Multivalued Treatment Research Articles

Combining machine learning and propensity score weighting to estimate causal effects in multivalued treatments

Interventions with multivalued treatments are common in medical and health research; examples include comparing the efficacy of competing interventions and contrasting various doses of a drug. In recent years, there has been growing interest in the development of methods that estimate multivalued treatment effects using observational data. This paper extends a previously described analytic framework for evaluating binary treatments to studies involving multivalued treatments utilizing a machine learning algorithm called optimal discriminant analysis (ODA). We describe the differences between regression-based treatment effect estimators and effects estimated using the ODA framework. We then present an empirical example using data from an intervention including three study groups to compare corresponding effects. The regression-based estimators produced statistically significant mean differences between the two intervention groups, and between one of the treatment groups and controls. In contrast, ODA was unable to discriminate between distributions of any of the three study groups. Optimal discriminant analysis offers an appealing alternative to conventional regression-based models for estimating effects in multivalued treatment studies because of its insensitivity to skewed data and use of accuracy measures applicable to all prognostic analyses. If these analytic approaches produce consistent treatment effect P values, this bolsters confidence in the validity of the results. If the approaches produce conflicting treatment effect P values, as they do in our empirical example, the investigator should consider the ODA-derived estimates to be most robust, given that ODA uses permutation P values that require no distributional assumptions and are thus, always valid.

Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations

This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to model selection errors and prove that they are valid uniformly over a large class of treatment effect models. The class allows for multivalued treatments with heterogeneous effects (in observables), general heteroskedasticity, and selection amongst (possibly) more covariates than observations. Our estimator attains the semiparametric efficiency bound under appropriate conditions. Precise conditions are given for any model selector to yield these results, and we show how to combine data-driven selection with economic theory. For implementation, we give a specific proposal for selection based on the group lasso and derive new technical results for high-dimensional, sparse multinomial logistic regression. A simulation study shows our estimator performs very well in finite samples over a wide range of models. Revisiting the National Supported Work demonstration data, our method yields accurate estimates and tight confidence intervals.

Robust inference on average treatment effects with possibly more covariates than observations

This paper concerns robust inference on average treatment effects following model selection. Under selection on observables, we construct confidence intervals using a doubly-robust estimator that are robust to model selection errors and prove their uniform validity over a large class of models that allows for multivalued treatments with heterogeneous effects and selection amongst (possibly) more covariates than observations. The semiparametric efficiency bound is attained under appropriate conditions. Precise conditions are given for any model selector to yield these results, and we specifically propose the group lasso, which is apt for treatment effects, and derive new results for high-dimensional, sparse multinomial logistic regression. Both a simulation study and revisiting the National Supported Work demonstration show our estimator performs well in finite samples.

Effects of farmer managed natural regeneration on livelihoods in semi-arid West Africa

This paper used a multivalued treatment framework to assess the effects of farmer managed natural regeneration (FMNR) on selected outcomes among 1080 rural household farmers in the Sahelian and Sudano-Sahelian ecozone of West Africa Sahel. The results indicate that keeping, protecting and managing trees in the farmland have significant effects on the livelihoods of the rural poor in the Sahelian countries. If 1000 households in a community decide to practice the FMNR continuously, it results in an increase in the gross income by US$ 72,000 per year. Noticeable changes are also observed on the value of tree products, with an observed significant increase in the value of the products harvested from tree by about 34–38 % among those actively practicing FMNR as compared to their counterparts. The results also lend support to the household resilience hypothesis of FMNR in that it leads to a significant increase of the dietary diversity by about 12–14 %. However, it also appeared that several factors impeded the regeneration of trees on farms. To foster the widespread dissemination and enhance the capacity of farmers to increase, diversify and sustain tree-based production systems, an enabling institutional, technical and policy environment needs to be promoted.

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.

