**Transcript of Cyberseminar**

**HERC Econometrics Course**

**Research Design**

**Presenter: Christine Pal Chee**

**October 9, 2013**

*This is an unedited transcript of this session. As such, it may contain omissions or errors due to sound quality or misinterpretation. For clarification or verification of any points in the transcript, please refer to the audio version posted at www.hsrd.research.va.gov/cyberseminars/catalog-archive.cfm or contact HERC at herc@va.gov.*

**Todd Wagner:**I just wanted to welcome everybody to the Research Design by Christine Chee. She is a new health economist here at HERC and I just wanted to—hopefully, I am not going to embarrass you, Christine. I am going to give – one of the things that particularly impressed me about her when we were interviewing her was that I was struggling with an econometric issue that not only I was struggling, but two biostats were struggling with. And during the hour-long meeting, she helped me fix the problem and identify the problem. So I am just thrilled that she took the job and she has been here for a little bit now and she is thrilled about teaching. And I am really pleased to have her teach today on Research Design. So thanks, Christine.

**Christine Pal Chee:**Thanks for the introduction, Todd. As Todd mentioned, the topic of today’s lecture is Research Design. This is a particularly important issue in Health Services Research because many of the questions we want to answer aim to establish a causal relationship.

Questions like, does the adoption of electronic medical records reduce healthcare costs? Or did the transition to Patient Aligned Care Teams improve quality of care and health outcomes? Or what effect will the Affordable Care Act have on the demand for VA services?

Each of these questions tests a causal relationship and is ideally studied through a randomized controlled trial although these are the gold standard when it comes to research design; and we will talk a little bit more about why that is the case, but not always possible.

An alternative event is to use observational data, which we have a lot of in the VA. The question then is, when can regression analysis of observational data answer these questions? This will be the focus of our lecture.

Before we begin, I thought it would be great to survey the group’s familiarity with research methods and regression analysis. So I put together a little poll. How would you describe your familiarity with regression analysis? You can select the first one, A, if you have an advanced understanding of research methods and have run many regressions. You can select B if you have a working knowledge of regression analysis and have run a few regressions, C if you have a basic understanding of regression analysis with the details and mechanics behind them are mysterious, and D if you have no prior knowledge of regression analysis.

**Heidi:**And it looks like those have settled down a little bit if you want to read through the results here.

**Christine Pal Chee:**Okay. And it looks like about—Heidi, am I reading this correctly—26 percent of the group ...

**Heidi:**Actually, that is 26 respondents and 27 percent.

**Christine Pal Chee:**Okay, thank you. So about 27 percent of the audience has an advanced understanding of regression analysis and 44 percent has a working knowledge of regression analysis, about 26 percent has a basic understanding of regression analysis, and 3 percent has no prior knowledge of regression analysis. So actually, it looks like there is a pretty good spread, but most people have at least some background in regression analysis.

Let me move through these. So for the rest of the time – actually, sorry. I am pushing the wrong button here. So the goal of this lecture is to provide a conceptual framework for research design. To do that, we will review the linear regression model that Todd covered last week. We will define the concepts of exogeneity and endogeneity, and we will discuss three common forms of endogeneity, omitted variable bias, sample selection and simultaneous causality.

Since the purpose of this lecture is to provide a conceptual framework for research design, I will focus the discussion more on definitions and examples of each of endogeneity and provide just a brief overview of possible methods and solutions for future reference.

So all research begins with a research question. This is the thing we are dying to know and arguably why researchers do what we do. In our context in Health Services, the basic form of the research question usually looks something like this? What is the effect of a particular X on some outcome Y? 

Throughout this lecture I will use a question drawn from my own research: what effect does receiving antiretroviral therapy or ARVs for HIV Aids have on substance use? In other words, does receiving ARVs increase, decrease or have no effect on the likelihood of substance use? 

This is an important question because substance use is high among HIV-positive patients and is detrimental to health. And the question to this answer [sic] may have policy implications for substance use frequent programs. 

Once we have established a research question, we need to construct a regression model to empirically answer our question. Here we will focus on the linear regression model, which Todd covered last lecture, although the concepts we cover today will generalize to other models as well.

