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NLME_Analysis_Full Report.Rmd
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NLME_Analysis_Full Report.Rmd
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---
title: '**The Utility of Mixed-Effect Models in the Evaluation of Complex Genomic Traits In-Vitro **'
author: '**Nathan Alade**'
date: '*`r format(Sys.Date(), format = "%B, %Y")`*'
output:
html_document:
code_folding: show
toc: yes
toc_float:
collapsed: yes
theme: flatly
css: CSS/style.css
highlight: zenburn
subtitle: '[Methods Supplement and R Code]'
bibliography: packages.bib
csl: American_Chemical_Society.csl
---
------------------------------------------------------------------------
------------------------------------------------------------------------
# **Introduction**
## Abstract
The use of human liver microsomes as a model system to evaluate the impact of complex genomic traits (i.e., linkage-disequilibrium patterns, coding, and non-coding variation, etc.) on drug metabolism remains challenging. To overcome these challenges, we propose the use of non-linear mixed effect models (NLME) as an unconventional approach to evaluate the impact of complex genomic traits on the metabolism of xenobiotics in vitro. In this in-silico study, we present a practical use case for such an approach using previously published in-vitro CYP2D6 data and explore the impact of sparse sampling, and experimental error on known kinetic parameter of CYP2D6 mediated formation of 4-hydroxy-atomoxetine in human liver microsomes.
## Objective
This supplement provides the `R` code used to conduct the *in-silico* portion of the study, as well as useful functions for evaluating/visualizing results.
------------------------------------------------------------------------
# **R Libraries and Packages**
```{r setup, include=FALSE, warning=FALSE}
# Setup ------
knitr::opts_chunk$set(echo = TRUE, cache = TRUE,
warning = FALSE,
message = FALSE,
eval = TRUE,
fig.align = 'center')
# Load Environment Quickly -----
# load("R Output/NLME_Analysis.RData")
```
```{r Packages, eval=T, message=FALSE}
# R Packages -----
library(nlme) # Non-Linear Mixed Effect Modeling
library(tidyverse) # Data Manipulation and Visualization
library(ggeasy) # Wrapper for Plot Manipulation
library(ggpubr) # Additional Tools for Plot Configuration
library(scales) # Additional Tools for Adjusting Plot Scales
library(cowplot) # Data Visualization Themes and Tools
library(kableExtra) # Additional Tools for Creating Custom Tables
# Package References -------
# knitr::write_bib(c(.packages()), "References/packages.bib")
```
------------------------------------------------------------------------
Citation information for R packages [@R-base; @R-cowplot; @R-dplyr; @R-ggeasy; @R-ggplot2; @R-ggpubr; @R-kableExtra; @R-nlme; @R-readr; @R-scales; @R-tibble; @R-tidyr; @R-tidyverse; @ggplot22016; @nlme2000; @tidyverse2019] used for data analysis can be found in the *References* section.
------------------------------------------------------------------------
# **Importing Data**
CYP2D6 mean estimates and frequencies (Dinh et. al., 2016) were imported and summarized by genotype (***referred to as diplotype in R script***). Additionally, an Eta table and parameter estimate table were also generated to be reference later on in the data analysis.
------------------------------------------------------------------------
```{r Data Import}
# Atomoxetine Dataset (Dinh et al., 2016)
atx.data <- readxl::read_xlsx("Input Data/Atomoxetine Data - 2016.xlsx")
# Summary of Atomoxetine Data by genotype ----
diplotype.data <- atx.data %>%
group_by(Diplotype) %>%
# Summarize mean estimates of the data
summarise(Vmax = mean(Vmax),
Km = mean(Km),
Score = unique(`Activity Score`),
n = n()) %>%
ungroup() %>%
mutate(Freq = n/sum(n),
Vmax.Eta = ifelse(Diplotype != "1/1",
round(Vmax-Vmax[Diplotype == "1/1"],
digits = 2),
round(Vmax, digits = 2)),
Km.Eta = ifelse(Diplotype != "1/1",
round(Km-Km[Diplotype == "1/1"],
digits = 2),
round(Km, digits = 2))) %>%
select(-n)
# Eta Table (Deviations from the reference group) -----
actual.eta <- diplotype.data %>%
select(Diplotype, Vmax.Eta, Km.Eta) %>%
rename("Vmax" = "Vmax.Eta",
"Km" = "Km.Eta") %>%
pivot_longer(Vmax:Km, names_to = "Parameter",
values_to = "Actual") %>%
arrange(desc(Parameter))
# mean estimates of Vmax and Km for each genotype -----
actual.est <- diplotype.data %>%
select(Diplotype, Vmax, Km) %>%
pivot_longer(Vmax:Km, names_to = "Parameter",
values_to = "Actual") %>%
mutate(Actual = round(Actual, digits = 2)) %>%
arrange(desc(Parameter))
```
------------------------------------------------------------------------
# **Virtual Population**
## Population Simulation Function
A custom simulation function `population.sim()` was scripted to generate a virtual population with a pre-defined distribution of *CYP2D6* genotypes, and to simulate Michaelis-Menten kinetics for each individual. The inputs for the function the `population.sim()` include the following:
- **n** - number of subjects per genotype group (default = 10).
- **CV%\_D** - Average standard deviation for each genotype group as a percentage of the true estimate for Vmax and Km (between subject variability for each genotype group) (default = 25).
- **CV%\_V** - Average coefficient of variation across all points for simulated Michaelis-Menten kinetics for each individual (residual error).
- **Start** - Starting concentration from Michaelis-Menten simulation (default = 0).