Doubly Robust Estimation of Causal Effects with Multivalued Treatments: An Application to the Returns to Schooling

SummaryThis paper provides doubly robust estimators for treatment effect parameters which are defined in a multivalued treatment effect framework. We apply this method to the unique dataset of the 1970 British Cohort Study (BCS70) to estimate returns to various levels of schooling. The analysis is carried out for female and male samples separately to capture possible gender differences. Average returns are estimated for the entire population, as well as conditional on having a specific educational achievement. For males, relative to no qualification, we find an average return to O‐levels of 6.3%, to A‐levels of 7.9% and to higher education of 25.4%. The estimated average returns to O‐level and A‐level relative to no qualification are insignificant for females, whereas the return to higher education is 19.9%.Copyright © 2014 John Wiley & Sons, Ltd.

Doubly Robust Estimation of Causal Effects with Multivalued Treatments

This paper provides doubly robust estimators for treatment effect parameters which are defined in multivalued treatment effect framework. We apply this method on a unique data set of British Cohort Study (BCS) to estimate returns to different levels of schooling. Average returns are estimated for entire population, as well as conditional on having a specific educational achievement. The analysis is carried out for female and male samples separately to capture possible gender differences. The results indicate that, on average, the percentage wage gain due to higher education versus any other lower educational attainment is higher for highly educated females than highly educated males.

Contracting for Innovation in Information Technology Outsourcing

The scope for innovations through outsourcing of information technology (IT), and more broadly, the challenges of sourcing innovations across firm boundaries has been an understudied area of literature. We study under what conditions certain contractual arrangements foster specific types of innovations in client organizations from IT outsourcing. We conceptualize two dimensions of innovation through outsourcing: process innovation and product innovations. Given the inherent uncertainty of innovative tasks, two distinct sets of contracting challenges could preclude firms from realizing business value through innovations. The ex ante problem is that of providing the vendor incentives for innovative services that raise the issue of appropriability of the gains from the innovation. The ex post challenge is the threat of holdup where the vendor, for example, is less willing to engage in the iterative collaboration needed for innovative tasks. We suggest two complementary solutions that simultaneously address both ex ante and ex post contractual problems: (i) credible commitments by outsourcing firms (clients) that act as reciprocal pledges, and (ii) contingent control rights that confer control contingent upon observed performance. We find that credible commitments are more important with process transformations while contingent control rights are more important with product innovations. We also find that the two contractual provisions are complementary. The impact of contractual provisions on post contract innovation performance is complicated by endogeneity. We employ methods from multi-valued treatment effects literature to deal with this issue. Our study suggests that portfolios of complementary contractual provisions need to simultaneously address ex ante and ex post hazards through contract design in the outsourcing of innovative tasks. Implications for practitioners and researchers are discussed.

Estimation of Multivalued Treatment Effects under Conditional Independence

This article discusses the poparms command, which implements two semiparametric estimators for multivalued treatment effects discussed in Cattaneo (2010, Journal of Econometrics 155: 138–154). The first is a properly reweighted inverse-probability weighted estimator, and the second is an efficient-influence-function estimator, which can be interpreted as having the double-robust property. Our implementation jointly estimates means and quantiles of the potential-outcome distributions, allowing for multiple, discrete treatment levels. These estimators are then used to estimate a variety of multivalued treatment effects. We discuss pre- and postestimation approaches that can be used in conjunction with our main implementation. We illustrate the program and provide a simulation study assessing the finite-sample performance of the inference procedures.

Identification in Nonlinear Difference in Difference Models with Multivalued Treatment Outcomes

We study the conditions to identify the joint distribution of outcomes for the treated group in absence of any treatment, avoiding to make assumptions that allow to identify each counterfac- tual marginal distribution. Our starting point is Athey & Imbens (2006)'s Changes-In-Changes Model, but we generalize it letting the treatment also affect the distribution of unobservables even within each group (e.g. treated and untreated). The key to achieve identification is re- place any identifying assumption on the marginal distribution of unobservables with identifying assumptions on the copula between all unobservables. We show that under a reasonable set of assumptions we can identify sharp bound for the counterfactual joint distribution of outcome variables. Moreover, if we restrict ourselves to copulas from the Archimedean family we can even achieve point identification.

