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an object of class \samp{Mods}, +#' see [Mods()] for details +#' +#' @return matrix y with all log hazard rates per dose level and per model +#' +#' @export +log_hazard_rates <- function(mods) { + y0 <- getResp(mods, doses = attr(mods, "doses")) + y <- y0[1:dim(y0)[1],] + return(y) +} +#' @examples +#' ## define 2 models, including the doses, direction decreasing in survival +#' contexts, +#' placEff is log hazard rate for placebo arm +#' and # difference between the response at the highest dose and placEff +#' mods <- Mods( +#' emax = c(1), +#' linear = NULL, +#' doses = c(0, 1, 1.5, 3), +#' direction = c("decreasing"), +#' placEff = log(0.6), +#' maxEff = log(0.3) - log(0.6) # difference between the response at the +#' highest dose and placEff +#' +#' log_hazard_rates(mods) log hazard rates +#' exp(log_hazard_rates(mods)) # hazard rates +``` + +```{r} +#' Data generation for Survival Data following exponential or Weibull distribution +#' +#' Simulate survival data using an exponential or Weibull distribution with the +#' true hazard rates from one model of \samp{mods}, +#' with event driven censoring after \samp{etotal} events happen and with +#' staggered study entry. +#' To implement the staggered study entry, an entry time for each patient is +#' computed and added to their event time. Then the event time is given in +#' calendar time. Then the data gets censored after the predefined number of +#' events and event time is again reduced by entry time to get the event time +#' in study time for the output +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param model wither Name or Number of the model from \samp{mods} of which +#' the hazards should be taken from +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param n sample size +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' @param staggered boolean variable, if true, study entry should be staggered +#' @param distribution character, either "exponential" or "weibull" +#' @param shape shape needed if "weibull" is chosen, if shape == 1, then equal +#' to exponential function +#' @param scale scale needed if "weibull" is chosen +#' +#' @return list of +#' - the data set including the variables \samp{group}, referring to the doses +#' (0 for placebo), \samp{hazard}, \samp{time} which is the event time and +#' \samp{status} which is 0 if censored and 1 if event was observed +#' - plot showing the distribution of time to event +#' @references Rühl 2022 (for staggered study entry and event times using +#' Weibull distribution) +#' @export +simulate_surv_data <- function(mods, + model, + ratio, + n, + etotal, + staggered = F, + distribution = c("exponential", "weibull"), + shape = 2, + scale = 3) { + set.seed(2026) + doses <- attr(mods, "doses") + y <- log_hazard_rates(mods) + mean_resp <- sample(y[, model], n, replace = T, prob = ratio) + # mean resp are log hazard rates + lambda0 <- exp(attr(mods, "placEff")) + + distribution <- match.arg(distribution) + if (staggered == T) { + if (distribution == "exponential") { + entry <- runif(n, 0, qexp(etotal / n, lambda0)) + event <- entry + rexp(n, exp(mean_resp)) # calendar time, hazard rates + text <- "Staggered Study Entry and Exponential Distribution of Event + Times" + } else if (distribution == "weibull") { + entry <- runif(n, 0, qweibull(etotal / n, shape, scale)) + event <- + entry + c(rweibull(n, shape, (scale / ( + exp(mean_resp) / lambda0 + )) ^ (1 / shape))) + text <- "Staggered Study Entry and Weibull Distribution of Event Times" + } + } else if (staggered == F) { + entry <- rep(0, n) + if (distribution == "exponential") { + event <- rexp(n, exp(mean_resp)) + text <- "NO Staggered Study Entry and Exponential Distribution of Event + Times" + } else if (distribution == "weibull") { + event <- + c(rweibull(n, shape, (scale / ( + exp(mean_resp) / lambda0 + )) ^ (1 / shape))) + text <- "NO Staggered Study Entry and Weibull Distribution of Event Times" + } + } + t_max_event <- sort(event)[etotal] + status <- (event <= t_max_event) + censoring <- pmin(event, t_max_event) + study_time <- censoring - entry # study time + + data <- data.frame( + group = names(mean_resp), + hazard = mean_resp, + time = study_time, + status = as.numeric(status) + ) + data$group <- factor(data$group, levels = as.character(doses)) + + plot <- ggplot(data, aes(x = time)) + + geom_histogram(bins = floor(max(data$time)) * 4, + color = "black", + fill = "white") + + ggtitle(paste("Distribution of Time to Event (in Study Time)\n ", text)) + + theme(plot.title = element_text(hjust = 0.5)) + + return(list(data, plot)) +} +#' +#' @examples +#' generate some survival data set that follows an exponential distributions +#' with hazards from the Emax model +#' simulation <- simulate_surv_data( +#' mods = mods, +#' model = 1, +#' ratio = c(1, 0.5, 0.5, 1), +#' n = 100, +#' etotal = 50, +#' staggered = T, +#' distribution = "exponential") +#' (data <- simulation[[1]]) +#' (data_plot <- simulation[[2]]) +``` + +```{r} +#' Compute the Covariance matrices S and S0 +#' +#' Forpower and sample size calculations in MCP-Mod, knowledge of the cavaraince +#' matrix for the estimators of the placebo-adjusted mean response among the +#' dose groups is needed. In survival settings, this can not be derived using +#' standard software. +#' Deng et al. derived an explicit form of the covariance matrix for the +#' estimators of the log hazard ratios. Those are needed to evaluate the power +#' analytically. +#' +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' +#' @return +#' - S, the covariance matrix adapted to the survival setting, to calculate the +#' optimal contrast coefficients and power +#' - S0, the covariance matrix adapted to the survival setting under H0, to +#' determine the critical value +#' @references Deng 2019 +#' @export +S_and_S0 <- function(mods, ratio, etotal) { + y <- log_hazard_rates(mods) + # second column of beta / for second model here + lambda0 <- attr(mods, "placEff") + beta <- y - lambda0 # placebo adjusted log hazard rates + nshape <- ncol(beta) + ngroup <- nrow(beta) + # 0.5 * beta = intermediate value between 0 and beta: + # See paper deng2019power (appendix last sentence) + p0 = 1 / apply(exp(0.5 * beta) * ratio, 2, sum) # sum of columns + pk = (exp(0.5 * beta) * ratio) %*% diag(p0) + + # S matrix + # Use S for calculating contrast and power + # Dimensions are reduced by 1 because the placebo group is excluded + # fill with 0s, 3-dimensional as given in c(...) + S <- array(0, c(ngroup - 1, ngroup - 1, nshape)) + for (i in 1:nshape) { + S[, , i] <- 1 / p0[i] + diag(S[, , i]) <- 1 / pk[-1, i] + 1 / p0[i] + } + S = S / etotal + + # S0 matrix + # use S0 to derive critical value + S0 <- diag(sum(ratio) + sum(ratio) / ratio[-1]) + S0[upper.tri(S0)] <- S0[lower.tri(S0)] <- sum(ratio) + S0 <- S0 / etotal + + return(list(S = S, S0 = S0)) +} + +#' @examples +#' S <- S_and_S0(mods = mods, ratio = c(1, 0.5, 0.5, 1), etotal = 50)$S +#' S0 <- S_and_S0(mods = mods, ratio = c(1, 0.5, 0.5, 1), etotal = 50)$S0 +``` + +```{r} +#' Extract information from the models defined +#' +#' Helper function to derive characteristics from the models defined with +#' \samp{Mods}. +#' Those are needed in following functions. +#' The functions \samp{log_hazard_rates} and \samp{S_andS0} defined above are +#' used here. +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' +#' @return +#' - matrix y: all log hazard rates per dose level and per model +#' - lambda 0: yearly hazard rate for Control/Placebo group +#' - nshape: number of models defined +#' - doses: vector of the doses, starting with 0 for the placebo group +#' - ngroup: number of dose groups +#' - S: covariance matrix for the survival setting +#' - S0: covariance matrix under H0 for the survival setting +#' - contMat: contrast matrix for all models and all dose groups computed using +#' the \samp{optContr} function from the \samp{DoseFinding} package +#' @export +model_info <- function(mods, ratio, etotal) { + y <- log_hazard_rates(mods) + lambda0 <- exp(attr(mods, "placEff")) + nshape <- dim(y)[2] + doses <- attr(mods, "doses") + ngroup <- length(doses) + + # S and S0 + sim <- S_and_S0(mods, ratio, etotal) + S <- sim$S # one for each model + S0 <- sim$S0 # one, independent of the model specifications + + return(list(y = y, lambda0 = lambda0, nshape = nshape, doses = doses, + ngroup = ngroup, S = S, S0 = S0)) +} +#' @examples +#' model_information <- model_info(mods = mods, ratio = c(1, 0.5, 0.5, 1), +#' etotal = 50) +``` + +```{r} +#' Compute power +#' +#' \samp{powMCT_TTE} is a modification of \samp{powMCT1} of Deng 2019 which is +#' a modification of the \samp{pow_MCT} function from the \samp{DoseFinding} +#' package. +#' Here, the function computes S and S0 using the subfunction \samp{S_and_S0}. +#' They are used as covariance matrix for the estimates. +#' This happens using S0 for the \samp{critVal} function from the +#' \samp{DoseFinding} package. With the critical value and with S, the power is +#' then +#' computed given a certain amount of events (\samp{etotal}) using the +#' \samp{powCalc} funciton from the \samp{DoseFinding} package. +#' \samp{cov2cor()} is used to scale a covariance matrix by its diagonal to +#' become the correlation matrix +#' The test is one sided using the significance level provided. +#' The calculations are based on the assumption of placebo-adjusted estimates, +#' the contrast matrix is +#' produced on placebo-adjusted scale +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details, defining the mean vectors +#' under which the power should be calculated +#' @param alpha Significance level to use +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' +#' @return Numeric vector containing the calculated power values under each +#' candidate model as well as the average +#' @references Pinheiro, J. C., Bornkamp, B., and Bretz, F. (2006). Design and +#' analysis of dose finding studies combining multiple comparisons and modeling +#' procedures, *Journal of Biopharmaceutical Statistics*, **16**, +#' Deng 2019 +#' @export +powMCT_TTE <- + function(mods, + alpha, + ratio, + etotal) { + set.seed(123) + model_information <- model_info(mods, ratio, etotal) + doses <- model_information$doses + nshape <- model_information$nshape + S <- model_information$S + S0 <- model_information$S0 + mcpmod_power <- rep(0, nshape) + contMat <- optContr(mods, + doses = doses[-1], + S = S[, , 1], + placAdj = T)[[1]] + contMat <- contMat[, 1, drop = F] + + if (nshape > 1) { + for (i in 2:nshape) { + contrast <- + optContr(mods, + doses = doses[-1], + S = S[, , i], + placAdj = T)[[1]] + contrast <- contrast[, i, drop = F] + contMat <- cbind(contMat, contrast) + } + } + for (j in 1:nshape) { + muMat <- getResp(mods)[,j, drop = FALSE] + # responses are expressed relative to the placebo. + muMat <- sweep(muMat, 2, muMat[1, ], "-") + muMat <- muMat[-1, , drop = FALSE] + deltaMat <- t(contMat) %*% muMat + covMat <- t(contMat) %*% S[, , j] %*% contMat + den <- sqrt(diag(covMat)) + deltaMat <- deltaMat / den + corMat <- cov2cor(covMat) + covMat0 <- t(contMat) %*% S0 %*% contMat + corMat0 <- cov2cor(covMat0) + critV <- critVal( + corMat0, + alpha, + df = 0, + alternative = "one.sided", + control = mvtnorm.control() + ) + pow <- DoseFinding:::powCalc( + alternative = "one.sided", + critV, + df = 0, + corMat, + deltaMat, + control = mvtnorm.control() + ) + mcpmod_power[j] <- pow + } + power_av <- round(mean(mcpmod_power), 4) + round(mcpmod_power, 5) + power_table <- data.frame(model = names(deltaMat[,1]), power = mcpmod_power) + # print(list(pow = pow, critV=critV, df=df, corMat=corMat, corMat0=corMat0, + # covMat=covMat, covMat0=covMat0, deltaMat=deltaMat)) + return(list(power_table = power_table, power_av = power_av)) + } +#' @examples +#' power_calc <- powMCT_TTE(mods = mods, alpha = 0.05, +#' ratio = c(1, 0.5, 0.5, 1), etotal = 30) +#' pow_sep <- power_calc$power_table +#' pow_av <- power_calc$power_av +#' +``` + +```{r} +#' compute the number of total events needed given a desired power +#' +#' \samp{no_events_given_pow function} computes the number of total events +#' needed given a desired power (\samp{des_pow}, in percent) using +#' the \samp{powMCT_TTE} function. It also provides a graph showing the average +#' power under the given models until the desired power is reached. +#' Starting at one event, the power is calculated. as long as the desired power +#' is not reached yet, the number of events gets raised by $1$. When the desired +#' power is reached, the loop ends. +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param alpha Significance level to use +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param des_pow desired power one wants to achieve +#' +#' @return +#' - number of total events needed given the desired power +#' - graph showing the average power under the given models until the desired +#' power is reached +#' @export +no_events_given_pow <- function(mods, alpha, ratio, des_pow){ + pow <- 0 + etotal_col <- c(0) + pow_col <- c(0) + + for (i in 1:1000){ + etotal <- i + pow <- powMCT_TTE(mods, alpha, ratio, etotal)$power_av + etotal_col[i] <- i + pow_col[i] <- pow + if(pow >= des_pow) break + } + dat <- data.frame(etotal_col, pow_col) + graf <- ggplot(data = dat, aes(x = etotal_col, y = pow_col, group = 1)) + + geom_line()+ + geom_point() + + xlab("Total Number of Events") + + ylab("Power") + + geom_hline(yintercept = des_pow, linetype="dashed") + + annotate("text", x = etotal / 6, y = des_pow - 0.02, + label = "Desired Power") + + ggtitle("Total Number of Events Needed to Reach the Desired Power") + + return(list(etotal = etotal, graf = graf)) +} +#' @examples +#' test <- no_events_given_pow(mods = mods, alpha = 0.25, +#' ratio = c(1, 0.5, 0.5, 1), des_pow = 0.8) +#' test$etotal +#' test$graf +``` + +```{r} +#' calculate the number of events given a certain sample size +#' +#' The \samp{no_events_given_samplesize} function calculates the number of +#' events given a certain sample size. +#' Therefore, the formula from Deng 2019 which is derived from equation 26 in +#' Lachin 1981 is used. +#' It is assumed that patients are recruited uniformly over the time period +#' $[0, \text{end_rec}]$ and that the survival time for group $k$ follows +#' the exponential distribution with hazard $\lambda_k$. +#' One model has to be chosen to compute the needed $\lambda_k$'s. +#' +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param end_rec end of recruitment period in years +#' @param end_stu endpoint of the study in years +#' @param model wither Name or Number of the model from \samp{mods} of which the +#' hazards should be taken from +#' @param n sample size +#' +#' @return +#' - total number of events +#' - vector with the number of events per group +#' @references Deng 2019, Lachin 1981 +#' @export +no_events_given_samplesize <- function(ratio, mods, end_rec, end_stu, model, n){ + y <- log_hazard_rates(mods) + ngroup <- length(ratio) + lambda <- exp(y)[,model] + rat <- ratio/sum(ratio) + D <- rep(0, ngroup) + for (i in 1:ngroup){ + D[i] <- (n * rat[i]) * (1 - ((exp(-lambda[i] * (end_stu - end_rec)) - + exp(-lambda[i] * end_stu)) / + (lambda[i] * end_rec))) + } + return(list(e_vec = D, etotal_samp = sum(D))) +} +#' @examples +#' no_events_given_samplesize(ratio = c(1, 0.5, 0.5, 1), +#' mods = mods, end_rec = 1, end_stu = 3, model = 2, n = 100) +``` + + +```{r} +#' calculate the total sample size needed to achieve a certain power +#' +#' \samp{samplesize_given_power} calculates the total sample size needed to +#' achieve a certain power. +#' Starting with a minimum number of patients (\samp{n_mind}) it computes the +#' number of events happening using the sample_size function. +#' With that number of events (\samp{etotal_int}) it computes the power this +#' study would have (\samp{pow}) using the \samp{powMCT_TTE} function. +#' The function stops when the desired power (\samp{des_pow}) is reached and +#' provides a plot showing the power for various sample sizes. +#' Here, the \samp{no_events_given_samplesize} is used to compute the number of +#' events. + +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param alpha Significance level to use +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param des_pow desired power one wants to achieve +#' @param end_rec end of recruitment period in years +#' @param end_stu endpoint of the study in years +#' @param model wither Name or Number of the model from \samp{mods} of which the +#' hazards should be taken from +#' @param n_mind minimum number of patients with which the loop starts, should +#' not be chosen too small, so meaningful allocaition can be computed and to +#' reduce running time +#' +#' @return +#' - number of total sample size needed given the desired power +#' - graph showing the average power under the given models until the desired +#' power is reached +#' - text explaining the output +#' @references Deng 2019, Lachin 1981 +#' @export +samplesize_given_power <- + function(mods, + alpha, + ratio, + des_pow, + end_rec, + end_stu, + model, + n_mind = 20) { + + pow <- 0 + n_col <- c(0) + pow_col <- c(0) + + for (i in (n_mind:1000)) { + n <- i + etotal_int <- + floor(no_events_given_samplesize(ratio, mods, end_rec, end_stu, model, + n = n)$etotal_samp) + pow <- + powMCT_TTE(mods, alpha, ratio, etotal = etotal_int)$power_av + n_col[i - n_mind] <- i + pow_col[i - n_mind] <- pow + if (pow >= des_pow) + break + } + + dat <- data.frame(n_col, pow_col) + graf <- + ggplot(data = dat, aes(x = n_col, y = pow_col, group = 1)) + + geom_line() + + geom_point() + + xlab("Total