- **End** - Ending concentration for Michaelis menten Kinetics (default = 100 uM).
- **By** - Simulated concentration increment (default = 0.5).
- **pop_freq** - TRUE or FALSE argument indicating whether to use true population frequency (default is FALSE).
- **seed** - Random number generator seed (for reproducibility, default = 23457).
- **data** - Dataframe to be used as reference for population averages. Must include genotype, Vmax, Km, and Frequency columns (default = `diplotype.data`).
Within-group between subject variability was set at 25% CV for each genotype (one standard deviation = 0.25 x mean of true value). Below is a simulated population containing 9000 individuals (1000 per diplotype groups) with mean and standard deviations for each group parameter.
------------------------------------------------------------------------
```{r Simulation Function}
population.sim <- function(
# Pre-define number of subjects per diplotype group
n = 10,
`CV%_D` = 25,
`CV%_V` = 0,
# Pre-define Michaelis Menten Kinetic Settings
Start = 0,
End = 100,
By = 0.5,
# Turn off or on use of true population frequency
## If set to true "n" will equal total population number
pop_freq = FALSE,
# Pre-define reference data, and set seed
data = diplotype.data,
seed = 23456){
# ======== Create Data Containers ========
datasets <- list()
pop.data <- tibble()
# ======== Create Datasets by Diplotype ========
for (i in seq_along(data[[1]])){
# Setting Population Specific Frequency
n_pop <- if_else(pop_freq == FALSE, n,
ifelse(pop_freq == TRUE,
round(n*data[[i, c("Freq")]]), 0))
# Specify Diplotype for current loop
Diplotype = rep(data[[i,1]], n_pop)
# Random assignment of Vmax values N(0,sigma)
set.seed(seed)
Vmax_eta <- rnorm(n_pop, sd = `CV%_D`)
Vmax = data[[i,2]] + (Vmax_eta/100)*data[[i,2]]
# Random assignment of Km values N(0,sigma)
set.seed(seed)
Km_eta <- rnorm(n_pop, sd = `CV%_D`)
Km = data[[i,3]] + (Km_eta/100)*data[[i,3]]
# Store each diplotype group in a list container
temp <- tibble(Diplotype, Vmax, Km)
datasets[[i]] <- temp
}
# ======== Combine Diplotype Datasets ========
for (i in seq_along(data[[1]])){
pop.data <- rbind(pop.data, datasets[[i]])
}
# ======== Simulate Michaelis Menten ========
set.seed(seed)
pop.data <- pop.data %>%
mutate(ID = factor(seq_along(Diplotype),
levels = seq_along(Diplotype))) %>%
relocate(ID) %>%
expand_grid(S = seq(Start, End, By)) %>%
mutate(V = round((Vmax*S)/(Km+S), digits = 2))%>%
group_by(ID) %>%
# Additon of Residual Error ------------
mutate(resid_pct = round(rnorm(n = length(S),sd = `CV%_V`),
digits = 3),
V_adj = V+(V*resid_pct/100)) %>%
ungroup()
return(pop.data)
}
```
------------------------------------------------------------------------
## Distribution of Virtual Population Parameters
```{r Vmax and Km Distribution, fig.asp=1.2, fig.keep='last', fig.cap= "Distribution of Michaelis-Menten Parameters for Virtual Population (n=9000) stratified by CYP2D6 genotype. Km represent the Michaelis-Menten constant, and Vmax represents maximal 4-OH Atomoxetine formation (pmol/min/mg protein) by CYP2D6 in human liver microsomes."}
dist.plot <- ggplot(
data = population.sim(n=1000,`CV%_D` = 25, Start = 0.5,
By = 5, pop_freq = F) %>%
group_by(ID) %>%
filter(S == min(S)),
aes(x = Vmax))+
geom_histogram(aes(fill = Diplotype), color = "black", bins = 100)+
ggeasy::easy_remove_legend_title()+
theme_bw(base_size = 14)+
xlab(bquote(V[max]))+
ylab("Population (n)")
dist.grb <- dist.plot +
ggeasy::easy_remove_legend() +
scale_x_log10()+
xlab("Log Scale")+
ylab("Count (n)")
dist.plot2 <- ggplot(
data = population.sim(n=1000,`CV%_D` = 25, Start = 0.5,
By = 5, pop_freq = F) %>%
group_by(ID) %>%
filter(S == min(S)),
aes(x = Km))+
geom_histogram(aes(fill = Diplotype), color = "black", bins = 100)+
ggeasy::easy_remove_legend_title()+
theme_bw(base_size = 14)+
xlab(bquote(K[m](uM)))+
ylab("Population (n)")+
scale_x_log10()
dist.grb2 <- dist.plot +
ggeasy::easy_remove_legend() +
scale_x_log10()+
xlab("Log Scale")+
ylab("Count (n)")
## Vmax and Km Distribution Plots
ggpubr::ggarrange(dist.plot +
annotation_custom(ggplotGrob(dist.grb),
xmin = 1000, xmax = 2500,
ymin = 250, ymax = 1250),
dist.plot2, ncol = 1, common.legend = T, legend = "right")
```
------------------------------------------------------------------------
## Virtual Population Vmax and Km Distribution Table
```{r Vmax and Km Distribution Table}
population.sim(n = 1000, End = 0,`CV%_D` = 25) %>%
group_by(Diplotype) %>%
summarise(Vmax_mean = round(mean(Vmax),2),
Vmax_sd = round(sd(Vmax),2),
Km_mean = round(mean(Km),2),
Km_sd = round(sd(Km),2),
`n` = length(Vmax),
Vmax = paste0(Vmax_mean," ± ",Vmax_sd),
Km = paste0(Km_mean," ± ",Km_sd)) %>%
ungroup() %>%
left_join(diplotype.data %>%
mutate(across(where(is.numeric), round, 2)) %>%
select(Diplotype, Vmax, Km) %>%
rename("Actual (Vmax)" = "Vmax", "Actual (Km)" = "Km"),
by = "Diplotype") %>%
select(Diplotype,`Actual (Vmax)`, Vmax, `Actual (Km)`,Km, n) %>%
rename("Simulated." = "Vmax",
"Simulated" = "Km",
"Actual." = "Actual (Vmax)",
"Actual" = "Actual (Km)") %>%
kbl(table.attr = "style='width:60%;'",
caption = "Simulated Population Parameter Estimates") %>%
kable_classic("striped", full_width = T) %>%
add_header_above(c(" ", "Vmax Estimate" = 2, "Km Estimate" = 2, " "))
```
------------------------------------------------------------------------
## Incorporation of Experimental Error
Residual error was added to simulated data using a constant coefficient of variation structure, where the observed metabolic rate (*V~obs~*)for the *i*^th^individual at the *j*^th^ substrate incubation concentration. The residual errors (*ε~i~*) were normally distributed with a mean of 0 and a standard deviation (*σ*) set at the following values: 0, 0.05, 0.10, or 0.2; corresponding to a coefficient of variation (CV%) of 0%, 5%, 10%, and 20%.
