MCP-Mod.Rmd

---
title: "MCP-Mod"
author: "liuc"
date: "2023-05-25"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


## MCP-Mod

> https://www.fda.gov/media/99313/download
> https://cran.r-project.org/web/packages/DoseFinding/vignettes/faq.html
> https://cran.r-project.org/web/packages/DoseFinding/vignettes/analysis_normal.html
> https://blog.statsols.com/mcp-mod
> https://www.lexjansen.com/pharmasug-cn/2019/CC/Pharmasug-China-2019-CC26.pdf



MCP-Mod (Multiple Comparisons Procedure - Modelling) is an increasingly popular statistical methodology. It can generate superior statistical evidence from Phase II trials with regards to dose selection. The FDA & EMA both recently approved this as fit-for-purpose (FFP).

It is noteworthy that the power of the MCP-Mod method was shown to be sensitive to the initial ‘guesses’ of model shapes. A minimum of 2 doses in addition to placebo is proposed but more than the minimum is desired.
Minimum: 2 active doses (for the MCP-step), 3 active doses (Mod step);
Recommendations (rules of thumb): 4-7 active doses, >10-fold dose range;
To gain most information on the compound, one should evaluate a dose-range that is as large as feasible in terms of lowest and highest dose. As a rule of thumb at minimum a dose-range of > 10-fold should be investigated (i.e., the ratio of highest versus lowest dose should be > 10).


*一般的理解：*
一个二期临床试验，一般的目的在于：
1. Establish that the drug works as intended
2. Determine the appropriate doses for Phase III testing
MCP-Mod方法，可以通过多重比对的方法，evaluate dose-response的信号是否存在(传统上多采用趋势检验、Bonferroni检验)；
然后用最优的模型去拟合一个参数分布，找到对与III期而言最好的dose，或者最efficacy的dose。

MCP: Rust, 但是受限于dose as nominal变量；
Mod: 灵活，但是受限于模型的选择；
而，MCP-Mod将此二者结合起来，一般的，其分析过程分为三个阶段：1，Design Stage，选择备选的模型，并为其的参数设置一个初始值
，以及生成optimal test；2，MCP Stage，选择最优模型，合适的contrasts，是否存在dose response这一趋势；3，Mod Stage，构建最优模型并find target dose.


*MCP-Mod trial design: *
首先是一般的二期试验的设计内容，包括受试人群的选择、研究终点的设置等等；依据相似化合物、mode of action等选择预设的 dose-response 曲线模型，优化模型shape；样本量计算、dose determination；然后一句trail得到的数据进行MCP-Mod分析。

- Define a suitable study population to represent the underlying true dose-response shape.
- Pre-Specify the candidate dose response models based on available information. These are based on assessment of relevant metrics such as type I error rate, power to detect a significant dose-response shape, and the power to find the minimal effective dose.
- Dose determination and sample size calculation to achieve targeted performance characteristics.




```{r, include=FALSE}
library(tidyverse)
library(DoseFinding)
```


### 官网示例，小小的模仿一下


```{r}
data(IBScovars)

str(IBScovars)
```


#### 第一步：

确定模型和猜测对应的模型的参数。

对于placebo的Eff值，可以考虑通过散点图查看其的中位值，或是均值来确定。
而对于每一个函数的参数的猜测，一般的：
- 对于Emax模型

```{r}
ggplot(IBScovars, aes(factor(dose), resp)) + 
  geom_boxplot() +
  geom_jitter() +
  labs(title = "resp by dose (jittered horizontally)") +
  xlab("dose [μg]") + ylab("response [l]")
```


```{r}
# The function “guesst” will pass the parameters of each model to function “Mods”, which will then produce a list that contains all information about candidate models.
?guesst

quad <- guesst(d = 1, p = 0.9, model = 'quadratic')
```

```{r}
## ?Mods
## perform (model based) multiple contrast test
## define candidate dose-response shapes
## 首先是设定你所欲考虑的模型。这里的问题在于the guesstimates for the theta2 parameters的值怎么去猜测？
## 还有关于placebo的部分需要注意，其默认的；两个值为0，1, placEff=0, maxEff=1
models <- Mods(linear = NULL, 
               linlog = NULL,
               emax = c(0.2, 1), 
               quadratic = -0.17,
               doses = c(0, 1, 2, 3, 4) # 需要加上placebo，也就是0
               )


## plot models
## It’s always a good idea to perform a visual sanity check of the functional relationships implied by the guesstimates.
plotMods(models)
```

Calculate optimal contrasts
```{r}
optC <- optContr(models, w=1)
print(optC)

plot(optC)
```

#### 第二步：

进行多重比对检验。Detect a significant dose response signal using a trend test.

Note that the type parameter defaults to type="normal", which means that we assume a homoscedastic ANOVA model for resp.

