Jekyll2023-02-17T05:48:18-08:00https://orozcodelpinopedro.github.io/feed.xmlHomeBiostatisticianPedro Orozco del Pino, Ph.D.porozco@umich.eduSensible choice of parameters to simulate a continuous outcome2022-01-11T00:00:00-08:002022-01-11T00:00:00-08:00https://orozcodelpinopedro.github.io/posts/2022/rsquared<p>Let’s say you want to make a simulation study to explore Method C (C for cool, because that is the best descriptor of your method). Your method assumes a continuous outcome $Y$ and a linear relationship with the vector $X$ through some coefficients $\beta$. Yes, this is the linear regression setup. You open your favorite coding program and start thinking. Ok, so you start by generating a matrix of covariates $X$. These covariates have a correlation matrix $\Sigma$. You think to yourself, I’m doing great, almost done. You are very proud because you have the mean of $Y$ perfectly specified. The only thing that you need is $\beta$. Is it?</p>
<p>Well, not really. You have to decide a value for the variance of the measurement error of $Y$; we will call it $\sigma^2$. Everything’s not lost. Just pick a number, and that is it. It is simple, choose a vector for $\beta$, select a number for $\sigma^2$, then you are done.</p>
<p>But wait a minute, that looks pretty arbitrary. How can you be sure you’ve chosen sensible values for these parameters?</p>
<p>Here is an idea. What if you fix the proportion of variance explained by your covariates (called $R^2$) and then set everything else. Here are two reasons why this is a good idea; the first is that it is much more interpretable than $\sigma^2$, and the second is very interpretable overall. I know, it is not two reasons but only one, but it is so good that it counts as two. You can choose $R^2$ according to the situations you expect your method to work.</p>
<p>Ok, a value of $R^2$ is a proportion, so it must be between 0 and 1. You think about all the situations that motivated your method. All those happy memories had $R^2$ between 0.2 and 0.3. You pick 0.25, and you are good to go. What next?</p>
<p>Remember the definition, $R^2$ is the proportion of the total variance of $Y$ explained by the covariates in your model. Your model is $Y=X\beta+\text{measurement error}$, and the covariates part is only $X\beta$, which gives us the following equation.</p>
\[R^2=\dfrac{var(X\beta)}{var(X\beta+\text{measurement error})}\]
<p>From here, you can get an expression of $\sigma^2$ as a function of $\beta$, $\Sigma$, and $R^2$ by following the algebra. You’ll finally get</p>
\[\sigma^2=\frac{\beta^T\Sigma\beta(1-R^2)}{R^2}\]
<p>Using this equation, you now have a sensible way to begin your simulation study, since fixing $R^2$ can be much less arbitrary than fixing $\sigma^2$.</p>
<p>Thanks for reading. Let me know if you have questions or corrections. Especially corrections.</p>Pedro Orozco del Pino, Ph.D.porozco@umich.eduLet’s say you want to make a simulation study to explore Method C (C for cool, because that is the best descriptor of your method). Your method assumes a continuous outcome $Y$ and a linear relationship with the vector $X$ through some coefficients $\beta$. Yes, this is the linear regression setup. You open your favorite coding program and start thinking. Ok, so you start by generating a matrix of covariates $X$. These covariates have a correlation matrix $\Sigma$. You think to yourself, I’m doing great, almost done. You are very proud because you have the mean of $Y$ perfectly specified. The only thing that you need is $\beta$. Is it?Picture a scientist documentary2021-08-10T00:00:00-07:002021-08-10T00:00:00-07:00https://orozcodelpinopedro.github.io/posts/2021/01/women-stem<h1 id="an-excellent-documentary">An excellent documentary</h1>
<p>I recently watched the documentary Picture a Scientist (https://www.pictureascientist.com). It is about the invisible (and often very visible) barriers that women have when they go into scientific careers.
After watching it I was shocked, but not surprised, about the stories and aweful situations most if not all women have to endure.
However, at this is not a critic of the documentary, I was also left with the question. What should we do? How do we solve this? What are the short, medium and long term actions that we have to take as a society?
I don’t know, but I hope there is plenty of research about it. I’ll look into it. For the moment I’m looking forward for the pannel discussion the School of Public Health at Michigan is going to have on the topic.</p>Pedro Orozco del Pino, Ph.D.porozco@umich.eduAn excellent documentary I recently watched the documentary Picture a Scientist (https://www.pictureascientist.com). It is about the invisible (and often very visible) barriers that women have when they go into scientific careers. After watching it I was shocked, but not surprised, about the stories and aweful situations most if not all women have to endure. However, at this is not a critic of the documentary, I was also left with the question. What should we do? How do we solve this? What are the short, medium and long term actions that we have to take as a society? I don’t know, but I hope there is plenty of research about it. I’ll look into it. For the moment I’m looking forward for the pannel discussion the School of Public Health at Michigan is going to have on the topic.A quick thought about inclusive teaching2021-04-07T00:00:00-07:002021-04-07T00:00:00-07:00https://orozcodelpinopedro.github.io/posts/2021/08/blog-post-1<h1 id="a-conversation-that-made-me-think">A conversation that made me think</h1>
<p>I had a fascinating talk today with a peer that sparked in me the idea of inclusive teaching. I mean that an inclusive teacher must develop many channels for students to participate in class. Only having one channel will benefit more those students that feel comfortable participating through that channel. This face of inclusive teaching is getting more common, especially with the increase of technology. Now you can reach out to professors through various methods, and it is not uncommon for them to have several of them available to students. However, I wonder how a teacher/professor can diversely evaluate students so that every student gets assessed so that their strengths shine more than their weaknesses. In all, so that grades reflect the best of all students and not just how well they can perform in a specific way.</p>
<p>This is a tough one. I don’t have an answer. If you do, please share it!</p>Pedro Orozco del Pino, Ph.D.porozco@umich.eduA conversation that made me think I had a fascinating talk today with a peer that sparked in me the idea of inclusive teaching. I mean that an inclusive teacher must develop many channels for students to participate in class. Only having one channel will benefit more those students that feel comfortable participating through that channel. This face of inclusive teaching is getting more common, especially with the increase of technology. Now you can reach out to professors through various methods, and it is not uncommon for them to have several of them available to students. However, I wonder how a teacher/professor can diversely evaluate students so that every student gets assessed so that their strengths shine more than their weaknesses. In all, so that grades reflect the best of all students and not just how well they can perform in a specific way.I got an internship!2021-03-01T00:00:00-08:002021-03-01T00:00:00-08:00https://orozcodelpinopedro.github.io/posts/2021/internship<h1 id="after-few-months-the-search-has-ended">After few months the search has ended.</h1>
<p>I’m going to be an Research Scientist for Eli Lilly Company during 12 weeks over the summer.
I’ll be working on simulations to assess methods of data integration for clinical trials.
I’m very happy for this opportunity.
If you want to read about my journey to get an internship <a href="https://docs.google.com/document/d/1wbdxtl1re1fuq8GiqybirVvxkVBJMNd1eXPzOnHWoI4/edit?usp=sharing">click here</a></p>Pedro Orozco del Pino, Ph.D.porozco@umich.eduAfter few months the search has ended. I’m going to be an Research Scientist for Eli Lilly Company during 12 weeks over the summer. I’ll be working on simulations to assess methods of data integration for clinical trials. I’m very happy for this opportunity. If you want to read about my journey to get an internship click here