Abstract
SummaryA problem that is frequently encountered in many areas of scientific research is that of estimating the effect of a non-randomized binary intervention on an outcome of interest by using time series data on units that received the intervention (‘treated’) and units that did not (‘controls’). One popular estimation method in this setting is based on the factor analysis (FA) model. The FA model is fitted to the preintervention outcome data on treated units and all the outcome data on control units, and the counterfactual treatment-free post-intervention outcomes of the former are predicted from the fitted model. Intervention effects are estimated as the observed outcomes minus these predicted counterfactual outcomes. We propose a model that extends the FA model for estimating intervention effects by jointly modelling the multiple outcomes to exploit shared variability, and assuming an auto-regressive structure on factors to account for temporal correlations in the outcome. Using simulation studies, we show that the method proposed can improve the precision of the intervention effect estimates and achieve better control of the type I error rate (compared with the FA model), especially when either the number of preintervention measurements or the number of control units is small. We apply our method to estimate the effect of stricter alcohol licensing policies on alcohol-related harms.
Highlights
In this work, we consider the problem of estimating the causal effect of an intervention on an outcome of interest in the setting where: i) the intervention is binary; ii) assignment of the sample units to the intervention is non-randomised; iii) only a small number of units are treated; and iv) there are multiple measurements of the outcome both before and after the intervention occurs.This problem is frequently encountered in various fields of scientific research, including econometrics, epidemiology, marketing, public health and political science
To answer question (i), we compare the results obtained from the multivariate FA (MVFA)+AR and MVFA models to the results obtained from the FA+AR and FA models, respectively
In settings where T1 < 40 and n1 ≥ 15 (i.e. Setups IV, V, VII and VIII), we see that joint modelling of outcomes leads to considerable gains in precision: the MVFA+AR and MVFA models decrease the standard error of the point estimates and the mean credible interval width in these settings
Summary
We consider the problem of estimating the causal effect of an intervention on an outcome of interest in the setting where: i) the intervention is binary; ii) assignment of the sample units to the intervention is non-randomised; iii) only a small number of units are treated; and iv) there are multiple measurements of the outcome both before and after the intervention occurs. Despite being similar in spirit to FA approaches, LCA-based causal inference methods cannot be used in the setting where i)-iv) apply, mainly because they require estimation of the propensity score, which is problematic when the number of treated units is small. These methods focus on the causal effect of the intervention on the probability that an individual belongs to a certain class, whereas in our problem the interest is in the effect of the intervention directly on the outcomes. The data that are analysed in the paper and the programs that were used to analyse them can be obtained from www.url.co.uk
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