------------------------------------------------------------------------
```{r fig.asp=0.9}
# Error Design Datatable -------
error_design.data <- rbind(population.sim(n=3, Start = 0, By = 0.1, `CV%_V` = 0) %>%
filter(Diplotype == "1/1") %>% mutate(Condition = "0% CV"),
population.sim(n=3, Start = 0, By = 0.1, `CV%_V` = 5) %>%
filter(Diplotype == "1/1") %>% mutate(Condition = "5% CV"),
population.sim(n=3, Start = 0, By = 0.1, `CV%_V` = 10) %>%
filter(Diplotype == "1/1") %>% mutate(Condition = "10% CV"),
population.sim(n=3, Start = 0, By = 0.1, `CV%_V` = 20) %>%
filter(Diplotype == "1/1") %>% mutate(Condition = "20% CV")) %>%
filter(S %in% c(0.1, 0.5, 1, 2, 5, 10, 15, 25, 40, 55, 70, 85, 100)) %>%
mutate(ID2 = paste("Subject",ID),
`Study Design` = "Rich Design (9 pts)")
# Assigning Condition as Ordered Factor -----------
error_design.data$Condition <- factor(error_design.data$Condition,
levels = c("0% CV","5% CV","10% CV","20% CV"))
# Simulation Grid ---------
error.nls <- nls(formula = V ~ (Vmax*S)/(Km + S), data = error_design.data,
start = list(Vmax = 350, Km = 2))
error.grid <- tibble(S = seq(0,100,0.1),
V = (coef(error.nls)[[1]]*S)/(coef(error.nls)[[2]]+S))
```
```{r eval=TRUE, fig.asp=1, fig.cap="Illustration of experimental error scenarios for 3 subjects with the same genotype. Black line represents the non-linear least-squares Michaelis-Menten fit for the genotype group."}
# Experimental Error Scenarios Plot -----------
ggplot(error_design.data %>% filter(S %in% c(0.1, 0.5, 1, 2.5, 5, 10, 25, 50, 100)),
aes(x = S, y = V))+
geom_line(data = error.grid, size = 1, alpha = 0.75)+
geom_point(aes(y = V_adj, group = ID2, color = ID2, shape = ID2), size = 2.5)+
facet_wrap(~Condition, ncol = 2, scales = "free")+
theme_bw(base_size = 14)+
xlab("[Substrate](uM)")+
ylab("Reaction Rate (V)\n")+
scale_color_viridis_d(option = "A", begin = 0.2, end = 0.7)+
ggeasy::easy_remove_legend_title()+
theme(legend.position = c(0.9,0.11), legend.box = "horizontal",
legend.background = element_rect(color = "grey"))+
labs(title = "Experimental Error Scenarios")
```
------------------------------------------------------------------------
# ***In-Silico*** **Experiments**
## Strategic Sampling Approach
A custom function, `update_data()`, was created to generate experimental data *in-silico* according to the specified experimental design and conditions. Two in-silico experimental designs (rich design, and sparse design) for two experimental conditions (UM/EM and IM/PM conditions) were incorporated into the function. Rich design experiments were conducted using 9 overlapping atomoxetine (ATX) incubation concentrations per subject, while sparse design experiments used 3-4 staggered incubation concentrations per subject , with both designs covering similar concentration ranges according to their experimental condition (UM/EM range: 0.10 - 100 uM, IM/PM range: 1-2000 uM). Additionally, each experimental design can subjected to variable degrees of experimental error using the `CV%` input. The inputs for the function the `update_data()` function include the following:
- **n_indiv** - number of subjects per diplotype group (default = 10).
- **CV%\_D** - Average standard deviation for each diplotype group as a percentage of the true estimate for Vmax and Km (between subject variability for each diplotype group) (default = 25).
- **CV%** - Average coefficient of variation across all points for simulated Michaelis-Menten kinetics for each individual (residual error).
- **start** - Starting concentration from Michaelis-Menten simulation (default = 0).
- **end** - Ending concentration for Michaelis-Menten kinetics (default = 100 uM).
- **by** - Simulated concentration increment (default = 0.5).
- **Pop_freq** - TRUE or FALSE argument indicating whether to use true population frequency (default is FALSE).
