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rm(list=ls()) # clear memory
# =========== Load R libraries (install them before loading) ====================
library(rstan)
library(tidyverse)
library(bayesplot)
library(deSolve)
library(readxl)
# ===================================Fitting all for Muc_func==========================================
WT_viral_load_data <- read_excel("Muc1/PR8-viral-load.xls", sheet = 1) %>% rename(Days = Days, ViralLoad = `Viral load`)
KO_viral_load_data <- read_excel("Muc1/PR8-viral-load.xls", sheet = 2) %>% rename(Days = Days, ViralLoad = `Viral load`)
WT_TNF_data <- read_excel("Muc1/TNF.xls", sheet = 1) %>% rename(Days = Days, TNFlevel = `TNF level`)
KO_TNF_data <- read_excel("Muc1/TNF.xls", sheet = 2) %>% rename(Days = Days, TNFlevel = `TNF level`)
WT_macrophage_data <- read_excel("Muc1/Macrophage.xls", sheet = 1) %>% rename(Days = Days, Macrophage = 'Macro level')
KO_macrophage_data <- read_excel("Muc1/Macrophage.xls", sheet = 2) %>% rename(Days = Days, Macrophage = 'Macro level')
time_data <- c(1,2,3,5,7)
V_data_WT <- WT_viral_load_data$ViralLoad
V_data_KO <- KO_viral_load_data$ViralLoad
TNF_data_WT <- WT_TNF_data$TNFlevel
TNF_data_KO <- KO_TNF_data$TNFlevel
time_data_macrophage <- c(1,3,5,7)
Macrophage_data_WT <- WT_macrophage_data$Macrophage
Macrophage_data_KO <- KO_macrophage_data$Macrophage
data_combined_muc1 <- list(N_T_WT = length(time_data),
N_V_WT = length(V_data_WT),
time_data_WT = time_data,
log_viral_load_data_WT = log(V_data_WT), # above V_WT
N_T_KO = length(time_data),
N_V_KO = length(V_data_KO),
time_data_KO = time_data,
log_viral_load_data_KO = log(V_data_KO), # above V_KO
N_T_TNF_WT = length(time_data),
N_TNF_WT = length(TNF_data_WT),
time_data_TNF_WT = time_data,
TNF_data_WT = TNF_data_WT, # above TNF_WT
N_T_TNF_KO = length(time_data),
N_TNF_KO = length(TNF_data_KO),
time_data_TNF_KO = time_data,
TNF_data_KO = TNF_data_KO, # above TNF_WT
N_T_Macrophage_WT = length(time_data_macrophage),
N_Macrophage_WT = length(Macrophage_data_WT),
time_data_Macrophage_WT = time_data_macrophage,
Macrophage_data_WT = log(Macrophage_data_WT), # above Macrophage_WT
N_T_Macrophage_KO = length(time_data_macrophage),
N_Macrophage_KO = length(Macrophage_data_KO),
time_data_Macrophage_KO = time_data_macrophage,
Macrophage_data_KO = log(Macrophage_data_KO), # above Macrophage_WT
t0 = 0,
T0 = 4e+8,
I0 = 0,
F0 = 0,
MR0 = 1e+6,
MA0 = 0)
init1 <- list(
theta = c(0.5, 0.5, 3.4e-5, 3.4, 7.9e-3, 2, 1e-5, 0.5, 0.5, 1e-5, 0.5,1e-2,1e-6,1e-6,1,3.5e-1),
sigma = c(0.5,0.5,0.5))
init2 <- list(
theta = c(0.8, 1, 1e-4, 5, 2.2e-3, 2, 1e-5, 0.8, 1, 1e-4, 0.5, 5e-2, 1e-4,1e-6, 1, 1.5e-1),
sigma = c(0.5,0.5,0.5))
options(mc.cores=parallel::detectCores()) # to utilise all cores available in your computer
Estimate_Full <- stan("Muc1/Muc1.stan",
data = data_combined_muc1,
pars = c("theta","theta_hat","sigma"),
seed = 90127, # set random seed for reproducibility
iter = 2000,
chains = 2,
init = list(init1,init2),
warmup = 1000,
control = list(adapt_delta = 0.99, max_treedepth = 15))
print(Estimate_Full, pars = c("theta","theta_hat","sigma"))
stan_dens(Estimate_Full, pars = c("theta","sigma"), separate_chains = TRUE)
