Notation
| (X_ {i}) | (Y_ {i} (0)) | (Y_ {i} (1)) |
| (X_ {1}) | (Y_ {1} (0)) | (Y_ {1} (1)) |
| (X_ {2}) | (Y_ {2} (0)) | (Y_ {2} (1)) |
| (X_ {3}) | (Y_ {3} (0)) | (Y_ {3} (1)) |
What is heterogeneous treatment effect (HTE)?
researchers interested in heterogeneous treatment effects are likely to encounter the problem of multiple comparisons: for example, when numerous subgroup analyses are conducted, the probability that at least one result looks statistically significant at the 5 percent level may be considerably greater than 5 percent even when the treatment has no …
Is there a pattern of heterogeneous treatment effects across strata ranks?
1 Heterogeneous Treatment Effects Same treatment may affect different individuals differently Conditional Average Treatment Effect (CATE) ˝(x) = E(Y i(1) Y i(0) jX i = x) where x 2X Individualized treatment rule f : X! f 0;1g We can never identify an individual causal effect ˝ i = Y i(1) Y i(0) Individualized treatment rule depends on the choice of X i
What instrumental variable is used to identify heterogeneous treatment effects?
Jan 25, 2021 · What are heterogeneous treatment effects? Intuitive definition When analyzing a randomized experiment or observational study, analysts often report the population average treatment effect (ATE) as the main —and often only— summary for …
Does the workhorse regression work for heterogeneous treatment effects?
Heterogeneous treatment effects: what does a regression estimate? Regressions that control for confounding factors are the workhorse of evaluation research. When treatment effects are heterogeneous, however, the workhorse regression leads to estimated treatment effects that lack behavioral interpretations even when the selection on observables assumption holds.
What is homogeneous treatment effect?
What is treatment response heterogeneity?
What are treatment effects in research?
How do you describe treatment effect?
What is heterogeneous effect?
What is heterogeneous medicine?
What is the difference between average treatment effect and average treatment effect on the treated?
What is the sample average treatment effect?
What is size of treatment effect?
What is a large treatment effect?
An estimate of how large the treatment effect is, that is how well the intervention worked in the. experimental group in comparison to the control. group. The larger the effect size, the stronger are the.
What is the average treatment effect on the untreated?
What is treatment effect in Anova?
What is heterogeneous treatment?
Hetoregenous literally means “diverse in character or content,” so when we talk about “heterogeneous treatment effects,” we acknowledge the fact that every experimental unit may have a different response to the intervention. In practice, however, it is extremely difficult to reliably assess the effect of the intervention on each individual unit, and we must instead settle on assessing the effect of the intervention on subgroups of units that share similar characteristics. For example, it is common in clinical trials to report separate estimates for how a drug impacts children and for how it impacts adults, to reflect the biological differences. Technology companies similarly track responses across different platforms and countries.
How to estimate heterogeneous effects?
We can estimate heterogeneous effects even when experiments where not run separately in each subgroup. Imagine we have a single binary covariate (for example, whether or not someone likes pie or whether or not someone is under the age of 18) that was recorded before the treatment assignment. Then, it is easy to measure the effect within the different values of this covariate. We simply group the units that like pie and the units that dislike pie and separately compute each group’s effect. We can carry out inference in the standard way, as discussed in our post on the potential outcomes framework. But, since we are testing multiple hypotheses, we need to perform a multiple comparison test adjustment to ensure that we control the overall type I error at the appropriate level. The simplest way to do this is via the Bonferroni correction that divides the nominal type I error by the number of tests.
Do people always agree with heterogeneous treatment effects?
People don’t always agree ; that is a fact of life. Similarly, when running an experiment, not everyone has the same reaction to the intervention! It’s critical that data scientists, academics, and the general public understand that the global average may not always be the most important or meaningful measure. Instead, it is often more informative to study how the effect of an intervention varies across different population subgroups. This post explains, at a high level, what heterogeneous treatment effects are, why they are essential, and how to think about them.
What is heterogeneous treatment effect?
A commonly analyzed heterogeneous treatment effect estimation problem is the identification of consumers which will be influenced the most by a particular advertising campaign. In political science, heterogeneous treatment effects have been used to illuminate how different get-out-the-vote text messaging strategies have had different effects on the actions of eligible voters. One of the first applications of heterogeneous treatment effect estimation was a paper written by causal inference pioneer William Cochran, which presented a methodology for understanding the ways in which smoking can differentially affect the mortality rates of smokers of different ages, nationalities, and smoking frequencies.
How to identify groups of individuals exposed and unexposed to treatment with similar respective values of particular confounding variables?
