Introduction to Field Experiments and Randomized Controlled Trials

Introduction to Field Experiments and Randomized Controlled Trials

Have you ever been curious about the methods researchers employ to determine causal relationships among various factors, ultimately leading to significant breakthroughs and progress in numerous fields? In this article, we offer an overview of field experimentation and its importance in discerning cause and effect relationships. We outline how randomized experiments represent an unbiased method for determining what works. Furthermore, we discuss key aspects of experiments, such as intervention, excludability, and non-interference. To illustrate these concepts, we present a hypothetical example of a randomized controlled trial evaluating the efficacy of an experimental drug called Covi-Mapp.

Why experiments?

Every day, we find ourselves faced with questions of cause and effect. Understanding the driving forces behind outcomes is crucial, ranging from personal decisions like parenting strategies to organizational challenges such as effective advertising. This blog aims to provide a systematic introduction to experimentation, igniting enthusiasm for primary research and highlighting the myriad of experimental applications and opportunities available.

The challenge for those who seek to answer causal questions convincingly is to develop a research methodology that doesn't require identifying or measuring all potential confounders. Since no planned design can eliminate every possible systematic difference between treatment and control groups, random assignment emerges as a powerful tool for minimizing bias. In the contentious world of causal claims, randomized experiments represent an unbiased method for determining what works. Random assignment means participants are assigned to different groups or conditions in a study purely by chance. Basically, each participant has an equal chance to be assigned to a control group or a treatment group. 

Field experiments, or randomized studies conducted in real-world settings, can take many forms. While experiments on college campuses are often considered lab studies, certain experiments on campus – such as those examining club participation – may be regarded as field experiments, depending on the experimental design. Ultimately, whether a study is considered a field experiment hinges on the definition of "the field."

Researchers may employ two main scenarios for randomization. The first involves gathering study participants and randomizing them at the time of the experiment. The second capitalizes on naturally occurring randomizations, such as the Vietnam draft lottery. 

Intervention, Excludability, and Non-Interference

Three essential features of any experiment are intervention, excludability, and non-interference. In a general sense, the intervention refers to the treatment or action being tested in an experiment. The excludability principle is satisfied when the only difference between the experimental and control groups is the presence or absence of the intervention. The non-interference principle holds when the outcome of one participant in the study does not influence the outcomes of other participants. Together, these principles ensure that the experiment is designed to provide unbiased and reliable results, isolating the causal effect of the intervention under study.

Omitted Variables and Non-Compliance

To ensure unbiased results, researchers must randomize as much as possible to minimize omitted variable bias. Omitted variables are factors that influence the outcome but are not measured or are difficult to measure. These unmeasured attributes, sometimes called confounding variables or unobserved heterogeneity, must be accounted for to guarantee accurate findings.

Non-compliance can also complicate experiments. One-sided non-compliance occurs when individuals assigned to a treatment group don't receive the treatment (failure to treat), while two-sided non-compliance occurs when some subjects assigned to the treatment group go untreated or individuals assigned to the control group receive the treatment. Addressing these issues at the design level by implementing a blind or double-blind study can help mitigate potential biases.

Achieving Precision through Covariate Balance

To ensure the control and treatment groups are comparatively similar in all relevant aspects, particularly when the sample size (n) is small, it is essential to achieve covariate balance. Covariance measures the association between two variables, while a covariate is a factor that influences the outcome variable. By balancing covariates, we can more accurately isolate the effects of the treatment, leading to improved precision in our findings.

Fictional Example of Randomized Controlled Trial of Covi-Mapp for COVID-19 Management

Let's explore a fictional example to better understand experiments: a one-week randomized controlled trial of the experimental drug Covi-Mapp for managing Covid. In this case, the control group receives the standard care for Covid patients, while the treatment group receives the standard care plus Covi-Mapp. The outcome of interest is whether patients have cough symptoms on day 7, as subsidizing cough symptoms is an encouraging sign in Covid recovery. We'll measure the presence of cough on day 0 and day 7, as well as temperature on day 0 and day 7. Gender is also tracked. The control represents the standard care for COVID-19 patients, while the treatment includes standard care plus the experimental drug.

