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There are many ways to control for variables. The easiest, and one you came up with, is to stratify your data so you have sub-groups with similar characteristics - there are then methods to pool those results together to get a single "answer". This works if you have a very small number of variables you want to control for, but as you've rightly discovered, ...

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1. Introduction I like @EpiGrad's answer (+1) but let me take a different perspective. In the following I am referring to this PDF document: "Multiple Regression Analysis: Estimation", which has a section on "A 'Partialling Out' Interpretation of Multiple Regression" (p. 83f.). Unfortunately, I have no idea who is the author of this chapter and I will refer ...

13

I think A and E aren't a good combination, because A says you should pick Mercy and E says you should pick Hope. A and D have the virtue of advocating the same choice. But, lets examine the line of reasoning in D in further detail, since that seems to be the confusion. The probability of success for the surgeries follows the same ordering at both ...

9

From Modern Epidemiology 3rd Edition by Rothman, Greenland and Lash: There are at least three forms of overmatching. The first refers to matching that harms statistical efficiency, such as case-control matching on a variable associated with exposure but not disease. The second refers to matching that harms validity, such as matching on an intermediate ...

7

Your question is actually a very hard one to answer. It is however good that you are asking before the study has been conducted - preferably well before the study is conducted. So this answer comes in a few parts: As many as you can possibly collect, given constraints of time and money. There is (almost) no such thing as too much data, and its harder to ...

7

Simpson's paradox is an extreme form of confounding where the apparent sign of correlation is reversed; you haven't said this is the position here. I can see at least three possibilities here: the heterogenity between the subgroups, the reduction in sample sizes in each, and poor definition of the subgroups which presuppose the results. Ignoring the third, ...

6

While I was ignorant of the "over-matching" terminology as well, one example of the same idea I have heard in Economic and Statistic lingo could be matching on an "intermediate" outcome. See Andrew Gelman's posts on the subject Amusing example of the fallacy of controlling for an intermediate outcome, or, the tyranny of statistical methodology and how it ...

6

In this case, it does not appear to have to do with sample sizes, since the CIs for the individual years do not even overlap with the CI for the whole period. It's hard to say exactly what's going on. Your code would help - did the model for the full data set include year as a IV? What is your dependent variable? What is your independent variable? It ...

5

I don't have a complete answer but can provide some thoughts: 1) Adjustment does remove the confounding effect, but only if the underlying causal pathways are correctly specified. There are occasions where adjustment can cause bias rather than decreasing biases. For more information on this issue, search for collider bias and directed acyclic graphs. 2) ...

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A confounding variable must: Be independently associated with the outcome; Be associated with the exposure Must not lie on the causal pathway between exposure and outcome. These are the criteria for considering a variable as a potential confounding variable. If the potential confounder is discovered (through stratification and adjustment testing) to ...

5

To expand on Peter Flom's answer (which is echoed in Michael Chernick's subsequent reply), this graphic may help the intuition. The following R code shows how it was produced. Briefly, it generates 400 data points per year, with values of variable $x$ ranging variously from $0$ to $2$ through $2$ to $4$, shifting upwards each year: this is one (mild) ...

4

First, it isn't terribly complicated to check for the association of Z on X or Y, even in survival analysis. Propensity scores and Inverse Probability of Treatment Weights (both common methods for adjusting for confounding in a survival context), along with other somewhat more esoteric methods are based on estimating the relationship between the covariate ...

4

No. One way to think of a confounding variable is as something that confuses the issues by making it unclear which of the various explanatory (sometimes confusingly called "independent") variables is actually relating to the response (sometimes, confusingly, called "dependent"). This is only possible if there is correlation between the candidate ...

3

I think the smaller sample size explains why some years are siginficant and others are not. Actually if you do multiplicity correction for doing 5 different test you may find that none of them are significant given a proper p-value adjustment to the tests. But Peter has hit on an important observation. The individual years give odds ratios that are close ...

3

First, a note: Randomized trials are not immune to confounding and other types of bias, though the randomization process helps protect them against it. Systematic flaws in the trial however, are just as serious as they are in observational studies. The answer to your question lies in how randomization works, and why we're doing it. The idea is to balance ...