Sample Size") + + ylab("Power") + + geom_hline(yintercept = des_pow, linetype = "dashed") + + annotate("text", x = etotal / 2, y = des_pow - 0.02, + label = "Desired Power") + + ggtitle("Total Sample Size Needed to Reach the Desired Power") + + text <- paste("To reach the desired power of", des_pow * 100, "%, ", n, + "patients are needed and", etotal_int, "events are expected.") + + return(list( + n = n, + etotal = etotal_int, + graf = graf, + data = dat, + text = text + )) + } +#' @examples +#' samplesize_given_power(mods = mods, alpha = 0.025, ratio, des_pow = 0.8, +#' end_rec = 1, end_stu = 3, model = 2, n_mind = 10) +``` \ No newline at end of file diff --git a/vignettes/LaTeX.Rmd b/vignettes/LaTeX.Rmd new file mode 100644 index 0000000..5bbdc3f --- /dev/null +++ b/vignettes/LaTeX.Rmd @@ -0,0 +1,137 @@ +--- +title: "LaTEX" +author: "Carina Miller" +date: "2025-08-19" +output: pdf_document +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE) +``` + +Underlying model for normally distributed data +$$ +\begin{aligned} +y_{ij} = f(d_i, \theta) + \epsilon_{ij}, \epsilon_{ij} \sim \mathcal{N}(0, \sigma^2) +\end{aligned} +$$ +with\ +- $y_{ij}$ response of the $j^{th}$ patient on dose $d_i$,\ +- $d_0, \ldots, d_k$ dose levels including placebo ($0$) with $n_i$ patients allocated to dose $d_i$,\ +- $k$ number of dose levels,\ +- $f(d_i, \theta)$ is a candidate dose-response model that represents the mean response $\mu(d_i)$ at dose $d_i$,\ +- $\theta$ vector of model parameters and\ +- $\epsilon_{ij}$ independent error terms. + +For general parametric models +$$ +\begin{aligned} +y_{ij} = F(\mu(d_i), z, \eta) +\end{aligned} +$$ +with\ +- $z$ are possible covariates,\ +- $\eta$ contains the nuisance parameters (e.g., $\eta = \sigma^2$ if $F$ is the normal distribution) and\ +- $\mu(d_i)$ dose-response parameter at different doses $i$ related through the dose-response model +$$ +\begin{aligned} +\mu(d_i) &= f(x, \theta) = \theta_0 + \theta_1f^0(d_i, \theta^0) +\end{aligned} +$$ +with\ +- $f^0$ standardized model function and\ +- $\theta^0$ parameter vector of $f^0$\ + + +with $ED_{50}$ = the dose at which half of the maximum effect is achieved\ + +optimal contrasts:\ + +$$ +c^{\textrm{opt}} \propto +S^{-1}\biggl(\mu^0_m - \frac{(\mu^0_m)^T S^{-1}1_K}{1_K^T S^{-1} 1_K}\biggr) +$$ +with\ +$K$ number of doses,\ +$1_K$ all-ones vector of length $K$ and\ +$S$ covariance matrix of the estimates at the doses\ + +\newpage + +Matrix containing the optimal contrasts: +$$ +C^{\textrm{opt}} = \left[c_1^{\textrm{opt}} \cdots c_M^{\textrm{opt}}\right] +$$ +Contrast estimates: +$$ +(C^{\textrm{opt}})' \hat{\mu} +$$ +are asymptotically normally distributed with mean: +$$ +(C^{\textrm{opt}})' \mu +$$ +and covariance matrix: +$$ +(C^{\textrm{opt}})'\hat{S}C^{\textrm{opt}} +$$ + +Test:\ + +$$ +H_0 : (c_m^{\textrm{opt}})'\mu = 0 \,\textrm{ vs. }\, H_1 : (c_m^{\textrm{opt}})'\mu > 0 +$$ + +$$ +z_m = \frac{(c_m^{\textrm{opt}})'\hat{\mu}}{\left[(C^{\textrm{opt}})'\hat{S}C^{\textrm{opt}}\right]_{m,m}^{1/2}} +$$ + + +with\ +- $\hat{\mu}$ vector of estimated dose-response parameters (e.g., means, log-odds, log-hazard ratios)\ +- $S$ estimated covariance matrix of $\hat{\mu}$\ +- $c_m^{\textrm{opt}}$ optimal contrast vector for model $m$\ +- $C^{\textrm{opt}} = \left[c_1^{\textrm{opt}} \cdots c_M^{\textrm{opt}}\right]$ matrix containing all optimal contrasts\ +- Contrast estimates $(C^{\textrm{opt}})' \hat{\mu} \sim \mathcal{N}((C^{\textrm{opt}})' \mu \,\,, (C^{\textrm{opt}})'\hat{S}C^{\textrm{opt}})$ + + +$$ +\mu_{d_i}, \,\,\,\,\,\,i = 1, \ldots, K +$$ + + +$$ +d_i +$$ + +$$ +\hat{\mu} +$$ + +$$ +\hat{\mu} \sim \mathcal{N}(\mu, S) +$$ + + +Formula Deng to compute sample size +$$ +n_k = D_k \bigg/ \left(1-\frac{\exp(-\lambda_k(\tau - R))\exp(-\lambda_k\tau)}{\lambda_kR}\right) +$$ + +with\ +$n_k$ patients needed per group $k$\ +$R$ end of recruiting period\ +$\tau$ total years of study duration\ +$D_k$ number of events in group $k$< +$\lambda_k$ hazard $\lambda$ in group $k$ + + +The power to detect the presence of dose response under candidate model $m$ is +$$ +\begin{aligned} +\pi_m &= 1 - \mathbb{P}\left(Z_i < cV, ..., Z_M < cV \,|\,\text{model }m\text{ is true}\right) +\end{aligned} +$$ + +with\ +- $Z_i, \ldots, Z_M$ contrast test statistics, asymptotically normal and\ +- $cV$ critical value\ diff --git a/vignettes/MCP TTE/Draft5.Rmd b/vignettes/MCP TTE/Draft5.Rmd new file mode 100644 index 0000000..45ee692 --- /dev/null +++ b/vignettes/MCP TTE/Draft5.Rmd @@ -0,0 +1,946 @@ +--- +title: "Time-to-Event Data MCP-Mod" +output: rmarkdown::html_vignette +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE) +rmarkdown.html_vignette.check_title = FALSE +``` + +```{r, echo=F, results='hide', message=FALSE} +library(`DoseFinding`, lib.loc = "~/RStudio/packages") +library(truncnorm) +library(dplyr) +library(survival) +library(ggsurvfit) +library(ggplot2) +``` + +In this vignette we illustrate how to use the `DoseFinding` package with survival endpoints. + +## Background and Data Set +Assume a dose-finding study is planned for an hypothetical investigational treatment. The endpoint of interest is time to a certain event. The treatment is tested with doses $0$ (placebo), $0.2$, $0.5$ and $1$, with a ratio of $2:1:1:2$. It is assumed that the yearly hazard rate for the placebo group is $\lambda_0 = 0.6$ and that the hazard ratio for the treatment effect on the highest dose, here $\text{HR} = 0.5$, is provided.\ +For calculations we need $\lambda_1$, the hazard rate for the treatment group on dose $1$. This can be derived by multiplication: +$$ +\begin{aligned} +\text{HR} = \frac{\lambda_1}{\lambda_0} +\Leftrightarrow \text{HR} \cdot \lambda_0 = \lambda_1 +\end{aligned} +$$ +In case median survival time $T_{0.5}$ is given, this can be transformed to a hazard rate using: +$$ +\begin{aligned} +\lambda = \frac{\ln(2)}{T_{0.5}} +\end{aligned} +$$ + +This can be derived from the definition of the survival function: +$$ +\begin{aligned} +S(T_{0.5}) &= 0.5 \\ +\Leftrightarrow \exp(-\lambda T_{0.5}) &= 0.5\\ +\Leftrightarrow \ln(\exp(-\lambda T_{0.5})) &= \ln(0.5)\\ +\Leftrightarrow -\lambda T_{0.5} &= \ln(0.5)\\ +\Leftrightarrow \lambda T_{0.5} &= - \ln(0.5)\\ +\Leftrightarrow \lambda T_{0.5} &= \ln(2)\\ +\Leftrightarrow T_{0.5} &= \frac{\ln(2)}{\lambda}\\ +\Leftrightarrow T_{0.5} \cdot \lambda &= \ln(2)\\ +\Leftrightarrow \lambda &= \frac{\ln(2)}{T_{0.5}}\\ +\end{aligned} +$$ + +We define some parameters for example data in the setting just described: +```{r} +lambda0 <- 0.6 # yearly hazard rate for Control/Placebo group +HR_treat <- 0.5 # hazard ratio for treatment effect on the highest dose +lambda3 <- lambda0 * HR_treat # hazard rate for Treatment group on highest dose +doses <- c(0, 0.2, 0.5, 1) # placebo or group and 3 treatment groups +ratio <- c(1, 0.5, 0.5, 1) # the first number is always 1 +ngroup <- length(doses) +n <- 100 # number of patients +etotal <- 50 # predefined total number of events +``` + + +## Candidate models +We will use the following candidate set of dose response models for the mean response: An $\text{E}_{max}$ model, a sigmoidal $\text{E}_{max}$ model, a quadratic, a n exponential and a linear model. For the $\text{E}_{max}$ model, $\text{ED}_{50}$ (the dose at +which half of the maximum effect is reached) of $1$ will be used as "guesstimates". For the +sigmoidal $\text{E}_{max}$, $\text{ED}_{50}$ will be $10$ with hill parameter $4$.\ +In survival context, it is important to remember that `direction` is `decreasing`. Alternatively, one can specify a negative `maxEff` argument.\ +`placEff` is expecting the log hazard rate of the placebo arm, so $\log\left(\lambda_0\right)$.