epo_pts.Rmd

---
title: "Probability of Technical Success - EPO IV/SC QW/TIW"
date: ""
author: "Metrum Research Group, LLC"
output: 
  html_document:
    css: docs/src/styles/styles.css
---

__Population Pharmacokinetic and Pharmacodynamic Model- Based Comparability Assessment of a Recombinant Human Epoetin Alfa and the Biosimilar HX575__

- Xiaoyu Yan, MS, Philip J. Lowe, PhD, Martin Fink, PhD, Alexander Berghout, PhD, Sigrid Balser, PhD, and Wojciech Krzyzanski, PhD

- J Clin Pharmacol. 2012 November ; 52(11): 1624–1644. 

- https://www.ncbi.nlm.nih.gov/pubmed/22162538


```{r, message = FALSE}
library(mrgsolve)
library(dplyr)
library(tidyr)
a <- config::get()
#source(a$functions)
#knitr_config()
set.seed(112)
```

```{r}
post <- readRDS(a$epo_post)
head(post)

sam <- dplyr::sample_n(post, 100)
dim(sam)
dim(post)
```

```{r}
mod <- mread_cache("epo", a$epo_project)
see(mod)

```


Drop the initial `HGB` by half
```{r}
mod <- param(mod, THETA19 = mod$THETA19/2)
post <- mutate(post, THETA19 = THETA19/2)
```

```{r}
qw <- ev(amt = 40000, ii = 168, addl = 3, rate = -2)

tiw <- ev_days(ev(amt = 7000, rate = -2), days="m,w,f", addl = 3)
tiw


qw <- filter(tiw, time==0) %>% mutate(amt = 40000)
qw
```

```{r}
data_sc <- bind_rows(tiw,qw) %>% mutate(ID = amt)
data_sc
```

## SC dosing

- When subcuteneous administration, 40,000 IU weekly has similar efficacy
to 100 IU/kg TIW
- We're looking out to 4 weeks here
```{r}
mod %>% 
  zero_re %>% 
  mrgsim(data = data_sc, end = 672) %>%
  plot(EPOi + HGBi~.)
```

```{r}
data_sc
data_iv <- mutate(data_sc, cmt = 2, rate = 0)
data_iv
```

## IV administration

- But when we look at the TIW versus QW comparison with IV administration,
the once-weekly is less effective than three-times-weekly

```{r}
mod %>% 
  zero_re %>% 
  mrgsim(data = data_iv, end = 672) %>%
  plot(EPOi + HGBi~.)
```

# Our task

Let's look at the probability of technical success for the QW versus TIW
dosing in the IV case

Let's ramp this up for PTS

## Population data sets

TIW data
```{r}
iv_tiw <- ev_rep(tiw, id = 1:250) %>% mutate(cmt = 2, rate = 0)
```

QW data
```{r}
iv_qw <- filter(iv_tiw, time==0) %>% mutate(amt = 40000, ID = ID + 1000)
```

If we bind this all together, we can simulate both regimens in one go
```{r}
data <- bind_rows(iv_tiw, iv_qw)

data
```

- What about simulating some variatility in Weight?


A simulation function

Arguments

- `i` replicate number
- `mod` the EPO model object
- `data` a template data set

```{r}
sim <- function(i, mod, data) {

 mod <- param(mod, slice(post,i))
 
 out <- mrgsim(mod, data = data, obsonly = TRUE,
               end = -1, add = 672)

  mutate(out, irep = i, qw = as.integer(ID >= 1000))
}
```


Test it out
```{r}
sim(2, mod, data)
```


## Simulate

- Remember to set a seed
- And change the `RNGkind`
- What about uncertainty in the random effect variances?

```{r}
set.seed(10020)
mcRNG()
out <- parallel::mclapply(1:101, mc.cores = 8, 
                          sim, mod, data) %>% bind_rows
```


## Summarize

Our target is HGB > 8.5

```{r}
sum1 <- 
out %>% 
  group_by(irep,qw) %>%
  summarise(success = mean(HGBi > 8.5)) 

sum1
```

Our success criteria is at least 40% of patients hitting the target
```{r}
sum2 <- 
  sum1 %>%
  group_by(qw) %>% 
  summarise(PR = mean(success > 0.4))
```


The bottom line
```{r}
sum2
```