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Exploring the underlying theory of the chi-square test through simulation – part 2

March 24, 2018
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Exploring the underlying theory of the chi-square test through simulation – part 2

In the last post, I tried to provide a little insight into the chi-square test. In particular, I used simulation to demonstrate the relationship between the Poisson distribution of counts and the chi-squared distribution. The key point in that post was the role conditioning plays in that relationship by reducing variance. To motivate some of the key issues, I talked...

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Exploring the underlying theory of the chi-square test through simulation – part 1

March 17, 2018
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Exploring the underlying theory of the chi-square test through simulation – part 1

Kids today are so sophisticated (at least they are in New York City, where I live). While I didn’t hear about the chi-square test of independence until my first stint in graduate school, they’re already talking about it in high school. When my kids came home and started talking about it, I did what I usually do when they...

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Another reason to be careful about what you control for

March 6, 2018
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Another reason to be careful about what you control for

Modeling data without any underlying causal theory can sometimes lead you down the wrong path, particularly if you are interested in understanding the way things work rather than making predictions. A while back, I described what can go wrong when you control for a mediator when you are interested in an exposure and an outcome. Here, I describe the...

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“I have to randomize by cluster. Is it OK if I only have 6 sites?”

February 20, 2018
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“I have to randomize by cluster. Is it OK if I only have 6 sites?”

The answer is probably no, because there is a not-so-low chance (perhaps considerably higher than 5%) you will draw the wrong conclusions from the study. I have heard variations on this question not so infrequently, so I thought it would be useful (of course) to do a few quick simulations to see what happens when we try to conduct...

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Have you ever asked yourself, “how should I approach the classic pre-post analysis?”

January 27, 2018
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Have you ever asked yourself, “how should I approach the classic pre-post analysis?”

Well, maybe not, but this comes up all the time. An investigator wants to assess the effect of an intervention on a outcome. Study participants are randomized either to receive the intervention (could be a new drug, new protocol, behavioral intervention, whatever) or treatment as usual. For each participant, the outcome measure is recorded at baseline - this is...

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Importance sampling adds an interesting twist to Monte Carlo simulation

January 17, 2018
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Importance sampling adds an interesting twist to Monte Carlo simulation

I’m contemplating the idea of teaching a course on simulation next fall, so I have been exploring various topics that I might include. (If anyone has great ideas either because you have taught such a course or taken one, definitely drop me a note.) Monte Carlo (MC) simulation is an obvious one. I like the idea of talking about...

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Simulating a cost-effectiveness analysis to highlight new functions for generating correlated data

January 7, 2018
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Simulating a cost-effectiveness analysis to highlight new functions for generating correlated data

My dissertation work (which I only recently completed - in 2012 - even though I am not exactly young, a whole story on its own) focused on inverse probability weighting methods to estimate a causal cost-effectiveness model. I don’t really do any cost-effectiveness analysis (CEA) anymore, but it came up very recently when some folks in the Netherlands contacted...

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When there’s a fork in the road, take it. Or, taking a look at marginal structural models.

December 10, 2017
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When there’s a fork in the road, take it. Or, taking a look at marginal structural models.

I am going to cut right to the chase, since this is the third of three posts related to confounding and weighting, and it’s kind of a long one. (If you want to catch up, the first two are here and here.) My aim with these three posts is to provide a basic explanation of the marginal structural model...

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When you use inverse probability weighting for estimation, what are the weights actually doing?

December 3, 2017
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When you use inverse probability weighting for estimation, what are the weights actually doing?

Towards the end of Part 1 of this short series on confounding, IPW, and (hopefully) marginal structural models, I talked a little bit about the fact that inverse probability weighting (IPW) can provide unbiased estimates of marginal causal effects in the context of confounding just as more traditional regression models like OLS can. I used an example based on...

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Characterizing the variance for clustered data that are Gamma distributed

November 26, 2017
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Characterizing the variance for clustered data that are Gamma distributed

Way back when I was studying algebra and wrestling with one word problem after another (I think now they call them story problems), I complained to my father. He laughed and told me to get used to it. “Life is one big word problem,” is how he put it. Well, maybe one could say any statistical analysis is really...

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