- **Seed** - Random number generator seed (for reproducibility, default = 23457).
- **type** - Experimental design to be simulated (options: rich sampling (9pt) = **"rich"**, sparse sampling (3pt) = **"sparse3pt"**, sparse sampling (4pt) = **"sparse4pt"**, rich sampling for poor metabolizers (16 pt) = **"PM"**, sparse sampling for poor metabolizer (3pt) = **"PM_3pt"**, sparse sampling for poor metabolizer (4pt) = **"PM_4pt"**.
------------------------------------------------------------------------
```{r Stategic Sampling Function}
update_data <-function(`CV%`, type, n_indiv = 10, `CV%.D` = 25, by = 0.1,
start = 0, end = 100, Seed = 23457, Pop.freq = FALSE){
# Sampling Information --------------
# Full Range Set
full_set <- c(0.1, 0.5, 1, 2.5, 5, 10, 25, 50, 100)
PM_range <- c(1, 5, 10, 15, 25, 30, 50, 60, 90, 100, 250, 500, 800, 1000, 1600, 2000)
# Strategic Sampling Sets ----
sparse3pt_set1 <- c(0.1, 2.5, 50)
sparse3pt_set2 <- c(1, 10, 100)
sparse4pt_set1 <- c(0.1, 2.5, 25, 50)
sparse4pt_set2 <- c(1, 10, 50, 100)
PM_3pt_set1 <- c(10,100,1000)
PM_3pt_set2 <- c(25,250,2000)
PM_4pt_set1 <- c(1,10,100,1000)
PM_4pt_set2 <- c(5,25,250,2000)
PM_range_set1 <- c(1,10,25,50,100,400,1000,2000)
PM_range_set2 <- c(5,15,30,60,90,200,800,1600)
# Rich Sampling Simulation ----------------
Rich <- population.sim(n = n_indiv, `CV%_D` = `CV%.D`, `CV%_V` = `CV%`, By = by,
Start = start, End = end, seed = Seed, pop_freq = Pop.freq) %>%
filter(S %in% full_set) %>%
mutate(Diplotype = as_factor(Diplotype),
V = round(V_adj, digits = 3)) %>%
select(ID, Diplotype, S, V)
# Sparse Sampling Simulation (3 point) ------------
Sparse3pt <- population.sim(n = n_indiv, `CV%_D` = `CV%.D`, `CV%_V` = `CV%`, By = by,
Start = start, End = end, seed = Seed, pop_freq = Pop.freq) %>%
filter(S %in% full_set) %>%
mutate(Set = if_else(as.numeric(ID) %% 2 == 0, "Set 2", "Set 1")) %>%
filter(if_else(Set == "Set 1", S %in% sparse3pt_set1, S %in% sparse3pt_set2)) %>%
mutate(Diplotype = as_factor(Diplotype),
V = round(V_adj, digits = 3)) %>%
select(ID, Diplotype, S, V)
# Sparse Sampling Simulation (4 point) --------------
Sparse4pt <- population.sim(n = n_indiv, `CV%_D` = `CV%.D`, `CV%_V` = `CV%`, By = by,
Start = start, End = end, seed = Seed, pop_freq = Pop.freq) %>%
filter(S %in% full_set) %>%
mutate(Set = if_else(as.numeric(ID) %% 2 == 0, "Set 2", "Set 1")) %>%
filter(if_else(Set == "Set 1", S %in% sparse4pt_set1, S %in% sparse4pt_set2)) %>%
mutate(Diplotype = as_factor(Diplotype),
V = round(V_adj, digits = 3)) %>%
select(ID, Diplotype, S, V)
PM <- population.sim(n = n_indiv, `CV%_D` = `CV%.D`, `CV%_V` = `CV%`, By = by,
Start = start, End = 2000, seed = Seed, pop_freq = Pop.freq) %>%
filter(S %in% c(PM_range)) %>%
mutate(Diplotype = as_factor(Diplotype),
V = round(V_adj, digits = 3)) %>%
select(ID, Diplotype, S, V)
PM_3pt <- population.sim(n = n_indiv, `CV%_D` = `CV%.D`, `CV%_V` = `CV%`, By = by,
Start = start, End = 2000, seed = Seed, pop_freq = Pop.freq) %>%
filter(S %in% c(PM_range)) %>%
mutate(Set = if_else(as.numeric(ID) %% 2 == 0, "Set 2", "Set 1")) %>%
filter(if_else(Set == "Set 1", S %in% PM_3pt_set1, S %in% PM_3pt_set2)) %>%
mutate(Diplotype = as_factor(Diplotype),
V = round(V_adj, digits = 3)) %>%
select(ID, Diplotype, S, V)
PM_4pt <- population.sim(n = n_indiv, `CV%_D` = `CV%.D`, `CV%_V` = `CV%`, By = by,
Start = start, End = 2000, seed = Seed, pop_freq = Pop.freq) %>%
filter(S %in% c(PM_range)) %>%
mutate(Set = if_else(as.numeric(ID) %% 2 == 0, "Set 2", "Set 1")) %>%
filter(if_else(Set == "Set 1", S %in% PM_4pt_set1, S %in% PM_4pt_set2)) %>%
mutate(Diplotype = as_factor(Diplotype),
V = round(V_adj, digits = 3)) %>%
select(ID, Diplotype, S, V)
# Output Selection ----------
switch(type,
"rich" = Rich,
"sparse3pt" = Sparse3pt,
"sparse4pt" = Sparse4pt,
"PM" = PM,
"PM_3pt" = PM_3pt,
"PM_4pt" = PM_4pt)
}
```
------------------------------------------------------------------------
## Representative Experimental Design Plots {.tabset .tabset-fade .tabset-pills}
Strategic sampling was accomplished by evenly dividing individuals falling under the same CYP2D6 genotype into two groups (Group 1 and Group 2). Each group was designated a pre-defined set of incubation concentrations to be used for the *in-silico* experiment with the total range of incubation concentrations dependent on the type of CYP2D6 metabolizer (as described in the *Strategic Sampling Approach* section above). Note: strategic sampling was not used for rich sample designs, meaning all subject were subjected to the same set of incubations concentrations.