# extract posterior samples for selected parameters
posterior_samples_all = rstan::extract(Estimate_Full_9_Sep, pars = c("theta"), inc_warmup = TRUE, permuted = FALSE)
posterior_samples_merged_after_burnin = rstan::extract(Estimate_Full_9_Sep, pars = c("theta"))
# show markov chains
color_scheme_set("brewer-Spectral")
mcmc_trace(posterior_samples_all, n_warmup = 200,
facet_args = list(nrow = 3, labeller = label_parsed))
# show all marginal posterior distributions
posterior_sample_table = data.frame(epsilon1 = posterior_samples_merged_after_burnin$theta[,1],
k1 = posterior_samples_merged_after_burnin$theta[,2],
beta = posterior_samples_merged_after_burnin$theta[,3],
delta_I = posterior_samples_merged_after_burnin$theta[,4],
p = posterior_samples_merged_after_burnin$theta[,5],
c = posterior_samples_merged_after_burnin$theta[,6],
epsilon2 = posterior_samples_merged_after_burnin$theta[,7],
k2 = posterior_samples_merged_after_burnin$theta[,8],
q_F = posterior_samples_merged_after_burnin$theta[,9],
delta_F = posterior_samples_merged_after_burnin$theta[,10],
V0 = posterior_samples_merged_after_burnin$theta[,11])
ggplot(posterior_sample_table, aes(x=epsilon1)) + geom_histogram(breaks=seq(0,1,1/30))+theme_bw()
ggplot(posterior_sample_table, aes(x=k1)) + geom_histogram(breaks=seq(0,2,1/30))+theme_bw()
ggplot(posterior_sample_table, aes(x=beta)) + geom_histogram(breaks=seq(0,0.03,0.03/30))+theme_bw()
ggplot(posterior_sample_table, aes(x=delta_I)) + geom_histogram(breaks=seq(0,2,2/30))+theme_bw()
ggplot(posterior_sample_table, aes(x=q_F)) + geom_histogram(breaks=seq(0,1e-6,1e-6/30))+theme_bw()
ggplot(posterior_sample_table, aes(x=delta_F)) + geom_histogram(breaks=seq(0,1,1/30))+theme_bw()
# show parameter correlations
pairs(posterior_samples_merged_after_burnin)
# posterior predictive check
Within_host_model_WT = function(t, y, param){
dydt1 = -(1 - param[1] * t^10/ (t^10 + param[2]^10)) * param[3] * y[1] * y[3]
dydt2 = (1 - param[1] * t^10/ (t^10 + param[2]^10)) * param[3] * y[1] * y[3] - param[4] * y[2]
dydt3 = param[5] * y[2] - param[6] * y[3]
dydt4 = (1 - param[7] * t^10/(t^10 + param[8]^10)) * param[9] * y[2] - param[10] * y[4]
list(c(dydt1, dydt2, dydt3, dydt4))
}
Within_host_model_KO = function(t, y, param){
dydt1 = -(1 - 0 * t^10/ (t^10 + param[2]^10)) * param[3] * y[1] * y[3]
dydt2 = (1 - 0 * t^10/ (t^10 + param[2]^10)) * param[3] * y[1] * y[3] - param[4] * y[2]
dydt3 = param[5] * y[2] - param[6] * y[3]
dydt4 = (1 - 0 * t^10/(t^10 + param[8]^10)) * param[9] * y[2] - param[10] * y[4]
list(c(dydt1, dydt2, dydt3, dydt4))
}
t_ppc = seq(0, 10, 0.1)
V_ppc_WT = matrix(, nrow = 1000, ncol = length(t_ppc))
F_ppc_WT = matrix(, nrow = 1000, ncol = length(t_ppc))
V_ppc_KO = matrix(, nrow = 1000, ncol = length(t_ppc))
F_ppc_KO = matrix(, nrow = 1000, ncol = length(t_ppc))
lower_95PI_WT = t_ppc
median_95PI_WT = t_ppc
upper_95PI_WT = t_ppc
lower_95PI_KO = t_ppc
median_95PI_KO = t_ppc
upper_95PI_KO = t_ppc
lower_95PI_WT_F = t_ppc
median_95PI_WT_F = t_ppc
upper_95PI_WT_F = t_ppc
lower_95PI_KO_F = t_ppc
median_95PI_KO_F = t_ppc
upper_95PI_KO_F = t_ppc
for (i in 1:1000){