Model-specific contrast tests with null hypotheses of a flat dose-response curve is performed by 'MCTtest' function.

```{r}
## perform multiple contrast test
## functions powMCT and sampSizeMCT provide tools for sample size
## calculation for multiple contrast tests
## 对所定义的每个模型都做一遍多重比对检验
## 对于此例而言，依照t值来说emax模型似乎拟合的最好。
test <- MCTtest(dose = dose, resp = resp, data = IBScovars, 
                models=models,# 上文定义的模型
                addCovars = ~ gender,# 协变量
                type = 'normal'
                )

test
```


*general test*
Generalization to non-normal data
```{r}
# fit a anova
fitlm <- lm(resp ~ factor(dose) - 1, data = IBScovars)
# get anova results
mu_hat <- coef(fitlm)
S_hat <- vcov(fitlm)
anova_df <- fitlm$df.residual

doses <- c(0,1,2,3,4)


test_general <- MCTtest(dose = doses, 
                        resp = mu_hat, 
                        S = S_hat, 
                        df = anova_df,
                        models = models, 
                        type = "general"
                        )
print(test_general)
```



#### 第三步：

下面选择Emax模型进行拟合，最小二乘法，Dose treated as continuous variable.
```{r}
## ?fitMod
fitemax <- fitMod(dose = dose, resp = resp, data=IBScovars, 
                  model="emax",
                  bnds = c(0.01,5)# upper and lower bound
                  )

## display fitted dose-effect curve
plot(fitemax, CI=TRUE, plotData="meansCI",level=0.95)
```
*interpret: *从图上的结果来看的话dose等于2的时候，resp就可以了。


```{r}
fitemax |> summary()
```


*The `MCPMod` function simultaneously conducts both steps. *
```{r}
set.seed(42, "L'Ecuyer")

res <- DoseFinding::MCPMod(dose = doses, resp = mu_hat, 
                           # data = IBScovars,
                           S = S_hat,
                           models = models,
                           type = 'general',
                           critV = TRUE,
                           alpha = 0.05,
                           alternative = 'two.sided',
                           Delta = 1,
                           selModel = 'AIC'
                           )

res$selMod
```

```{r}
res$doseEst
```

```{r}
doseVec <- seq(1,10,by=1)


pred <- predict(fitemax, se.fit = TRUE, predType = 'ls-means')

pred |> str()
```



### kx826 1002 实战

很明显的，本二期临床试验采用的是传统的pairwise comparisons方法衡量的dose，而且其所设置的dose剃度仅为2+1个。 有一些模型不是很适合。

对于MMRM类的数据，似乎可以通过MMRM分析，比如R包`mmrm::mmrm`或SAS`PROC Mixed`提取对应的协方差矩阵等。

```{r, include=FALSE}
final_data_wider <- read_csv(
  '~/OneDrive/kintor/Daily_Work/KX826_CN1002/final_data_wider.csv') %>% 
  mutate(dislevel = case_when(
    dislevel == 'IIIvertex' ~ 'III',
    dislevel == 'Ⅴ级' ~ 'V',
    dislevel == 'Ⅳ级' ~  'IV'
  ))
```


```{r}
demo <- final_data_wider %>%
  filter(arm %in% c('placeboBID', '2.5mgBID','5mgBID')) %>%
  mutate(resp = dW24, dose = case_when(
    arm == "placeboBID" ~ 0,
    arm == "2.5mgBID" ~ 2.5,
    arm == "5mgBID" ~ 5,
    TRUE ~ NA_integer_
  )) %>% 
  drop_na(resp) %>% as.data.frame()

demo
```

```{r}
ggplot(demo, aes(factor(dose), resp)) + 
  geom_boxplot() +
  geom_jitter() +
  labs(title = "resp by dose (jittered horizontally)") +
  xlab("dose [μg]") + ylab("response [chg]")
```


```{r}
quad <- guesst(d = 3, p = 0.9, model = 'quadratic')
exp <- guesst(d = 3, p = 0.9, model = 'exponential', Maxd = 3)
emax <- guesst(d = 3, p = 0.9, model = 'emax')
sigemax <- guesst(d = c(2.5, 4), p = c(0.3, 0.9), model = 'sigEmax')
logis <- guesst(d = c(2.5, 4), p = c(0.3, 0.9), model = 'logistic')
```

```{r}
mods <- Mods(
  linear = NULL,
  linlog = NULL,
  emax = c(emax, 2.5),
  quadratic = quad,
  exponential = exp,
  # sigEmax = sigemax,
  # logistic = logis,
  doses = c(0, 2.5, 5)
)

plot(mods)
```

```{r}
optC <- optContr(mods, w=1)
print(optC)

plot(optC)
```

```{r}
test <- MCTtest(dose = dose, resp = resp, data = demo, 
                models=mods,
                # addCovars = ~ gender,# 协变量
                type = 'normal'
                )

test
```
*结果不妙：*从设定好的p值来看的话，不具有计量的量效关系。


```{r}
fit_best <- fitMod(dose = dose, resp = resp, data=demo, 
                  model="exponential"
                  )

## display fitted dose-effect curve
plot(fit_best, CI=TRUE, plotData="meansCI",level=0.95)
```

```{r}
# fit an anova
fitlm <- lm(resp ~ factor(dose) - 1, data = demo)
# get anova results
mu_hat <- coef(fitlm)
S_hat <- vcov(fitlm)
anova_df <- fitlm$df.residual

doses <- c(0, 2.5, 5)


test_general <- MCTtest(dose = doses, 
                        resp = mu_hat, 
                        S = S_hat, 
                        df = anova_df,
                        models = mods, 
                        type = "general"
                        )
print(test_general)
```

```{r}
set.seed(42, "L'Ecuyer")

res <- DoseFinding::MCPMod(dose = doses, resp = mu_hat, 
                           # data = IBScovars,
                           S = S_hat,
                           models = mods,
                           type = 'general',
                           critV = TRUE,
                           alpha = 0.025,
                           alternative = 'one.sided',
                           Delta = 1,
                           selModel = 'AIC'
                           )

res$selMod
```