\ +`maxEff` is the maximum effect size within the dose-range. It is expecting the difference between the response at the highest dose and `placEff`, the log(HR): + +$$ +\begin{aligned} +\text{HR} = \frac{\lambda_1}{\lambda_0} +\Leftrightarrow \log(\text{HR}) = \log\left(\lambda_1\right) - \log\left(\lambda_0\right) +\end{aligned} +$$ +We use log hazard rates here because dose-response models in the `DoseFinding` package assume additive effects when specifying responses. +```{r, fig.width = 9, out.width = '100%'} +mods <- Mods( + emax = c(1), + sigEmax = rbind(c(10, 4)), + quadratic = -0.5, + exponential = 0.7, + linear = NULL, + doses = doses, + direction = c("decreasing"), # decreasing in survival contexts + placEff = log(lambda0), # log hazard rate for placebo arm + maxEff = log(lambda3) - log(lambda0) + # difference between the response at the highest dose and placEff +) + +plotMods(mods, superpose = T, ylab = 'log (hazard rates)') +``` + + +```{r} +#' Extracts the log hazard rates for all doses per defined model +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' +#' @return matrix y with all log hazard rates per dose level and per model +#' +#' @export +log_hazard_rates <- function(mods) { + y0 <- getResp(mods, doses = attr(mods, "doses")) + y <- y0[1:dim(y0)[1],] + return(y) +} +#' @examples +#' ## define 2 models, including the doses, direction decreasing in survival +#' contexts, +#' placEff is log hazard rate for placebo arm +#' and # difference between the response at the highest dose and placEff +#' mods <- Mods( +#' emax = c(1), +#' linear = NULL, +#' doses = c(0, 1, 1.5, 3), +#' direction = c("decreasing"), +#' placEff = log(0.6), +#' maxEff = log(0.3) - log(0.6) # difference between the response at the +#' highest dose and placEff +#' +#' log_hazard_rates(mods) log hazard rates +#' exp(log_hazard_rates(mods)) # hazard rates +``` + +## Data generation +```{r} +#' Data generation for Survival Data following exponential or Weibull distribution +#' +#' Simulate survival data using an exponential or Weibull distribution with the +#' true hazard rates from one model of \samp{mods}, +#' with event driven censoring after \samp{etotal} events happen and with +#' staggered study entry. +#' To implement the staggered study entry, an entry time for each patient is +#' computed and added to their event time. Then the event time is given in +#' calendar time. Then the data gets censored after the predefined number of +#' events and event time is again reduced by entry time to get the event time +#' in study time for the output +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param model wither Name or Number of the model from \samp{mods} of which +#' the hazards should be taken from +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param n sample size +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' @param staggered boolean variable, if true, study entry should be staggered +#' @param distribution character, either "exponential" or "weibull" +#' @param shape shape needed if "weibull" is chosen, if shape == 1, then equal +#' to exponential function +#' @param scale scale needed if "weibull" is chosen +#' +#' @return list of +#' - the data set including the variables \samp{group}, referring to the doses +#' (0 for placebo), \samp{hazard}, \samp{time} which is the event time and +#' \samp{status} which is 0 if censored and 1 if event was observed +#' - plot showing the distribution of time to event +#' @references Rühl 2022 (for staggered study entry and event times using +#' Weibull distribution) +#' @export +simulate_surv_data <- function(mods, + model, + ratio, + n, + etotal, + staggered = F, + distribution = c("exponential", "weibull"), + shape = 2, + scale = 3) { + set.seed(2026) + doses <- attr(mods, "doses") + y <- log_hazard_rates(mods) + mean_resp <- sample(y[, model], n, replace = T, prob = ratio) + # mean resp are log hazard rates + lambda0 <- exp(attr(mods, "placEff")) + + distribution <- match.arg(distribution) + if (staggered == T) { + if (distribution == "exponential") { + entry <- runif(n, 0, qexp(etotal / n, lambda0)) + event <- entry + rexp(n, exp(mean_resp)) # calendar time, hazard rates + text <- "Staggered Study Entry and Exponential Distribution of Event + Times" + } else if (distribution == "weibull") { + entry <- runif(n, 0, qweibull(etotal / n, shape, scale)) + event <- + entry + c(rweibull(n, shape, (scale / ( + exp(mean_resp) / lambda0 + )) ^ (1 / shape))) + text <- "Staggered Study Entry and Weibull Distribution of Event Times" + } + } else if (staggered == F) { + entry <- rep(0, n) + if (distribution == "exponential") { + event <- rexp(n, exp(mean_resp)) + text <- "NO Staggered Study Entry and Exponential Distribution of Event + Times" + } else if (distribution == "weibull") { + event <- + c(rweibull(n, shape, (scale / ( + exp(mean_resp) / lambda0 + )) ^ (1 / shape))) + text <- "NO Staggered Study Entry and Weibull Distribution of Event Times" + } + } + t_max_event <- sort(event)[etotal] + status <- (event <= t_max_event) + censoring <- pmin(event, t_max_event) + study_time <- censoring - entry # study time + + data <- data.frame( + group = names(mean_resp), + hazard = mean_resp, + time = study_time, + status = as.numeric(status) + ) + data$group <- factor(data$group, levels = as.character(doses)) + + plot <- ggplot(data, aes(x = time)) + + geom_histogram(bins = floor(max(data$time)) * 4, + color = "black", + fill = "white") + + ggtitle(paste("Distribution of Time to Event (in Study Time)\n ", text)) + + theme(plot.title = element_text(hjust = 0.5)) + + return(list(data, plot)) +} +#' +#' @examples +#' generate some survival data set that follows an exponential distributions +#' with hazards from the Emax model +#' simulation <- simulate_surv_data( +#' mods = mods, +#' model = 1, +#' ratio = c(1, 0.5, 0.5, 1), +#' n = 100, +#' etotal = 50, +#' staggered = T, +#' distribution = "exponential") +#' (data <- simulation[[1]]) +#' (data_plot <- simulation[[2]]) +``` + +```{r} +simulation <- simulate_surv_data( + mods, + model = 1, + ratio, + n = 100, + etotal = 80, + staggered = F, + distribution = "weib", + shape = 2, + scale = 5) + +data <- simulation[[1]] +data_plot <- simulation[[2]] +``` + + +```{r, fig.width = 5, out.width = '100%', echo=FALSE} +model <- 1 +ratio <- c(1, 0.2, 0.5, 1) +n <- 100 +etotal <- 90 +shape <- 2 +scale <- 5 + +(data_plot_F_exp <- simulate_surv_data(mods, model, ratio, n, etotal, shape, + scale, staggered = F, + distribution = "exp")[[2]]) +(data_plot_F_weib <- simulate_surv_data(mods, model, ratio, n, etotal, shape, + scale, staggered = F, + distribution = "weib")[[2]]) +(data_plot_T_exp <- simulate_surv_data(mods, model, ratio, n, etotal, shape, + scale, staggered = T, + distribution = "exp")[[2]]) +(data_plot_T_weib <- simulate_surv_data(mods, model, ratio, n, etotal, shape, + scale, staggered = T, + distribution = "weib")[[2]]) + +mean(simulate_surv_data(mods, model, ratio, n, etotal, shape, scale, + staggered = F, distribution = "exp")[[1]] $ time) +mean(simulate_surv_data(mods, model, ratio, n, etotal, shape, scale, + staggered = F, distribution = "weib")[[1]] $ time) +mean(simulate_surv_data(mods, model, ratio, n, etotal, shape, scale, + staggered = T, distribution = "exp")[[1]] $ time) +mean(simulate_surv_data(mods, model, ratio, n, etotal, shape, scale, + staggered = T, distribution = "weib")[[1]] $ time) +``` + +Look at the survival data with a Kaplan-Meier plot: +```{r, fig.width = 5, out.width = '100%'} +survfit2(Surv(time, status) ~ group, data = data) %>% + ggsurvfit() + + labs(x = "Years", + y = "Survival Probability", + title = "Kaplan-Meier Estimator by Dose", + ) + + theme(plot.title = element_text(hjust = 0.5)) +``` + +## Cox's Semiparametric Regression Model +The Cox's semiparametric regression model expresses the hazard rate like this +$$ +\begin{aligned} +\lambda \left(t|x_1,\ldots, x_p\right) = \lambda_0\left(t\right)\exp\left(\beta_1x_1+ \ldots \beta_px_p\right) +\end{aligned} +$$ + +with\ +$\lambda_0\left(t\right)$ baseline hazard,\ +$x_1,\ldots, x_p$ covariates,\ +$\beta_1,\ldots\beta_p$ regression coefficients (effects) of the covariates\ +$\exp\left(\beta_1x_1+ \ldots \beta_px_p\right)$ and hazard ratio\ +(Book ABG)\ +here: $x$ refers to the doses, so\ +$$ +\begin{aligned} +\lambda \left(t|\text{doses}\right) &= \lambda_0\left(t\right)\exp\left(\beta_1 \cdot 0\, + \beta_2 \cdot 0.2\, + \beta_3 \cdot 0.5\, + \beta_4 \cdot 1\,\right) \\ +\end{aligned} +$$ +Run Cox PH Model:\ +Fit the Cox Proportional Hazards model to the survival data. Evaluate whether the treatment has a significant effect on survival: +```{r} +cox <- coxph(Surv(time, status) ~ group, data = data) +summary(cox) +``` + +Coefficients are estimates. Contain the estimated log hazard ratios for each dose group relative to the reference group, typically placebo: +```{r} +coef <- cox$coef +``` + +Variance-covariance matrix of the estimated coefficients from the Cox Proportional Hazards Model +```{r} +cov <- cox$var +``` + +# Analysis +The Cox's regression model provides the estimated coefficients and their estimated covariance matrix. This is used for some analyses.\ +NOW: Everything placAdj = TRUE !!! + +## Multiple Contrast Test +How well do the different potential dose-response models fit the data compared to the null hypothesis $H_0$: "No dose-response relationship"?\ +Evaluate dose-response relationships using the MCPMod approach. Tests for significant differences across doses +```{r} +mct <- + MCTtest( + dose = doses[-1], # placebo adjusted + resp = coef, + S = cov, + models = mods, + type = 'general', + alternative = "one.sided", + placAdj = TRUE # placebo-adjusted estimates are specified in ‘⁠resp⁠’ + ) +mct +``` + +The first table shows the same matrix as `optContr` containing optimal contrasts for candidate shapes. It shows how much weight each dose contributes to the test for each hypothesized model.