Covariate balancing based on kernel density estimates for controlled experiments

Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes.A completely randomised design is usually used to randomly assign treatment levels to experimental units.When covariates of the experimental units are available,the experimental design should achieve covariate balancing among the treatment groups,such that the statistical inference of the treatment effects is not confounded with any possible effects of covariates.However,covariate imbalance often exists,because the experiment is carried out based on a single realisation of the complete randomisation.It is more likely to occur and worsen when the size of the experimental units is small or moderate.In this paper,we introduce a new covariate balancing criterion,which measures the differences between kernel density estimates of the covariates of treatment groups.To achieve covariate balance before the treatments are randomly assigned,we partition the experimental units by minimising the criterion,then randomly assign the treatment levels to the partitioned groups.Through numerical examples,weshow that the proposed partition approach can improve the accuracy of the difference-in-mean estimator and outperforms the complete randomisation and rerandomisation approaches.

Pharmacological Treatment of Adult Attention-Deficit/Hyperactivity Disorder(ADHD)in a Longitudinal Observational Study:Estimated Treatment Effect Strengthened by Improved Covariate Balance

An improved method for estimation of causal effects from observational data is demonstrated. Applications in medicine have been few, and the purpose of the present study is to contribute new clinical insight by means of this new and more sophisticated analysis. Long term effect of medication for adult ADHD patients is not resolved. A model with causal parameters to represent effect of medication was formulated, which accounts for time-varying confounding and selection-bias from loss to follow-up. The popular marginal structural model (MSM) for causal inference, of Robins et al., adjusts for time-varying confounding, but suffers from lack of robustness for misspecification in the weights. Recent work by Imai and Ratkovic?[1][2] achieves robustness in the MSM, through improved covariate balance (CBMSM). The CBMSM (freely available software) was compared with a standard fit of a MSM and a naive regression model, to give a robust estimate of the true treatment effect in 250 previously non-medicated adults, treated for one year, in a specialized ADHD outpatient clinic in Norway. Covariate balance was greatly improved, resulting in a stronger treatment effect than without this improvement. In terms of treatment effect per week, early stages seemed to have the strongest influence. An estimated average reduction of 4 units on the symptom scale assessed at 12 weeks, for hypothetical medication in the 9 - 12 weeks period compared to no medication in this period, was found. The treatment effect persisted throughout the whole year, with an estimated average reduction of 0.7 units per week on symptoms assessed at one year, for hypothetical medication in the last 13 weeks of the year, compared to no medication in this period. The present findings support a strong and causal direct and indirect effect of pharmacological treatment of adults with ADHD on improvement in symptoms, and with a stronger treatment effect than has been reported.

CBPS-Based Inference in Nonlinear Regression Models with Missing Data

In this article, to improve the doubly robust estimator, the nonlinear regression models with missing responses are studied. Based on the covariate balancing propensity score (CBPS), estimators for the regression coefficients and the population mean are obtained. It is proved that the proposed estimators are asymptotically normal. In simulation studies, the proposed estimators show improved performance relative to usual augmented inverse probability weighted estimators.

Recent advances in statistical methodologies in evaluating program for high-dimensional data

The era of big data brings opportunities and challenges to developing new statistical methods and models to evaluate social programs or economic policies or interventions. This paper provides a comprehensive review on some recent advances in statistical methodologies and models to evaluate programs with high-dimensional data. In particular, four kinds of methods for making valid statistical inferences for treatment effects in high dimensions are addressed. The first one is the so-called doubly robust type estimation, which models the outcome regression and propensity score functions simultaneously. The second one is the covariate balance method to construct the treatment effect estimators. The third one is the sufficient dimension reduction approach for causal inferences. The last one is the machine learning procedure directly or indirectly to make statistical inferences to treatment effect. In such a way, some of these methods and models are closely related to the de-biased Lasso type methods for the regression model with high dimensions in the statistical literature. Finally, some future research topics are also discussed.

Comparison of Covariate Balance Weighting Methods in Estimating Treatment Effects

Different covariate balance weighting methods have been proposed by researchers from different perspectives to estimate the treatment effects.This paper gives a brief review of the covariate balancing propensity score method by Imai and Ratkovic(2014),the stable balance weighting procedure by Zubizarreta(2015),the calibration balance weighting approach by Chan,et al.(2016),and the integrated propensity score technique by Sant’Anna,et al.(2020).Simulations are conducted to illustrate the finite sample performance of both the average treatment effect and quantile treatment effect estimators based on different weighting methods.Simulation results show that in general,the covariate balance weighting methods can outperform the conventional maximum likelihood estimation method while the performance of the four covariate balance weighting methods varies with the data generating processes.Finally,the four covariate balance weighting methods are applied to estimate the treatment effects of the college graduate on personal annual income.

Multi-arm covariate-adaptive randomization

Simultaneously investigating multiple treatments in a single study achieves considerable efficiency in contrast to the traditional two-arm trials.Balancing treatment allocation for influential covariates has become increasingly important in today’s clinical trials.The multi-arm covariate-adaptive randomized clinical trial is one of the most powerful tools to incorporate covariate information and multiple treatments in a single study.Pocock and Simon’s procedure has been extended to the multi-arm case.However,the theoretical properties of multi-arm covariate-adaptive randomization have remained largely elusive for decades.In this paper,we propose a general framework for multi-arm covariate-adaptive designs which also includes the two-arm case,and establish the corresponding theory under widely satisfied conditions.The theoretical results provide new insights into the balance properties of covariate-adaptive randomization procedures and make foundations for most existing statistical inferences under two-arm covariate-adaptive randomization.Furthermore,these open a door to study the theoretical properties of statistical inferences for clinical trials based on multi-arm covariateadaptive randomization procedures.

SURFACE IMBALANCE ENERGY CALCULATED AND ANALYZED WITH THE DATA OF EBEX-2000

Mainly.three methods have been developed to calculate turbulence heat flux.They are eddy covariance method,Bowen ratio/energy balance method and aerodynamic method.In this paper, all the three methods have been used to calculate sensible heat flux,latent heat flux and imbalance energy near the surface with the experiment data of EBEX-2000.Then comparisons of the three methods and some possible explanations of the surface imbalance energy are given.