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Aug 19 • 14 tweets • 4 min read
I've been revisiting several probability, statistics & clinical research concepts that I've learned through simulation & visualization over the past years. Full list pinned below - I hope this can be helpful for others who also learn this way! #epitwitter #statstwitter #RStats
The "birthday problem"

The Monty Hall problem

Bootstrap resampling

Universality of the uniform / inverse transform sampling

Propensity score matching & the propensity score paradox

Directed acyclic graphs (DAGs) and the four "elemental confounds"

Information entropy, Kullback-Liebler divergence and the Poisson distribution

Comparison of difficulty in identifying continuous vs. dichotomous interaction effects

Interactive application for Bayesian re-analysis of clinical trial data

Gaussian distribution and information entropy

Covariate adjustment to improve power in RCTs

The normality assumption in statistical models

Bayesian analysis of RCT data to derive patient-specific efficacy estimates

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More from @BenYAndrew

Ben Andrew Profile picture
May 3, 2019
The assumption of normality in many statistical models refers to the model residuals and not the dependent variable. @oscar_olvera100 has a great post about this topic (linked). I tried to expand on his thoughts through some additional simulation/visualization. #epitwitter 1/n
In these examples, we’ll look at a simple linear model Y ~ X, where X is dichotomous and Y is continuous. This first plot shows, for two relative effect sizes, the distributions of:

1. Y stratified by X
2. Y without stratification
3. Residuals from the linear model Y ~ X

2/n
We can "test" the normality assumption using the Shapiro-Wilk test. We find that if we look at only the dependent variable, the normality assumption is "violated" (SW p < 0.05) when the effect size is large (Cohen's d = 2), but not for smaller effect sizes (Cohen's d = 0.75). 3/n
Read 13 tweets
Ben Andrew Profile picture
Apr 15, 2019
I took a crack at reworking @statsepi’s RCT adjustment post (bit.ly/2Pd1JkH) w/ added simulation & visualization. To pique interest, here is a redacted version of the final image. Stick around for a walkthrough of how to get there & what it means. #epitwitter #rstats 1/n
Let's say we are studying the effect of a treatment on a continuous outcome (Y). In this field of study, 20 continuous patient variables are commonly reported (i.e., are found in the typical table 1). 2/n
Next, let's say that 10 of these variables are causally unrelated to Y (and thus are non-predictors of Y; call these N) and 10 have true causal effects on Y (and thus are predictors of Y; call these C). 3/n
Read 32 tweets

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