---
title: "Multi-stage group-sequential multi-arm clinical trial design for a normally distributed primary outcome"
date: "`r format(Sys.time(), '%d/%m/%Y')`"
params:
  alpha:       NA
  beta:        NA
  delta0:      NA
  delta1:      NA
  e:           NA
  efix:        NA
  f:           NA
  ffix:        NA
  integer:     NA
  J:           NA
  K:           NA
  lower:       NA
  maxN:        NA
  n10:         NA
  n1:          NA
  opchar:      NA
  plots:       NA
  power:       NA
  ratio_type:  NA
  ratio_init:  NA
  ratio:       NA
  sigma:       NA
  stopping:    NA
  swss:        NA
  upper:       NA
  boundaries:  NA
  equal_error: NA
  equal_power: NA
  equal_other: NA
  equal_sample_size: NA
  shifted_power:     NA
  shifted_sample_size:     NA
  pmf_N:     NA
---

```{r, include = F}
knitr::opts_chunk$set(echo = F, results = "asis")
```

# Design setting

The trial will be designed to compare $K$ experimental treatments to a shared control arm.
Response $X_{ik}$, from patient $i=1,\dots,n_k$ in arm $k=0,\dots,K$, will be assumed to be distributed as $X_{ik} \sim N(\mu_k,\sigma_k^2)$. Then, the hypotheses to be tested will be:
$$ H_k : \tau_k = \mu_k - \mu_0 \le 0,\ k=1,\dots,K.$$
The *global null hypothesis*, $H_G$, will be:
$$ \tau_1 = \cdots = \tau_K = 0. $$
The *global alternative hypothesis*, $H_A$, will be:
$$ \tau_1 = \cdots = \tau_K = \delta_1. $$
The *least favourable configuration* for experimental arm $k$, $LFC_k$, will be:
$$ \tau_k = \delta_1,\ \tau_1 = \cdots = \tau_{k-1} = \tau_{k+1} = \cdots = \tau_K = \delta_0. $$
Here, $\delta_1$ and $\delta_0$ are *interesting* and *uninteresting* treatment effects respectively.

# Inputs

```{r, echo = F, results = "asis"}
alpha       <- params$alpha
beta        <- params$beta
delta0      <- params$delta0
delta1      <- params$delta1
e           <- params$e
efix        <- params$efix
f           <- params$f
ffix        <- params$ffix
integer     <- params$integer
J           <- params$J
K           <- params$K
lower       <- params$lower
maxN        <- params$maxN
n10         <- params$n10
n1          <- params$n1
opchar      <- params$opchar
plots       <- params$plots
power       <- params$power
ratio_type  <- params$ratio_type
ratio_init  <- params$ratio_init
ratio       <- params$ratio
sigma       <- params$sigma
stopping    <- params$stopping
swss        <- params$swss
upper       <- params$upper
```

```{r input_text, echo = FALSE, results = "asis"}
if (power == "marginal") {
  power_type_text     <- "marginal power for each null hypothesis"
  power_scenario_text <-
    "each of their respective least favourable configurations"
} else {
  power_scenario_text <- "the global alternative hypothesis"
  if (power == "conjunctive") {
    power_type_text   <- "conjunctive power"
  } else if (power == "disjunctive") {
    power_type_text   <- "disjunctive power"
  }
}

if (ratio_type == "equal_all") {
  ratio_text          <- "the same as the control arm"
} else if (ratio_type == "equal_exp") {
  ratio_text          <- paste0(ratio_init[1], " times that of the control arm")
} else {
  ratio_text          <- paste0(round(1/sqrt(K), 3),
                                " times that of the control arm")
}

if (lower == "fixed") {
  lower_prelim <- "fixed value"
} else if (lower == "obf") {
  lower_prelim <- "O'Brien-Fleming"
} else if (lower == "pocock") {
  lower_prelim <- "Pocock"
} else if (lower == "triangular") {
  lower_prelim <- "triangular"
}

if (upper == "fixed") {
  upper_prelim <- "fixed value"
} else if (upper == "obf") {
  upper_prelim <- "O'Brien-Fleming"
} else if (upper == "pocock") {
  upper_prelim <- "Pocock"
} else if (upper == "triangular") {
  upper_prelim <- "triangular"
}

if (lower == "fixed") {
  lower_text          <- paste0(lower_prelim, ", with a fixed value of ", ffix)
} else {
  lower_text          <- lower_prelim
}

if (upper == "fixed") {
  upper_text          <- paste0(upper_prelim, ", with a fixed value of ", efix)
} else {
  upper_text          <- upper_prelim
}

if (integer) {
  integer_text        <- "will"
} else {
  integer_text        <- "will not"
}

if (plots) {
  plot_text           <- "will"
} else {
  plot_text           <- "will not"
}
```

```{r output_text, echo = F, results = "asis"}
FWER                  <- round(opchar$FWERI1[1], 3)
if (power == "marginal") {
  power_type_text     <- "minimum marginal power"
  power_value         <-
    round(min(diag(as.matrix(opchar[-(1:2), (K + 3):(2*K + 2)]))), 3)
} else {
  power_scenario_text <- "the global alternative hypothesis."
  if (power == "conjunctive") {
    power_type_text   <- "conjunctive power"
    power_value       <- round(opchar$Pcon[2], 3)
  } else if (power == "disjunctive") {
    power_type_text   <- "disjunctive power"
    power_value       <- round(opchar$Pdis[2], 3)
  }
}
if (swss == "fixed") {
  swss_text  <- "is"
  swss_text2 <- round(n1, 3)
} else {
  swss_text  <- "to the control arm is"
  swss_text2 <- round(n10, 3)
}
```