**Extensive and Ultra-Rapid Metabolizers**
*Incubation Concentrations - Rich (9pt)* - Set: 0.1, 0.5, 1, 2.5, 5, 10, 25, 50, and 100 uM
*Incubation Concentrations - Sparse (3pt)* - Set 1: 0.1, 2.5, and 50 uM - Set 2: 1, 10, and 100 uM
*Incubation Concentrations - Sparse (4pt)* - Set 1: 0.1, 2.5, 25, and 50 uM - Set 2: 1, 10, 50, and 100 uM
**Intermediate and Poor Metabolizers**
*Incubation Concentrations - Rich (16pt)* - Set: 1, 5, 10, 15, 25, 30, 50, 60, 90, 100, 250, 500, 800, 1000, 1600, and 2000 uM
*Incubation Concentrations - Sparse (3pt)* - Set 1: 10,100, and 1000 uM - Set 2: 25, 250, and 2000 uM
*Incubation Concentrations - Sparse (4pt)* - Set 1: 1,10,100, and 1000 uM - Set 2: 5,25,250, and 2000 uM
------------------------------------------------------------------------
```{r Design Strategies Datasets}
# Generating Representative Data sets =========
## Representative data comes from 2 wild-type subjects.
rich_design.data <- update_data(`CV%` = 0, type = "rich") %>%
filter(Diplotype == "1/1", ID %in% c(1,2)) %>%
mutate(ID2 = paste("Subject",ID),
`Study Design` = "Rich Design (9 pts)")
sparse_3pt_design.data <- update_data(`CV%` = 0, type = "sparse3pt")%>%
filter(Diplotype == "1/1", ID %in% c(1,2)) %>%
mutate(ID2 = paste("Subject",ID),
`Study Design` = "Sparse Design (3 pts)")
sparse_4pt_design.data <- update_data(`CV%` = 0, type = "sparse4pt")%>%
filter(Diplotype == "1/1", ID %in% c(1,2)) %>%
mutate(ID2 = paste("Subject",ID),
`Study Design` = "Sparse Design (4 pts)")
PM_design.data <- update_data(`CV%` = 0, type = "PM") %>%
filter(Diplotype == "4/5", ID %in% c(81,82)) %>%
mutate(ID2 = paste("Subject",ID),
`Study Design` = "Rich Design (16 pts)")
PM3pt_design.data <- update_data(`CV%` = 0, type = "PM_3pt") %>%
filter(Diplotype == "4/5", ID %in% c(81,82)) %>%
mutate(ID2 = paste("Subject",ID),
`Study Design` = "Sparse Design (3 pts)")
PM4pt_design.data <- update_data(`CV%` = 0, type = "PM_4pt") %>%
filter(Diplotype == "4/5", ID %in% c(81,82)) %>%
mutate(ID2 = paste("Subject",ID),
`Study Design` = "Sparse Design (4 pts)")
# Solution Grid
design.nls <- nls(formula = V ~ (Vmax*S)/(Km + S), data = rich_design.data,
start = list(Vmax = 350, Km = 2))
grid <- tibble(S = seq(0,100,0.1),
V = (coef(design.nls)[[1]]*S)/(coef(design.nls)[[2]]+S))
design_PM.nls <- nls(formula = V ~ (Vmax*S)/(Km + S), data = PM_design.data,
start = list(Vmax = 20, Km = 50))
grid_pm <- tibble(S = seq(0,2000,0.1),
V = (coef(design_PM.nls)[[1]]*S)/(coef(design_PM.nls)[[2]]+S))
```
```{r Design Plots, fig.asp=1}
# UM/EM STRATEGIC SAMPLING DESIGN FIGURE ================
## Representative plots contain data for 2 wild-type subjects.
# Rich Design--------
D1<- ggplot(rich_design.data, aes(x = S, y = V))+
geom_line(data = grid, size = 1.5, alpha = 0.75)+
geom_point(aes(color=ID2, shape = ID2), size = 3.5)+
theme_bw(base_size = 14)+
ggeasy::easy_remove_legend_title()+
theme(legend.position = c(0.7,0.2))+
facet_wrap(~`Study Design`, ncol = 1)+
labs(title = "Conventional")+
xlab("[Substrate](uM)")+
ylab("Reaction Rate (V)\n")+
scale_color_viridis_d(option = "A", begin = 0.2, end = 0.6)
# Sparse Design (3pt)----------
D2<- ggplot(sparse_3pt_design.data, aes(x = S, y = V))+
geom_line(data = grid, size = 1.5, alpha = 0.75)+
geom_point(aes(color=ID2, shape = ID2), size = 3.5)+
theme_bw(base_size = 14)+
ggeasy::easy_remove_legend_title()+
theme(legend.position = c(0.7,0.2))+
facet_wrap(~`Study Design`, ncol = 1)+
labs(title = "Strategic Scenario (2)")+
xlab("[Substrate](uM)")+
ylab("Reaction Rate (V)\n")+
scale_color_viridis_d(option = "A", begin = 0.2, end = 0.6)
# Sparse Design (4pt)------------
D3 <- ggplot(sparse_4pt_design.data, aes(x = S, y = V))+
geom_line(data = grid, size = 1.5, alpha = 0.75)+
geom_point(aes(color=ID2, shape = ID2), size = 3.5)+
theme_bw(base_size = 14)+
ggeasy::easy_remove_legend_title()+
theme(legend.position = c(0.7,0.2))+
facet_wrap(~`Study Design`, ncol = 1)+
labs(title = "Strategic Scenario (1)")+
xlab("[Substrate](uM)")+
ylab("Reaction Rate (V)\n")+
scale_color_viridis_d(option = "A", begin = 0.2, end = 0.6)
