Controlled Direct and Mediated Effects: Definition,Identification and Bounds

Abstract. Results are given which provide bounds for controlled direct effects when nounmeasured confounding assumptions required for the identification of these effects do not hold. Previous results concerning bounds for controlled direct effects rely on monotonicity relationships between the treatment, mediator and the outcome themselves; the results presented in this article instead assume that monotonicity relationships hold between the unmeasured confounding variable or variables and the treatment, mediator and outcome. Whereas prior results give bounds that contain the null hypothesis of no direct effect, the results presented here will in many instances yield bounds that do not contain the null hypothesis of no direct effect. For contexts in which a set of variables intercepts all paths between a treatment and an outcome, it is possible to provide a definition for a controlled mediated effect. We discuss the identification of these controlled mediated effects; the bounds for controlled direct effects are applicable also to controlled mediated effects. An example is given to illustrate how the results in the article can be used to draw inferences about direct and mediated effects in the presence of unmeasured confounding variables.     

The Identification of Direct and Indirect Effects in Studies with an Unmeasured Intermediate Variable

This paper considers the identification problem of direct and indirect effects of treatment on a response, when observed data are available but an important intermediate variable is unmeasured. To solve this problem, we propose identification conditions for direct and indirect effects based on (conditionally independent) proxy variables of the unmeasured intermediate variable. This paper establishes feasible approaches for evaluating direct and indirect effects in studies with a single unmeasured intermediate variable.     

Efficient crossover designs in the presence of interactions between direct and carry-over treatment effects

Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of application, there is also the possible presence of a residual, or carry-over, effect of a treatment from one or more previous periods. We use a model in which the residual effect from a treatment depends upon the treatment applied in the succeeding period; that is, a model which includes interactions between the treatment direct and residual effects. We assume that residual effects do not persist further than one succeeding period.A particular class of strongly balanced repeated measurements designs with n=t² units and which are uniform on the periods is examined. A lower bound for the A-efficiency of the designs for estimating the direct effects is derived and it is shown that such designs are highly efficient for any number of periods p=2,…,2t.     

A comparison of the type I error rates of three assessment methods for indirect effects

Mediation analysis is a popular statistical analysis verifying the relation between an independent variable and a dependent variable through a mediator. There are three traditional tests to assess indirect effects: the Baron and Kenny test (BK), the Sobel test (ST) and the bootstrap method (BT). Previous studies have showed that the BT is more powerful and more conceptually appropriate. However, no study has systematically compared these tests regarding the type I error rate. A Monte-Carlo simulation is carried out with 19 scenarios varying paths (but no indirect effect), 9 scenarios varying the direct effect, and 6 sample sizes (1056 different scenarios). Results show that the BT had an overall good performance even for small sample size and whatever the effect sizes. The ST and the BK test were conservative, especially with small sample size and low effect sizes. In conclusion, these tests should be avoided, and the BT is recommended.     

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ABSTRACT

In the class of stochastic volatility (SV) models, leverage effects are typically specified through the direct correlation between the innovations in both returns and volatility, resulting in the dynamic leverage (DL) model. Recently, two asymmetric SV models based on threshold effects have been proposed in the literature. As such models consider only the sign of the previous return and neglect its magnitude, this paper proposes a dynamic asymmetric leverage (DAL) model that accommodates the direct correlation as well as the sign and magnitude of the threshold effects. A special case of the DAL model with zero direct correlation between the innovations is the asymmetric leverage (AL) model. The dynamic asymmetric leverage models are estimated by the Monte Carlo likelihood (MCL) method. Monte Carlo experiments are presented to examine the finite sample properties of the estimator. For a sample size of T = 2000 with 500 replications, the sample means, standard deviations, and root mean squared errors of the MCL estimators indicate only a small finite sample bias. The empirical estimates for S&;P 500 and TOPIX financial returns, and USD/AUD and YEN/USD exchange rates, indicate that the DAL class, including the DL and AL models, is generally superior to threshold SV models with respect to AIC and BIC, with AL typically providing the best fit to the data.     

Dynamic path analysis for event time data: large sample properties and inference

We consider the situation with a survival or more generally a counting process endpoint for which we wish to investigate the effect of an initial treatment. Besides the treatment indicator we also have information about a time-varying covariate that may be of importance for the survival endpoint. The treatment may possibly influence both the endpoint and the time-varying covariate, and the concern is whether or not one should correct for the effect of the dynamic covariate. Recently Fosen et al. (Biometrical J 48:381–398, 2006a) investigated this situation using the notion of dynamic path analysis and showed under the Aalen additive hazards model that the total effect of the treatment indicator can be decomposed as a sum of what they termed a direct and an indirect effect. In this paper, we give large sample properties of the estimator of the cumulative indirect effect that may be used to draw inferences. Small sample properties are investigated by Monte Carlo simulation and two applications are provided for illustration. We also consider the Cox model in the situation with recurrent events data and show that a similar decomposition of the total effect into a sum of direct and indirect effects holds under certain assumptions.     

