ouR data generation

I am involved with a stepped-wedge designed study that is exploring whether we can improve care for patients with end-stage disease who show up in the emergency room. The plan is to train nurses and physicians in palliative care. (A while ago, I described what the stepped wedge design is.)

Under this design, 33 sites around the country will receive the training at some point, which is no small task (and fortunately as the statistician, this is a part of the study I have little involvement). After hearing about this ambitious plan, a colleague asked why we didn’t just randomize half the sites to the intervention and conduct a more standard cluster randomized trial, where a site would either get the training or not. I quickly simulated some data to see what we would give up (or gain) if we had decided to go that route. (It is actually a moot point, since there would be no way to simultaneously train 16 or so sites, which is why we opted for the stepped-wedge design in the first place.)

The odds ratio always confounds: while it may be constant across different groups or clusters, the risk ratios or risk differences across those groups may vary quite substantially. This makes it really hard to interpret an effect. And then there is inconsistency between marginal and conditional odds ratios, a topic I seem to be visiting frequently, most recently last month.

My aim here is to generate a few figures that might highlight some of these issues.

Maybe this should be filed under topics that are so obvious that it is not worth writing about. But, I hate to let a good simulation just sit on my computer. I was recently working on a paper investigating the relationship of emotion knowledge (EK) in very young kids with academic performance a year or two later. The idea is that kids who are more emotionally intelligent might be better prepared to learn. My collaborator suspected that the relationship between EK and academics would be different for immigrant and non-immigrant children, so we agreed that this would be a key focus of the analysis.

This afternoon, I was looking over some simulations I plan to use in an upcoming lecture on multilevel models. I created these examples a while ago, before I started this blog. But since it was just about a year ago that I first wrote about this topic (and started the blog), I thought I’d post this now to mark the occasion.

The code below provides another way to visualize the difference between marginal and conditional logistic regression models for clustered data (see here for an earlier post that discusses in greater detail some of the key issues raised here.) The basic idea is that both models for a binary outcome are valid, but they provide estimates for different quantities.

In health services research, experiments are often conducted at the provider or site level rather than the patient level. However, we might still be interested in the outcome at the patient level. For example, we could be interested in understanding the effect of a training program for physicians on their patients. It would be very difficult to randomize patients to be exposed or not to the training if a group of patients all see the same doctor. So the experiment is set up so that only some doctors get the training and others serve as the control; we still compare the outcome at the patient level.

It is grant season around here (actually, it is pretty much always grant season), which means another series of problems to tackle. Even with the most straightforward study designs, there is almost always some interesting twist, or an approach that presents a subtle issue or two. In this case, the investigator wants compare two interventions, but doesn’t feel the need to show that one is better than the other. He just wants to see if the newer intervention is not inferior to the more established intervention.

I recently described why we might want to conduct a multi-factorial experiment, and I alluded to the fact that this approach can be quite efficient. It is efficient in the sense that it is possible to test simultaneously the impact of multiple interventions using an overall sample size that would be required to test a single intervention in a more traditional RCT. I demonstrate that here, first with a continuous outcome and then with a binary outcome.

A reader recently inquired about functions in simstudy that could generate data for a balanced multi-factorial design. I had to report that nothing really exists. A few weeks later, a colleague of mine asked if I could help estimate the appropriate sample size for a study that plans to use a multi-factorial design to choose among a set of interventions to improve rates of smoking cessation. In the course of exploring this, I realized it would be super helpful if the function suggested by the reader actually existed. So, I created genMultiFac. And since it is now written (though not yet implemented), I thought I’d share some of what I learned (and maybe not yet learned) about this innovative study design.

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 a bit about recycling. I asked you to imagine a set of bins placed in different locations to collect glass bottles. I will stick with this scenario, but instead of just glass bottle bins, we now also have cardboard, plastic, and metal bins at each location. In this expanded scenario, we are interested in understanding the relationship between location and material. A key question that we might ask: is the distribution of materials the same across the sites? (Assume we are still just counting items and not considering volume or weight.)

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 come home asking about a new statistical concept. I opened up R and started generating some data. Of course, they rolled their eyes, but when the evening was done, I had something that might illuminate some of what underlies the theory of this ubiquitous test.