Our standard regression model usually looks something like this on the first line. We have Y, some outcome variable of interest; which is determined by X1 some explanatory variable of interest; X2, which is an additional control variable or it can be another explanatory variable of interest; and we can have any number of these additional variables. 

And here we see that the first three terms of the right-hand side β0 + β1X1 + β2X2 are used to predict the value of the outcome variable Y. And so the lasts term, e, which is the error term, contains all other factors besides X1 and X2 that determine the value of Y.

Since we cannot perfectly predict each value of Y, there is some stuff that is left over after we account for X1 and X2, and all of that stuff is contained in this error term. Another way to think about the error term is that it is the difference between the observed and predicted values of Y. So this is the difference between what we have observed and what we can predict with X1 and X2.

Most of our lecture will focus on this error term and its relationship to the other explanatory variables and the outcome variable of interest.

β1 is the  coefficient that we are most interested in, and it is the change in Y that is associated with the unit change in X1, holding constant X2. And for the rest of our lecture, I will refer to β1 hat as our regression estimate of β1. This is what the regression equation or the regression analysis will give us as our estimate of what β1 is from the observed data we have. 

And it is important to know that the regression model specifies all meaningful determinates of our outcome variable Y. I will elaborate more on what I mean by “all meaningful determinates” in just a little bit.

But to see the regression model in action, let us consider our example of ARVs and substance use. Here we can use a very simple regression analysis. Here we have that substance use is predicted by just one explanatory variable and that is whether or not a person receives ARVs. 

In here e, the error term, contains all other factors besides receiving ARVs that determine substance use. And β1 here is the change in the likelihood of substance use associated with receiving ARVs. The question then is, when does β1, or our estimate of β1, estimate the causal effect of receiving ARVs on substance use?

It must be the case that receiving ARVs is exogenous. For a variable X in a regression model to be exogenous, it must be the case that the conditional expectation of the error term given X is equal to 0. We say that the conditional mean of e, the error term, given X is 0. 

When this is true, we say that X is exogenous. I recognize that this concept and the formula are a little bit cryptic, but what it tactically means is that for a given value of X, the average value of the error term is 0. So this means that knowing what X is does not help us predict the error term.

And remember, the error term is the difference between the observed and predicted values of Y. It contains all other factors besides X that determine the value of Y.

So it means that information other than X does not tell us anything more about Y.

So in this case, in a simple regression model with just one explanatory variable X, X is the only meaningful determinate of Y within this context. This implies that X and the error term e cannot be correlated. If they are correlated, then X is no longer exogenous.

In the context of a randomized controlled trial, we can run a very simple regression using the following model where we have outcome dependent on treatment. Here the error term e can include things like age, gender, preexisting conditions, income, education, anything else that might affect the outcome variable that we are interested in. 

But because in a randomized controlled trial, treatment is randomly assigned, we know that treatment and the error term so everything else that is included in the error term are independent. This implies that treatment is exogenous.

In observational studies, X or a treatment is not randomly assigned, and the best that we can hope for is that treatment is as if it were randomly assigned in the sense that all other factors other than treatment do not tell us anything more about what the value of the outcome variable is. 

In our example, in order for β1 hat to estimate the causal effect of ARVs on substance use, the variable ARV must be exogenous. That means all other factors when receiving ARVs do not tell us anything more about whether or not a person engages in substance use. In the context of a randomized controlled trial where treatment with ARVs is randomized, ARV is exogenous. The question is, is the same true in the context of observational studies?

Actually, in observational studies, it is not uncommon for our explanatory variable to fail the exogeneity condition. If that is the case, we say that X is endogenous. 

X is always endogenous when X, our explanatory variable of interest, is correlated with the error term e. When X is exogenous, our estimate, β1 hat, is biased.

We say that β1 hat is unbiased if the expected value of the estimate is equal to the true value of β1. So in other words, an estimator β1 hat is unbiased if on average it is equal to the true causal effect that we are interested in.

If the β1 hat is biased, we will not estimate a causal effect of X and Y. In that case, what we have is a measure of the correlation between X and Y. And you have probably heard this many times before, but correlation does not imply causation. For a silly example of why this is the case, consider the correlation between the number of people who bring umbrellas to work and whether or not it is raining that day. There is a very strong and positive correlation between the two. If lots of people bring umbrellas to work, then it is very likely that it is raining outside.

