Although the overarching goal of such evaluation may be to assess the impact of such intervention in reducing the prevalence of smoking in the general population i. ATE , researchers and policymakers might be interested in explicitly evaluating the effect of the intervention on those who actually received the intervention i. ATT but not that on those among whom the intervention was never intended. Alternatively, researchers may be interested in estimating the potential impact of an existing program in a new target sub- population.
For instance, one might wish to project the effect of the smoking cessation intervention in a city that did not receive the intervention in order to gauge its potential impact when such intervention is actually implemented. This latter quantity is referred to as the average treatment effect on the untreated ATU. All three quantities will be equal when the covariate distribution is the same among the treated and the untreated e.
Among these, the marginal structural models MSMs were designed to estimate marginal quantities i. The parameters of a MSM can be consistently estimated using two classes of estimators: the g-computation algorithm [ 4 ] and the inverse-probability of treatment weighting IPTW [ 5 ].
G-computation is often seen as a viable alternative to IPTW because g-computation produces more efficient i. To date, there are several didactic demonstrations for g-computation [ 7 , 8 ] and applied examples for projecting the impact of hypothetical interventions aimed at reducing risk factors for coronary heart diseases [ 9 ] or diabetes in adult populations [ 10 ], or at reducing early childhood adiposity [ 11 ].
In the remaining, we will use capital letters to refer to random variables and lowercase letters to represent the specific realizations of the corresponding random variables.
Each subject in the population has a pair of potential outcomes, one being observed and the other being counterfactual. When the assumptions of consistency [ 12 ], conditional exchangeability given C [ 13 ], and positivity [ 14 ] are met, the target causal parameters ATE, ATT and ATU on the risk difference scale can be estimated using observational data and the following estimators:.
Step 1: Fit a flexible model for Y on A and covariates C i. Step 2: Re-sample the original data with replacement K times e. Create two copies of this pooled dataset and stack them. For ATT, assign the potential outcome Y a for treated i. This latter counterfactual outcome is simulated under non-treatment, based on the outcome model and regression coefficients from step 1. This counterfactual outcome Y a is simulated under treatment, based on the outcome model and regression coefficients from step 1.
Note that the g-computation of the ATT or ATU involves imputing or simulating only half of the potential outcomes under the counterfactual treatment since by consistency under factual treatment the potential outcome is observed. Step 3: For ATT and ATU respectively, regress the corresponding potential outcome variable on the intervention variable A for the entire pooled simulated sample to obtain the point estimate. Repeat steps 1 to 3 on J e.
The standard deviation of these J point estimates is taken as the standard error and the corresponding 2. Nonparametric bootstrapping [ 15 ] can also be used to obtain bias-corrected and accelerated CIs. An alternative g-computation technique without simulation is included in the Additional file 1 : Section2.
Samples were probabilistically selected with every individual being assigned to a known non-zero selection probability. All participants were interviewed face-to-face with the standardized WHS survey, which included questions regarding demographic, socioeconomic and behavioral factors.
Details of dataset description and variable creation can be found elsewhere [ 17 ]. Table 1 displays the estimates for ATT, ATU and ATE on the risk difference and odds ratio scale respectively for binary education treatment and binary angina indicator outcome , accounting for age and gender covariates.
We were interested in estimating the impact of a hypothetical intervention aimed at ensuring that the target study participants have at least a high school education on angina diagnosis. The intervention could be implemented i universally in the whole population of India ATE , ii among individuals of a sub-population of India who actually completed high school or had higher educational attainment ATT , or iii among individuals of a sub-population of India who had less than a high school education ATU when the survey was conducted.
Detailed steps and the accompanying SAS codes for this illustrative example are included in the Additional file 1 : Section 3 and Additional file 1 : Section 5. In the illustration, participants with at least a high school education were less likely to report having an angina diagnosis compared to those with less than a high school education, based on both risk difference RD and odds ratio OR measures Table 1.
Similar results obtained via g-computation without simulation are presented in the Additional file 1 : Table S1. When generating the potential outcomes in step 2, the potential outcome will be the same as the observed outcome if the intervention assignment e. Accordingly, the counterfactual outcome for the same subjects will be imputed simulated based on the outcome from those who received the alternative to treatment e.
In step 2 of the alternative g-computation approach that does not require simulation, the predicted outcomes [i. While the approach via simulation clearly demonstrates the importance of the two core assumptions—consistency and conditional exchangeability—to estimate causal parameters from observational data, the approach without simulation is less computationally intensive. We also need the positivity assumption which requires that there exist participants who experienced all levels of the treatment such as being treated or untreated for every combination of the values of the observed confounders in the population under study [ 14 ].
This latter assumption needs to be supported by the data at hand. Steps for implementing g-computation for ATT and ATU allow us to better understand the importance of assumptions that are often listed but seldom discussed.
Besides the consistency, conditional exchangeability and positivity assumptions, other implicit assumptions such as the absence of other biases selection bias and measurement error and correct model specification need to be satisfied in order to estimate ATE, ATT and ATU consistently. G-computation relies heavily on outcome model specification as shown in the above steps, in which we used the regression coefficients we obtained from the outcome regression model in step 1 to predict potential outcomes.
On the contrary, the IPTW method relies on correct exposure model specification assumptions. Therefore, these two g-methods can sometimes yield different results. Their strengths and limitations, and performance under violation of the positivity assumption have also been discussed in the literature [ 6 , 18 ].
When possible, researchers could use both methods, or use doubly robust methods [ 19 — 21 ] where consistent estimates for the target effects can be obtained as long as either the outcome or exposure model is correctly specified. It should be used in modern epidemiologic teaching and practice. Imbens GW. Nonparametric estimation of average treatment effects under exogeneity: a review. Rev Econ Stat.
Article Google Scholar. Heckman JJ, Vytlacil E. Policy-Relevant Treatment Effects. Am Econ Rev. Robins JM.
New York: Springer; Chapter Google Scholar. Robins J. A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect. Math Model. Marginal structural models and causal inference in epidemiology. Methods for dealing with time-dependent confounding. Stat Med. Implementation of G-computation on a simulated data set: demonstration of a causal inference technique.
Am J Epidemiol. The parametric g-formula for time-to-event data: intuition and a worked example. Intervening on risk factors for coronary heart disease: an application of the parametric g-formula. Int J Epidemiol. Hypothetical midlife interventions in women and risk of type 2 diabetes.
Projecting the impact of hypothetical early life interventions on adiposity in children living in low-income households. Pediatr Obes.
PubMed Google Scholar. The consistency statement in causal inference: a definition or an assumption? Article PubMed Google Scholar. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Please can anyone help me understand why they are different and, more importantly, what the differences mean eg. As you see the ATT and the more general ATE are referring by definition to different portions of the population of interest. These are very strong assumptions which are commonly violated in observational studies and therefore the ATT and the ATE are not expected to be equal.
Especially in the cases where the individuals self-select to enter the treatment group or not eg. In scenarios like this even talking about ATE is probably ill-defined eg.
The inequality of the two suggests that the treatment assignment mechanism was potentially not random. In general, in an observational study because the above-mentioned assumptions do not generally hold, we either partition our sample accordingly or we control for difference through "regression-like" techniques. The ATT is the effect of the treatment actually applied. Medical studies typically use the ATT as the designated quantity of interest because they often only care about the causal effect of drugs for patients that receive or would receive the drugs.
For another example, ATT tells us how much the typical soldier gained or lost as a consequence of military service, while ATE tells us how much the typical applicant to the military gained or lost. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 4 years ago. Active 6 months ago. Viewed 48k times. Improve this question.
Add a comment. Active Oldest Votes.
0コメント