In nlmixrdevelopment/nlmixr.examples: Nonlinear Mixed Effects Models in Population Pharmacokinetics and Pharmacodynamics

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
  )

## These options cache the models and the model simulations in R
## To run the actual models on your system, take the save options off.
options(nlmixr.save=TRUE,
        nlmixr.save.dir=system.file(package="nlmixr.examples"));

This shows an example of integrated workflow between xgxr nlmixr and ggPmx

library(nlmixr)
library(xgxr)
library(readr)
library(ggplot2)
library(dplyr)
library(tidyr)
library(ggPMX)

Load the data

pkpd_data <- case1_pkpd %>%
  arrange(DOSE) %>%
  select(-IPRED) %>%
  mutate(TRTACT_low2high = factor(TRTACT, levels = unique(TRTACT)),
         TRTACT_high2low = factor(TRTACT, levels = rev(unique(TRTACT))),
         DAY_label = paste("Day", PROFDAY),
         DAY_label = ifelse(DAY_label == "Day 0","Baseline",DAY_label))

pk_data <- pkpd_data %>%
  filter(CMT == 2)

pk_data_cycle1 <- pk_data %>%
    filter(CYCLE == 1)

Exploratory analysis using ggplot and xgx helper functions

Use xgxr for simplified concentration over time, colored by Dose, mean +/- 95% CI

Often in exploring data it is worthwhile to plot by dose by each nominal time and add the 95% confidence interval. This typical plot can be cumbersome and lack some nice features that xgxr can help with. Note the following helper functions:

• xgx_theme_set() this sets the theme to black and white color theme and other best pratices in xgxr.

• xgx_geom_ci() which creates the Confidence Interval and mean plots in a simple interface.

• xgx_scale_y_log10() which creates a log-scale that includes the minor grids that immediately show the viewer that the plot is a semi-log plot without carefully examining the y axis.

• xgx_scale_x_time_units which creates an appropriate scale based on your times observed and the units you use. It also allows you to convert units easily for the right display.

• xgx_annote_status() which adds a DRAFT annotation which is often considered best practice when the data or plots are draft.

xgx_theme_set() # This uses black and white theme based on xgxr best
                # pratices

# flag for labeling figures as draft
status <- "DRAFT"

time_units_dataset <- "hours"
time_units_plot    <- "days"
trtact_label       <- "Dose"
dose_label         <- "Dose (mg)"
conc_label         <- "Concentration (ng/ml)" 
auc_label          <- "AUCtau (h.(ng/ml))"
concnorm_label     <- "Normalized Concentration (ng/ml)/mg"
sex_label          <- "Sex"
w100_label         <- "WEIGHTB>100"
pd_label           <- "FEV1 (mL)"
cens_label         <- "Censored"


ggplot(data = pk_data_cycle1, aes(x     = NOMTIME,
                                  y     = LIDV,
                                  group = DOSE,
                                  color = TRTACT_high2low)) +
    xgx_geom_ci(conf_level = 0.95) + # Easy CI with xgxr
    xgx_scale_y_log10() + # semi-log plots with semi-log grid minor lines
    xgx_scale_x_time_units(units_dataset = time_units_dataset,
                           units_plot = time_units_plot) +
    # The last line creates an appropriate x scale based on time-units
    # and time unit scale
    labs(y = conc_label, color = trtact_label) +
    xgx_annotate_status(status) #  Adds draft status to plot

With this plot you see the mean concentrations confidence intervals stratified by dose

Concentration over time, faceted by Dose, mean +/- 95% CI, overlaid on gray spaghetti plots

Not only is it useful to look at the mean concentrations, it is often useful to look at the mean concentrations and their relationship between actual individual profiles. Using ggplot coupled with the xgxr helper functions used above, we can easily create these plots as well:

ggplot(data = pk_data_cycle1, aes(x = NOMTIME, y = LIDV)) +
  geom_line(aes(group = ID), color = rgb(0.5, 0.5, 0.5), size = 1, alpha = 0.3) +
  scale_shape_manual(values = c(1, 8)) +
  scale_color_manual(values = c("grey50", "red")) +
  xgx_geom_ci(aes(x = NOMTIME, color = NULL, group = NULL), conf_level = 0.95) +
  xgx_scale_y_log10() +
  xgx_scale_x_time_units(units_dataset = time_units_dataset, units_plot = time_units_plot) +
  labs(y = conc_label, color = trtact_label) +
  theme(legend.position = "none") +
  facet_grid(.~TRTACT_low2high) +
  xgx_annotate_status(status)

To me it appears the variability seems to be higher with higher doses and higher with later times.

Exploring the dose linearity

A common way to explore the dose linearity is to normalize by the dose. If the confidence intervals overlap, often this is a dose linear example.

ggplot(data = pk_data_cycle1,
       aes(x = NOMTIME,
           y = LIDV / as.numeric(as.character(DOSE)),
           group = DOSE,
           color = TRTACT_high2low)) +
  xgx_geom_ci(conf_level = 0.95, alpha = 0.5, position = position_dodge(1)) +
  xgx_scale_y_log10() +
  xgx_scale_x_time_units(units_dataset = time_units_dataset, units_plot = time_units_plot) +
  labs(y = concnorm_label, color = trtact_label) +
    xgx_annotate_status(status)

This example seems to be dose-linear, with the exception of the censored data. This can be made even more clear by removing the censored data for this plot:

ggplot(data = pk_data_cycle1 %>% filter(CENS == 0),
       aes(x = NOMTIME,
           y = LIDV / as.numeric(as.character(DOSE)),
           group = DOSE,
           color = TRTACT_high2low)) +
  xgx_geom_ci(conf_level = 0.95, alpha = 0.5, position = position_dodge(1)) +
  xgx_scale_y_log10() +
  xgx_scale_x_time_units(units_dataset = time_units_dataset, units_plot = time_units_plot) +
  labs(y = concnorm_label, color = trtact_label) +
    xgx_annotate_status(status)

The lowest dose, with the most censoring, is the one that seems to be the outlier. That is likely an artifact of censoring.

