R/mixmodel_int_cont.R

In pavlakrotka/NCC: Simulation and Analysis of Platform Trials with Non-Concurrent Controls

#' Mixed regression model analysis for continuous data using the covariates treatment and period as fixed effects and the interaction between them as a random effect
#'
#' @description This function performs linear mixed model regression taking into account all trial data until the arm under study leaves the trial and adjusting for periods as random factors.
#'
#' @param data Data frame with trial data, e.g. result from the `datasim_cont()` function. Must contain columns named 'treatment', 'response' and 'period'.
#' @param arm Integer. Index of the treatment arm under study to perform inference on (vector of length 1). This arm is compared to the control group.
#' @param alpha Double. Significance level (one-sided). Default=0.025.
#' @param ci Logical. Indicates whether confidence intervals should be computed. Default=FALSE.
#' @param ncc Logical. Indicates whether to include non-concurrent data into the analysis. Default=TRUE.
#' @param check Logical. Indicates whether the input parameters should be checked by the function. Default=TRUE, unless the function is called by a simulation function, where the default is FALSE.
#' @param ... Further arguments passed by wrapper functions when running simulations.
#'
#' @importFrom lmerTest lmer
#' @importFrom stats pt
#' @importFrom stats coef
#' @importFrom stats confint
#'
#' @export
#'
#' @examples
#'
#' trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
#' theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")
#'
#' mixmodel_int_cont(data = trial_data, arm = 3, ci = TRUE)
#'
#' @return List containing the following elements regarding the results of comparing `arm` to control:
#'
#' - `p-val` - p-value (one-sided)
#' - `treat_effect` - estimated treatment effect in terms of the difference in means
#' - `lower_ci` - lower limit of the (1-2*`alpha`)*100% confidence interval
#' - `upper_ci` - upper limit of the (1-2*`alpha`)*100% confidence interval
#' - `reject_h0` - indicator of whether the null hypothesis was rejected or not (`p_val` < `alpha`)
#' - `model` - fitted model
#'
#' @author Pavla Krotka

mixmodel_int_cont <- function(data, arm, alpha=0.025, ci=FALSE, ncc=TRUE, check=TRUE, ...){

  if (check) {
    if (!is.data.frame(data) | sum(c("treatment", "response", "period") %in% colnames(data))!=3) {
      stop("The data frame with trial data must contain the columns 'treatment', 'response' and 'period'!")
    }

    if(!is.numeric(arm) | length(arm)!=1){
      stop("The evaluated treatment arm (`arm`) must be one number!")
    }

    if(!is.numeric(alpha) | length(alpha)!=1 | alpha>=1 | alpha<=0){
      stop("The significance level (`alpha`) must be one number between 0 and 1!")
    }

    if(!is.logical(ci) | length(ci)!=1){
      stop("The indicator whether confidence intervals should be computed (`ci`) must be TRUE or FALSE!")
    }

    if(!is.logical(ncc) | length(ncc)!=1){
      stop("The indicator of including NCC data to the analysis (`ncc`) must be TRUE or FALSE!")
    }
  }

  min_period <- min(data[data$treatment==arm,]$period)
  max_period <- max(data[data$treatment==arm,]$period)

  if (ncc) {
    data_new <- data[data$period %in% c(1:max_period),]
  } else {
    data_new <- data[data$period %in% c(min_period:max_period),]
  }

  data_new$treatment_aux <- ifelse(data_new$treatment==arm, 0, data_new$treatment) # create an auxiliary treatment variable for the interaction

  # fit linear mixed model
  if(length(unique(data_new$period))==1){ # if only one period in the data, don't use period as covariate
    mod <- lm(response ~ as.factor(treatment), data_new)
    res <- summary(mod)

    # one-sided p-value
    p_val <- pt(coef(res)[paste0("as.factor(treatment)", arm), "t value"], mod$df, lower.tail = FALSE)

  } else {
    mod <- lmer(response ~ as.factor(treatment) + as.factor(period) + (1 | treatment_aux:period), data_new) # using lmerTest
    res <- summary(mod)

    # one-sided p-value
    p_val <- pt(coef(res)[paste0("as.factor(treatment)", arm), "t value"], coef(res)[paste0("as.factor(treatment)", arm), "df"], lower.tail = FALSE)

  }


  # treatment effect
  treat_effect <- res$coefficients[paste0("as.factor(treatment)", arm), "Estimate"]

  reject_h0 <- (p_val < alpha)

  # confidence intervals
  if (ci) {
    lower_ci <- confint(mod, level = 1-(2*alpha), parallel="no")[paste0("as.factor(treatment)", arm), 1]
    upper_ci <- confint(mod, level = 1-(2*alpha), parallel="no")[paste0("as.factor(treatment)", arm), 2]
  }

  return(list(p_val = p_val,
              treat_effect = treat_effect,
              lower_ci = ifelse(exists("lower_ci"), lower_ci, "not computed"),
              upper_ci = ifelse(exists("upper_ci"), upper_ci, "not computed"),
              reject_h0 = reject_h0,
              model = mod))
}