#### Inputs

The following choices were made:

- $K = \boldsymbol{`r K`}$ experimental treatments will initially be included in the trial.
- A maximum of $J = \boldsymbol{`r J`}$ stages will be allowed in the trial.
- A __`r stopping`__ stopping rule will be used.
- The stage-wise sample size will be __`r swss`__.
- The lower stopping boundaries will be __`r lower_text`__.
- The upper stopping boundaries will be __`r upper_text`__.
- A family-wise error-rate of $\alpha = \boldsymbol{`r alpha`}$ will be used.
- The __`r power_type_text`__ will be controlled to level $1-\beta = \boldsymbol{`r 1 - beta`}$ under __`r power_scenario_text`__.
- The interesting and uninteresting treatment effects will be: $\delta_1 = \boldsymbol{`r round(delta1, 3)`}$ and $\delta_0 = \boldsymbol{`r round(delta0, 3)`}$ respectively.
- The standard deviations of the responses will be assumed to be: $(\sigma_0,\dots,\sigma_K) = \boldsymbol{(`r paste(round(sigma, 3), collapse = ", ")`)}$.
- The target allocation to each of the experimental arms will be: __`r ratio_text`__.
- The sample size in each arm __`r integer_text`__ be required to be an integer.
- Plots __`r plot_text`__ be produced.

#### Outputs

- The maximum required sample size is: $\boldsymbol{`r round(maxN, 3)`}$.
- The stage-wise sample size __`r swss_text`__: __`r swss_text2`__.
- The realised allocation ratios to the experimental arms are: $(r_1,\dots,r_K) = \boldsymbol{(`r paste(rep(round(ratio, 3), K), collapse = ", ")`)}$.
- The maximum familywise error-rate is: $\boldsymbol{`r FWER`}$.
- The __`r power_type_text`__ is: $\boldsymbol{`r power_value`}$.
- The lower stopping boundaries are: $\boldsymbol{`r paste0("(", paste(round(f, 3), collapse = ", "), ")")`}$.
- The upper stopping boundaries are: $\boldsymbol{`r paste0("(", paste(round(e, 3), collapse = ", "), ")")`}$.

# Operating characteristcs

```{r, echo = F, results = "asis"}
library(knitr)
kable(round(opchar[, c(1:K, (2*K + 3):(4*K + 2))]), digits = 3)
kable(round(opchar[, 1:(2*K + 2)]), digits = 3)
kable(round(opchar[, -((K + 1):(4*K + 2))]), digits = 3)
```

# Plots

```{r, echo = F, results = "asis", dpi = 600}
if (params$plots) {
  print(params$boundaries)
  cat("\n \n \n \n \n \n")
  print(params$equal_error)
  cat("\n \n \n \n \n \n")
  print(params$equal_power)
  cat("\n \n \n \n \n \n")
  print(params$equal_other)
  cat("\n \n \n \n \n \n")
  print(params$equal_sample_size)
  cat("\n \n \n \n \n \n")
  print(params$shifted_power)
  cat("\n \n \n \n \n \n")
  print(params$shifted_sample_size)
  cat("\n \n \n \n \n \n")
  print(params$pmf_N)
} else {
  cat("Not chosen for output: select the box next to 'Plot power curves' to",
      "add plots to the report.")
}
```