我国城镇居民收入分配机会不平等因何而生

本文借鉴Roemer的环境和努力二元因素分析框架,采用CHIP数据,构建相对全面的环境集,然后借助事前法构造的反事实收入来间接测度我国城镇居民收入分配机会不平等程度及其具体生成渠道,并选取年龄、性别和地区三大环境因素,进一步剖析城镇居民收入分配机会不平等的异质性特征。结果发现：（1）城镇居民收入不平等中的23.2%是由环境因素所引致的机会不平等。城镇机会不平等程度随年龄增加而逐步积累,但在51-60岁时有所缓和,呈现倒U型特征;女性的机会不平等程度高于男性;机会不平等程度在东部、中部、西部地区依次递减。（2）从生成渠道来看,机会不平等中的78.3%源于环境因素的直接渠道影响,剩余21.7%为环境因素的间接渠道影响。两种渠道的相对程度在不同年龄间差异明显,间接渠道对女性机会不平等的解释力是男性的2倍以上,间接渠道相对程度在东部、中部、西部地区依次递减。旨在缩小机会不平等的政策应致力于补偿年龄、性别和地区等环境因素差异,尽可能使所有人的同等努力得到同等回报。     

资本技能互补与技术进步的技能偏向决定

本文基于三要素双层嵌套式CES生产函数和质量阶梯型技术创新模型，通过对企业行为的理论分析，揭示了决定技术进步方向的各种因素，发现技术进步的方向取决于技术进步的直接效应、资本技能互补的间接效应和劳动力市场内部的规模效应。其中，资本技能互补效应引致技术进步偏向于技能的机制有二：一是通过体现于资本的技术水平提高偏向于技能劳动，二是通过资本规模的扩大偏向于技能劳动。运用贝叶斯参数估计方法对中国1991-2016年期间技术进步技能偏向指数的实证测算结果表明，资本技能互补效应对于决定技术进步的技能偏向作用巨大，尽管在此期间直接效应偏向于非技能劳动，但是由于资本技能互补的间接效应和要素配置的规模效应偏向于技能劳动，且二者的作用强度均大于直接效应，从而使得中国的技术整体呈现出技能劳动偏向。     

A simpler approach for mediation analysis for dichotomous mediators in logistic regression

Mediation is a hypothesized causal chain among three variables. Mediation analysis for continuous response variables is well developed in the literature, and it can be shown that the indirect effect is equal to the total effect minus the direct effect. However, mediation analysis for categorical responses is still not fully developed. The purpose of this article is to propose a simpler method of analysing the mediation effect among three variables when the dependent and mediator variables are both dichotomous. We propose using the latent variable technique which in turn will adjust for the necessary condition that indirect effect is equal to the total effect minus the direct effect. An intensive simulation study is conducted to compare the proposed method with other methods in the literature. Our theoretical derivation and simulation study show that the proposed approach is simpler to use and at least as good as other approaches provided in the literature. We illustrate our approach to test for the potential mediators on the relationship between depression and obesity among children and adolescents compared to the method in Winship and Mare using National children health survey data 2011–2012.     

An Odd Couple: Monotone Instrumental Variables and Binary Treatments

This article investigates Monotone Instrumental Variables (MIV) and their ability to aid in identifying treatment effects when the treatment is binary in a nonparametric bounding framework. I show that an MIV can only aid in identification beyond that of a Monotone Treatment Selection assumption if for some region of the instrument the observed conditional-on-received-treatment outcomes exhibit monotonicity in the instrument in the opposite direction as that assumed by the MIV in a Simpson's Paradox-like fashion. Furthermore, an MIV can only aid in identification beyond that of a Monotone Treatment Response assumption if for some region of the instrument either the above Simpson's Paradox-like relationship exists or the instrument's indirect effect on the outcome (as through its influence on treatment selection) is the opposite of its direct effect as assumed by the MIV. The implications of the main findings for empirical work are discussed and the results are highlighted with an application investigating the effect of criminal convictions on job match quality using data from the 1997 National Longitudinal Survey of the Youth. Though the main results are shown to hold only for the binary treatment case in general, they are shown to have important implications for the multi-valued treatment case as well.     