### kx826 cn1004


```{r}
fake_data <- read_csv(
  '~/OneDrive/kintor/Daily_Work/KX826_CN1004/data_wider.csv'
) %>% 
  filter(ARM %in% c('placeboQD','2.5mgQD','5mgQD')) %>%
  # filter(ARM %in% c('placeboBID','2.5mgBID','5mgBID')) %>%
  mutate(resp = dW24, 
         dose = case_when(ARM == "placeboQD" ~ 0,
                                       ARM == "2.5mgQD" ~ 2.5,
                                       ARM == "5mgQD" ~ 5,
                                       TRUE ~ NA_integer_),
         # dose = case_when(ARM == "placeboBID" ~ 0,
         #                               ARM == "2.5mgBID" ~ 2.5,
         #                               ARM == "5mgBID" ~ 5,
         #                               TRUE ~ NA_integer_)
         ) %>% drop_na(resp) %>% as.data.frame()

fake_data
```

```{r}
ggplot(fake_data, aes(factor(dose), resp)) + 
  geom_boxplot() +
  geom_jitter() +
  labs(title = "resp by dose (jittered horizontally)") +
  xlab("dose [μg]") + ylab("response [chg]")
```

```{r}
quad <- guesst(d = c(2.5, 5), p = 0.9, model = 'quadratic')
exp <- guesst(d = 3, p = 0.9, model = 'exponential', Maxd = 3)
emax <- guesst(d = 3, p = 0.9, model = 'emax')
sigemax <- guesst(d = c(2.5, 4), p = c(0.3, 0.9), model = 'sigEmax')
logis <- guesst(d = c(2.5, 4), p = c(0.3, 0.9), model = 'logistic')

mods <- Mods(
  linear = NULL,
  linlog = NULL,
  emax = c(emax, 2.5),
  quadratic = quad,
  exponential = exp,
  # sigEmax = sigemax,
  # logistic = logis,
  doses = c(0, 2.5, 5)
)

plot(mods)
```

```{r}
test <- MCTtest(dose = dose, resp = resp, data = fake_data, 
                models=mods,
                # addCovars = ~ gender,# 协变量
                type = 'normal'
                )

test
```

拟合最优模型：
```{r}
fit_best <- fitMod(dose = dose, resp = resp, data=fake_data, 
                  model="exponential"
                  )

## display fitted dose-effect curve
plot(fit_best, CI=TRUE, plotData="meansCI",level=0.95)
```

*use general: *
```{r}
# fit an anova
fitlm <- lm(resp ~ factor(dose) - 1, data = fake_data)
# get anova results
mu_hat <- coef(fitlm)
S_hat <- vcov(fitlm)
anova_df <- fitlm$df.residual

doses <- c(0, 2.5, 5)


test_general <- MCTtest(dose = doses, 
                        resp = mu_hat, 
                        S = S_hat, 
                        df = anova_df,
                        models = mods, 
                        type = "general"
                        )
print(test_general)
```

```{r}
set.seed(42, "L'Ecuyer")

res <- DoseFinding::MCPMod(dose = doses, resp = mu_hat, 
                           # data = IBScovars,
                           S = S_hat,
                           models = mods,
                           type = 'general',
                           critV = TRUE,
                           alpha = 0.025,
                           alternative = 'one.sided',
                           Delta = 1,
                           selModel = 'maxT'
                           )

res$selMod
```

```{r}
res$doseEst
```


```{r}
DoseFinding::ED(fit_best, p = 0.9)

DoseFinding::TD(fit_best)
```


所选出的最佳剂量反应曲线模型，可通过试验结果数据估计模型的参数，进而由逆回归方法推估感兴趣的剂量:
inverse regression equation

```{r}
# 也即是通过Y的值去推测X的值
# 以下对线形模型适用，但对此模型似乎不行
# xval <- approx(x = fit_best$fitted, y = x, xout = 9.1)$y
# points(xval, 9.1, col = "blue", lwd = 5)


ypredict <- 9.1

fun <- function(x1, y1, mod) {
    predict(mod, newdata=data.frame(days=x1)) - y1
    }    
                
(xpred <- sapply(ypredict, function(z) uniroot(fun, interval=c(0, 500), mod=fit_best, y1=z)$root))
        

```