y_init = c(data_combined_muc1_WT$T0, data_combined_muc1_WT$I0, posterior_sample_table$V0[i], data_combined_muc1_WT$F0)
param_fit = c(posterior_sample_table$epsilon1[i],
posterior_sample_table$k1[i],
posterior_sample_table$beta[i],
posterior_sample_table$delta_I[i],
posterior_sample_table$p[i],
posterior_sample_table$c[i],
posterior_sample_table$epsilon2[i],
posterior_sample_table$k2[i],
posterior_sample_table$q_F[i],
posterior_sample_table$delta_F[i])
param_fit_hat = c(posterior_sample_table$epsilon1[i]*0,
posterior_sample_table$k1[i],
posterior_sample_table$beta[i],
posterior_sample_table$delta_I[i],
posterior_sample_table$p[i],
posterior_sample_table$c[i],
posterior_sample_table$epsilon2[i]*0,
posterior_sample_table$k2[i],
posterior_sample_table$q_F[i],
posterior_sample_table$delta_F[i])
model_output_WT = ode(times = t_ppc, y = y_init, func = Within_host_model_WT, parms = param_fit, method = "bdf")
model_output_KO = ode(times = t_ppc, y = y_init, func = Within_host_model_WT, parms = param_fit_hat, method = "bdf")
V_ppc_WT[i,] = model_output_WT[,4]
F_ppc_WT[i,] = model_output_WT[,5]
V_ppc_KO[i,] = model_output_KO[,4]
F_ppc_KO[i,] = model_output_KO[,5]
}
for (i in 1:length(t_ppc)){
temp_WT = unname(quantile(V_ppc_WT[,i], probs = c(0.025, 0.5, 0.975)))
temp_KO = unname(quantile(V_ppc_KO[,i], probs = c(0.025, 0.5, 0.975)))
temp_WT_F = unname(quantile(F_ppc_WT[,i], probs = c(0.025, 0.5, 0.975)))
temp_KO_F = unname(quantile(F_ppc_KO[,i], probs = c(0.025, 0.5, 0.975)))
lower_95PI_WT[i] = temp_WT[1]
median_95PI_WT[i] = temp_WT[2]
upper_95PI_WT[i] = temp_WT[3]
lower_95PI_KO[i] = temp_KO[1]
median_95PI_KO[i] = temp_KO[2]
upper_95PI_KO[i] = temp_KO[3]
lower_95PI_WT_F[i] = temp_WT_F[1]
median_95PI_WT_F[i] = temp_WT_F[2]
upper_95PI_WT_F[i] = temp_WT_F[3]
lower_95PI_KO_F[i] = temp_KO_F[1]
median_95PI_KO_F[i] = temp_KO_F[2]
upper_95PI_KO_F[i] = temp_KO_F[3]
}
data_plot = data.frame(time = rep(c(1,2,3,5,7), each = 5),
V_WT = log10(exp(data_combined_muc1_WT$log_viral_load_data_WT)),
V_KO = log10(exp(data_combined_muc1_WT$log_viral_load_data_KO)))
fit_plot = data.frame(time = t_ppc,
lower_95PI_WT = lower_95PI_WT,
V_WT = median_95PI_WT,
upper_95PI_WT = upper_95PI_WT,
lower_95PI_KO = lower_95PI_KO,
V_KO = median_95PI_KO,
upper_95PI_KO = upper_95PI_KO)
ggplot(fit_plot, aes(time))+
geom_point(data = data_plot, aes(time, V_WT), size = 3) +
geom_line(data = fit_plot, aes(time, log10(V_WT))) +
geom_ribbon(aes(ymin = log10(lower_95PI_WT), ymax = log10(upper_95PI_WT)), alpha = 0.5, na.rm = TRUE) +
theme_bw() # V_WT
ggplot(fit_plot, aes(time))+
geom_point(data = data_plot, aes(time, V_KO), size = 3) +
geom_line(data = fit_plot, aes(time, log10(V_KO))) +
geom_ribbon(aes(ymin = log10(lower_95PI_KO), ymax = log10(upper_95PI_KO)), alpha = 0.5, na.rm = TRUE) +
theme_bw() # V_KO
data_plot_F_WT = data.frame(time = rep(c(1,2,3,5,7), c(2,4,5,4,4)),
F_WT = data_combined_muc1_WT$TNF_data_WT)
data_plot_F_KO = data.frame(time = rep(c(1,2,3,5,7), c(2,3,6,4,5)),
F_KO = data_combined_muc1_WT$TNF_data_KO)
fit_plot_F = data.frame(time = t_ppc,
lower_95PI_WT_F = lower_95PI_WT_F,
F_WT = median_95PI_WT_F,
upper_95PI_WT_F = upper_95PI_WT_F,
lower_95PI_KO_F = lower_95PI_KO_F,
