Binary response panel data models with sample selection and self‐selection

Semiparametric and nonparametric estimation of sample selection models under symmetry

Estimation of Sample Selection Models with Spatial Dependence

Estimation of spatial sample selection models: A partial maximum likelihood approach

The literature on the estimation of treatment effects has matured in economics. The potential outcomes framework guides the estimation of the causal effect of economic choices or policy interventions. The application of methods from the treatment effects literature has spread from the analysis of the effects of labor market programs and the wage return to education to other areas in economics. This special issue involves methodological developments and state-of-the art applications of methods to estimate treatment effects in various areas of economics. The contributions illustrate the emphasis within the treatment effects literature on the separate but related issues of heterogeneous treatment effects and identification. The careful, high-quality substantive applications collected here show just how much applied work on policy-relevant topics has benefitted from the methodological developments in the treatment effects literature. At the same time, many of the substantive papers make important methodological contributions as well.

ABSTRACTLongitudinal binary data are commonly encountered in clinical trials. Multiple imputation is an approach for getting a valid estimation of treatment effects under an assumption of missing at random mechanism. Although there are a variety of multiple imputation methods for the longitudinal binary data, a limited number of researches have reported on relative performances of the methods. Moreover, when focusing on the treatment effect throughout a period that has often been used in clinical evaluations of specific disease areas, no definite investigations comparing the methods have been available. We conducted an extensive simulation study to examine comparative performances of six multiple imputation methods available in the SAS MI procedure for longitudinal binary data, where two endpoints of responder rates at a specified time point and throughout a period were assessed. The simulation study suggested that results from naive approaches of a single imputation with non-responders and a complete case analysis could be very sensitive against missing data. The multiple imputation methods using a monotone method and a full conditional specification with a logistic regression imputation model were recommended for obtaining unbiased and robust estimations of the treatment effect. The methods were illustrated with data from a mental health research.

Precise estimation of treatment effects is crucial for accurately evaluating the intervention. While deep learning models have exhibited promising performance in learning counterfactual representations for treatment effect estimation (TEE), a major limitation in most of these models is that they often overlook the diversity of treatment effects across potential subgroups that have varying treatment effects and characteristics, treating the entire population as a homogeneous group. This limitation restricts the ability to precisely estimate treatment effects and provide targeted treatment recommendations. In this paper, we propose a novel treatment effect estimation model, named SubgroupTE, which incorporates subgroup identification in TEE. SubgroupTE identifies heterogeneous subgroups with different responses and more precisely estimates treatment effects by considering subgroup-specific treatment effects in the estimation process. In addition, we introduce an expectation–maximization (EM)-based training process that iteratively optimizes estimation and subgrouping networks to improve both estimation and subgroup identification. Comprehensive experiments on the synthetic and semi-synthetic datasets demonstrate the outstanding performance of SubgroupTE compared to the existing works for treatment effect estimation and subgrouping models. Additionally, a real-world study demonstrates the capabilities of SubgroupTE in enhancing targeted treatment recommendations for patients with opioid use disorder (OUD) by incorporating subgroup identification with treatment effect estimation.

Summary Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper we consider estimation of the local average treatment effect under the binary instrumental variable model. We discuss the challenges of causal estimation with a binary outcome and show that, surprisingly, it can be more difficult than in the case with a continuous outcome. We propose novel modelling and estimation procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness and efficiency. Our approach is illustrated via simulation studies and a real data analysis.

In longitudinal studies, the inverse probability of treatment weighted (IPTW) method is commonly employed to estimate the effect of time-dependent treatments on an outcome of interest. However, it has been documented that when the confounders are subject to measurement error, the naive IPTW method which simply ignores measurement error leads to biased treatment effect estimation. In the existing literature, there is a lack of measurement error correction methods that fully remove measurement error effect and produce consistent treatment effect estimation. In this article, we develop a novel consistent IPTW estimation procedure for longitudinal studies. The key step of the proposed method is to use the observed data to construct a corrected function that is unbiased of the unknown IPTW function. Simulation studies reveal that the proposed method outperforms the existing consistent and approximate measurement error correction methods for IPTW estimation of the average treatment effect. Finally, we apply the proposed method to analyze a real dataset.

BackgroundThe classical linear model is widely used in the analysis of clinical trials with continuous outcomes. However, required model assumptions are frequently not met, resulting in estimates of treatment effect that can be inefficient and biased. In addition, traditional models assess treatment effect only on the mean response, and not on other aspects of the response, such as the variance. Distributional regression modelling overcomes these limitations. The purpose of this paper is to demonstrate its usefulness for the analysis of clinical trials, and superior performance to that of traditional models.MethodsDistributional regression models are demonstrated, and contrasted with normal linear models, on data from the LIPID randomized controlled trial, which compared the effects of pravastatin with placebo in patients with coronary heart disease. Systolic blood pressure (SBP) and the biomarker midregional pro-adrenomedullin (MR-proADM) were analysed. Treatment effect was estimated in models that used response distributions more appropriate than the normal (Box-Cox-t and Johnson’s Su for MR-proADM and SBP, respectively), applied censoring below the detection limit of MR-proADM, estimated treatment effect on distributional parameters other than the mean, and included random effects for longitudinal observations. A simulation study was conducted to compare the performance of distributional regression models with normal linear regression, under conditions mimicking the LIPID study. The R package gamlss (Generalized Additive Models for Location, Scale and Shape), which implements maximum likelihood estimation for distributional regression modelling, was used throughout.ResultsIn all cases the distributional regression models fit the data well, in contrast to poor fits obtained for traditional models; for MR-proADM a small but significant treatment effect on the mean was detected by the distributional regression model and not the normal model; and for SBP a beneficial treatment effect on the variance was demonstrated. In the simulation study distributional models strongly outperformed normal models when the response variable was non-normal and heterogeneous; and there was no disadvantage introduced by the use of distributional regression modelling when the response satisfied the normal linear model assumptions.ConclusionsDistributional regression models are a rich framework, largely untapped in the clinical trials world. We have demonstrated a sample of the capabilities of these models for the analysis of trials. If interest lies in accurate estimation of treatment effect on the mean, or other distributional features such as variance, the use of distributional regression modelling will yield superior estimates to traditional normal models, and is strongly recommended.Trial registrationThe LIPID trial was retrospectively registered on ANZCTR on 27/04/2016, registration number ACTRN12616000535471.