# IM/PM STRATEGIC SAMPLING DESIGN FIGURE ================
## Representative plots contain data for 2 wild-type subjects.
# PM Sparse Design (4pt)---------
D4 <- ggplot(PM4pt_design.data, aes(x = S, y = V))+
geom_line(data = grid_pm, size = 1.5, alpha = 0.75)+
geom_point(aes(color=ID2, shape = ID2), size = 3.5)+
theme_bw(base_size = 14)+
ggeasy::easy_remove_legend_title()+
theme(legend.position = c(0.7,0.2))+
facet_wrap(~`Study Design`, ncol = 1)+
labs(title = "")+
xlab("[Substrate](uM)")+
ylab("Reaction Rate (V)\n")+
scale_color_viridis_d(option = "A", begin = 0.2, end = 0.6)
# Extensize metabolizer model---------
D5 <- D3 + labs(title = "") #4pt
D6 <- D2 + labs(title = "") #3pt
D7 <- D1 + labs(title = "Extensive Metabolizer") #9pt
# PM Sparse Design (3pt)---------
D8 <- ggplot(PM3pt_design.data, aes(x = S, y = V))+
geom_line(data = grid_pm, size = 1.5, alpha = 0.75)+
geom_point(aes(color=ID2, shape = ID2), size = 3.5)+
theme_bw(base_size = 14)+
ggeasy::easy_remove_legend_title()+
theme(legend.position = c(0.7,0.2))+
facet_wrap(~`Study Design`, ncol = 1)+
labs(title = "")+
xlab("[Substrate](uM)")+
ylab("Reaction Rate (V)\n")+
scale_color_viridis_d(option = "A", begin = 0.2, end = 0.6)
# PM Rich Design (16pt)---------
D9 <- ggplot(PM_design.data, aes(x = S, y = V))+
geom_line(data = grid_pm, size = 1.5, alpha = 0.75)+
geom_point(aes(color=ID2, shape = ID2), size = 3.5)+
theme_bw(base_size = 14)+
ggeasy::easy_remove_legend_title()+
theme(legend.position = c(0.7,0.2))+
facet_wrap(~`Study Design`, ncol = 1)+
labs(title = "Poor Metabolizers")+
xlab("[Substrate](uM)")+
ylab("Reaction Rate (V)\n")+
scale_color_viridis_d(option = "A", begin = 0.2, end = 0.6)
```
### **UM/EM Design**
```{r fig.asp=1}
## Extensive Metabolizers
ggpubr::ggarrange(D7,D5,D6,ncol = 2, nrow = 2, labels = "AUTO")
```
### **IM/PM Design**
```{r fig.asp=1}
## Poor Metabolizers
ggpubr::ggarrange(D9,D4,D8, ncol = 2, nrow = 2, labels = "AUTO")
```
------------------------------------------------------------------------
# **Population Modeling (UM/EM)**
## Generation of Experimental Data (Base Model - 0% CV)
```{r Base Model Experimental Data}
# Population Datasets (CV = 0%)
rich.data <- update_data(`CV%` = 0, type = "rich") %>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse3pt.data <- update_data(`CV%` = 0, type = "sparse3pt") %>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse4pt.data <- update_data(`CV%` = 0, type = "sparse4pt") %>%
filter(!Diplotype %in% c("4/41", "4/5"))
```
------------------------------------------------------------------------
## Individual-Fits of Experimental Data (Base Model - 0% CV)
A grouped data frame was created for each experiment where reaction rate (V) is predicted by substrate concentration (S) according to subject (ID). Individual fits (un-weighted) and parameter estimates for the data sets were obtained using non-linear least squares function `nlsList()`. Values obtained from the `nlsList()` were used as initial estimates for the non-linear mixed effect model.
------------------------------------------------------------------------
```{r Base Model NLS Fit}
# Grouped Data frame -------------
rich_data.grp <- groupedData(V~S|ID, rich.data)
sparse3pt.grp <- groupedData(V~S|ID, sparse3pt.data)
sparse4pt.grp <- groupedData(V~S|ID, sparse4pt.data)
# Fit Model ((Non-Linear Least Squares) ------------
rich_fit.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = rich_data.grp)
sparse3pt_fit.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse3pt.grp)
sparse4pt_fit.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse4pt.grp)
```
------------------------------------------------------------------------
## Non-Linear Mixed Effect Modeling (Base Model - 0% CV)
Non-linear mixed effect modeling was conducted using the `nlme()` package version 3.1 (Bates et al., 2000). The `nlsList()` fits were used as initial estimates for the NLME model. Individual level random effects were applied to both Vmax and Km. A diagonal variance-covariance structure was assigned to each model using the `pdDiag()` function.
