2022-04-19 14:19:44

Talk Overview

  • Part 1: Introduction
  • Part 2: Past work
  • Part 3: Norovirus
  • Part 4: Influenza
  • Part 5: More stuff

Part 1 - Introduction

What we know

https://xkcd.com/

https://xkcd.com/

  • Inoculum dose is an important determinant of infection and vaccination outcomes.
  • For infection, higher dose is often associated with greater risk of infection (ID50) and more severe outcomes (LD50).
  • For vaccines, dose is thought to impact both immunogenicity/efficacy and side effects (morbidity).

What we don’t know

  • Not much is known about the impact of dose given infection.
  • There might be non-monotone relations between infection or vaccination dose and outcomes.
  • There might be trade-offs between vaccine availability/safety and efficacy.

Part 2 - Past work

Modeling dose and virus load

Adenovirus type 5 (ADV) infections of cotton rats.

\[ \begin{aligned} \dot U & = - bUV \\ \dot I & = bUV - dI \\ \dot V & = pI - cV \end{aligned} \]

Modeling dose and virus load

Modeling dose and immune response

Human parainfluenza virus (HPIV) in cotton rats

Human parainfluenza virus (HPIV) in cotton rats

Modeling dose and immune response

Modeling dose and immune response

\[ \begin{aligned} \textrm{Uninfected cells} \qquad \dot{U} & = - bUV \\ \textrm{Infected cells} \qquad \dot{I} & = bUV - d_I I \\ \textrm{Dead cells} \qquad \dot{D} & = d_I I \\ \textrm{Virus} \qquad \dot{V} & = \frac{pI}{1+s_F F} - (d_V V + k^{'}_{A}A + b^{'} U)V\\ \textrm{Innate response} \qquad \dot{F} & = p_F - d_F F + \frac{g_F (F_{max} - F)V}{V+h_V} \\ \textrm{B cells} \qquad \dot{B} & = \frac{F V}{FV+h_F} g_B B \\ \textrm{Antibodies} \qquad \dot{A} & = r_A B - d_A A - k_{A}AV \\ \end{aligned} \]

Modeling dose and immune response

Model fit to HPIV data

Model fit to HPIV data

Modeling dose and immune response

Part 3 - Norovirus

Data I

  • 57 volunteers challenged with 4 doses of norovirus.
  • 20 infected, only one at lowest dose. We dropped them.
  • 6/7/6 individuals infected at low/medium/high dose.
  • Followed for 96h in facility, up to 91 days at home.
  • Tracking of virus, symptoms and antibodies.

Data II

  • Individuals received a norovirus vaccine candidate at 4 doses (2 shots each).
  • Different types of antibodies to virus vaccine components G1.1 and G2.4 were tracked.

Models I

\[ \begin{align*} \textrm{Likelihood: } & \\ & y_{i} \sim \textrm{Normal} \left(\mu_{i}, \sigma \right) \\ \textrm{Linear model: } & \\ & \mu_{i} = \alpha_i + \beta x_i \\ \textrm{Priors: } & \\ & \sigma \sim \textrm{Half-Cauchy} \left(0,2 \right) \\ & \beta \sim \textrm{Normal} \left(0, 1 \right) \\ & \alpha_i \sim \textrm{Normal} \left(\delta, \gamma \right) \\ & \delta \sim \textrm{Normal} \left(25, 5 \right) \\ & \gamma \sim \textrm{Half-Cauchy} \left(0, 2 \right) \\ \end{align*} \]

  • \(y_i\) is outcome for individual \(i\), \(x_i\) is the dose (either continuous or categorical).
  • Depending on outcome, prior distributions and the likelihood distribution changes (e.g. Gamma-Poisson for for positive counts).

Models II

Additional details for time-series data fitting

\[ \begin{align*} \textrm{Likelihood: } & \\ & y_{i,t} \sim \textrm{Normal} \left(\mu_{i,t}, \sigma \right) \\ \textrm{Time-series model: } & \\ & \mu_{i,t} = \log\left( \frac{m_i \exp(-d_i t)}{1 + \exp ( -g_i (t - s_i) )} \right) \\ \textrm{Parameter equations: } & \\ p_{i} & = p_{0,i} + p_1 x_i \\ g_{i} & = g_{0,i} + g_1 x_i \\ T_{i} & = T_{0,i} + s_1 x_i \\ d_{i} & = d_{0,i} + d_1 x_i \\ \end{align*} \]

Population-level priors for dose parameters. Multi-level, adaptive priors for intercept parameters.

Dose and virus shedding I

A) fecal shedding during first 96 hours. B) total fecal shedding. C) shedding through vomit.

  1. fecal shedding during first 96 hours. B) total fecal shedding. C) shedding through vomit.

Dose and virus shedding II

Dose and virus shedding II

Dose and symptoms

Dose and immune response I

Dose and immune response II

Dose and immune response III

Part 4 - Influenza Vaccines

Setup

  • The default influenza vaccine was the trivalent or quadrivalent standard dose (SD, 15µg) Fluzone vaccine.
  • Individuals >=65 years were offered the high-dose (HD, 60µg) trivalent vaccine.
  • We evaluated immune response following vaccination, specifically antibodies as measured by hemagglutination inhibition assay (HAI).

Question: What is the impact of standard dose (SD) versus high dose (HD) vaccine on antibodies?

Study population

“Raw” data - homologous responses

“Raw” data - heterologous responses

Outcomes of interest

We investigate 4 antibody titer outcomes for each strain:

  • Titer increase following vaccination
  • Post-vaccination titer
  • Seroconversion, defined as pre-vaccination HAI titer <1:10 (limit of detection) and post-vaccination titer >= 1:40 OR a >=4-fold increase
  • Seroprotection, defined as post-vaccination HAI >= 1:40

All HAI titer dilution values are converted to a scale from 0 - N with limit of detection = 0, lowest dilution (1:10) = 1, etc. up to highest dilution (1:20480) = 12.

Results - homologous response

Median and 89% equal-tailed credible interval

Median and 89% equal-tailed credible interval

Heterologous H1N1 titer increase

Heterologous H1N1 seroconversion

Part 5 - some other projects

R packages to make modeling easier

Online modeling/analysis courses

Acknowledgements

  • Collaborators:
    • Prior work: See published papers
    • Ongoing work: Yang Ge, Zane Billings, Ye Shen, Ted Ross, Ben Lopman, Katia Koelle, Robert Atmar, several others…
  • Funding:
    • NIH

Questions?