However, we cannot say that bringing umbrellas to work actually causes it to rain. All we can say is that bringing umbrellas to work is correlated with it raining.

For the rest of our time, we will focus on this issue of endogeneity and more specifically, we will cover three examples or three forms, omitted variable bias, sample selection and simultaneous causality by a detailed discussion of each form with definition and examples, and then just a brief overview of possible solutions.

So first, omitted variable bias. This arises when two conditions are true. First, a variable omitted from the regression model is a determinate of the dependent variable Y. So this omitted variable is contained in the error term.

Next, the omitted variable is correlated with the regressor X. This leads our estimate β1 hat to be biased, and that is because β1 hat also captures the correlation between the omitted variable and the dependent variable, not just the relationship between the explanatory variable we are interested in and the dependent variable.

To demonstrate this, let us return to our basic regression model where we have just one explanatory variable X. Let us say another factor, W, determines Y. If W determines Y and is not explicitly included in the regression, then it is included in the error term e. And if X and W are correlated, then it is also the case that X and the error term are correlated; and that is because the error term includes W.

If X and the error term are correlated, then it is the case that X is endogenous and our estimate β1 hat is biased, and that is because it captures the correlation between W and Y. We cannot say that we have a causal relationship between X and Y. We have some measure of the relationship between X and W and Y. 

Returning to our example of substance use and ARVs, if we rely on the simple model which has ARVs as the explanatory variable, we need to ask two questions. First, besides receiving ARVs, do any other factors determine substance use? And second, are those factors correlated with receiving ARVs? We will consider two factors: education and health.

First, let us look at education. Does education determine or affect substance use? Well, it is the case that individuals who are more highly educated are less likely to engage in substance use. So yes, it is the case that education determines substance use.

Next, is education correlated with receiving ARVs? Actually, individuals who are more highly educated are also more likely to receive ARVs or medical care in general. 

So we have the case that both conditions are met, and so education is likely an omitted variable from our regression model.

Next we will consider health. It is the case that individuals who are in poorer health are less likely to engage in substance use. If someone is very sick in bed, they are probably less likely to be doing many things. It is also the case that individuals who are in poorer health are also more likely to receive ARVs. 

To see what omitted variable bias might look like in this case, I have run a very simple regression using data from the HIV Cost and Services Utilization Survey. It is a representative sample of HIV-positive patients in the US.

First, I run a regression of substance use on only the explanatory variable ARV. And here we see that receiving ARVs is associated with a 2.5 percentage point decrease in substance use. Now when I include education as a control, I find that receiving ARVs is associated with a 3.2 percentage point decrease in substance use. This is a 25 percent increase in the magnitude of the effect.

Now when I control for health, I find that receiving ARVs is associated with a 1.3 percentage point decrease in substance use. This is a 50 percent decrease in the magnitude from the original model that includes only ARVs as the explanatory variable.

So the change in the estimate of β1 hat suggests that our simple model, which just includes ARV as the explanatory variable, suffers from omitted variable bias. And the initial estimate of the decrease of 2.5 percentage points of substance use is actually biased.

Now how do we deal with omitted variable bias? One option is to run a randomized control trial. In our example we have randomly assigned treatment to ARVs to a population of HIV-positive patients. That is not always feasible.

So an alternative is to perform multiple linear regressions. So here after we have identified our key explanatory variable of interest, we need to identify likely sources of omitted variable bias. We should include all relevant factors in the regression model so that we have conditional mean independence. So here, in our example, we can include education, health and other factors like age or income, that might also affect the dependent variable substance use.

The important part here is that we must have conditional mean independence. That means after accounting for all the included regressors, the explanatory variable is as if it were randomly assigned in our population. 

One way to check that is to compare descriptive statistics of those who receive treatment and those who do not. If they differ in any way that are not included in our regression model, there is reason to believe that we might be suffering from omitted variable bias.