A Longitudinal Analysis of the Relationship Between Fertility Timing and Schooling

This article quantifies the contribution of pre-treatment dynamic selection to the relationship between fertility timing and postsecondary attainment, after controlling for a rich set of predetermined characteristics. Eventual mothers and nonmothers are matched using their predicted birth hazard rate, which shares the desirable properties of a propensity score but in a multivalued treatment setting. I find that eventual mothers and matched nonmothers enter college at the same rate, but their educational paths diverge well before the former become pregnant. This pre-pregnancy divergence creates substantial differences in ultimate educational attainment that cannot possibly be due to the childbirth itself. Controls for predetermined characteristics and fixed effects do not address this form of dynamic selection bias. A dynamic model of the simultaneous childbirth-education sequencing decision is necessary to address it.

A Semi-Parametric Two-Stage Projection Type Estimator of Multi-Valued Treatment Effects

One of the most well documented regularities in evaluation literature like returns to schooling(or funding for programs) is that several factors come together to confound the measurement of its effect. First, in observational studies the true return is often individual specific, and so it is almost impossible to use a traditional treatment effect models with randomly assigned treatment and control groups. This endogeneity in the model further exacerbates our inability to conduct such trials. Second, the problem is not a classical treatment effect measurement problem where we have discrete or more often binary treatments. Hence, techniques like measuring the Local Average Treatment Effect (LATE) cannot be implemented as it is not very well defined for the continuous treatment case. Third, a traditional 2SLS approach might be misleading because of the non-Gaussian nature of response distribution, in particular, if different quantiles of response have differential effects. However, their technique is also not defined for continuous treatments, and cannot measure if different distributions of the treatment might have different effects on the response variable. In this paper, we propose the effects of different multi-valued treatment variable after conditioning for other covariates.

Efficient semiparametric estimation of multi-valued treatment effects under ignorability

This paper studies the efficient estimation of a large class of multi-valued treatment effects as implicitly defined by a collection of possibly over-identified non-smooth moment conditions when the treatment assignment is assumed to be ignorable. Two estimators are introduced together with a set of sufficient conditions that ensure their n -consistency, asymptotic normality and efficiency. Under mild assumptions, these conditions are satisfied for the Marginal Mean Treatment Effect and the Marginal Quantile Treatment Effect, estimands of particular importance for empirical applications. Previous results for average and quantile treatments effects are encompassed by the methods proposed here when the treatment is dichotomous. The results are illustrated by an empirical application studying the effect of maternal smoking intensity during pregnancy on birth weight, and a Monte Carlo experiment.

Survival analysis using inverse probability of treatment weighted methods based on the generalized propensity score

In survival analysis, treatment effects are commonly evaluated based on survival curves and hazard ratios as causal treatment effects. In observational studies, these estimates may be biased due to confounding factors. The inverse probability of treatment weighted (IPTW) method based on the propensity score is one of the approaches utilized to adjust for confounding factors between binary treatment groups. As a generalization of this methodology, we developed an exact formula for an IPTW log-rank test based on the generalized propensity score for survival data. This makes it possible to compare the group differences of IPTW Kaplan-Meier estimators of survival curves using an IPTW log-rank test for multi-valued treatments. As causal treatment effects, the hazard ratio can be estimated using the IPTW approach. If the treatments correspond to ordered levels of a treatment, the proposed method can be easily extended to the analysis of treatment effect patterns with contrast statistics. In this paper, the proposed method is illustrated with data from the Kyushu Lipid Intervention Study (KLIS), which investigated the primary preventive effects of pravastatin on coronary heart disease (CHD). The results of the proposed method suggested that pravastatin treatment reduces the risk of CHD and that compliance to pravastatin treatment is important for the prevention of CHD.

Evaluating Nonexperimental Estimators for Multiple Treatments: Evidence from Experimental Data

This paper assesses the effectiveness of unconfoundedness-based estimators of mean effects for multiple or multivalued treatments in eliminating biases arising from nonrandom treatment assignment. We evaluate these multiple treatment estimators by simultaneously equalizing average outcomes among several control groups from a randomized experiment. We study linear regression estimators as well as partial mean and weighting estimators based on the generalized propensity score (GPS). We also study the use of the GPS in assessing the comparability of individuals among the different treatment groups, and propose a strategy to determine the overlap or common support region that is less stringent than those previously used in the literature. Our results show that in the multiple treatment setting there may be treatment groups for which it is extremely difficult to find valid comparison groups, and that the GPS plays a significant role in identifying those groups. In such situations, the estimators we consider perform poorly. However, their performance improves considerably once attention is restricted to those treatment groups with adequate overlap quality, with difference-in-difference estimators performing the best. Our results suggest that unconfoundedness-based estimators are a valuable econometric tool for evaluating multiple treatments, as long as the overlap quality is satisfactory.

