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d-morrison
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📖 https://ucd-serg.github.io/serodynamics/preview/pr88 |
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Looks good so far! See comments
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Please don't track the pdf version
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Don't track the .tex version either
| $$ | ||
| \frac{dy}{dt} = | ||
| \begin{cases} | ||
| \mu_1 b(t), & t < t_1 \\ | ||
| - \alpha y(t)^r, & t \ge t_1 | ||
| \end{cases} | ||
| \quad \text{with } | ||
| \frac{db}{dt} = \mu_0 b(t) - c y(t) b(t) |
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before introducing this new revised model, can you summarize the Teunis 2016 and 2023 models?
# add references bib file # Remove tracked PDF and .tex files and add to .gitignore
# spelling correction # update WORDLIST
Merge branch 'main' of https://github.com/UCD-SERG/serodynamics into beamer # Conflicts: # .gitignore
Kwan-Jenny
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sschildhauer
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sschildhauer
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Currently, there are three .qmd files in the articles folder, but Antibody_Kinetics.qmd is the most up-to-date version. Therefore, only Antibody_Kinetics.qmd needs to be reviewed. However, I am unsure whether I should delete the other two .qmd files. @d-morrison, should I delete the other two and keep only this one? |
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This looks great Kwan! Just a few small clarifications. After reviewing you can re request from me and I will try to review in a more timely manner.
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| title: "Hierarchical Bayesian Model" | |||
| author: "Our Study Group" | |||
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| author: "Our Study Group" | |
| author: "Kwan Ho Lee, UC Davis SeroEpidemiology Research Group" |
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| ## Big Picture: What Are We Modeling? | ||
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| We are modeling **how antibody levels change over time** in response to infection, using data from multiple individuals and multiple **biomarkers** (10 antigen-isotype combinations, so ( j = 1, 2, ..., 10 )). |
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| We are modeling **how antibody levels change over time** in response to infection, using data from multiple individuals and multiple **biomarkers** (10 antigen-isotype combinations, so ( j = 1, 2, ..., 10 )). | |
| We are modeling **how antibody levels change over time** in response to infection for different antigen-isotype (biomarker) combinations (ex. anti-LPS IgG), using longitudinal serologic data from multiple individuals (10 antigen-isotype combinations, so ( j = 1, 2, ..., 10 )). |
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| ## Big Picture: What Are We Modeling? | ||
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| We are modeling **how antibody levels change over time** in response to infection, using data from multiple individuals and multiple **biomarkers** (10 antigen-isotype combinations, so ( j = 1, 2, ..., 10 )). |
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Why is this 10 antigen-isotype combinations? Couldn't it technically be any number of combinations?
| We want to: | ||
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| - Understand the average pattern for each biomarker | ||
| - Allow each person’s response to vary |
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| - Allow each person’s response to vary | |
| - Allow each person’s response to vary as a random effect |
| \end{bmatrix} | ||
| $$ | ||
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| These describe the antibody curve for person ( $i$ ) and biomarker ( $j$ ): the starting level, how fast it rises, peaks, and decays. |
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| These describe the antibody curve for person ( $i$ ) and biomarker ( $j$ ): the starting level, how fast it rises, peaks, and decays. | |
| These describe the antibody kinetic curve for each person ( $i$ ) and biomarker ( $j$ ): the baseline antibody level, rate of increase, peaks antibody level, and decay (waning) rate. |
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| Higher $\nu_j$ $\rightarrow$ more informative prior (stronger prior). | ||
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| Lower $\nu_j$ $\rightarrow$ more weakly informative (broader prior or weaker prior). |
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| Lower $\nu_j$ $\rightarrow$ more weakly informative (broader prior or weaker prior). | |
| Lower $\nu_j$ $\rightarrow$ less informative (broader prior or weaker prior). |
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| The model is built hierarchically across five conceptual levels: | ||
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| 1. **Observed data:** noisy log antibody concentrations from serum samples |
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| 1. **Observed data:** noisy log antibody concentrations from serum samples | |
| 1. **Observed data:** log antibody concentrations from serum samples |
| The model is built hierarchically across five conceptual levels: | ||
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| 1. **Observed data:** noisy log antibody concentrations from serum samples | ||
| 2. **Latent individual parameters:** hidden antibody dynamics $\theta_{ij}$ for each subject-biomarker pair |
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What does "hidden" mean here? Does it mean unobserved?
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| 2. **Middle Level**: | ||
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| - For each person $i$, their parameters: |
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| - For each person $i$, their parameters: | |
| - Each person $i$ has their parameters: |
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| 3. **Bottom Level**: | ||
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| - Their actual observed antibody levels are noisy measurements of predictions from $\theta_{ij}$: |
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| - Their actual observed antibody levels are noisy measurements of predictions from $\theta_{ij}$: | |
| - Observed antibody levels are noisy measurements of predictions from $\theta_{ij}$: |
3 participants
This pull request adds the finalized Beamer presentation materials for the April 14th meeting, including:
Beamer_Antibody_Kinetics.qmd: Full 32-slide presentation in Quarto Beamer formatBeamer_Antibody_Kinetics.pdf: Compiled version for presentationPlease let me know if you want me to change anything in here.