In this Covi-Mapp example, the intervention is the Covi-Mapp drug, the excludability principle is satisfied if the only difference in patient care between the groups is the drug administration, and the non-interference principle holds if one patient's outcome doesn't affect another's.

First, let's assume we have a dataset containing the relevant information for each patient, including cough status on day 0 and day 7, temperature on day 0 and day 7, treatment assignment, and gender. We'll read the data and explore the dataset:

Simple treatment effect of the experimental drug

Without any covariates, let's first look at the estimated effect of the treatment on the presence of cough on day 7. The estimated proportion of patients with a cough on day 7 for the control group (not receiving the experimental drug) is 0.847458. In other words, about 84.7% of patients in the control group are expected to have a cough on day 7, all else being equal. The estimated effect of the experimental drug on the presence of cough on day 7 is -0.23. This means that, on average, receiving the experimental drug reduces the proportion of patients with a cough on day 7 by 23.8% compared to the control group.

We know that a patient's initial condition would affect the final outcome. If the patient has a cough and a fever on day 0, they might not fare well with the treatment. To better understand the treatment's effect, let's add these covariates:

The output shows the results of a linear regression model, estimating the effect of the experimental drug (treat_covid_mapp) on the presence of cough on day 7, adjusting for cough on day 0 and temperature on day 0. The experimental drug significantly reduces the presence of cough on day 7 by approximately 16.6% compared to the control group (p-value = 0.046242). The presence of cough on day 0 does not significantly predict the presence of cough on day 7 (p-value = 0.717689). A one-unit increase in temperature on day 0 is associated with a 20.6% increase in the presence of cough on day 7, and this effect is statistically significant (p-value = 0.009859).

Should we add day 7 temperature as a covariate? By including it, we might find that the treatment is no longer statistically significant since the temperature on day 7 could be affected by the treatment itself. It is a post-treatment variable, and by including it, the experiment loses value as we used something that was affected by intervention as our covariate.

However, we'd like to investigate if the treatment affects men or women differently. Since we collected gender as part of the study, we could check for Heterogeneous Treatment Effect (HTE) for male vs. female. The experimental drug has a marginally significant effect on the outcome variable for females, reducing it by approximately 23.1% (p-value = 0.05391).

Which group, those coded as male == 0 or male == 1, have better health outcomes (cough) in control? What about in treatment? How does this help to contextualize any heterogeneous treatment effect that might have been estimated?

Stargazer is a popular R package that enables users to create well-formatted tables and reports for statistical analysis results.

Looking at this regression report, we see that males in control have a temperature of 102; females in control have a temperature of 98.6 (which is very nearly a normal temperature). So, in control, males are worse off. In treatment, males have a temperature of 102 - 2.59 = 99.41. While this is closer to a normal temperature, this is still elevated. Females in treatment have a temperature of 98.5 - .32 = 98.18, which is slightly lower than a normal temperature, and is better than an elevated temperature. It appears that the treatment is able to have a stronger effect among male participants than females because males are *more sick* at baseline.

In conclusion, experimentation offers a fascinating and valuable avenue for primary research, allowing us to address causal questions and enhance our understanding of the world around us. Covariate control helps to isolate the causal effect of the treatment on the outcome variable, ensuring that the observed effect is not driven by confounding factors. Proper control of covariates enhances the internal validity of the study and ensures that the estimated treatment effect is an accurate representation of the true causal relationship. By exploring and accounting for sub groups in data, researchers can identify whether the treatment has different effects on different groups, such as men and women or younger and older individuals. This information can be critical for making informed policy decisions and developing targeted interventions that maximize the benefits for specific groups. The ongoing investigation of experimental methodologies and their potential applications represents a compelling and significant area of inquiry. 

References

1. Gerber, A. S., & Green, D. P. (2012). Field Experiments: Design, Analysis, and Interpretation. W. W. Norton.

2. “DALL·E 2.” OpenAI, https://openai.com/product/dall-e-2

3. “Data Science 241. Experiments and Causal Inference.” UC Berkeley School of Information, https://www.ischool.berkeley.edu/courses/datasci/241