional odds model

In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.     

Semiparametric Transformation Rate Model for Recurrent Event Data

In this article, we propose a class of semiparametric transformation rate models for recurrent event data subject to right censoring and potentially stopped by a terminating event (e.g., death). These transformation models include both additive rates model and proportional rates model as special cases. Respecting the property that no recurrent events can occur after the terminating event, we model the conditional recurrent event rate given survival. Weighted estimating equations are constructed to estimate the regression coefficients and baseline rate function. In particular, the baseline rate function is approximated by wavelet function. Asymptotic properties of the proposed estimators are derived and a data-dependent criterion is proposed for selecting the most suitable transformation. Simulation studies show that the proposed estimators perform well for practical sample sizes. The proposed methods are used in two real-data examples: a randomized trial of rhDNase and a community trial of vitamin A.     

Nonlinear response surface in the study of interaction analysis of three combination drugs

Few articles have been written on analyzing three‐way interactions between drugs. It may seem to be quite straightforward to extend a statistical method from two‐drugs to three‐drugs. However, there may exist more complex nonlinear response surface of the interaction index () with more complex local synergy and/or local antagonism interspersed in different regions of drug combinations in a three‐drug study, compared in a two‐drug study. In addition, it is not possible to obtain a four‐dimensional (4D) response surface plot for a three‐drug study. We propose an analysis procedure to construct the dose combination regions of interest (say, the synergistic areas with ). First, use the model robust regression method (MRR), a semiparametric method, to fit the entire response surface of the , which allows to fit a complex response surface with local synergy/antagonism. Second, we run a modified genetic algorithm (MGA), a stochastic optimization method, many times with different random seeds, to allow to collect as many feasible points as possible that satisfy the estimated values of . Last, all these feasible points are used to construct the approximate dose regions of interest in a 3D. A case study with three anti‐cancer drugs in an in vitro experiment is employed to illustrate how to find the dose regions of interest.     

Additive Damage Models for Cellular Pharmacodynamics of Radiation–Chemotherapy Combinations

Many cancer patients receive combination treatments with radiation and chemotherapy. Available mathematical models for cellular pharmacodynamics have limited ability to represent observed in vitro responses to radiochemotherapy. Here, a family of additive damage models is proposed to describe cell kill resulting from radiochemotherapy with fixed schedule and variable doses. The pathways by which the agents produce cellular damage are assumed to converge in a single cell death process, so that survival depends on total damage, which can be represented as a sum of contributions from the various damage pathways. Heterogeneity in response across the cell population is ascribed to variations in the damage threshold for cell kill. The family of proposed models includes effects of one or two pathways of damage for each agent, saturation in drug responses, and cooperative or antagonistic interactions between agents. Models from this family with 4–7 unknown parameters are tested for their ability to fit 218 in vitro literature data sets for a range of drugs and cell lines. Overall, the additive damage models are found to outperform models based on the existing concept of independent cell kill, according to the corrected Akaike Information Criterion. The results are used to assess the importance of the various effects included in the models. These additive damage models have potential applications to the optimization of treatment and to the analysis and interpretation of in vitro screening data for new drug–radiation combinations.     

Bayesian variable selection and estimation in semiparametric joint models of multivariate longitudinal and survival data

This paper presents a novel semiparametric joint model for multivariate longitudinal and survival data (SJMLS) by relaxing the normality assumption of the longitudinal outcomes, leaving the baseline hazard functions unspecified and allowing the history of the longitudinal response having an effect on the risk of dropout. Using Bayesian penalized splines to approximate the unspecified baseline hazard function and combining the Gibbs sampler and the Metropolis–Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates in SJMLS. Simulation studies are conducted to investigate the finite sample performance of the proposed techniques. An example from the International Breast Cancer Study Group (IBCSG) is used to illustrate the proposed methodologies.     

Semiparametric regression analysis of longitudinal data with informative drop-outs

Informative drop-out arises in longitudinal studies when the subject's follow-up time depends on the unobserved values of the response variable. We specify a semiparametric linear regression model for the repeatedly measured response variable and an accelerated failure time model for the time to informative drop-out. The error terms from the two models are assumed to have a common, but completely arbitrary joint distribution. Using a rank-based estimator for the accelerated failure time model and an artificial censoring device, we construct an asymptotically unbiased estimating function for the linear regression model. The resultant estimator is shown to be consistent and asymptotically normal. A resampling scheme is developed to estimate the limiting covariance matrix. Extensive simulation studies demonstrate that the proposed methods are suitable for practical use. Illustrations with data taken from two AIDS clinical trials are provided.