Optimal Circular Block Designs for Neighbouring Competition Effects

Competition or interference occurs when the responses to treatments in experimental units are affected by the treatments in neighbouring units. This may contribute to variability in experimental results and lead to substantial losses in efficiency. The study of a competing situation needs designs in which the competing units appear in a predetermined pattern. This paper deals with optimality aspects of circular block designs for studying the competition among treatments applied to neighbouring experimental units. The model considered is a four-way classified model consisting of direct effect of the treatment applied to a particular plot, the effect of those treatments applied to the immediate left and right neighbouring units and the block effect. Conditions have been obtained for the block design to be universally optimal for estimating direct and neighbour effects. Some classes of balanced and strongly balanced complete block designs have been identified to be universally optimal for the estimation of direct, left and right neighbour effects and a list of universally optimal designs for v<20 and r<100 has been prepared.     

The 1970 US draft lottery revisited: a spatial analysis

Summary.  We revise the result of the 1970 selective service draft lottery in the USA following an open question that was suggested by Fienberg in a paper published in Science in 1971. The result of the drawings can be viewed as a particular spatial pattern which can be analysed by using general spatial tools adapted to our context. Approaches for assessing the complete spatial randomness for this spatial process on a finite support are proposed. More specifically, these approaches involve the number of events in a square window and a k ( r )-based function used to analyse stationary spatial point processes.     

Indirect comparisons in the comparative efficacy and non-inferiority settings

International Conference on Harmonization E10 concerns non-inferiority trials and the assessment of comparative efficacy, both of which often involve indirect comparisons. In the non-inferiority setting, there are clinical trial results directly comparing an experimental treatment with an active control, and clinical trial results directly comparing the active control with placebo, and there is an interest in the indirect comparison of the experimental treatment with placebo. In the comparative efficacy setting, there may be separate clinical trial results comparing each of two treatments with placebo, and there is interest in an indirect comparison of the treatments. First, we show that the sample size required for a trial intended to demonstrate superiority through an indirect comparison is always greater than the sample size required for a direct comparison. In addition, by introducing the concept of preservation of effect, we show that the hypothesis addressed in the two settings is identical. Our main result concerns the logical inconsistency between a reasonable criterion for preference of an experimental treatment to a standard treatment and existing regulatory guidance for approval of the experimental treatment on the basis of an indirect comparison. Specifically, the preferred treatment will not always meet the criterion for regulatory approval. This is due to the fact that the experimental treatment bears the burden of overcoming the uncertainty in the effect of the standard treatment. We consider an alternative approval criterion that avoids this logical inconsistency.     

Communication of risk: health hazards from mobile phones

Summary. Possible health hazards from mobile phones arise from the use of the phones themselves and via the base stations that relay signals. Except for an increase in traffic accidents induced by the use of mobile phones in cars the evidence for a health hazard is at most indirect, but it cannot be entirely dismissed; the phones have not been widely used for sufficiently long for direct epidemiological studies to have high sensitivity for detecting any induced incidence of cancer, for example. The background and evidence are briefly reviewed and the steps taken in the UK to make information widely available described.     

研发投入对企业绩效影响的门槛效应:以广东省为例

一般认为,研发投入会对企业绩效产生影响,但并不是简单的促进或抑制作用,而与企业研发投入强度有关。文章基于广东省2015—2020年A股上市企业的面板数据,运用门槛模型对R&D投入与企业绩效之间的非线性关系进行实证分析。结果表明,无论是基于全样本还是民营上市企业样本,R&D投入对企业绩效均存在显著的三重门槛效应,R&D投入对企业绩效的影响在不同门槛区间内存在方向、系数值上的明显差异。同时,企业规模、企业营运能力以及资本结构等控制变量均对企业绩效具有显著影响,股权集中度在全样本回归中不具有显著性。因此,政府整体上仍应鼓励企业加强R&D投入,具体方式包括直接补贴和间接税收优惠,对R&D投入位于低水平的民营企业而言,应侧重从降低企业研发成本的角度给予支持。     

Optimal two treatment repeated measurement designs for three periods

Repeated Measurement Designs, with two treatments, n (experimental) units and p periods are examined, the two treatments are denoted A and B. The model with independent observations within and between treatment sequences is used. Optimal designs are derived for: (i) the difference of direct treatment effects and the difference of residual effects, (ii) the difference of direct treatment effects, and (iii) the difference of residual effects. We prove that for three periods when n is odd the optimal design in the three cases (i), (ii), and (iii) is determined by taking the sequences BAA and ABB in numbers differing by one. If n is even, the optimal design in cases (i), (ii), and (iii) is again the same, by taking the sequences ABB and BAA in equal numbers. In case (i), for n even or odd, in the optimal design there is no correlation between the two estimated parameters. For n even, case (i) was solved by Cheng and Wu in 1980. The above imply that with two treatments in practice are preferable to use three periods instead of two.     