\ +(like book p.220 Table 12.3)\ + +The second table contains the result of the contrast test. It shows how similar or related the estimated contrasts for each model are.\ +High correlations (near 1) between models (e.g., emax1 and emax2) suggest these models produce similar dose-response patterns.\ +(like book p.220 Table 12.4 or p.222 Table 12.6).\ + +The third table gives the $t$-statistics and adjusted $p$-values for each model.\ +It shows how strong the evidence for the corresponding model is.\ +A higher $t$-statistic suggests better compatibility between the model and the observed data.\ +Small adjusted $p$-values ($< 0.05$) indicate strong evidence for the model fitting better than the null hypothesis ("no dose-response relationship"). Here, all adjusted $p$-values are small, so this gives a strong evidence for the existence of a dose-response effect.\ + +The model with smallest $p$-value and highest $t$-statistic is considered the best model, with the strongest statistical evidence for detecting the dose-response pattern. Here, this would be emax2 which makes sense as this is the distribution used for data generation. + +## Find the best model (see book p. 219) +Plot of estimated dose-response curve (book p. 220)\ +Like plot in book p.221, Fig 12.2 + +```{r, fig.width = 6.9, out.width = '100%'} +fitEmax <- fitMod( + dose = doses[-1], + resp = coef, + S = cov, + model = 'emax', + type = 'general', + placAdj = TRUE +) +plot(fitEmax, title = "TITEL") +aic_emax <- gAIC(fitEmax) + +fitSigEmax <- fitMod( + dose = doses[-1], + resp = coef, + S = cov, + model = 'sigEmax', + type = 'general', + placAdj = TRUE +) + +plot(fitSigEmax) +aic_sigemax <- gAIC(fitSigEmax) + +ifelse(aic_emax <= aic_sigemax, + paste('Emax model fits better than SigEmax regarding the gAIC values of + the models.'), + paste('SigEmax model fits better than Emax regarding the gAIC values of + the models.')) +``` +Preferred model is the one with the minimum AIC value.\ + +## Find the best dose (see book p. 220) +Here, decreasing response is beneficial (as before).\ +Find a dose that achieves a certain percentage of the full effect size over placebo, usually $0.9$ as it is close to the plateau. +```{r} +percentage_dose_emax <- ED(fitEmax, p = 0.9, direction = 'decreasing') +percentage_dose_emax + +percentage_dose_sigemax <- ED(fitSigEmax, p = 0.9, direction = 'decreasing') +percentage_dose_sigemax +``` + + +Predict the effect of more doses, e.g. $0.3$ and $1.5$ (book p. 220) +```{r} +pred_emax <- predict(fitEmax, doseSeq = c(0.3, 1.5), + predType = 'effect-curve', se.fit = T) +pred_emax + +pred_sigemax <- predict(fitSigEmax, doseSeq = c(0.3, 1), + predType = 'effect-curve', se.fit = T) +pred_sigemax +``` + + +# Power and sample size +Contrasts help assess whether a dose-response relationship exists by comparing the effects of different doses in the trial.\ +Use $w = 1$ if homoscedastic residuals with equal group sizes, which is not the case here.\ +```{r, fig.width = 6.9, out.width = '100%'} +contMat <- optContr(mods, w = ratio) +summary(contMat) # cols add up to ~0 +plotContr(contMat) # display contrasts using ggplot2 +``` + +For the functions `sampSizeMCT` and `powN` there is `sigma` needed which we have to derive like in (deng2019power) for survival settings.\ +They derived the covariance matrix $S$ of $\hat{\beta}$: +$$ +\begin{aligned} +S \approx D^{-1} +\begin{pmatrix}{} +p_0^{-1} + p_1^{-1} & p_0^{-1} & \ldots & p_0^{-1} \\ +p_0^{-1} & p_0^{-1} + p_2^{-1} & \ldots & p_0^{-1} \\ +\vdots & \vdots & \vdots & \vdots\\ +p_0^{-1} & p_0^{-1} & \ldots & p_0^{-1} + p_K^{-1} \\ +\end{pmatrix} +\end{aligned} +$$ +with +$$ +\begin{aligned} +p_k = \frac{\frac{n_k}{n_0}\exp(\beta_k)}{1 + \sum_{i = 1}^{K}\frac{n_i}{n_0}\exp(\beta_i)}, +\end{aligned} +$$ +$n_k$ the number of patients in dose group $k$ for $k = 0, 1, \ldots, K$, $k = 0$ placebo,\ +$n = n_0 + n_1 + \ldots + n_k$,\ +$\beta_0 = 0$\ + +Under $H_0$, $S$, say, $S_0$, then has the following structure:\ +$$ +\begin{aligned} +S_0 \approx \frac{n}{D} +\begin{pmatrix}{} +n_0^{-1} + n_1^{-1} & n_0^{-1} & \ldots & n_0^{-1} \\ +n_0^{-1} & n_0^{-1} + n_2^{-1} & \ldots & n_0^{-1} \\ +\vdots & \vdots & \vdots & \vdots\\ +n_0^{-1} & n_0^{-1} & \ldots & n_0^{-1} + n_K^{-1} \\ +\end{pmatrix} +\end{aligned} +$$ + +with $D =$ total number of events (before named `etotal`)\ + +(see everything paper deng2019power) +# here: for all models +```{r} +#' Compute the Covariance matrices S and S0 +#' +#' Forpower and sample size calculations in MCP-Mod, knowledge of the cavaraince +#' matrix for the estimators of the placebo-adjusted mean response among the +#' dose groups is needed. In survival settings, this can not be derived using +#' standard software. +#' Deng et al. derived an explicit form of the covariance matrix for the +#' estimators of the log hazard ratios. Those are needed to evaluate the power +#' analytically. +#' +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' +#' @return +#' - S, the covariance matrix adapted to the survival setting, to calculate the +#' optimal contrast coefficients and power +#' - S0, the covariance matrix adapted to the survival setting under H0, to +#' determine the critical value +#' @references Deng 2019 +#' @export +S_and_S0 <- function(mods, ratio, etotal) { + y <- log_hazard_rates(mods) + # second column of beta / for second model here + lambda0 <- attr(mods, "placEff") + beta <- y - lambda0 # placebo adjusted log hazard rates + nshape <- ncol(beta) + ngroup <- nrow(beta) + # 0.5 * beta = intermediate value between 0 and beta: + # See paper deng2019power (appendix last sentence) + p0 = 1 / apply(exp(0.5 * beta) * ratio, 2, sum) # sum of columns + pk = (exp(0.5 * beta) * ratio) %*% diag(p0) + + # S matrix + # Use S for calculating contrast and power + # Dimensions are reduced by 1 because the placebo group is excluded + # fill with 0s, 3-dimensional as given in c(...) + S <- array(0, c(ngroup - 1, ngroup - 1, nshape)) + for (i in 1:nshape) { + S[, , i] <- 1 / p0[i] + diag(S[, , i]) <- 1 / pk[-1, i] + 1 / p0[i] + } + S = S / etotal + + # S0 matrix + # use S0 to derive critical value + S0 <- diag(sum(ratio) + sum(ratio) / ratio[-1]) + S0[upper.tri(S0)] <- S0[lower.tri(S0)] <- sum(ratio) + S0 <- S0 / etotal + + return(list(S = S, S0 = S0)) +} + +#' @examples +#' S <- S_and_S0(mods = mods, ratio = c(1, 0.5, 0.5, 1), etotal = 50)$S +#' S0 <- S_and_S0(mods = mods, ratio = c(1, 0.5, 0.5, 1), etotal = 50)$S0 +``` + + +Power estimation using the calculated S and S0: +```{r} +S <- S_and_S0(mods, ratio, etotal)$S +S0 <- S_and_S0(mods, ratio, etotal)$S0 +alpha <- 0.05 + +contMat <- optContr(mods, doses = doses[-1], S = S[,, 1], placAdj = T)[[1]] +``` + +```{r} +#' Extract information from the models defined +#' +#' Helper function to derive characteristics from the models defined with +#' \samp{Mods}. +#' Those are needed in following functions. +#' The functions \samp{log_hazard_rates} and \samp{S_andS0} defined above are +#' used here. +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' +#' @return +#' - matrix y: all log hazard rates per dose level and per model +#' - lambda 0: yearly hazard rate for Control/Placebo group +#' - nshape: number of models defined +#' - doses: vector of the doses, starting with 0 for the placebo group +#' - ngroup: number of dose groups +#' - S: covariance matrix for the survival setting +#' - S0: covariance matrix under H0 for the survival setting +#' - contMat: contrast matrix for all models and all dose groups computed using +#' the \samp{optContr} function from the \samp{DoseFinding} package +#' @export +model_info <- function(mods, ratio, etotal) { + y <- log_hazard_rates(mods) + lambda0 <- exp(attr(mods, "placEff")) + nshape <- dim(y)[2] + doses <- attr(mods, "doses") + ngroup <- length(doses) + + # S and S0 + sim <- S_and_S0(mods, ratio, etotal) + S <- sim$S # one for each model + S0 <- sim$S0 # one, independent of the model specifications + + return(list(y = y, lambda0 = lambda0, nshape = nshape, doses = doses, + ngroup = ngroup, S = S, S0 = S0)) +} +#' @examples +#' model_information <- model_info(mods = mods, ratio = c(1, 0.5, 0.5, 1), +#' etotal = 50) +``` + +```{r} +model_information <- model_info(mods, ratio, etotal) +``` + +```{r} +#' Compute power +#' +#' \samp{powMCT_TTE} is a modification of \samp{powMCT1} of Deng 2019 which is +#' a modification of the \samp{pow_MCT} function from the \samp{DoseFinding} +#' package. +#' Here, the function computes S and S0 using the subfunction \samp{S_and_S0}. +#' They are used as covariance matrix for the estimates. +#' This happens using S0 for the \samp{critVal} function from the +#' \samp{DoseFinding} package. With the critical value and with S, the power is +#' then +#' computed given a certain amount of events (\samp{etotal}) using the +#' \samp{powCalc} funciton from the \samp{DoseFinding} package. +#' \samp{cov2cor()} is used to scale a covariance matrix by its diagonal to +#' become the correlation matrix +#' The test is one sided using the significance level provided. +#' The calculations are based on the assumption of placebo-adjusted estimates, +#' the contrast matrix is +#' produced on placebo-adjusted scale +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details, defining the mean vectors +#' under which the power should be calculated +#' @param alpha Significance level to use +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param etotal number of events after which event driven censoring is +#' implemented, time cutoff when etotal of event being observed +#' +#' @return Numeric vector containing the calculated power values under each +#' candidate model as well as the average +#' @references Pinheiro, J. C., Bornkamp, B., and Bretz, F. (2006). Design and +#' analysis of dose finding studies combining multiple comparisons and modeling +#' procedures, *Journal of Biopharmaceutical Statistics*, **16**, +#' Deng 2019 +#' @export +powMCT_TTE <- + function(mods, + alpha, + ratio, + etotal) { + set.seed(123) + model_information <- model_info(mods, ratio, etotal) + doses <- model_information$doses + nshape <- model_information$nshape + S <- model_information$S + S0 <- model_information$S0 + mcpmod_power <- rep(0, nshape) + contMat <- optContr(mods, + doses = doses[-1], + S = S[, , 1], + placAdj = T)[[1]] + contMat <- contMat[, 1, drop = F] + + if (nshape > 1) { + for (i in 2:nshape) { + contrast <- + optContr(mods, + doses = doses[-1], + S = S[, , i], + placAdj = T)[[1]] + contrast <- contrast[, i, drop = F] + contMat <- cbind(contMat, contrast) + } + } + for (j in 1:nshape) { + muMat <- getResp(mods)[,j, drop = FALSE] + # responses are expressed relative to the placebo. + muMat <- sweep(muMat, 2, muMat[1, ], "-") + muMat <- muMat[-1, , drop = FALSE] + deltaMat <- t(contMat) %*% muMat + covMat <- t(contMat) %*% S[, , j] %*% contMat + den <- sqrt(diag(covMat)) + deltaMat <- deltaMat / den + corMat <- cov2cor(covMat) + covMat0 <- t(contMat) %*% S0 %*% contMat + corMat0 <- cov2cor(covMat0) + critV <- critVal( + corMat0, + alpha, + df = 0, + alternative = "one.sided", + control = mvtnorm.control() + ) + pow <- DoseFinding:::powCalc( + alternative = "one.sided", + critV, + df = 0, + corMat, + deltaMat, + control = mvtnorm.control() + ) + mcpmod_power[j] <- pow + } + power_av <- round(mean(mcpmod_power), 4) + round(mcpmod_power, 5) + power_table <- data.frame(model = names(deltaMat[,1]), power = mcpmod_power) + # print(list(pow = pow, critV=critV, df=df, corMat=corMat, corMat0=corMat0, + # covMat=covMat, covMat0=covMat0, deltaMat=deltaMat)) + return(list(power_table = power_table, power_av = power_av)) + } +#' @examples +#' power_calc <- powMCT_TTE(mods = mods, alpha = 0.05, +#' ratio = c(1, 0.5, 0.5, 1), etotal = 30) +#' pow_sep <- power_calc$power_table +#' pow_av <- power_calc$power_av +#' +``` +The function provides the power for each model separately (pow_sep) as well as the average power over all models (pow_av): +```{r} +power_calc <- powMCT_TTE(mods, alpha, ratio, etotal = 30) +pow_sep <- power_calc$power_table # power under each candidate model +pow_av <- power_calc$power_av # average power + +pow_sep +pow_av +``` + + +```{r} +#' compute the number of total events needed given a desired power +#' +#' \samp{no_events_given_pow function} computes the number of total events +#' needed given a desired power (\samp{des_pow}, in percent) using +#' the \samp{powMCT_TTE} function. It also provides a graph showing the average +#' power under the given models until the desired power is reached. +#' Starting at one event, the power is calculated. as long as the desired power +#' is not reached yet, the number of events gets raised by $1$. When the desired +#' power is reached, the loop ends. +#' +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param alpha Significance level to use +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param des_pow desired power one wants to achieve +#' +#' @return +#' - number of total events needed given the desired power +#' - graph showing the average power under the given models until the desired +#' power is reached +#' @export +no_events_given_pow <- function(mods, alpha, ratio, des_pow){ + pow <- 0 + etotal_col <- c(0) + pow_col <- c(0) + + for (i in 1:1000){ + etotal <- i + pow <- powMCT_TTE(mods, alpha, ratio, etotal)$power_av + etotal_col[i] <- i + pow_col[i] <- pow + if(pow >= des_pow) break + } + dat <- data.frame(etotal_col, pow_col) + graf <- ggplot(data = dat, aes(x = etotal_col, y = pow_col, group = 1)) + + geom_line()+ + geom_point() + + xlab("Total Number of Events") + + ylab("Power") + + geom_hline(yintercept = des_pow, linetype="dashed") + + annotate("text", x = etotal / 6, y = des_pow - 0.02, + label = "Desired Power") + + ggtitle("Total Number of Events Needed to Reach the Desired Power") + + return(list(etotal = etotal, graf = graf)) +} +#' @examples +#' test <- no_events_given_pow(mods = mods, alpha = 0.25, +#' ratio = c(1, 0.5, 0.5, 1), des_pow = 0.8) +#' test$etotal +#' test$graf +``` + + +```{r, fig.width = 6.9, out.width = '100%'} +des_pow <- 0.8 +test <- no_events_given_pow(mods, alpha, ratio, des_pow) +test$etotal +test$graf +``` + +```{r} +#' calculate the number of events given a certain sample size +#' +#' The \samp{no_events_given_samplesize} function calculates the number of +#' events given a certain sample size. +#' Therefore, the formula from Deng 2019 which is derived from equation 26 in +#' Lachin 1981 is used. +#' It is assumed that patients are recruited uniformly over the time period +#' $[0, \text{end_rec}]$ and that the survival time for group $k$ follows +#' the exponential distribution with hazard $\lambda_k$. +#' One model has to be chosen to compute the needed $\lambda_k$'s. +#' +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param end_rec end of recruitment period in years +#' @param end_stu endpoint of the study in years +#' @param model wither Name or Number of the model from \samp{mods} of which the +#' hazards should be taken from +#' @param n sample size +#' +#' @return +#' - total number of events +#' - vector with the number of events per group +#' @references Deng 2019, Lachin 1981 +#' @export +no_events_given_samplesize <- function(ratio, mods, end_rec, end_stu, model, n){ + y <- log_hazard_rates(mods) + ngroup <- length(ratio) + lambda <- exp(y)[,model] + rat <- ratio/sum(ratio) + D <- rep(0, ngroup) + for (i in 1:ngroup){ + D[i] <- (n * rat[i]) * (1 - ((exp(-lambda[i] * (end_stu - end_rec)) - + exp(-lambda[i] * end_stu)) / + (lambda[i] * end_rec))) + } + return(list(e_vec = D, etotal_samp = sum(D))) +} +#' @examples +#' no_events_given_samplesize(ratio = c(1, 0.5, 0.5, 1), +#' mods = mods, end_rec = 1, end_stu = 3, model = 2, n = 100) +``` + +```{r} +no_events_given_samplesize(ratio, mods, end_rec = 1, end_stu = 3, model = 2, + n = 100) +``` + +```{r} +#' calculate the total sample size needed to achieve a certain power +#' +#' \samp{samplesize_given_power} calculates the total sample size needed to +#' achieve a certain power. +#' Starting with a minimum number of patients (\samp{n_mind}) it computes the +#' number of events happening using the sample_size function. +#' With that number of events (\samp{etotal_int}) it computes the power this +#' study would have (\samp{pow}) using the \samp{powMCT_TTE} function. +#' The function stops when the desired power (\samp{des_pow}) is reached and +#' provides a plot showing the power for various sample sizes. +#' Here, the \samp{no_events_given_samplesize} is used to compute the number of +#' events. + +#' @param mods Set of dose-response models; an object of class \samp{Mods}, +#' see [Mods()] for details +#' @param alpha Significance level to use +#' @param ratio Vector of Sample Size allocation ratio, according to doses used +#' in \samp{mods}, first number must be 1 +#' @param des_pow desired power one wants to achieve +#' @param end_rec end of recruitment period in years +#' @param end_stu endpoint of the study in years +#' @param model wither Name or Number of the model from \samp{mods} of which the +#' hazards should be taken from +#' @param n_mind minimum number of patients with which the loop starts, should +#' not be chosen too small, so meaningful allocaition can be computed and to +#' reduce running time +#' +#' @return +#' - number of total sample size needed given the desired power +#' - graph showing the average power under the given models until the desired +#' power is reached +#' - text explaining the output +#' @references Deng 2019, Lachin 1981 +#' @export +samplesize_given_power <- + function(mods, + alpha, + ratio, + des_pow, + end_rec, + end_stu, + model, + n_mind = 20) { + + pow <- 0 + n_col <- c(0) + pow_col <- c(0) + + for (i in (n_mind:1000)) { + n <- i + etotal_int <- + floor(no_events_given_samplesize(ratio, mods, end_rec, end_stu, model, + n = n)$etotal_samp) + pow <- + powMCT_TTE(mods, alpha, ratio, etotal = etotal_int)$power_av + n_col[i - n_mind] <- i + pow_col[i - n_mind] <- pow + if (pow >= des_pow) + break + } + + dat <- data.frame(n_col, pow_col) + graf <- + ggplot(data = dat, aes(x = n_col, y = pow_col, group = 1)) + + geom_line() + + geom_point() + + xlab("Total Sample Size") + + ylab("Power") + + geom_hline(yintercept = des_pow, linetype = "dashed") + + annotate("text", x = etotal / 2, y = des_pow - 0.02, + label = "Desired Power") + + ggtitle("Total Sample Size Needed to Reach the Desired Power") + + text <- paste("To reach the desired power of", des_pow * 100, "%, ", n, + "patients are needed and", etotal_int, "events are expected.") + + return(list( + n = n, + etotal = etotal_int, + graf = graf, + data = dat, + text = text + )) + } +#' @examples +#' samplesize_given_power(mods = mods, alpha = 0.025, ratio, des_pow = 0.8, +#' end_rec = 1, end_stu = 3, model = 2, n_mind = 10) +``` + +```{r, fig.width = 6.9, out.width = '100%'} +final_result <- samplesize_given_power(mods, alpha = 0.025, ratio, des_pow = 0.8, end_rec = 1, + end_stu = 3, model = 2, n_mind = 10) +final_result$text +final_result$graf +``` + + + + diff --git a/vignettes/MCP TTE/Draft5_files/127530FF3BDB0B67DA2C3178F5D342B0.cache.js.download b/vignettes/MCP TTE/Draft5_files/127530FF3BDB0B67DA2C3178F5D342B0.cache.js.download new file mode 100755 index 0000000..80d4def --- /dev/null +++ b/vignettes/MCP 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r=t.inputState;if(r.operator){if(r.operator==n.operator){r.motion="expandToLine",r.motionArgs={linewise:!0},this.evalInput(e,t);return}pt(e)}r.operator=n.operator,r.operatorArgs=kt(n.operatorArgs),n.keys.length>1&&(r.operatorShortcut=n.keys),n.exitVisualBlock&&(t.visualBlock=!1,Kt(e)),t.visualMode&&this.evalInput(e,t)},processOperatorMotion:function(e,t,n){var r=t.visualMode,i=kt(n.operatorMotionArgs);i&&r&&i.visualLine&&(t.visualLine=!0),this.processOperator(e,t,n),r||this.processMotion(e,t,n)},processAction:function(e,t,n){var r=t.inputState,i=r.getRepeat(),s=!!i,o=kt(n.actionArgs)||{};r.selectedCharacter&&(o.selectedCharacter=r.selectedCharacter),n.operator&&this.processOperator(e,t,n),n.motion&&this.processMotion(e,t,n),(n.motion||n.operator)&&this.evalInput(e,t),o.repeat=i||1,o.repeatIsExplicit=s,o.registerName=r.registerName,pt(e),t.lastMotion=null,n.isEdit&&this.recordLastEdit(t,r,n),Tt[n.action](e,o,t)},processSearch:function(e,t,n){function a(r,i,s){at.searchHistoryController.pushInput(r),at.searchHistoryController.reset();try{In(e,r,i,s)}catch(o){Hn(e,"Invalid regex: "+r),pt(e);return}yt.processMotion(e,t,{type:"motion",motion:"findNext",motionArgs:{forward:!0,toJumplist:n.searchArgs.toJumplist}})}function f(e){a(e,!0,!0);var t=at.macroModeState;t.isRecording&&or(t,e)}function l(t,n,i){var s=m.keyName(t),o,a;s=="Up"||s=="Down"?(o=s=="Up"?!0:!1,a=t.target?t.target.selectionEnd:0,n=at.searchHistoryController.nextMatch(n,o)||"",i(n),a&&t.target&&(t.target.selectionEnd=t.target.selectionStart=Math.min(a,t.target.value.length))):s!="Left"&&s!="Right"&&s!="Ctrl"&&s!="Alt"&&s!="Shift"&&at.searchHistoryController.reset();var f;try{f=In(e,n,!0,!0)}catch(t){}f?e.scrollIntoView(zn(e,!r,f),30):(Xn(e),e.scrollTo(u.left,u.top))}function c(t,n,r){var i=m.keyName(t);i=="Esc"||i=="Ctrl-C"||i=="Ctrl-["||i=="Backspace"&&n==""?(at.searchHistoryController.pushInput(n),at.searchHistoryController.reset(),In(e,o),Xn(e),e.scrollTo(u.left,u.top),m.e_stop(t),pt(e),r(),e.focus()):i=="Up"||i=="Down"?m.e_stop(t):i=="Ctrl-U"&&(m.e_stop(t),r(""))}if(!e.getSearchCursor)return;var r=n.searchArgs.forward,i=n.searchArgs.wholeWordOnly;xn(e).setReversed(!r);var s=r?"/":"?",o=xn(e).getQuery(),u=e.getScrollInfo();switch(n.searchArgs.querySrc){case"prompt":var h=at.macroModeState;if(h.isPlaying){var p=h.replaySearchQueries.shift();a(p,!0,!1)}else jn(e,{onClose:f,prefix:s,desc:"(JavaScript regexp)",onKeyUp:l,onKeyDown:c});break;case"wordUnderCursor":var d=nn(e,!1,!0,!1,!0),v=!0;d||(d=nn(e,!1,!0,!1,!1),v=!1);if(!d)return;var p=e.getLine(d.start.line).substring(d.start.ch,d.end.ch);v&&i?p="\\b"+p+"\\b":p=Rt(p),at.jumpList.cachedCursor=e.getCursor(),e.setCursor(d.start),a(p,!0,!1)}},processEx:function(e,t,n){function r(t){at.exCommandHistoryController.pushInput(t),at.exCommandHistoryController.reset(),Yn.processCommand(e,t),e.state.vim&&pt(e)}function i(t,n,r){var i=m.keyName(t),s,o;if(i=="Esc"||i=="Ctrl-C"||i=="Ctrl-["||i=="Backspace"&&n=="")at.exCommandHistoryController.pushInput(n),at.exCommandHistoryController.reset(),m.e_stop(t),pt(e),r(),e.focus();i=="Up"||i=="Down"?(m.e_stop(t),s=i=="Up"?!0:!1,o=t.target?t.target.selectionEnd:0,n=at.exCommandHistoryController.nextMatch(n,s)||"",r(n),o&&t.target&&(t.target.selectionEnd=t.target.selectionStart=Math.min(o,t.target.value.length))):i=="Ctrl-U"?(m.e_stop(t),r("")):i!="Left"&&i!="Right"&&i!="Ctrl"&&i!="Alt"&&i!="Shift"&&at.exCommandHistoryController.reset()}n.type=="keyToEx"?Yn.processCommand(e,n.exArgs.input):t.visualMode?jn(e,{onClose:r,prefix:":",value:"'<,'>",onKeyDown:i,selectValueOnOpen:!1}):jn(e,{onClose:r,prefix:":",onKeyDown:i})},evalInput:function(e,t){var n=t.inputState,r=n.motion,i=n.motionArgs||{},s=n.operator,o=n.operatorArgs||{},u=n.registerName,a=t.sel,f=Dt(t.visualMode?Ct(e,a.head):e.getCursor("head")),l=Dt(t.visualMode?Ct(e,a.anchor):e.getCursor("anchor")),c=Dt(f),h=Dt(l),p,d,v;s&&this.recordLastEdit(t,n),n.repeatOverride!==undefined?v=n.repeatOverride:v=n.getRepeat();if(v>0&&i.explicitRepeat)i.repeatIsExplicit=!0;else if(i.noRepeat||!i.explicitRepeat&&v===0)v=1,i.repeatIsExplicit=!1;n.selectedCharacter&&(i.selectedCharacter=o.selectedCharacter=n.selectedCharacter),i.repeat=v,pt(e);if(r){var m=bt[r](e,f,i,t,n);t.lastMotion=bt[r];if(!m)return;if(i.toJumplist){!s&&e.ace.curOp!=null&&(e.ace.curOp.command.scrollIntoView="center-animate");var g=at.jumpList,y=g.cachedCursor;y?(sn(e,y,m),delete g.cachedCursor):sn(e,f,m)}m instanceof Array?(d=m[0],p=m[1]):p=m,p||(p=Dt(f));if(t.visualMode){if(!t.visualBlock||p.ch!==Infinity)p=Ct(e,p,c);d&&(d=Ct(e,d)),d=d||h,a.anchor=d,a.head=p,Kt(e),vn(e,t,"<",Ht(d,p)?d:p),vn(e,t,">",Ht(d,p)?p:d)}else s||(e.ace.curOp&&(e.ace.curOp.vimDialogScroll="center-animate"),p=Ct(e,p,c),e.setCursor(p.line,p.ch))}if(s){if(o.lastSel){d=h;var b=o.lastSel,E=Math.abs(b.head.line-b.anchor.line),x=Math.abs(b.head.ch-b.anchor.ch);b.visualLine?p=new w(h.line+E,h.ch):b.visualBlock?p=new w(h.line+E,h.ch+x):b.head.line==b.anchor.line?p=new w(h.line,h.ch+x):p=new w(h.line+E,h.ch),t.visualMode=!0,t.visualLine=b.visualLine,t.visualBlock=b.visualBlock,a=t.sel={anchor:d,head:p},Kt(e)}else t.visualMode&&(o.lastSel={anchor:Dt(a.anchor),head:Dt(a.head),visualBlock:t.visualBlock,visualLine:t.visualLine});var T,N,C,k,L;if(t.visualMode){T=Bt(a.head,a.anchor),N=jt(a.head,a.anchor),C=t.visualLine||o.linewise,k=t.visualBlock?"block":C?"line":"char";var A=S(e,T,N);L=Qt(e,{anchor:A.start,head:A.end},k);if(C){var O=L.ranges;if(k=="block")for(var M=0;Mf&&i.line==f)return hn(e,t,n,r,!0);var l=e.ace.session.getFoldLine(u);return l&&(n.forward?u>l.start.row&&(u=l.end.row+1):u=l.start.row),n.toFirstChar&&(s=tn(e.getLine(u)),r.lastHPos=s),r.lastHSPos=e.charCoords(new w(u,s),"div").left,new w(u,s)},moveByDisplayLines:function(e,t,n,r){var i=t;switch(r.lastMotion){case this.moveByDisplayLines:case this.moveByScroll:case this.moveByLines:case this.moveToColumn:case this.moveToEol:break;default:r.lastHSPos=e.charCoords(i,"div").left}var s=n.repeat,o=e.findPosV(i,n.forward?s:-s,"line",r.lastHSPos);if(o.hitSide)if(n.forward)var u=e.charCoords(o,"div"),a={top:u.top+8,left:r.lastHSPos},o=e.coordsChar(a,"div");else{var f=e.charCoords(new w(e.firstLine(),0),"div");f.left=r.lastHSPos,o=e.coordsChar(f,"div")}return r.lastHPos=o.ch,o},moveByPage:function(e,t,n){var r=t,i=n.repeat;return e.findPosV(r,n.forward?i:-i,"page")},moveByParagraph:function(e,t,n){var r=n.forward?1:-1;return gn(e,t,n.repeat,r)},moveBySentence:function(e,t,n){var r=n.forward?1:-1;return bn(e,t,n.repeat,r)},moveByScroll:function(e,t,n,r){var i=e.getScrollInfo(),s=null,o=n.repeat;o||(o=i.clientHeight/(2*e.defaultTextHeight()));var u=e.charCoords(t,"local");n.repeat=o,s=bt.moveByDisplayLines(e,t,n,r);if(!s)return null;var a=e.charCoords(s,"local");return e.scrollTo(null,i.top+a.top-u.top),s},moveByWords:function(e,t,n){return cn(e,t,n.repeat,!!n.forward,!!n.wordEnd,!!n.bigWord)},moveTillCharacter:function(e,t,n){var r=n.repeat,i=pn(e,r,n.forward,n.selectedCharacter),s=n.forward?-1:1;return on(s,n),i?