------------------------------------------------------------------------
```{r Base Model NLME Fit}
# Fit Model ((Non-Linear Mixed-Effect) ------------
rich.nlme <- nlme(rich_fit.nls, random = pdDiag(Vmax + Km ~ 1))
sparse3pt.nlme <- nlme(sparse3pt_fit.nls, random = pdDiag(Vmax + Km ~ 1))
sparse4pt.nlme <- nlme(sparse4pt_fit.nls, random = pdDiag(Vmax + Km ~ 1))
# Model Fixed Effect comparisons
fixef.table <- rbind(fixef(rich.nlme),
fixef(sparse3pt.nlme),
fixef(sparse4pt.nlme)) %>%
as_tibble() %>%
mutate(Model = c("Rich","Sparse (3pt)","Sparse (4pt)")) %>%
relocate(Model)
fixef.table %>%
mutate(across(where(is.numeric), round, 2)) %>%
kbl( table.attr = "style='width:60%;'",
caption = "Base Model: Mixed Effect Michaelis-Menten") %>%
kable_classic("striped")
```
------------------------------------------------------------------------
## Non-Linear Mixed Effect Modeling (Covariate Model - 0% CV)
*CYP2D6* genotype was incorporated as a categorical covariate in the model by adding it as a fixed effect that impacts both Vmax and Km. The extracted population level fixed effects for Vmax and Km from the base model (described in the previous section) were used as initial estimates for the covariate model.
------------------------------------------------------------------------
```{r Inclusion of Genotype as Covariate}
#Models with genotype as a Covariate -----
rich.fxf <- fixef.table[1,2:3]
sparse3pt.fxf <- fixef.table[2,2:3]
sparse4pt.fxf <- fixef.table[3,2:3]
rich_covar.nlme <- update(rich.nlme, fixed = Vmax + Km ~ Diplotype,
start = c(rich.fxf[[1]], rep(0,6),
rich.fxf[[2]], rep(0,6)))
sparse3pt_covar.nlme <- update(sparse3pt.nlme, fixed = Vmax + Km ~ Diplotype,
start = c(sparse3pt.fxf[[1]], rep(0,6),
sparse3pt.fxf[[2]], rep(0,6)))
sparse4pt_covar.nlme <- update(sparse4pt.nlme, fixed = Vmax + Km ~ Diplotype,
start = c(sparse4pt.fxf[[1]], rep(0,6),
sparse4pt.fxf[[2]], rep(0,6)))
```
------------------------------------------------------------------------
## Base Model and Covariate Model Evaluation (0% CV)
The impact of adding CYP2D6 genotype as a (covariate on both Vmax and Km) and the whether adding covariates to the model improved fit compared to baseline was assessed using analysis of variance `anova()`.
### Overall Impact of adding covariates to base model
```{r Base vs Covariate Model ANOVA, eval=FALSE}
anova(rich.nlme, rich_covar.nlme)
anova(sparse3pt.nlme, sparse3pt_covar.nlme)
anova(sparse4pt.nlme, sparse4pt_covar.nlme)
```
------------------------------------------------------------------------
### Impact of adding covariate to Vmax and Km
```{r Covariate Model ANOVA, warning = F, eval=FALSE}
anova(rich_covar.nlme) %>%
kbl(caption = "Rich Model (w/Covariates)",
table.attr = "style='width:60%;'") %>%
kable_classic(full_width = T, "striped")
anova(sparse3pt_covar.nlme)%>%
kbl(caption = "Sparse 3pt Model (w/Covariates)",
table.attr = "style='width:60%;'") %>%
kable_classic(full_width = T, "striped")
anova(sparse4pt_covar.nlme)%>%
kbl(caption = "Sparse 4pt Model (w/Covariates)",
table.attr = "style='width:60%;'") %>%
kable_classic(full_width = T, "striped")
```
------------------------------------------------------------------------
## Summary Tables of Fixed Effects Estimates (Covariate Model - 0% CV) {.tabset .tabset-fade .tabset-pills}
### **Table of Covariate Model Estimates**
```{r}
# Covariate Analysis Summary Table ------------
covaref.table <- rbind(fixef(rich_covar.nlme),
fixef(sparse3pt_covar.nlme),
fixef(sparse4pt_covar.nlme)) %>%
as_tibble() %>%
mutate(`Covariate Model` = c("Rich","Sparse (3pt)","Sparse (4pt)")) %>%
pivot_longer(`Vmax.(Intercept)`:`Km.Diplotype2/4`,
names_to = "Parameter",
values_to = "Value") %>%
pivot_wider(names_from = `Covariate Model`, values_from = Value) %>%
separate(Parameter, sep = "\\.", into = c("Parameter","Diplotype"), remove = T) %>%
mutate(Diplotype = recode(Diplotype, "(Intercept)" = "Reference (1/1)"),
across(where(is.numeric), round, 2))
```
------------------------------------------------------------------------
### **Reference Group (\*1/\*1) Parameter Estimates**
```{r}
# Reference Estimates -----------
covaref.table %>%
filter(Diplotype == "Reference (1/1)")%>%
kbl(caption = "Reference Population Estimates",
table.attr = "style='width:60%;'") %>%
kable_classic(full_width = T, "striped")
```
------------------------------------------------------------------------
### **Variant Group ETAs Table**
```{r}
# CYP2D6 Genotype Effects --------
covaref.table%>%
kbl(caption = "Michaelis Menten Mixed-Effect Model (w/Covariates)",
table.attr = "style='width:60%;'") %>%
kable_classic(full_width = T, "striped") %>%
pack_rows("Vmax Estimate (Population)", 1,1) %>%
pack_rows("Covariate (Vmax Eta)", 2, 7)%>%
pack_rows("Km Estimate (Population)", 8,8) %>%
pack_rows("Covariate (Km Eta)", 9, 14)
```
### **Covariate Model 95% Confidence Interval Table (0% CV)**
```{r }
# Function to Extract Confidence Interval Info ----------
extract_CI <- function(int.data, name){
