scholarly journals Inference under covariate‐adaptive randomization with multiple treatments

2019 ◽  
Vol 10 (4) ◽  
pp. 1747-1785 ◽  
Author(s):  
Federico A. Bugni ◽  
Ivan A. Canay ◽  
Azeem M. Shaikh
Keyword(s):  
Linear Regression ◽  
Null Hypothesis ◽  
Fixed Effects ◽  
Asymptotic Variance ◽  
Consistent Estimator ◽  
Nominal Level ◽  
Adaptive Randomization ◽  
Rejection Probability ◽  
Multiple Treatments ◽  
Baseline Covariates

This paper studies inference in randomized controlled trials with covariate‐adaptive randomization when there are multiple treatments. More specifically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni, Canay, and Shaikh (2018), covariate‐adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve “balance” within each stratum. Importantly, in contrast to Bugni, Canay, and Shaikh (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a “fully saturated” linear regression, that is, a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are invalid in the sense that they may have limiting rejection probability under the null hypothesis strictly greater than the nominal level; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact in the sense that they have limiting rejection probability under the null hypothesis equal to the nominal level. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with “strata fixed effects,” that is, a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are conservative in the sense that they have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact, thereby generalizing results in Bugni, Canay, and Shaikh (2018) for the case of a single treatment to multiple treatments. A simulation study and an empirical application illustrate the practical relevance of our theoretical results.

OLS and 2SLS in Randomized and Conditionally Randomized Experiments

2018 ◽  
Vol 238 (3-4) ◽  
pp. 243-293 ◽  
Author(s):  
Jason Ansel ◽  
Han Hong ◽  
and Jessie Li
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
Randomized Experiments ◽  
Adaptive Randomization ◽  
Working Paper ◽  
Average Treatment ◽  
Local Average Treatment Effect ◽  
Effect Parameter ◽  
Multiple Treatments ◽  
Local Average

Abstract We investigate estimation and inference of the (local) average treatment effect parameter when a binary instrumental variable is generated by a randomized or conditionally randomized experiment. Under i.i.d. sampling, we show that adding covariates and their interactions with the instrument will weakly improve estimation precision of the (local) average treatment effect, but the robust OLS (2SLS) standard errors will no longer be valid. We provide an analytic correction that is easy to implement and demonstrate through Monte Carlo simulations and an empirical application the interacted estimator’s efficiency gains over the unadjusted estimator and the uninteracted covariate adjusted estimator. We also generalize our results to covariate adaptive randomization where the treatment assignment is not i.i.d., thus extending the recent contributions of Bugni, F., I.A. Canay, A.M. Shaikh (2017a), Inference Under Covariate-Adaptive Randomization. Working Paper and Bugni, F., I.A. Canay, A.M. Shaikh (2017b), Inference Under Covariate-Adaptive Randomization with Multiple Treatments. Working Paper to allow for the case of non-compliance.

THE INFORMATION BOUND OF A DYNAMIC PANEL LOGIT MODEL WITH FIXED EFFECTS

2001 ◽  
Vol 17 (5) ◽  
pp. 913-932 ◽  
Author(s):  
Jinyong Hahn
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Fixed Effects ◽  
Dynamic Panel Data ◽  
Consistent Estimator ◽  
Likelihood Estimator ◽  
Dynamic Panel ◽  
Conditional Maximum Likelihood ◽  
Information Bound ◽  
Conditional Maximum

In this paper, I calculate the semiparametric information bound in two dynamic panel data logit models with individual specific effects. In such a model without any other regressors, it is well known that the conditional maximum likelihood estimator yields a √n-consistent estimator. In the case where the model includes strictly exogenous continuous regressors, Honoré and Kyriazidou (2000, Econometrica 68, 839–874) suggest a consistent estimator whose rate of convergence is slower than √n. Information bounds calculated in this paper suggest that the conditional maximum likelihood estimator is not efficient for models without any other regressor and that √n-consistent estimation is infeasible in more general models.

Is the classical Wald test always suitable under response-adaptive randomization?

2016 ◽  
Vol 27 (8) ◽  
pp. 2294-2311 ◽  
Author(s):  
Alessandro Baldi Antognini ◽  
Alessandro Vagheggini ◽  
Maroussa Zagoraiou
Keyword(s):  
Sample Size ◽  
Power Function ◽  
Wald Test ◽  
Correct Choice ◽  
Consistent Estimator ◽  
Initial Sample ◽  
Normal Response ◽  
Adaptive Randomization ◽  
Classical Test ◽  
The Impact

The aim of this paper is to analyze the impact of response-adaptive randomization rules for normal response trials intended to test the superiority of one of two available treatments. Taking into account the classical Wald test, we show how response-adaptive methodology could induce a consistent loss of inferential precision. Then, we suggest a modified version of the Wald test which, by using the current allocation proportion to the treatments as a consistent estimator of the target, avoids some degenerate scenarios and so it should be preferable to the classical test. Furthermore, we show both analytically and via simulations how some target allocations may induce a locally decreasing power function. Thus, we derive the conditions on the target guaranteeing its monotonicity and we show how a correct choice of the initial sample size allows one to overcome this drawback regardless of the adopted target.