F_KO = median_95PI_KO_F,
upper_95PI_KO_F = upper_95PI_KO_F)
ggplot(fit_plot_F, aes(time))+
geom_point(data = data_plot_F_WT, aes(time, F_WT), size = 3) +
geom_line(data = fit_plot_F, aes(time, F_WT)) +
geom_ribbon(aes(ymin = lower_95PI_WT_F, ymax = upper_95PI_WT_F), alpha = 0.5, na.rm = TRUE) +
theme_bw() # F_WT
ggplot(fit_plot_F, aes(time))+
geom_point(data = data_plot_F_KO, aes(time, F_KO), size = 3)+
geom_line(data = fit_plot_F, aes(time, F_KO))+
geom_ribbon(aes(ymin = lower_95PI_KO_F, ymax = upper_95PI_KO_F), alpha = 0.5, na.rm = TRUE) +
theme_bw() # F_KO
# =============== Save the fitting results and generate outputs in CSV file ===================
write.csv(posterior_samples_merged_after_burnin, file="Muc1_fit_results2.csv")
save.image(file = "fitting_results_Mu1")
#================ only fit viral load data to the model ===================
data_combined_muc1_WT_V <- list(N_T_WT = length(time_data),
N_V_WT = length(V_data_WT),
time_data_WT = time_data,
log_viral_load_data_WT = log(V_data_WT), # above V_WT
N_T_KO = length(time_data),
N_V_KO = length(V_data_KO),
time_data_KO = time_data,
log_viral_load_data_KO = log(V_data_KO), # above V_KO
t0 = 0,
T0 = 4e+8,
I0 = 0)
#plot_df <- data.frame(time = as.factor(rep(c(1,2,3,5,7,1,2,3,5,7),each = 5)), Viral_load = c( log10(V_data_WT) ,log10(V_data_KO)), type = rep(as.factor(c("WT", "KO")), each = 25))
#ggplot(plot_df, aes(x = time, y = Viral_load, fill = type)) + geom_boxplot()
init1 <- list(
theta = c(0.5, 1, 6e-5, 2.1, 2.2e-3, 3, 0.33),
sigma = 0.5)
init2 <- list(
theta = c(0.1, 2, 1.4e-5, 3, 2.2e-3, 3, 0.33),
sigma = 0.5)
#init2 <- list(
# theta = c(runif(1,0.1,0.9), runif(1,0.1,2), runif(1,3.8e-6,1.6e-4), runif(1,2.1,11.2), runif(1,3.2e-3,7.1e-2), runif(1,2.1,4.2),
# runif(1,1.4e-3,9.1e-1)),
# sigma = 0.5)
Estimate_V <- stan("Muc1_Virus.stan",
data = data_combined_muc1_WT_V,
pars = c("theta","theta_hat","sigma"),
seed = 90127, # set random seed for reproducibility
iter = 2000,
chains = 1,
init = list(init1),
warmup = 1000,
control = list(adapt_delta = 0.99, max_treedepth = 20))
print(Estimate_V, pars = c("theta","theta_hat","sigma"))
stan_dens(Estimate_V, pars = c("theta","sigma"), separate_chains = TRUE) # +
# xlab("theta[1:7] = c(epsilon1,k1,theta,delta_I, p, delta_V)")
# extract posterior samples for selected parameters
posterior_samples_all = rstan::extract(Estimate_V, pars = c("theta","sigma"), inc_warmup = TRUE, permuted = FALSE)
posterior_samples_merged_after_burnin = rstan::extract(Estimate_V, pars = c("theta","sigma"))
# show markov chains
color_scheme_set("brewer-Spectral")
mcmc_trace(posterior_samples_all, n_warmup =1000,
facet_args = list(nrow = 3, labeller = label_parsed))
# show all marginal posterior distributions
posterior_sample_table = data.frame(epsilon1 = posterior_samples_merged_after_burnin$theta[,1],
k1 = posterior_samples_merged_after_burnin$theta[,2],
beta = posterior_samples_merged_after_burnin$theta[,3],
delta_I = posterior_samples_merged_after_burnin$theta[,4],
p = posterior_samples_merged_after_burnin$theta[,5],
c = posterior_samples_merged_after_burnin$theta[,6],
V0 = posterior_samples_merged_after_burnin$theta[,7])
