Visualizing lmer and limits [Study As­sess­ment]

posted by mittyri – Russia, 2019-01-06 17:00  – Posting: # 19735
Views: 8,485

Dear Shuanghe, Dear Detlew,

Happy New Year!

Here's my attempt to visualize the results of lmer.
I tried to add the acceptance criteria to the plot.
What do you think? Is that suitable? Did I understand the article correctly?

library(lme4)
# the next one has A LOT of dependencies
# I added it to visualize confidence limits for each observation, by the way for the ribbon only max and min are used for each dose level
library(merTools)
library(ggplot2)
library(dplyr)
lowBind <- 0.8
Subj   <- c(1, 2, 4, 5, 6, 4, 5, 6, 7, 8, 9, 7, 8, 9)
Dose   <- c(25, 25, 50, 50, 50, 250, 250, 250, 75, 75, 75, 250, 250, 250)
AUC    <- c(326.40, 437.82, 557.47, 764.85, 943.59, 2040.84, 2989.29,
            4107.58, 1562.42, 982.02, 1359.68, 3848.86, 4333.10, 3685.55)
Cmax   <- c(64.82, 67.35, 104.15, 143.12, 243.63, 451.44, 393.45,
            796.57, 145.13, 166.77, 296.90, 313.00, 387.00, 843.00)
resp   <- data.frame(Subj, Dose, Cmax, AUC)
resp$Subj <- factor(resp$Subj)

muddle <- lmer(log(Cmax) ~ log(Dose) + (1|Subj), data=resp)

coefs <- data.frame(summary(muddle)$coefficients)
pred <- cbind(resp, predictInterval(muddle, resp, level=0.9)) %>%
  mutate(minDose = min(Dose),
         lowL = exp(coefs['(Intercept)','Estimate'])*Dose^(1+log(lowBind)/log(Dose/minDose)),
         upL = exp(coefs['(Intercept)','Estimate'])*Dose^(1+log(1/lowBind)/log(Dose/minDose))
         ) %>%
  group_by(Dose) %>%
  mutate(ymax = max(upr),
            ymin = min(lwr))

ggplot(pred,aes(x = log(Dose), y = log(Cmax))) +
  geom_point(shape = Subj, size = 2)+
  geom_point(aes(y = fit), shape = Subj, size = 2, colour = 'blue')+
  geom_ribbon(aes(ymin = ymin, ymax = ymax), fill = 'blue', alpha = .2) +
  geom_abline(intercept = coefs['(Intercept)','Estimate'], slope = coefs['log(Dose)','Estimate'], size = 2, color = 'blue', linetype = 'dashed') +
  geom_abline(intercept = coefs['(Intercept)','Estimate'] - qt(1-0.05, coefs['(Intercept)', 't.value']) * coefs['(Intercept)', 'Std..Error'],
              slope = coefs['log(Dose)', 'Estimate'] - qt(1-0.05, coefs['log(Dose)', 't.value']) * coefs['log(Dose)', 'Std..Error'], size = 2, color = 'blue', linetype = 'dotdash' ) +
  geom_abline(intercept = coefs['(Intercept)','Estimate'] + qt(1-0.05, coefs['(Intercept)', 't.value']) * coefs['(Intercept)', 'Std..Error'],
              slope = coefs['log(Dose)', 'Estimate'] + qt(1-0.05, coefs['log(Dose)', 't.value']) * coefs['log(Dose)', 'Std..Error'], size = 2, color = 'blue', linetype = 'dotdash') +
  geom_line(aes(y=log(lowL)), colour = 'red', size = 2) +
  geom_line(aes(y=log(upL)), colour = 'red', size = 2) +
  scale_y_continuous(labels = function(x) paste0(signif(x,4), "(", signif(exp(x), 4), ")")) +
  scale_x_continuous(breaks=log(Dose), labels = function(x) paste0(signif(x,4), "(", signif(exp(x), 4), ")")) 

[image]
Black dots: Observed values
Blue dots: Predicted values
Blue area: 90% prediction area for all observations
Blue dashed line: fitted regression line
Blue dot-dashed lines: 90% limits built using 90% CIs for the slope and intercept
Red lines: 80-125% acceptance limits

Kind regards,
Mittyri

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