Academia
"Science is organized knowledge. Wisdom is organized life."-
Direct and Indirect Causal Effects
Causal effects are comparisons of potential outcomes under different treatment on a common set of units. The use of the concept of ‘direct’ versus ‘indirect’ causal effects is common in statistics, social, economics, and biomedical fields. The most straightforward way to clarify the direct and indirect causality is by using potential outcomes to define causal effects. Here we use two example studies to illustrate the widespread acceptance and application of the potential outcomes framework, also known as the Rubin causal model (RCM), in direct and indirect causal inference.
Figure 1. Simplified set-up with two levels of vaccination: low versus high. Figure from Rubin 2004
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Two-way ANOVA and test for interaction without replications
In this post, we will generalize over one-way ANOVA to two-way and multi-way ANOVA, and discuss a few solutions to test for interaction terms when there is no replication.
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A quick Intro to one-way ANOVA
ANOVA is parametrized by a regression framework. \(Y = X \cdot \beta + \epsilon\)
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Start learning causal inference from an easy classical question
Recently I am taking a class of causal inference, and we did an easy exercise during the class. Despite the fact that this is a basic regression question, it helps us understand how to interpret the coefficients gained in different models, and how the observed coefficients indicate the causal relationship.
question background and models
So let’s first take an look of the background of the question and the models:
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Journal Club -- discussion on antagonistic QTLs
We did a journal club discussing the paper “Tightly-linked antagonistic-effect loci underlie polygenic demographic variation in C. elegans “ on bioRxiv.
Summary of the paper
In this paper Bernstein et al. used the experimental genetics to show most genomic regions carry variants with detectable effects on complex traits. They measured the fitness effects of Ceanorhabditis elegans under Nickel stress using a high-throughput phenotyping method that characterize demography as a multivariate trait in growing populations. They then focused on a 1.4-Mb region of the X chromosome using the near isogenic lines (NILs) that subdivide the region into fifteen intervals. They found that eleven of intervals have significant effects, indicating potential adjacent QTLs with antagonistic effects.