temp <- int.data$fixed %>%
as_tibble() %>%
mutate(across(where(is.numeric), round, 2),
`CI (95%)` = paste0("(",lower,", ",upper,")")) %>%
select(est., `CI (95%)`)
colnames(temp) <- c(paste(name, " Estimate"), paste(name, " CI (95%)"))
temp
}
# Confidence Interval by Sampling Scenario -------
rich_covar.intervals <- intervals(rich_covar.nlme, which = "fixed")
sparse3pt_covar.intervals <- intervals(sparse3pt_covar.nlme, which = "fixed")
sparse4pt_covar.intervals <- intervals(sparse4pt_covar.nlme, which = "fixed")
# Summary Table of Confidence Intervals by Diplotype and Scenario -----------
covar_ci.table <- cbind(extract_CI(rich_covar.intervals, name = "Rich"),
extract_CI(sparse3pt_covar.intervals, name = "Sparse 3pt"),
extract_CI(sparse4pt_covar.intervals, name = "Sparse 4pt")) %>%
mutate(Parameter = rownames(rich_covar.intervals$fixed)) %>%
relocate(Parameter) %>%
separate(Parameter, remove = T, sep = "\\.", into = c("Parameter", "Diplotype"))%>%
mutate(Diplotype = recode(Diplotype, "(Intercept)" = "Reference (1/1)"))
colnames(covar_ci.table)<- c("Parameter", "Diplotype",
"Estimate","CI (95%)",
"Estimate", "CI (95%)",
"Estimate", "CI (95%)")
covar_ci.table%>%
kbl(caption = "Michaelis Menten Mixed-Effect Model (w/Covariates)") %>%
kable_classic(full_width = T, "striped")%>%
pack_rows("Vmax Estimate (Population)", 1,1) %>%
pack_rows("Covariate (Vmax Eta)", 2, 7)%>%
pack_rows("Km Estimate (Population)", 8,8) %>%
pack_rows("Covariate (Km Eta)", 9, 14) %>%
add_header_above(c(" ", " ",
"Rich (9pt)" = 2,
"Sparse (3pt)" = 2,
"Sparse (4pt)" = 2))
```
------------------------------------------------------------------------
# **Impact of Residual Error**
Data sets which include increasing degrees of residual error (5, 10, and 20% CV) were generated using the `update_data()` function described earlier (see *In-Silico Experiments* section for full description). Additonally, the same methodology for model analysis used in the the previous section (*Population Michaelis-Menten Modeling (UM/EM)*) was applied here to evaluate the impact of increasing experimental error on parameter estimates.
## Generation of Experimental Data (Base Model - 5-20% CV)
```{r}
# Population Data sets (CV = 5%) ----------------
rich_CV5.data <- update_data(`CV%` = 5, type = "rich")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse3pt_CV5.data <- update_data(`CV%` = 5, type = "sparse3pt")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse4pt_CV5.data <- update_data(`CV%` = 5, type = "sparse4pt")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
# Population Data sets (CV = 10%) ----------------
rich_CV10.data <- update_data(`CV%` = 10, type = "rich")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse3pt_CV10.data <- update_data(`CV%` = 10, type = "sparse3pt")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse4pt_CV10.data <- update_data(`CV%` = 10, type = "sparse4pt")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
# Population Data sets (CV = 20%) ----------------
rich_CV20.data <- update_data(`CV%` = 20, type = "rich")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse3pt_CV20.data <- update_data(`CV%` = 20, type = "sparse3pt")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
sparse4pt_CV20.data <- update_data(`CV%` = 20, type = "sparse4pt")%>%
filter(!Diplotype %in% c("4/41", "4/5"))
```
------------------------------------------------------------------------
## Inidividual-Fits of Experimental Data (Base Model - 5-20% CV)
```{r}
# Grouped Data frame =============================
rich_CV5_data.grp <- groupedData(V~S|ID, rich_CV5.data)
sparse3pt_CV5.grp <- groupedData(V~S|ID, sparse3pt_CV5.data)
sparse4pt_CV5.grp <- groupedData(V~S|ID, sparse4pt_CV5.data)
rich_CV10_data.grp <- groupedData(V~S|ID, rich_CV10.data)
sparse3pt_CV10.grp <- groupedData(V~S|ID, sparse3pt_CV10.data)
sparse4pt_CV10.grp <- groupedData(V~S|ID, sparse4pt_CV10.data)
rich_CV20_data.grp <- groupedData(V~S|ID, rich_CV20.data)
sparse3pt_CV20.grp <- groupedData(V~S|ID, sparse3pt_CV20.data)
sparse4pt_CV20.grp <- groupedData(V~S|ID, sparse4pt_CV20.data)
# Fit Model ((Non-Linear Least Squares) =====================
rich_CV5.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = rich_CV5_data.grp)
sparse3pt_CV5.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse3pt_CV5.grp)
sparse4pt_CV5.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse4pt_CV5.grp)
rich_CV10.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = rich_CV10_data.grp)
sparse3pt_CV10.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse3pt_CV10.grp)
sparse4pt_CV10.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse4pt_CV10.grp)
rich_CV20.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = rich_CV20_data.grp)
sparse3pt_CV20.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse3pt_CV20.grp)
sparse4pt_CV20.nls <- nlsList(V~SSmicmen(S,Vmax,Km), data = sparse4pt_CV20.grp)