BackgroundMulticentre randomized controlled trials (RCTs) routinely use randomization and analysis stratified by centre to control for differences between centres and to improve precision. No consensus has been reached on how to best analyze correlated continuous outcomes in such settings. Our objective was to investigate the properties of commonly used statistical models at various levels of clustering in the context of multicentre RCTs.MethodsAssuming no treatment by centre interaction, we compared six methods (ignoring centre effects, including centres as fixed effects, including centres as random effects, generalized estimating equation (GEE), and fixed- and random-effects centre-level analysis) to analyze continuous outcomes in multicentre RCTs using simulations over a wide spectrum of intraclass correlation (ICC) values, and varying numbers of centres and centre size. The performance of models was evaluated in terms of bias, precision, mean squared error of the point estimator of treatment effect, empirical coverage of the 95% confidence interval, and statistical power of the procedure.ResultsWhile all methods yielded unbiased estimates of treatment effect, ignoring centres led to inflation of standard error and loss of statistical power when within centre correlation was present. Mixed-effects model was most efficient and attained nominal coverage of 95% and 90% power in almost all scenarios. Fixed-effects model was less precise when the number of centres was large and treatment allocation was subject to chance imbalance within centre. GEE approach underestimated standard error of the treatment effect when the number of centres was small. The two centre-level models led to more variable point estimates and relatively low interval coverage or statistical power depending on whether or not heterogeneity of treatment contrasts was considered in the analysis.ConclusionsAll six models produced unbiased estimates of treatment effect in the context of multicentre trials. Adjusting for centre as a random intercept led to the most efficient treatment effect estimation across all simulations under the normality assumption, when there was no treatment by centre interaction.

This paper applies both parametric and semiparametric methods to the estimation of wage and participation equations for married women in Portugal. The semiparametric estimators considered are the two‐stage estimators proposed by Newey (1991) and Andrews and Schafgans (1998). The selection equation results are compared using the specification tests proposed by Horowitz (1993), Horowitz and Härdle (1994), and the wage equation results are compared using a Hausman test. Significant differences between the two approaches indicate the inappropriateness of the standard parametric methods to the estimation of the model and for the purpose of policy simulations. The greater departure seems to occur in the range of the low values of the index corresponding to a specific group of women. Copyright © 2001 John Wiley & Sons, Ltd.

The econometric issue of sample selection concerns the possible biases that arise when a nonrandomly sampled set of observations from a population is used as if the sample were random to make inferences about that population. Current literature, with a few exceptions noted below, has focused on, and finely tuned, the known results relating to this issue in the framework of the linear regression model and analysis of a continuous dependent variable, such as hours worked or wages. This paper will examine an extension of the sample selection model to the Poisson regression model for discrete, count data, such as numbers of patents, of children, of visits to facilities such as shops or recreation sites, of convictions for crimes committed, and so on.

Summary Sample selection models are important for correcting the effects of non-random sampling. This paper is about semiparametric estimation using a series approximation to the correction term. Regression spline and power series approximations are considered. Asymptotic normality and consistency of an asymptotic variance estimator are shown.

This paper assesses the causal impact of late-term (8th month) maternal smoking on birthweight using data from a randomized clinical trial, in which some women were encouraged not to smoke, while others were not. The estimation of treatment effects in this case is made difficult as a result of the presence of non-compliers, women who would not change their smoking status, regardless of the receipt of encouragement. Because these women are not at risk of changing treatment status, treatment effect distributions may be difficult to construct for them. Consequently, the paper focuses on obtaining the distribution of treatment impacts for the sub-set of compliers found in the data. Because compliance status is not observed for all subjects in the sample, a Bayesian finite mixture model is estimated that recovers the treatment effect parameters of interest. The complier average treatment effect implies that smokers give birth to infants weighing 348 g less than those of non-smokers, on average, although the 95% posterior density interval contains zero. The treatment effect is stronger for women who were moderate smokers prior to pregnancy, implying a birthweight difference of 430 g. However, the model predicts that only about 22% of the women in the sample were at risk of changing their smoking behaviour in response to encouragement to quit.

Statistical heterogeneity and small-study effects are 2 major issues affecting the validity of meta-analysis. In this article, we introduce the concept of a limit meta-analysis, which leads to shrunken, empirical Bayes estimates of study effects after allowing for small-study effects. This in turn leads to 3 model-based adjusted pooled treatment-effect estimators and associated confidence intervals. We show how visualizing our estimators using the radial plot indicates how they can be calculated using existing software. The concept of limit meta-analysis also gives rise to a new measure of heterogeneity, termed G(2), for heterogeneity that remains after small-study effects are accounted for. In a simulation study with binary data and small-study effects, we compared our proposed estimators with those currently used together with a recent proposal by Moreno and others. Our criteria were bias, mean squared error (MSE), variance, and coverage of 95% confidence intervals. Only the estimators arising from the limit meta-analysis produced approximately unbiased treatment-effect estimates in the presence of small-study effects, while the MSE was acceptably small, provided that the number of studies in the meta-analysis was not less than 10. These limit meta-analysis estimators were also relatively robust against heterogeneity and one of them had a relatively small coverage error.