A Bayesian propensity score adjustment for latent variable modeling and MCMC algorithm

The estimation of the differences among groups in observational studies is frequently inaccurate owing to a bias caused by differences in the distributions of covariates. In order to estimate the average treatment effects when the treatment variable is binary, Rosenbaum and Rubin [1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41–55] proposed an adjustment method for pre-treatment variables using propensity scores. Imbens [2000. The role of the propensity score in estimating dose-response functions. Biometrika 87, 706–710] extended the propensity score methodology for estimation of average treatment effects with multivalued treatments. However, these studies focused only on estimating the marginal mean structure. In many substantive sciences such as the biological and social sciences, a general estimation method is required to deal with more complex analyses other than regression, such as testing group differences on latent variables. For latent variable models, the EM algorithm or the traditional Monte Carlo methods are necessary. However, in propensity score adjustment, these methods cannot be used because the full distribution is not specified. In this paper, we propose a quasi-Bayesian estimation method for general parametric models that integrate out the distributions of covariates using propensity scores. Although the proposed Bayes estimates are shown to be consistent, they can be calculated by existing Markov chain Monte Carlo methods such as Gibbs sampler. The proposed method is useful to estimate parameters in latent variable models, while the previous methods were unable to provide valid estimates for complex models such as latent variable models. We also illustrated the procedure using the data obtained from the US National Longitudinal Survey of Children and Youth (NLSY1979–2002) for estimating the effect of maternal smoking during pregnancy on the development of the child's cognitive functioning.

On the use of discrete choice models for causal inference

Methodology for causal inference based on propensity scores has been developed and popularized in the last two decades. However, the majority of the methodology has concentrated on binary treatments. Only recently have these methods been extended to settings with multi-valued treatments. We propose a number of discrete choice models for estimating the propensity scores. The models differ in terms of flexibility with respect to potential correlation between treatments, and, in turn, the accuracy of the estimated propensity scores. We present the effects of discrete choice models used on performance of the causal estimators through a Monte Carlo study. We also illustrate the use of discrete choice models to estimate the effect of antipsychotic drug use on the risk of diabetes in a cohort of adults with schizophrenia.

The role of the propensity score in estimating dose-response functions

SUMMARY Estimation of average treatment effects in observational studies often requires adjustment for differences in pre-treatment variables. If the number of pre-treatment variables is large, standard covariance adjustment methods are often inadequate. Rosenbaum & Rubin (1983) propose an alternative method for adjusting for pre-treatment variables for the binary treatment case based on the so-called propensity score. Here an extension of the propensity score methodology is proposed that allows for estimation of average casual effects with multi-valued treatments. Estimation of average treatment effects in observational studies often requires adjustment for differences in pre-treatment variables. If the number of pre-treatment variables is large and their distribution varies substantially with treatment status, standard adjustment methods such as covari- ance adjustment are often inadequate. Rosenbaum & Rubin (1983, 1984) propose an alternative method for adjusting for pre-treatment variables based on the propensity score, the conditional probability of receiving the treatment given pre-treatment variables. They demonstrate that adjusting solely for the propensity score removes all bias associated with differences in the pre- treatment variables. The Rosenbaum-Rubin proposals deal exclusively with binary-valued treat- ments. In many cases of interest, however, treatments take on more than two values. Here an extension of the propensity score methodology is proposed that allows for estimation of average causal effects with multi-valued treatments. The key insight is that for estimation of average causal effects it is not necessary to divide the population into subpopulations where causal comparisons are valid, as the propensity score does; it is sufficient to divide the population into subpopulations where average potential outcomes can be estimated.