**Todd Wagner:**Can I interrupt for a second, Christine?

**Christine Pal Chee:**Yes.

**Todd Wagner:**So I know that grant cycles are coming up and there is often this question that comes into grant cycles about conceptual models. Well, sometimes conceptual models provide information on what variables should be in your analysis. So you might ask the question, or ask Christine a question about, what variables do I want to include? There are a whole lot of variables I could include. Well, hopefully you have some theoretical reason for including the variables that you are including. You can use empirical tests as well, but perhaps the conceptual models add relevance in that case.

**Christine Pal Chee:**Yeah, thanks, Todd. I totally agree. What is most important is the contextual knowledge of the context we are looking at. So here the clinical knowledge and economic knowledge and background are really important. What we want is to – what the regression model does is it models all meaningful determinants of our outcome variables. So if there is a theoretical reason to include something, it should be included.

**Todd Wagner:**We have a question that just came in.

**Christine Pal Chee:**Mm hm.

**Todd Wagner:**And then one question was: How about clinical rationale? I think you sort of addressed that. I think it can be a theoretical rationale or a clinical rational that you should include.

**Christine Pal Chee:**Yeah.

**Todd Wagner:**I mean you are probably in hot water if you do not have data on things that are important. And then the other one is, does omitted variable equal a confounder?

**Christine Pal Chee:**Yes. So an omitted variable is by definition a potential confounder. And if we do not include it, our estimates will be biased.

**Todd Wagner:**Hence the definite of it is a confounder, yes?

**Christine Pal Chee:**Yes.

**Todd Wagner:**And then how do you deal with multicollinearity when the independent variables are correlated?

**Christine Pal Chee:**They have to be very correlated to suffer from multicollinearity. And in general, I think the rule from on there is to include everything that is clinically or theoretically meaningful, and then we kind of just have to see what the data pans out to be. Is there a reason to believe that they are multicollinear? So some of them perfectly explain – some variable perfectly explains another set of variables. Then we will have to omit some of them. And that will be fine, since by definition multicollinearity means a set of variables or one variable explains another set. So they would be redundant in the regression equation anyway.

**Todd Wagner:**May I add into that ..

**Christine Pal Chee:**Mm hm.

**Todd Wagner:**... there will be two types of multicollinearity that I see in data. One is multicollinear by accident. You have constructed two variables to be the same thing, although you have given them different names; and most of the time, for example, if you are working with data instead to draw something out, that is one of the reasons it is happening. 

The other issue is that multicollinear—and Christine, you can speak to this—is really a function of your sample size. So if you have a huge sample, you are still able to estimate things that are highly correlated.

**Christine Pal Chee:**Yes, and that is just because we have more variation in each of the variables. With less variation it is more likely to have some overlap between the different variables.

**Todd Wagner:**Great. That is all the questions for now. Thanks.

**Christine Pal Chee:**Great. Thanks, Todd.

Returning to our slides, what if it not possible to include omitted variables in the regression? Actually, in our example with substance use and ARVs, one big concern is health because a lot of health is unobserved; and if it is unobserved, we do not have data on it and we cannot include it in the regression model. In that case, what do we do?

An option there is to utilize panel data, and this is data that contains the same observational unit observed at different points in time. In our case we could have one patient that is observed in multiple years or multiple months.

Using panel data, we can perform fixed effects regression. Doing this, it is possible to control for unobserved omitted variables as long as those omitted variables do not change over time. Stock and Watson actually provide an excellent introduction to fixed effects regression for anyone who is interested more in that.

Another option is to utilized instrumental variables regression. Here, if we can find an instrument variable that is correlated with the independent variable of interest, here like to find an instrumental variable that is correlated with whether or not a person receives ARVs, but is uncorrelated with the omitted variables. So here the instrument would have to be uncorrelated with say unobserved health that we are not able to control for in our regression model.

The idea behind instrumental variable is that it affects the outcome variable Y only through X. Because it is not correlated with the omitted variables, we get around the issue of having the explanatory variable X correlated with the error term e. We will talk more about this in the Instrumental Variables Regression lecture on October 30.

The next form of endogeneity is sample selection. This arises when a selection process influences the availability of data, or the data that we observe, and the selection process is related to the dependent variable Y beyond depending on X. This leads our estimate β1 hat to be biased, and so we no longer are able to estimate the true causal effect.

