ESTIMATION AND TESTING FOR PARTIALLY LINEAR SINGLE-INDEX MODELS

Partial-linear single-index transformation models with censored data

In studies with time-to-event outcomes, multiple, inter-correlated, and time-varying covariates are commonly observed. It is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk. A class of semiparametric transformation (ST) models offers flexible specifications of the intensity function and can be a general framework to accommodate nonlinear covariate effects. In this paper, we propose a partial-linear single-index (PLSI) transformation model that reduces the dimensionality of multiple covariates into a single index and provides interpretable estimates of the covariate effects. We develop an iterative algorithm using the regression spline technique to model the nonparametric single-index function for possibly nonlinear joint effects, followed by nonparametric maximum likelihood estimation. We also propose a nonparametric testing procedure to formally examine the linearity of covariate effects. We conduct Monte Carlo simulation studies to compare the PLSI transformation model with the standard ST model and apply it to NYU Langone Health de-identified electronic health record data on COVID-19 hospitalized patients' mortality and a Veteran's Administration lung cancer trial.

Relative contrast estimation and inference for treatment recommendation

When there are resource constraints, it may be necessary to rank individualized treatment benefits to facilitate the prioritization of assigning different treatments. Most existing literature on individualized treatment rules targets absolute conditional treatment effect differences as a metric for the benefit. However, there can be settings where relative differences may better represent such benefit. In this paper, we consider modeling such relative differences formed as scale-invariant contrasts between the conditional treatment effects. By showing that all scale-invariant contrasts are monotonic transformations of each other, we posit a single index model for a particular relative contrast. We then characterize semiparametric estimating equations, including the efficient score, to estimate index parameters. To achieve semiparametric efficiency, we propose a two-step approach that minimizes a doubly robust loss function for initial estimation and then performs a one-step efficiency augmentation procedure. Careful theoretical and numerical studies are provided to show the superiority of our proposed approach.

Multi-Response Based Personalized Treatment Selection with Data from Crossover Designs for Multiple Treatments

In this work we propose a novel method for treatment selection based on individual covariate information when the treatment response is multivariate and data are available from a crossover design. Our method covers any number of treatments and it can be applied for a broad set of models. The proposed method uses a rank aggregation technique to estimate an ordering of treatments based on ranked lists of treatment performance measures such as smooth conditional means and conditional probability of a response for one treatment dominating others. An empirical study demonstrates the performance of the proposed method in finite samples.

Towards multi-label classification: Next step of machine learning for microbiome research

Machine learning (ML) has been widely used in microbiome research for biomarker selection and disease prediction. By training microbial profiles of samples from patients and healthy controls, ML classifiers constructs data models by community features that highly correlated with the target diseases, so as to determine the status of new samples. To clearly understand the host-microbe interaction of specific diseases, previous studies always focused on well-designed cohorts, in which each sample was exactly labeled by a single status type. However, in fact an individual may be associated with multiple diseases simultaneously, which introduce additional variations on microbial patterns that interferes the status detection. More importantly, comorbidities or complications can be missed by regular ML models, limiting the practical application of microbiome techniques. In this review, we summarize the typical ML approaches of single-label classification for microbiome research, and demonstrate their limitations in multi-label disease detection using a real dataset. Then we prospect a further step of ML towards multi-label classification that potentially solves the aforementioned problem, including a series of promising strategies and key technical issues for applying multi-label classification in microbiome-based studies.

High-dimensional single-index models with censored responses

In this article, we study the estimation of high-dimensional single index models when the response variable is censored. We hybrid the estimation methods for high-dimensional single-index models (but without censorship) and univariate nonparametric models with randomly censored responses to estimate the index parameters and the link function and apply the proposed methods to analyze a genomic dataset from a study of diffuse large B-cell lymphoma. We evaluate the finite sample performance of the proposed procedures via simulation studies and establish large sample theories for the proposed estimators of the index parameter and the nonparametric link function under certain regularity conditions.

A family of partial-linear single-index models for analyzing complex environmental exposures with continuous, categorical, time-to-event, and longitudinal health outcomes

BACKGROUND

Statistical methods to study the joint effects of environmental factors are of great importance to understand the impact of correlated exposures that may act synergistically or antagonistically on health outcomes. This study proposes a family of statistical models under a unified partial-linear single-index (PLSI) modeling framework, to assess the joint effects of environmental factors for continuous, categorical, time-to-event, and longitudinal outcomes. All PLSI models consist of a linear combination of exposures into a single index for practical interpretability of relative direction and importance, and a nonparametric link function for modeling flexibility.