3

"How much" matters a great deal! The adjustment is unlikely to be zero, after all; this would only happen if z were totally uncorrelated with x or y. By common convention one would test the statistical significance of the relationship between z and y as a way of deciding whether it is necessary to use z to adjust x's coefficient. That said, significance ...

3

Yes, the weaknesses of associations found in epidemiological studies also apply to a failure to find an association. You've already eliminated the first go-to problem, that of a study being underpowered, so at the moment we're just talking about bias. Two issues that may mean your study is failing to find a true association: Confounding. There are ...

3

The key to understanding lies in the word "conditional" in the phrase "conditional odds ratio". Basically, the statement means that the model assumes that $\beta$ doesn't vary across different levels of $Z$. If conditional independence of $Y$ and $X$ given $Z$ holds, then $\beta = 0$, so testing for $\beta = 0$ tests one of the implications of ...

3

I agree with @Michelle. In general, experimental control allows for causal inferences, but statistical control does not. In principle, statistically controlling for all confounding variables would allow you to make valid causal inferences, but in practice you have two problems: First, fishing through a lot of different candidate predictors, and fitting ...

3

summary(lm(...)) reports tests based on Type 3 SS summary(aov(...)) reports based on Type 1 SS T1 tests the variables in the order they are entered in the model, eg/ CVa CVb|CVa CVc|CVa,CVb etc T3 tests the variables effectively conditional on all other variables in the model, eg/ CVa|Cvb,CVc,etc CVb|Cva,CVc,etc This is why you are getting different ...

2

None of the answers are entirely baseless. But they ALL assume significant external knowledge and can't be taken to be correct strictly on the basis of the statistics. A, B, D, and E all require assumptions about the factors the cause patients to choose one hospital over another; the process by which doctors and patients are matched up, the extent to which ...

2

@gung gave a very thorough answer, but there is one more reason why D is a correct answer to the question: Better hospitals do more of the difficult operations because they are better. That is, if a person comes into Hope Hospital for operation D (the hardest) they may send him/her to Mercy because they at Hope don't know how to do it. This even happens in ...

2

This strategy for finding 'confounders' has been seriously challenged in the past few years. It is likely to result in confidence intervals for exposure effects that do not have the claimed properties. There is really no need to be parsimonious when adjusting for confounding. The H&L strategy has also been shown to be arbitrary. For one thing it ...

2

This is one of the major subjects of Pearl's work, and is why it is standard in the field of epidemiology. His approach is to build a causal model with links indicating all considered causal relationships. Then, to evaluate your question: whether treatment has an effect on staying drug free, one wants to basically find out whether evidence flows along the ...

2

I wouldn't call observed correlations spurious, but rather false causal inferences drawn from those correlations. Problems with ratios are of a kind with other types of confounding. If you define random variables $U=\frac{X}{Q}$ & $V=\frac{Y}{Q}$, where $X$, $Y$, & $Q$ are independent, then $X$ & $Y$ are correlated. This could mislead you into ...

2

This project will take an excellent understanding of statistics. This is not really a software question. Briefly, it is not useful to think of adjusting variables to produce new variables. You need to adjust for variables in the context of a statistical model. Only in the very special case of ordinary regression with no interactions and all effects ...

2

In the context of multiple linear regression, "adjusting" for a covariate simply means including it as an explanatory variable. There is an equivalent way of understanding multiple linear regression that provides insight into this question. To regress, say, $Z$ on $X$ and $Y$, we may (arbitrarily) select one of the explanatory variables (let it be $X$) and ...

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A few examples from clinical research might be variables that arise after randomization - randomization doesn't protect you from those at all. A few off the top of my head, that have been raised as either possibilities or been noted: Changes in behavior post voluntary adult male circumcision for the prevention of HIV Differential loss to follow-up between ...

1

If you have infected and uninfected individuals and a level of exposure (in this case Cytokine levels) you should be able to calculate a relative risk, and an appropriate 95% CI after adjustment. These can then be used in a plot that looks very similar to a boxplot if your levels are organized categorically, or a line diagram if your cytokine levels are more ...

1

Your intuition is correct; there is a link between main and interaction effects. "For example, it's possible to have a non-significant interaction that is still substantial enough to make it look like you have main effects when you don't have main effects." How to interpret main effects when the interaction effect is not significant?

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