Sample selection is a form of omitted variable bias. The selection process is captured by the error term, and because that is [inaud.], it induces a correlation between the regressor X and the error term e. To provide some motivation for this, I will go over two classic examples from economics and then a few examples within the VA.

One thing economists have been historically interested in is the effect of unionization on wages. So does union membership increase over gross wages?

So a very simple regression model here will regress wages on just one explanatory variable unionization. The issue here is that a worker’s decision to join a union is not random and is highly endogenous and that it may depend on many factors that also affect wages. The concern here is that workers who choose to join unions are probably more likely to benefit from union status to begin with; they probably are more likely to experience higher wages as a result of joining unions. And it might also be the case that workers who do not join unions are not likely to have that same benefit in wages.

So that is the case, and we compare the wages of people who choose to join a union and those who choose not to join a union. We will probably be overestimating the effect of union status on wages.

A very similar example involves the return to college education, and economists have also been interested in the effect of college education on wages. So does going to college give you *[no speech from 00:31:39 to 00:31: 40]* here on.

Here is our simple regression model. It can include wages as the dependent variable and just one explanatory variable, college.

The issue here is really similar. A person’s decision to go to college is also not random and highly endogenous. Those who go to college are probably most likely to benefit from college or most able to go to college and that way will also overestimate the effect of college on wages if we just compare people who choose to go to college and those who choose not to go to college.

Now let us consider some examples in the VA. Let us say we want to evaluate the effect of a new tobacco dependence treatment program on quitting smoking. Our simple regression model can look at the relationship between quitting and whether or not a veteran participates in one of these treatment programs. The concern here is that individuals who participate in the program may be more likely to quit to begin with. If that is the case, we will also overestimate the effect of treatment, if we just compare people who enroll in the programs and those who do not enroll in the programs.

Next, we might be interested in evaluating the effect of home-based primary care on nursing home use; and our regression model here is also very similar. We want to look at the effect of home-based primary care on nursing home use.

The issue here is that individuals who use home-based primary care may be more plugged into the VA in general and more likely to know about and use other available programs that might also affect nursing home use. Or it could be the case that facilities that adopt home-based primary care may already have other supportive programs to begin with. These supportive programs might also affect nursing home use.

In both of these examples, individuals choose into treatment based on ways that affect the outcome variable.

How do we deal with sample selection? Again we can run or we can conduct a randomized controlled trial. Because that is not always feasible, an alternative is to utilize sample selection and treatment effect models. These models attempt to model the structure of the selection process so that the selection process is no longer—sorry—so that the selection decision is no longer endogenous because we explicitly account for them. Green and Wooldridge both provide more information on these models.

Another alternative is instrumental variables regression, and we will talk more about this in the Instrumental Variables Regression lecture in a few weeks.

**Todd Wagner:**Christine?

**Christine Pal Chee:**Yes?

**Todd Wagner:**Can you go back one slide? For the question on the – understanding sample selection on the Green and Wooldridge, you do not see this frequently in health services research. Is that predominantly you expect because understanding sample selection is really hard and multifaceted, or is there another reason that you expect?

**Christine Pal Chee:**Yes. I think sample selection is very complex. I also have to say that the sample selection and treatment effects models are also or can be quite complicated, and they actually impose pretty strong assumptions. You have to properly model the structure of the selection process, otherwise the results will also be biased.

**Todd Wagner:**Okay. Thank you.

**Christine Pal Chee:**Yes. The third form of endogeneity that we will discuss is simultaneous causality. This arises when there is a causal link from X to Y as we expect. We are interested in the effects of X on Y. However, there is also a causal link from Y to X. So not only does X affect Y; Y also affects X. This is also referred to as simultaneous equations bias and it leads our estimate β1 hat to be biased. That is because the reversed causal relationship from Y to X leads our estimate β1 hat to pick up both effects.

Let us return to our examples of estimating the effect of receiving ARVs on substance use. In our basic regression model, we have that substance use is affected by ARVs. 

If it is the case that substance use in turn affects the likelihood of receiving ARVs, we also have the case that the second equation is true. We have that ARVs are determined by substance use.

But both these equations are necessary to understand the relationship between ARVs and substance use. It would be incomplete for us to only consider the first equation. To see why this is the case, we can walk through an example.