METHODS

We presented PLSI linear regression and PLSI quantile regression for continuous outcome, PLSI generalized linear regression for categorical outcome, PLSI proportional hazards model for time-to-event outcome, and PLSI mixed-effects model for longitudinal outcome. These models were demonstrated using a dataset of 800 subjects from NHANES 2003-2004 survey including 8 environmental factors. Serum triglyceride concentration was analyzed as a continuous outcome and then dichotomized as a binary outcome. Simulations were conducted to demonstrate the PLSI proportional hazards model and PLSI mixed-effects model. The performance of PLSI models was compared with their counterpart parametric models.

RESULTS

PLSI linear, quantile, and logistic regressions showed similar results that the 8 environmental factors had both positive and negative associations with triglycerides, with a-Tocopherol having the most positive and trans-b-carotene having the most negative association. For the time-to-event and longitudinal settings, simulations showed that PLSI models could correctly identify directions and relative importance for the 8 environmental factors. Compared with parametric models, PLSI models got similar results when the link function was close to linear, but clearly outperformed in simulations with nonlinear effects.

CONCLUSIONS

We presented a unified family of PLSI models to assess the joint effects of exposures on four commonly-used types of outcomes in environmental research, and demonstrated their modeling flexibility and effectiveness, especially for studying environmental factors with mixed directional effects and/or nonlinear effects. Our study has expanded the analytical toolbox for investigating the complex effects of environmental factors. A practical contribution also included a coherent algorithm for all proposed PLSI models with R codes available.

Sparse Single Index Models for Multivariate Responses

Joint models are popular for analyzing data with multivariate responses. We propose a sparse multivariate single index model, where responses and predictors are linked by unspecified smooth functions and multiple matrix level penalties are employed to select predictors and induce low-rank structures across responses. An alternating direction method of multipliers (ADMM) based algorithm is proposed for model estimation. We demonstrate the effectiveness of proposed model in simulation studies and an application to a genetic association study.

Personalized treatment selection using data from crossover designs with carry-over effects

In this work, we propose a semiparametric method for estimating the optimal treatment for a given patient based on individual covariate information for that patient when data from a crossover design are available. Here, we assume there are carry-over effects for patients switching from one treatment to another. For the K treatment (K ≥ 2) scenario, we show that nonparametric estimation of carry-over effects can have the undesirable property that comparison of treatment means can only be done using independent outcome measurements from different groups of patients rather than using available joint measurements for each patient. To overcome this barrier, we compare probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient-specific scores constructed from patient covariates. We suggest single-index models as appropriate models connecting outcome variables to covariates and our empirical investigations show that frequencies of correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a single-index model structure. We also conduct a real data analysis to show the applicability of the proposed procedure.

Bi-level feature selection in high dimensional AFT models with applications to a genomic study

We propose a new bi-level feature selection method for high dimensional accelerated failure time models by formulating the models to a single index model. The method yields sparse solutions at both the group and individual feature levels along with an expedient algorithm, which is computationally efficient and easily implemented. We analyze a genomic dataset for an illustration, and present a simulation study to show the finite sample performance of the proposed method.

Statistical regression modeling for energy consumption in wastewater treatment

Wastewater treatment is one of critical issues faced by water utilities, and receives more and more attentions recently. The energy consumption modeling in biochemical wastewater treatment was investigated in the study via a general and robust approach based on Bayesian semi-parametric quantile regression. The dataset was derived from a municipal wastewater treatment plant, where the energy consumption of unit chemical oxygen demand (COD) reduction was the response variable of interest. Via the proposed approach, the comprehensive regression pictures of the energy consumption and truly influencing factors, i.e., the regression relationships at lower, median and higher energy consumption levels were characterized respectively. Meanwhile, the proposals for energy saving in different cases were also facilitated specifically. First, the lower level of energy consumption was closely associated with the temperature of influent wastewater, and the chroma-rich wastewater also showed helpful in the execution of energy saving. Second, at median energy consumption level, the COD-rich wastewater played a determinative role in the reduction of energy consumption, while the higher quality of treated water led to slightly energy intensive. Third, the higher level of energy consumption was most likely to be attributed to the relatively high temperature of wastewater and total nitrogen (TN)-rich wastewater, and both of the factors were preferably to be avoided to alleviate the burden of energy consumption. The study provided an efficient approach to controlling the energy consumption of wastewater treatment in the perspective of statistical regression modeling, and offered valuable suggestions for the future energy saving.