(i.ch+=s,i):null},moveToCharacter:function(e,t,n){var r=n.repeat;return on(0,n),pn(e,r,n.forward,n.selectedCharacter)||t},moveToSymbol:function(e,t,n){var r=n.repeat;return fn(e,r,n.forward,n.selectedCharacter)||t},moveToColumn:function(e,t,n,r){var i=n.repeat;return r.lastHPos=i-1,r.lastHSPos=e.charCoords(t,"div").left,dn(e,i)},moveToEol:function(e,t,n,r){return hn(e,t,n,r,!1)},moveToFirstNonWhiteSpaceCharacter:function(e,t){var n=t;return new w(n.line,tn(e.getLine(n.line)))},moveToMatchedSymbol:function(e,t){var n=t,r=n.line,i=n.ch,s=e.getLine(r),o;for(;i]/.test(s[i])?/[(){}[\]<>]/:/[(){}[\]]/,f=e.findMatchingBracket(new w(r,i+1),{bracketRegex:a});return f.to}return n},moveToStartOfLine:function(e,t){return new w(t.line,0)},moveToLineOrEdgeOfDocument:function(e,t,n){var r=n.forward?e.lastLine():e.firstLine();return n.repeatIsExplicit&&(r=n.repeat-e.getOption("firstLineNumber")),new w(r,tn(e.getLine(r)))},moveToStartOfDisplayLine:function(e){return e.execCommand("goLineLeft"),e.getCursor()},moveToEndOfDisplayLine:function(e){e.execCommand("goLineRight");var t=e.getCursor();return t.sticky=="before"&&t.ch--,t},textObjectManipulation:function(e,t,n,r){var i={"(":")",")":"(","{":"}","}":"{","[":"]","]":"[","<":">",">":"<"},s={"'":!0,'"':!0,"`":!0},o=n.selectedCharacter;o=="b"?o="(":o=="B"&&(o="{");var u=!n.textObjectInner,a;if(i[o])a=wn(e,t,o,u);else if(s[o])a=En(e,t,o,u);else if(o==="W")a=nn(e,u,!0,!0);else if(o==="w")a=nn(e,u,!0,!1);else if(o==="p"){a=gn(e,t,n.repeat,0,u),n.linewise=!0;if(r.visualMode)r.visualLine||(r.visualLine=!0);else{var f=r.inputState.operatorArgs;f&&(f.linewise=!0),a.end.line--}}else if(o==="t")a=rn(e,t,u);else{if(o!=="s")return null;var l=e.getLine(t.line);t.ch>0&&Y(l[t.ch])&&(t.ch-=1);var c=yn(e,t,n.repeat,1,u),h=yn(e,t,n.repeat,-1,u);G(e.getLine(h.line)[h.ch])&&G(e.getLine(c.line)[c.ch-1])&&(h={line:h.line,ch:h.ch+1}),a={start:h,end:c}}return e.state.vim.visualMode?Jt(e,a.start,a.end):[a.start,a.end]},repeatLastCharacterSearch:function(e,t,n){var r=at.lastCharacterSearch,i=n.repeat,s=n.forward===r.forward,o=(r.increment?1:0)*(s?-1:1);e.moveH(-o,"char"),n.inclusive=s?!0:!1;var u=pn(e,i,s,r.selectedCharacter);return u?(u.ch+=o,u):(e.moveH(o,"char"),t)}},St={change:function(e,t,n){var r,i,s=e.state.vim,o=n[0].anchor,u=n[0].head;if(!s.visualMode){i=e.getRange(o,u);var a=s.lastEditInputState||{};if(a.motion=="moveByWords"&&!G(i)){var f=/\s+$/.exec(i);f&&a.motionArgs&&a.motionArgs.forward&&(u=Lt(u,0,-f[0].length),i=i.slice(0,-f[0].length))}var l=new w(o.line-1,Number.MAX_VALUE),c=e.firstLine()==e.lastLine();u.line>e.lastLine()&&t.linewise&&!c?e.replaceRange("",l,u):e.replaceRange("",o,u),t.linewise&&(c||(e.setCursor(l),m.commands.newlineAndIndent(e)),o.ch=Number.MAX_VALUE),r=o}else if(t.fullLine)u.ch=Number.MAX_VALUE,u.line--,e.setSelection(o,u),i=e.getSelection(),e.replaceSelection(""),r=o;else{i=e.getSelection();var h=Et("",n.length);e.replaceSelections(h),r=Bt(n[0].head,n[0].anchor)}at.registerController.pushText(t.registerName,"change",i,t.linewise,n.length>1),Tt.enterInsertMode(e,{head:r},e.state.vim)},"delete":function(e,t,n){var r,i,s=e.state.vim;if(!s.visualBlock){var o=n[0].anchor,u=n[0].head;t.linewise&&u.line!=e.firstLine()&&o.line==e.lastLine()&&o.line==u.line-1&&(o.line==e.firstLine()?o.ch=0:o=new w(o.line-1,It(e,o.line-1))),i=e.getRange(o,u),e.replaceRange("",o,u),r=o,t.linewise&&(r=bt.moveToFirstNonWhiteSpaceCharacter(e,o))}else{i=e.getSelection();var a=Et("",n.length);e.replaceSelections(a),r=Bt(n[0].head,n[0].anchor)}return at.registerController.pushText(t.registerName,"delete",i,t.linewise,s.visualBlock),Ct(e,r)},indent:function(e,t,n){var r=e.state.vim;if(e.indentMore){var i=r.visualMode?t.repeat:1;for(var s=0;s1&&e.setSelection(n[0].anchor,n[n.length-1].head),e.execCommand("indentAuto"),bt.moveToFirstNonWhiteSpaceCharacter(e,n[0].anchor)},changeCase:function(e,t,n,r,i){var s=e.getSelections(),o=[],u=t.toLower;for(var a=0;af.top?(a.line+=(u-f.top)/i,a.line=Math.ceil(a.line),e.setCursor(a),f=e.charCoords(a,"local"),e.scrollTo(null,f.top)):e.scrollTo(null,u);else{var l=u+e.getScrollInfo().clientHeight;l=i.anchor.line?s=Lt(i.head,0,1):s=new w(i.anchor.line,0)}else if(r=="inplace"){if(n.visualMode)return}else r=="lastEdit"&&(s=Kn(e)||s);e.setOption("disableInput",!1),t&&t.replace?(e.toggleOverwrite(!0),e.setOption("keyMap","vim-replace"),m.signal(e,"vim-mode-change",{mode:"replace"})):(e.toggleOverwrite(!1),e.setOption("keyMap","vim-insert"),m.signal(e,"vim-mode-change",{mode:"insert"})),at.macroModeState.isPlaying||(e.on("change",ur),m.on(e.getInputField(),"keydown",cr)),n.visualMode&&Yt(e),Wt(e,s,o)},toggleVisualMode:function(e,t,n){var r=t.repeat,i=e.getCursor(),s;if(!n.visualMode){n.visualMode=!0,n.visualLine=!!t.linewise,n.visualBlock=!!t.blockwise,s=Ct(e,new w(i.line,i.ch+r-1));var o=S(e,i,s);n.sel={anchor:o.start,head:o.end},m.signal(e,"vim-mode-change",{mode:"visual",subMode:n.visualLine?"linewise":n.visualBlock?"blockwise":""}),Kt(e),vn(e,n,"<",Bt(i,s)),vn(e,n,">",jt(i,s))}else n.visualLine^t.linewise||n.visualBlock^t.blockwise?(n.visualLine=!!t.linewise,n.visualBlock=!!t.blockwise,m.signal(e,"vim-mode-change",{mode:"visual",subMode:n.visualLine?"linewise":n.visualBlock?"blockwise":""}),Kt(e)):Yt(e)},reselectLastSelection:function(e,t,n){var r=n.lastSelection;n.visualMode&&$t(e,n);if(r){var i=r.anchorMark.find(),s=r.headMark.find();if(!i||!s)return;n.sel={anchor:i,head:s},n.visualMode=!0,n.visualLine=r.visualLine,n.visualBlock=r.visualBlock,Kt(e),vn(e,n,"<",Bt(i,s)),vn(e,n,">",jt(i,s)),m.signal(e,"vim-mode-change",{mode:"visual",subMode:n.visualLine?"linewise":n.visualBlock?"blockwise":""})}},joinLines:function(e,t,n){var r,i;if(n.visualMode){r=e.getCursor("anchor"),i=e.getCursor("head");if(Ht(i,r)){var s=i;i=r,r=s}i.ch=It(e,i.line)-1}else{var o=Math.max(t.repeat,2);r=e.getCursor(),i=Ct(e,new w(r.line+o-1,Infinity))}var u=0;for(var a=r.line;a1)var r=Array(t.repeat+1).join(r);var p=i.linewise,d=i.blockwise;if(d){r=r.split("\n"),p&&r.pop();for(var v=0;ve.lastLine()&&e.replaceRange("\n",new w(C,0));var k=It(e,C);ka.length&&(s=a.length),o=new w(i.line,s)}var f=S(e,i,o);i=f.start,o=f.end;if(r=="\n")n.visualMode||e.replaceRange("",i,o),(m.commands.newlineAndIndentContinueComment||m.commands.newlineAndIndent)(e);else{var l=e.getRange(i,o);l=l.replace(/[\uD800-\uDBFF][\uDC00-\uDFFF]/g,r),l=l.replace(/[^\n]/g,r);if(n.visualBlock){var c=(new Array(e.getOption("tabSize")+1)).join(" ");l=e.getSelection(),l=l.replace(/[\uD800-\uDBFF][\uDC00-\uDFFF]/g,r),l=l.replace(/\t/g,c).replace(/[^\n]/g,r).split("\n"),e.replaceSelections(l)}else e.replaceRange(l,i,o);n.visualMode?(i=Ht(u[0].anchor,u[0].head)?u[0].anchor:u[0].head,e.setCursor(i),Yt(e,!1)):e.setCursor(Lt(o,0,-1))}},incrementNumberToken:function(e,t){var n=e.getCursor(),r=e.getLine(n.line),i=/(-?)(?:(0x)([\da-f]+)|(0b|0|)(\d+))/gi,s,o,u,a;while((s=i.exec(r))!==null){o=s.index,u=o+s[0].length;if(n.ch=1)return!0}else e.nextCh===e.reverseSymb&&e.depth--;return!1}},section:{init:function(e){e.curMoveThrough=!0,e.symb=(e.forward?"]":"[")===e.symb?"{":"}"},isComplete:function(e){return e.index===0&&e.nextCh===e.symb}},comment:{isComplete:function(e){var t=e.lastCh==="*"&&e.nextCh==="/";return e.lastCh=e.nextCh,t}},method:{init:function(e){e.symb=e.symb==="m"?"{":"}",e.reverseSymb=e.symb==="{"?"}":"{"},isComplete:function(e){return e.nextCh===e.symb?!0:!1}},preprocess:{init:function(e){e.index=0},isComplete:function(e){if(e.nextCh==="#"){var t=e.lineText.match(/^#(\w+)/)[1];if(t==="endif"){if(e.forward&&e.depth===0)return!0;e.depth++}else if(t==="if"){if(!e.forward&&e.depth===0)return!0;e.depth--}if(t==="else"&&e.depth===0)return!0}return!1}}};tt("pcre",!0,"boolean"),Sn.prototype={getQuery:function(){return at.query},setQuery:function(e){at.query=e},getOverlay:function(){return this.searchOverlay},setOverlay:function(e){this.searchOverlay=e},isReversed:function(){return at.isReversed},setReversed:function(e){at.isReversed=e},getScrollbarAnnotate:function(){return this.annotate},setScrollbarAnnotate:function(e){this.annotate=e}};var An={"\\n":"\n","\\r":"\r","\\t":" "},Mn={"\\/":"/","\\\\":"\\","\\n":"\n","\\r":"\r","\\t":" ","\\&":"&"},Rn=0,Qn=function(){this.buildCommandMap_()};Qn.prototype={processCommand:function(e,t,n){var r=this;e.operation(function(){e.curOp.isVimOp=!0,r._processCommand(e,t,n)})},_processCommand:function(e,t,n){var r=e.state.vim,i=at.registerController.getRegister(":"),s=i.toString();r.visualMode&&Yt(e);var o=new m.StringStream(t);i.setText(t);var u=n||{};u.input=t;try{this.parseInput_(e,o,u)}catch(a){throw Hn(e,a.toString()),a}var f,l;if(!u.commandName)u.line!==undefined&&(l="move");else{f=this.matchCommand_(u.commandName);if(f){l=f.name,f.excludeFromCommandHistory&&i.setText(s),this.parseCommandArgs_(o,u,f);if(f.type=="exToKey"){for(var c=0;c@~])/);return 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