So we start with two simultaneous equations now because we have causality that runs in both directions. So let us start with the first equation, equation one. Let us suppose that there is some positive factor in the error term in equation one that leads to a higher value of the variable substance. So if there is a large positive factor in e, the left-hand side variable substance will also increase.

A higher value of the variable substance leads to a higher value of the variable ARV if the second equation is also true.

That means that if there is a positive factor or positive error e, we also have a higher value of the variable ARV. So explicitly, an increase in e will lead to an increase in the variable ARV. That means that the variables ARV and the error term are correlated. So in the very first equation in our basic regression model that we are relying on, we have this explanatory variable ARV that is correlated with the error term, which violates our exogeneity assumption.

And when that is the case, our estimate, β1 from equation one, the effect of ARVs on substance use, is biased. We are no longer estimating the causal effect of receiving ARVs in substance use.

So how do we deal with simultaneous causality? I am going to sound like a broken record, but again we can conduct a randomized controlled trial where the reverse causality channel is eliminated. So if we were to randomize treatment with ARVs, this would mean that treatment with ARVs is independent of substance use. And it would remove that reverse causality channel.

Because that is not always possible, we can also utilize instrumental variables regression. In here, we can utilize an instrumental variable that is correlated with our explanatory variable X. In here, we have an instrumental variable that determines whether or not a person receives ARVs.

At the same time, this instrumental variable cannot be correlated with the error term. Since the error term contains all other factors that determine Y, this means that the instrumental variable does not otherwise determine Y. So in this case, the instrumental variable does not affect substance use. We will talk more about this on the Instrumental Variables Regression lecture on Oct. 30.

**Todd Wagner:**Christine?

**Christine Pal Chee:**Yes?

**Todd Wagner:**We have had two questions come in ...

**Christine Pal Chee:**Okay.

**Todd Wagner:**... both related to the sample selection model specifically, but more about propensity scores, and you have highlighted ways of handling selection as well as this issue of endogeneity. But you have not talked about propensity scores. And so the questions can be: Can you handle sample selection in an omitted variable bias by using propensity scores?

**Christine Pal Chee:**Yes, you can. Propensity scores, I think, are a form of Campbell selection models, and they do account or attempt to account for the selection process. So we try to predict. Using the information we have, we try to predict whether or not a person receives treatment, and we control – we explicitly control for that.

Todd, I think next week or in two weeks you will be talking more about propensity scores?

**Todd Wagner:**Yes. I am actually going to give the exact opposite answer that you just gave, which is – and I think it is more like the sample selection model. I am going to say, no, you cannot in part because I am never comfortable with the assumptions that are made in propensity score models about sample selection. And so I think that they generally place a lot of strong assumptions about understanding selection, and I have yet to be comfortable with those. But that might be my personal bias.

**Christine Pal Chee:**Actually, I totally agree and I was going to say that the propensity score models come with a caveat, and that is the same caveat that goes with sample selection treatment effect models, and it is that being made a very strong assumption. And that assumption is that we can perfectly or adequately model the selection process. If we are not able to, then our estimates will still be biased.

An alternative is just to utilize multiple linear regression and just to control for possible omitted variable biases or possible factors that might predict treatment.

**Todd Wagner:**And thanks for plugging the propensity score lecturing in a couple weeks. Thank you.

**Christine Pal Chee:**Oh, no problem. Was there another question, Todd?

**Todd Wagner:**That is it for right now.

**Christine Pal Chee:**Okay. Well, we are nearing the end of this lecture. But during this time, we considered the concepts of exogeneity and endogeneity and discussed common forms of endogeneity that will lead our regression estimate to be biased. 

An important point underlying this is that good research design requires a thorough understanding of how the dependent variable is determined. Here clinical knowledge, economic knowledge, any background knowledge is really important and necessary in order to adequately and properly construct our regression model.

In constructing our regression model, we need to ask, is the explanatory variable of interest exogenous? More specifically, are there omitted variables left out in our regression model? Is there sample selection? And is there simultaneous causality that leaves the dependent variable to determine the explanatory variable?