The Finite Sample Performance of Inference Methods for Propensity Score Matching and Weighting Estimators

ABSTRACT

This article investigates the finite sample properties of a range of inference methods for propensity score-based matching and weighting estimators frequently applied to evaluate the average treatment effect on the treated. We analyze both asymptotic approximations and bootstrap methods for computing variances and confidence intervals in our simulation designs, which are based on German register data and U.S. survey data. We vary the design w.r.t. treatment selectivity, effect heterogeneity, share of treated, and sample size. The results suggest that in general, theoretically justified bootstrap procedures (i.e., wild bootstrapping for pair matching and standard bootstrapping for “smoother” treatment effect estimators) dominate the asymptotic approximations in terms of coverage rates for both matching and weighting estimators. Most findings are robust across simulation designs and estimators.     

On the Predictive Distributions of Outcome Gains in the Presence of an Unidentified Parameter

In this article we describe methods for obtaining the predictive distributions of outcome gains in the framework of a standard latent variable selection model. Although most previous work has focused on estimation of mean treatment parameters as the method for characterizing outcome gains from program participation, we show how the entire distributions associated with these gains can be obtained in certain situations. Although the out-of-sample outcome gain distributions depend on an unidentified parameter, we use the results of Koop and Poirier to show that learning can take place about this parameter through information contained in the identified parameters via a positive definiteness restriction on the covariance matrix. In cases where this type of learning is not highly informative, the spread of the predictive distributions depends more critically on the prior. We show both theoretically and in extensive generated data experiments how learning occurs, and delineate the sensitivity of our results to the prior specifications. We relate our analysis to three treatment parameters widely used in the evaluation literature—the average treatment effect, the effect of treatment on the treated, and the local average treatment effect—and show how one might approach estimation of the predictive distributions associated with these outcome gains rather than simply the estimation of mean effects. We apply these techniques to predict the effect of literacy on the weekly wages of a sample of New Jersey child laborers in 1903.     

Neighbor-Balanced Row-column Designs

In this article, row-column designs incorporating directional neighbor effects have been studied. A row-column design is said to be neighbor balanced if every treatment has all other treatments appearing as a neighbor a constant number of times. We considered here three different situations under row-column setup incorporating neighbor effects viz., row-column design with one-sided neighbor effect, two-sided neighbor effect, and four-sided neighbor effect. The information matrices for all the situations for estimating the direct and neighbor effects of treatments have been derived. Methods of constructing neighbor-balanced row-column designs have been developed and its characterization properties have been studied.     

Does congress realign or smoothly adjust? A discrete switching model of congressional partisan regimes

Studies of development and change in partisan fortunes in the US emphasize epochs of partisan stability, separated by critical events or turning points. In this paper we study partisan electoral changes in the US Congress using the method of Markov switching. Our estimates are based on election changes from 1854, roughly the date of the establishment of the modern incarnation of the two-party system, to the present. For the Senate, we estimate partisan balance both from 1856 and from 1914, the period of direct elections. Our discrete-state method performs better than one based on smooth cycles, and is more consistent with the existing theory.We use the Markov switching method to estimate an underlying unobserved state parameter, ‘partisan regime’. The method allows the direct estimation of critical transition points between Republican and Democratic partisan coalitions. Republican regimes characterized House elections during three periods: 1860 through 1872, 1894 through 1906, and 1918 through 1928. Senate results were roughly similar. Every recession caused a realignment prior to 1932, but since then none has.For the Senate, the two-state model does not fit adequately. We estimate a three-state model in which a Republican regime dominated from 1914 through 1928; a Democratic regime characterized the period 1930–1934, and a Democratic-leaning regime characterized the period 1938 to the present (1936 is a transition year).The driver for historical realignments up to 1930 seems to have been economic distress, at least for the House. Each recession before 1930 is associated with a realignment, but after 1930, no recession produced a realignment. Since then, however, economic downturns have not led to realignments. We speculate that better economic management since World War II, resulting in shallower recessions, is the cause. For the Senate, however, we detect only one fundamental regime shift: that during the Great Depression.