Another way causal inference analysts try to identify groups of individuals exposed and unexposed to treatment with similar respective values of particular confounding variables is matching . Matching consists of selecting pairs of similar observed individuals, of which one is exposed to treatment and one is not. The “similarity” of these individuals in pairs can be measured in a variety of ways but this metric is generally calculated as the distance between the values of their confounding variables. Within these pairs, called matched samples, the values of confounding variables are approximately constant across individuals, and thus an analyst can estimate the extent of a treatment effect conditional on these confounding variables, by comparing the outcomes of each pair’s observed individual that is exposed to treatment and its observed individual that is not.
How does confounding bias affect treatment effects?
Much like any estimation of a causal effect, estimations of conditional average treatment effects are susceptible to distortions from confounding bias, which distorts the estimate of a causal effect by adding additional correlation between an explanatory variable and an outcome variable within a causal relationship of interest. Additionally recall from my confounding bias post that in order to achieve an unbiased estimate of a causal effect an analyst must estimate the extent of the effect while “conditioning” on all confounding variables. This is because treatment and potential outcomes of an observed individual are conditionally independent given these confounding variables, meaning that when these confounding variables are constant, there is no additional correlation distorting an analysts estimate of a causal effect.
How to estimate conditional average treatment effects?
One way an analyst can estimate conditional average treatment effects is subclassification, which splits observed individuals into subclassifications along variation in their respective values of confounding variables. For example, if an analyst wishes to understand the effect of their treatments on different genders, they may split their population of observed individuals by gender, and estimate causal effects within each defined gender. Once observed individuals have been split into subclassifications, an analyst can estimate causal effects within these groups by leveraging the simple difference in mean outcomes (SDO) calculation discussed in my post covering average treatment effect estimation. As the name suggests, leveraging the SDO requires an analyst to calculate the difference in the mean outcomes within each group with value#N#≈ z#N#color {#7A28CB} approx z ≈ z in order to estimate#N#τ ( z)#N#color {#7A28CB} tau (z) τ (z). An analyst can use this to estimate CATE as a result of a useful theorem from probability theory#N#E [ A − B] = E [ A] − E [ B]#N#E [A - B] = E [A] - E [B] E[A−B]= E[A]−E[B], and thus:
Is past behavior a confounding variable?
Note that Past Behavior, Demographic Data, and Psychographic Data are all confounding variables, as described in a previous blog post. These variables have an effect on both the explanatory variable and outcome variable I am interested in.
What chapter is the report of heterogeneity?
Chapter 3Estimation and Reporting of Heterogeneity of Treatment Effects
What is the effect of exposure on outcome?
If two or more exposure variables act in concert to cause disease, we will observe that the effect of exposure on outcome (treatment effect) differs according to the level of the other factor(s). A number of terms have been used to describe this phenomenon, including “joint” effects, “synergism,” “antagonism,” “interaction,” “effect modification,” and “effect measure modification.” Where effect modification exists, sound inferences will require accounting for factors that modify the effect of the exposure of primary interest. Accounting for this HTE may be required even when the variable that modifies treatment effect is not a risk factor for the outcome in the untreated group (e.g., a receptor that determines how a drug is metabolized).
Why is HTE important?
Understanding HTE is critical for decisions that are based on knowing how well a treatment is likely to work for an individual or group of similar individuals, and is relevant to stakeholders including patients, clinicians, and policymakers . It also has implications for applicability to individual patients (personalized medicine) of findings from pragmatic trials and observational comparative effectiveness research (CER). Pragmatic trials are large and simple experiments on treatments, with broad eligibility criteria, from which evidence is expected to be generalizable. While these designs incorporate heterogeneity in the risk of outcome among the subjects, they may also lead to HTE for the treatments that are applied. These studies may be more likely to yield null ATE than efficacy trials, where stricter inclusion criteria produce relatively homogeneous study populations. Therefore, understanding major sources of variations in treatment response is essential. For a formal general definition of HTE, see Box 3.1.
How can observational studies be challenging?
The study of treatment effects can be challenging in observational studies. Observational studies are susceptible to confounding by indication, ascertainment biases in exposure to treatment, measurement error in assessment of health outcomes, and lack of information on important prognostic variables (in studies using existing data). These biases and measurement errors can introduce apparent HTE when in fact none is present, or conversely, obscure true HTE. Because heterogeneity in observational studies can be due to chance or bias, investigators must evaluate the observed HTE to determine whether a finding is indicative of true heterogeneity. To do this, chance findings should be evaluated by testing for interaction; biases should be avoided by adhering to sound study design principles and by evaluating balance on covariates within subgroups to assess the potential for confounding.