This exogeneity commission is important because it is necessary for the estimation of a causal treatment effect. Otherwise, the best we can do is estimate the correlation between the dependent variable and the explanatory variable.

It is my hope that understanding sources of exogeneity can help us understand what our regression estimates actually estimate, and the potential limitations of our analyses, and can perhaps point us to appropriate methods to use to answer our research questions. We will cover some of these methods in the rest of the course this fall.

That is all I have for now. Todd, were there any other questions?

**Todd Wagner:**Not yet, but it is usually good to hold on for two minutes and as people start typing the followup questions, people can ask those questions. So thank you for a very clear presentation. And if people were there for my talk last week, it ties in very nicely and I think you went into much more detail about omitted variable bias and selection and so forth, so thank you.

Can you explain best practices in your opinion for pilot study sample size? And I am not sure if that means powers – the writer of that can talk a little bit more. Do you mean power analysis for sample size or perhaps you can give a little bit more context on those.

And another question came in, and, Heidi, this is more for you. It is, how do we download the slides?

**Heidi:** I am going to send out that link to everyone right now.

**Todd Wagner:**Okay. And I am a little bit about the question on sample size, a little bit unclear about the best practice, but a little bit more context. There is clearly minimal sample size requirements, but luckily in this day of mostly big data or the other extreme.

Yeah, so the question for you, Christine, is, can you say a little bit more about power minimum size, effect size determination, best practices? How much effect do you want, so forth, with observational data.

**Christine Pal Chee:**Sure. So there is a very large literature on this topic. And, Todd, like you mentioned when we were working with large datasets, that is not a large concern for us. But if we are working with pilot data or even studies and implementation science or quality improvements where we are working with specific sites or specific programs and the sample sizes are much smaller, power is actually a huge concern. We want to be able to have a sufficient sample size to statistically say something about a clinically meaningful effect size. And there is a trade-off between sample size and the number of variables that you include in your regression and even the research design that you use.

I am not quite sure specifically if I have more to add. If there are more specific questions, I am happy to look into them or help answer them.

**Todd Wagner:**Yes. One of the—if I could just offer to provide just my opinion. [Clears throat] I apologize. One of the things that I would say is the talks in a reason for polling multiple years of data is that you might be interested in our particular type of surgery that is not widely conducted at a particular medical center. But by pooling your data across two years or three years, you will get enough information to say something about that surgical technique at that facility. 

I would also say that power means two different things. When you are doing an experimental design, power is really helping you understand the likelihood of a Type I error, which keep in mind is confirming a difference when it does not really exist; and a Type II error, which is just confirming a difference that exists. 

And in today’s world of big data, I think power is usually more than sufficient and we are not asking often the right questions about how do we know if it is minimally clinically important, and I think we are finding things that are very, very significant that may not be meaningful. So I think you run the risk of saying something that is highly significant but that is not very important in that regard. So be careful when you start pulling down millions of records about how much data you actually have.

There are a bunch more questions that came in. So is it true to say that endogeneity is almost always present in all regression models using retrospective data?

**Christine Pal Chee:**[Laughter] That is a good question. I think it is not uncommon. The question, then, is how severe is the problem and what the nature of the problem is. And if we can understand that, we can better understand probably the direction of our bias, so whether we are overestimating or underestimating the treatment effect, and the magnitude of the bias. 

If we expect a priority or using good and sound clinical and theoretical background, we expect a small bias. Perhaps we do not need to be as concerned about it. But if we expect a large bias, then we should be concerned about it. 

And there are ways to test for endogeneity. I mentioned one way and that was to check the scripted statistics of groups of people who receive treatment and those who do not. A lot of it actually just relies on good clinical knowledge and background.

**Todd Wagner:**Great. And I love your answer to it. There is also a little bit of a cultural answer, too, in economics and also in some health economics fields. You are correct that we assume it is there and often we say it is fatal if it is there unless you can figure out some very clever way of fixing it. And so most PhD students are on the path to try to figure out some clever way to fix it, whereas in health services we often say it is there and then wave our hands in the limitation section.

Another question came in ...