Locally Optimal Properties of the Durbin-Watson Test

1988 ◽  
Vol 4 (3) ◽  
pp. 509-516 ◽  
Author(s):  
Maxwell L. King ◽  
Merran A. Evans
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Spatial Autocorrelation ◽  
Linear Regression Model ◽  
Null Hypothesis ◽  
Cycle Model ◽  
Disturbance Processes ◽  
Watson Test

Although originally designed to detect AR(1) disturbances in the linear-regression model, the Durbin-Watson test is known to have good power against other forms of disturbance behavior. In this paper, we identify disturbance processes involving any number of parameters against which the Durbin–Watson test is approximately locally best invariant uniformly in a range of directions from the null hypothesis. Examples include the sum of q independent ARMA(1,1) processes, certain spatial autocorrelation processes involving up to four parameters, and a stochastic cycle model.

scholarly journals A new and intuitive test for zero modification

2018 ◽  
Vol 19 (4) ◽  
pp. 341-361 ◽  
Author(s):  
Paul Wilson ◽  
Jochen Einbeck
Keyword(s):  
Null Hypothesis ◽  
Statistical Tests ◽  
Ratio Test ◽  
Nominal Level ◽  
Number Of Zeros ◽  
Data Regression ◽  
Poisson Binomial Distribution ◽  
The Mean ◽  
Direct Use ◽  
Hybrid Estimator

Abstract: While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a novel non-asymptotic test is introduced which makes direct use of the fact that the distribution of the number of zeros under the null hypothesis of no zero modification can be described by a Poisson-binomial distribution. The computation of critical values from this distribution requires estimation of the mean parameter under the null hypothesis, for which a hybrid estimator involving a zero-truncated mean estimator is proposed. Power and nominal level attainment rates of the new test are studied, which turn out to be very competitive to those of the likelihood ratio test. Illustrative data examples are provided.

scholarly journals Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects

2020 ◽  
Vol 110 (9) ◽  
pp. 2964-2996 ◽  
Author(s):  
Clément de Chaisemartin ◽  
Xavier D’Haultfœuille
Keyword(s):  
Linear Regression ◽  
Fixed Effects ◽  
Treatment Effects ◽  
Regression Coefficient ◽  
Weighted Sums ◽  
Linear Regression Coefficient ◽  
Heterogeneous Treatment Effects ◽  
Average Treatment Effects ◽  
Linear Regression Estimator ◽  
Linear Regressions

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate weighted sums of the average treatment effects (ATE ) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator. (JEL C21, C23, D72, J31, J51, L82)

scholarly journals On shrinkage and model extrapolation in the evaluation of clinical center performance

Biostatistics ◽  
2014 ◽  
Vol 15 (4) ◽  
pp. 651-664 ◽  
Author(s):  
Machteld Varewyck ◽  
Els Goetghebeur ◽  
Marie Eriksson ◽  
Stijn Vansteelandt
Keyword(s):  
Fixed Effects ◽  
Patient Specific ◽  
Care Level ◽  
Entire Study ◽  
Dichotomous Outcome ◽  
Clinical Center ◽  
Study Population ◽  
Doubly Robust ◽  
Baseline Covariates ◽  
Stroke Register

Abstract We consider statistical methods for benchmarking clinical centers based on a dichotomous outcome indicator. Borrowing ideas from the causal inference literature, we aim to reveal how the entire study population would have fared under the current care level of each center. To this end, we evaluate direct standardization based on fixed versus random center effects outcome models that incorporate patient-specific baseline covariates to adjust for differential case-mix. We explore fixed effects (FE) regression with Firth correction and normal mixed effects (ME) regression to maintain convergence in the presence of very small centers. Moreover, we study doubly robust FE regression to avoid outcome model extrapolation. Simulation studies show that shrinkage following standard ME modeling can result in substantial power loss relative to the considered alternatives, especially for small centers. Results are consistent with findings in the analysis of 30-day mortality risk following acute stroke across 90 centers in the Swedish Stroke Register.

scholarly journals Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization

2020 ◽  
Vol 11 (3) ◽  
pp. 957-982
Author(s):  
Yichong Zhang ◽  
Xin Zheng
Keyword(s):  
Propensity Score ◽  
Quantile Regression ◽  
Standard Error ◽  
Wald Test ◽  
Estimation Methods ◽  
Compact Set ◽  
Nominal Level ◽  
Adaptive Randomization ◽  
Asymptotic Size ◽  
Quantile Treatment Effect

In this paper, we study the estimation and inference of the quantile treatment effect under covariate‐adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error underrejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate‐adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.

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