Why are exclusion criteria used in observational studies?
Exclusion criteria also serve to protect patients who might be harmed by a treatment (such as those with a contraindication to the treatment). Since the aim of many observational studies is to describe the effect of treatment as actually used , fewer exclusions are typically applied, and those that are often applied are for the purpose of improved confounder control. As a result, observational studies often include patients for whom no randomized data of treatment effect exists. For example, a patient with a relative contraindication for a treatment might be excluded from a randomized trial, but a treating clinician may decide that the benefits outweigh the risks for this patient and apply the therapy.
Is streptokinase safe for older people?
The ISIS-2 study conducted additional subgroup analyses to assess the consistency of the subgroup findings from an earlier randomized trial of streptokinase (GISSI) that found no benefit of streptokinase among persons older than 65, those with a previous infarct, and those presenting more than 6 hours after the onset of pain. In contrast to GISSI, the ISIS-2 study found a mortality benefit for streptokinase among these subgroups, a finding that further underscores the need for caution when drawing inferences from subgroup results.When there are plausible a priori reasons that a treatment may not be effective (such as in patients with contraindications to the therapy) and subgroup analyses find no benefit in that subgroup, stronger inferences might be drawn.
Does a statistical test of interaction correspond to an assessment of biological interaction?
It should also be noted that a statistical test of interaction does not correspond to an assessment of biological interaction. The presence or absence of statistical interaction depends on various mathematical aspects of the regression model (e.g., scale of dependent variable, covariates present in the model, distributional assumptions). These considerations are largely irrelevant for biological interactions.3
Abstract
Heterogeneous treatment effect (HTE) analysis focuses on examining varying treatment effects for individuals or subgroups in a population. For example, an HTE-informed understanding can critically guide physicians to individualize the medical treatment for a certain disease.
INTRODUCTION
Treatment effect refers to the causal effect of a treatment or intervention (e.g., administering an anticancer drug) on an outcome of interest (e.g., health or disease progression of the patient) based on the counterfactuals (e.g., difference in outcomes with/without using the drug).
METHODS
In this section, after describing the basic principle of treatment effect, we introduce the concept of HTE and graphically illustrate the differences between no treatment heterogeneity and HTE.
RESULTS
In this section, a case example with nonlinear HTE was simulated to demonstrate HTE analysis conducted by causal forest and the two-step method. By stipulating Equation ( 1 ), the example case was simulated based on the model , where , and heterogeneity covariates and have interactions with the treatment ( T) in a nonlinear form, ( ).
DISCUSSION
This study introduced an ML-based HTE analysis and presented a systematic evaluation of HTE analysis methods. HTE analysis demonstrated its ability to address questions on the individualized counterfactual treatment effects.
CONCLUSION
Given its resilience in handling complex data (e.g., nonlinear and/or high-dimensional data), the causal forest HTE method, an ML approach derived from a random forest algorithm, provides a unique opportunity for scientists to assess and predict heterogeneity for treatment effect for real-world applications.
DISCLAIMER
The opinions expressed in this manuscript are those of the authors and should not be interpreted as the position of the US Food and Drug Administration.
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Conditional Average Treatment Effects
- The particular heterogeneous treatment effect I am interested in estimating are conditional average treatment effects (CATE), or the expected treatment effect of a particular consumer conditional on a set of explanatory variables describing them, such as Past Behavior, Demographic Data, and Psychographic Data. Formally, one can define a conditional...
Estimating Conditional Average Treatment Effects
- In order to estimate Yi1−Yi0\color{#EF3E36}Y^1_i - Y^0_iYi1−Yi0 for an individual consumer an analyst will often leverage variation in the value of an explanatory variable Xi\color{#7A28CB}X_iXi of interest as is common with many causal inference methods. Particularly, an analyst will leverage variation in treatment within groups of observed individuals with similar values of conf…
Bias in Estimation of Cate
- Much like any estimation of a causal effect, estimations of conditional average treatment effects are susceptible to distortions from confounding bias, which distorts the estimate of a causal effect by adding additional correlation between an explanatory variable and an outcome variable within a causal relationship of interest. Additionally recall from my confounding bias post that i…
Lifting The Curse
- What machine learning strategies exist for selecting the optimal set of confounding variables for an analyst to condition their CATE estimates on? What is the evaluation metric for such strategies? For example, how would such a strategy identify which confounding variables have the greatest effect on Exposed To Ad and Purchases Flight? All this and more will be revealed in my …