**Christine Pal Chee:**Oh, Todd, sorry. Can I mention one other thing?

**Todd Wagner:**Sure.

**Christine Pal Chee:**Actually, in the field of economics, there has been more interest in probably the last five or ten years in research design in finding new methods to get around some of these issues of endogeneity. These include fixed effects regressions. It includes the difference and differences model. It includes instrumental variables. It includes regression discontinuity. So increasingly, there are more tools to help us deal with it. The challenge for us as researchers is to figure out which tool can help us answer the question we are interested in and kind of get around the issues that are unique to our current study in context.

**Todd Wagner:**Correct. There is a question about sample selection bias. You say sample selection bias leads to correlation of X and error. Can you please provide a specific example of this problem?

**Christine Pal Chee:**Yes. So let us return to the example in a VA of wanting to estimate the effect of tobacco dependence treatment programs on quitting smoking. In our basic regression, we will have whether or not a person quits as our dependent variable and our independent variable will be whether or not a person participates in one of these treatment programs. If that is the only variable we are controlling for in our regression, we could have the case because of selection that the variable treatment so whether or not a person participates in the treatment program is correlated with the error term. And that can be true if the most motivated veteran enroll in one of these programs. In that case, in our error term we have motivation. Each person’s level of motivation or each person’s desire to quit is included in the error term that we are not including in the regression model. But these factors, how motivated a person is or how much they want to quit, actually affects whether or not they receive treatment. So that is one specific example of how selection can induce a correlation between explanatory variable and the error term. Hopefully that makes sense.

**Todd Wagner:**Yeah, that is a great example. I was thinking of an example as you were talking, and the one that often comes up is in economics. It is sort of the return on investment in education. It is clearly not something you can randomize. You cannot randomize someone to say, sorry, you are going to stop at grade five or you are going to go on to grade eight and you are going to go to graduate school. There has been a lot of interest among economists in trying to understand sort of the benefits or the selection effects of education. They are very, very thorny issues because there are so many unobserved things that fall into the decision to get more education. So in that case it is a very challenging discussion econometrically. Hopefully that helped.

Another question that came up: In one of the exogeneity slides you wrote, Information other than Xi does not tell us anything about Y. But you said that the error term contains factors that determine Y. Thus, is not the error term always telling you something about Y, even in the case of exogeneity?

**Christine Pal Chee:**Yes. So I am looking at that slide and actually exogeneity – or X being exogenous and by the information other than X does not tell us anything more about Y. So we will use information about X to predict Y. And for each prediction of Y, we have an error term; because if we have the observed value of Y and we have the predicted value of Y, so for each data point we have an error term.

**Todd Wagner:**So go back to your slide on exogeneity.

**Christine Pal Chee:**Thank you. [Laughter] 

Todd:The other thing to keep in mind is that you are trying to understand a specific question, which is a causal relationship between your outcome and your independent variable. So you are right that there might be other variables of interest in the error term, that determinate; and often you might end up with a randomized trial that is showing something that is totally exogeneity but you have a very low R2, and that is okay.

**Christine Pal Chee:**Yes. So what is important—I am trying to find the slide. Here it is. 

**Todd Wagner:**Right.

**Christine Pal Chee:**So here I say that knowing X does not help us predict the error term. And remember that the error term is the difference between the observed value of Y and our predicted value of Y. So we start with the predicted value of Y and then we add the error term, and then we get our observed value of Y. So information outside of X does not tell us anything more about Y. So that means the error terms on average, what we have is, a couple of lines up is that the conditional average. So once we control for X or we look at a given value of X, any other information is not meaningful in that our predicted error is zero. So on average we are actually doing the best we can to predict Y. If that makes sense.

**Todd Wagner:**That was perfect. That is all the questions that have come in so far and I feel a little bit like Click and Clack for those of you who listen to that radio show. You have wasted another perfectly good hour listening to us here. So...   I do not know if Christine is Click and I am Clack ...

**Christine Pal Chee:**[Laughter]

**Todd Wagner:**... but it was a great presentation, Christine, thank you so much.

**Christine Pal Chee:**It was my pleasure.

**Moderator:**And for the audience, I am just about to put up a feedback form. If you could take a few moments to fill that out, we would definitely appreciate your feedback. Thank you, everyone, for joining us for today’s HSR&D Cyber Seminar. Thank you.

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