ggplot(posterior_sample_table, aes(x=epsilon1)) + geom_histogram(breaks=seq(0,1,1/30))+theme_bw()
ggplot(posterior_sample_table, aes(x=k1)) + geom_histogram(breaks=seq(0,2,1/30))+theme_bw()
ggplot(posterior_sample_table, aes(x=beta)) + geom_histogram(breaks=seq(0,1e-4,1e-5/30))+theme_bw()
# show parameter correlations
pairs(posterior_samples_merged_after_burnin$theta[,1:6], labels = c("epsilon1","k1","theta","delta_I", "p", "delta_V"), col = c( "blue", "red"))
# posterior predictive check
Within_host_model_WT = function(t, y, param){
dydt1 = -(1 - param[1] * t^10/ (t^10 + param[2]^10)) * param[3] * y[1] * y[3]
dydt2 = (1 - param[1] * t^10/ (t^10 + param[2]^10)) * param[3] * y[1] * y[3] - param[4] * y[2]
dydt3 = param[5] * y[2] - param[6] * y[3]
list(c(dydt1, dydt2, dydt3))
}
t_ppc = seq(0, 10, 0.1)
V_ppc_WT = matrix(, nrow = 1000, ncol = length(t_ppc))
lower_95PI_WT = t_ppc
median_95PI_WT = t_ppc
upper_95PI_WT = t_ppc
V_ppc_KO = matrix(, nrow = 1000, ncol = length(t_ppc))
lower_95PI_KO = t_ppc
median_95PI_KO = t_ppc
upper_95PI_KO = t_ppc
for (i in 1:1000){
y_init = c(data_combined_muc1_WT_V$T0, data_combined_muc1_WT_V$I0, posterior_sample_table$V0[i])
param_fit_WT = c(posterior_sample_table$epsilon1[i],
posterior_sample_table$k1[i],
posterior_sample_table$beta[i],
posterior_sample_table$delta_I[i],
posterior_sample_table$p[i],
posterior_sample_table$c[i])
param_fit_KO = c(posterior_sample_table$epsilon1[i] * 0,
posterior_sample_table$k1[i],
posterior_sample_table$beta[i],
posterior_sample_table$delta_I[i],
posterior_sample_table$p[i],
posterior_sample_table$c[i])
model_output_WT = ode(times = t_ppc, y = y_init, func = Within_host_model_WT, parms = param_fit_WT, method = "bdf")
model_output_KO = ode(times = t_ppc, y = y_init, func = Within_host_model_WT, parms = param_fit_KO, method = "bdf")
V_ppc_WT[i,] = model_output_WT[,4]
V_ppc_KO[i,] = model_output_KO[,4]
}
for (i in 1:length(t_ppc)){
temp_WT = unname(quantile(V_ppc_WT[,i], probs = c(0.025, 0.5, 0.975)))
lower_95PI_WT[i] = temp_WT[1]
median_95PI_WT[i] = temp_WT[2]
upper_95PI_WT[i] = temp_WT[3]
temp_KO = unname(quantile(V_ppc_KO[,i], probs = c(0.025, 0.5, 0.975)))
lower_95PI_KO[i] = temp_KO[1]
median_95PI_KO[i] = temp_KO[2]
upper_95PI_KO[i] = temp_KO[3]
}
data_plot = data.frame(time = rep(c(1,2,3,5,7), each = 5),
V_WT = log10(exp(data_combined_muc1_WT_V$log_viral_load_data_WT)),
V_KO = log10(exp(data_combined_muc1_WT_V$log_viral_load_data_KO)))
fit_plot = data.frame(time = t_ppc,
lower_95PI_WT = lower_95PI_WT,
V_WT = median_95PI_WT,
upper_95PI_WT = upper_95PI_WT,
lower_95PI_KO = lower_95PI_KO,
V_KO = median_95PI_KO,
upper_95PI_KO = upper_95PI_KO)
ggplot(fit_plot, aes(time))+
geom_point(data = data_plot, aes(time, V_WT), size = 3) +
geom_line(data = fit_plot, aes(time, log10(V_WT))) +
geom_ribbon(aes(ymin = log10(lower_95PI_WT), ymax = log10(upper_95PI_WT)), alpha = 0.5, na.rm = TRUE) +
theme_bw()
ggplot(fit_plot, aes(time))+
geom_point(data = data_plot, aes(time, V_KO), size = 3) +
geom_line(data = fit_plot, aes(time, log10(V_KO))) +
geom_ribbon(aes(ymin = log10(lower_95PI_KO), ymax = log10(upper_95PI_KO)), alpha = 0.5, na.rm = TRUE) +
theme_bw()