Other ways to explore the data include by looking at normalized Cmax and AUC values (which we will skip in this vignette).

Exploring Covariates in the dataset

Using the xgx helper functions to ggplot you can explore the effect of high baseline weight. This particular plot is shown below:

ggplot(data = pk_data_cycle1, aes(x = NOMTIME,
                                  y = LIDV,
                                  group = WEIGHTB > 100,
                                  color = WEIGHTB > 100)) + 
    xgx_geom_ci(conf_level = 0.95) +
    xgx_scale_y_log10() +
    xgx_scale_x_time_units(units_dataset = time_units_dataset, units_plot = time_units_plot) +
    facet_grid(.~DOSE) +
    labs(y = conc_label, color = w100_label) +
    xgx_annotate_status(status)

It seems that the weight effect is not extreme for either dose group

Summary of exploratory analysis findings

From the exploratory analysis we see: - The doses seem proportional - The PK seems to have a 2-compartment model - Censoring has a large effect on the PK data.

Fitting the data with nlmixr

First we need to subset to the PK only data and rename LIDV to DV

dat <- case1_pkpd %>%
    rename(DV=LIDV) %>%
    filter(CMT %in% 1:2) %>%
    # Filter (for now) since CENS supprot in nlmixr is in development
    filter(CENS == 0) %>%
    filter(TRTACT != "Placebo")

Next create a 2 compartment model

## Use 2 compartment model
cmt2 <- function(){
    ini({
        lka <- log(0.1) # log Ka
        lv <- log(10) # Log Vc
        lcl <- log(4) # Log Cl
        lq <- log(10) # log Q
        lvp <- log(20) # Log Vp

        eta.ka ~ 0.01
        eta.v ~ 0.1
        eta.cl ~ 0.1
        logn.sd = 10
    })
    model({
        ka <- exp(lka + eta.ka)
        cl <- exp(lcl + eta.cl)
        v <- exp(lv + eta.v)
        q <- exp(lq)
        vp <- exp(lvp)
        linCmt() ~ lnorm(logn.sd)
    })
}

## Check parsing
cmt2m <- nlmixr(cmt2)
print(cmt2m)

## First try log-normal (since the variabilitiy seemed proportional to concentration)
cmt2fit.logn <- nlmixr(cmt2m, dat, "saem", table=tableControl(npde=TRUE,cwres=TRUE))


## Now try proportional
cmt2fit.prop <- cmt2fit.logn %>%
    update(linCmt() ~ prop(prop.sd)) %>%
    nlmixr(est="saem", table=tableControl(npde=TRUE, cwres=TRUE))

## now try add+prop
cmt2fit.add.prop <- cmt2fit.prop %>%
    update(linCmt() ~ prop(prop.sd) + add(add.sd)) %>%
    nlmixr(est="saem", table=tableControl(npde=TRUE, cwres=TRUE))

Now that we have run 3 different estimation methods, we can compare the results side-by-side

library(huxtable)

as_hux("lognormal"=cmt2fit.logn, "proportional"=cmt2fit.prop, "add+prop"=cmt2fit.add.prop)

Note that the additive and proportional model has the additive component approach zero. When comparing the objective functions of log-normal and proportional models, the proportional model has the lowest objective function value. (Since we modeled log-normal without data transformation it is appropriate to compare the AIC/Objective function values)

You may wish to see a visual comparison of the parameters:

library(dotwhisker)
## exponentiate=NA causes the parameters to be back-transformed
dwplot(list("lognormal"=cmt2fit.logn, "proportional"=cmt2fit.prop), exponentiate=NA) +
    ## Notice we can use some xgx functions post analysis as well,
    ## since they are ggplot helper functions
    xgx_scale_x_log10() +
    ggtitle("Comparison between lognormal and proportional models",
            "On backtransformed scales")

Model Diagnostics with ggPMX

## The controller then can be piped into a specific plot
ctr <- pmx_nlmixr(cmt2fit.logn, conts = c("WEIGHTB"), cats="TRTACT")

ctr %>% pmx_plot_dv_ipred

ctr %>% pmx_plot_dv_pred

ctr %>% pmx_plot_abs_iwres_ipred

ctr %>% pmx_plot_individual(1)

ctr %>% pmx_plot_iwres_dens

ctr %>% pmx_plot_npde_qq

ctr %>% pmx_plot_npde_pred

ctr %>% pmx_plot_npde_time

ctr %>% pmx_plot_eta_qq

ctr %>% pmx_plot_vpc

ctr %>% pmx_plot_eta_box

ctr %>% pmx_plot_eta_hist

ctr %>% pmx_plot_eta_matrix

## Create a report of all the plots you generated from the controller
ctr %>% pmx_report("nlmixr_report",".")

unlink("nlmixr_report.Rmd") # Remove this file so it isn't confused with vignettes

This creates 2 reports, both a pdf and word document.

nlmixrdevelopment/nlmixr.examples documentation built on Nov. 4, 2019, 10:08 p.m.