R/CvMcens.R

In GofCens: Goodness-of-Fit Methods for Complete and Right-Censored Data

CvMcens <- function(times, cens = rep(1, length(times)),
                    distr = c("exponential", "gumbel", "weibull", "normal",
                              "lognormal", "logistic", "loglogistic", "beta"),
                    betaLimits = c(0, 1), igumb = c(10, 10), degs = 3, BS = 999,
                    params0 = list(shape = NULL, shape2 = NULL,
                                   location = NULL, scale = NULL),
                    prnt = TRUE, outp = "list", tol = 1e-04) {
  if (!is.numeric(times)) {
    stop("Variable times must be numeric!")
  }
  if (any(times <= 0)) {
    stop("Times must be strictly positive!")
  }
  if (any(!cens %in% 0:1)) {
    stop("Status indicator must be either 0 or 1!")
  }
  if (prnt && !outp %in% c("list", "table")) {
    stop("Invalid value of outp. Use 'table' or 'list'.")
  }
  if (!is.list(params0)) {
    stop("params0 must be a list!")
  }
  distr <- match.arg(distr)
  if (distr == "beta" && any(times < betaLimits[1] | times > betaLimits[2])) {
    msg <- paste0("Times must be within limits! Try with 'betaLimits = c(",
                  pmax(0, min(times) - 1), ", ", ceiling(max(times) + 1), ")'.")
    stop(msg)
  }
  if (!all(sapply(params0, is.null))) {
    if (distr == "exponential" && is.null(params0$scale)) {
      stop("Argument 'params0' requires a value for the scale parameter.")
    }
    if (distr %in% c("weibull", "loglogistic") &&
        (is.null(params0$shape) || is.null(params0$scale))) {
      stop("Argument 'params0' requires values for the shape and scale parameters.")
    }
    if (distr %in% c("gumbel", "normal", "lognormal", "logistic") &&
        (is.null(params0$location) || is.null(params0$scale))) {
      stop("Argument 'params0' requires values for the location and scale parameters.")
    }
    if (distr == "beta" && (is.null(params0$shape) || is.null(params0$shape2))) {
      stop("Argument 'params0' requires values for both shape parameters.")
    }
  }
  rnd <- -log(tol, 10)
  times <- round(pmax(times, tol), rnd)
  dd <- data.frame(left = as.vector(times), right = ifelse(cens == 1, times, NA))
  alpha0 <- params0$shape
  gamma0 <- params0$shape2
  mu0 <- params0$location
  beta0 <- params0$scale
  alphaML <- gammaML <- muML <- betaML <- NULL
  censKM <- survfit(Surv(times, 1 - cens) ~ 1)
  if (distr == "exponential") {
    if (!is.null(beta0)) {
      hypo <- c(scale = beta0)
    }
    muu <- unname(coefficients(survreg(Surv(times, cens) ~ 1,
                                       dist = "exponential")))
    betaML <- 1 / exp(-muu)
    expStat <- function(dat) {
      if (is.null(beta0)) {
        muu <- unname(coefficients(survreg(Surv(dat$times, dat$cens) ~ 1,
                                           dist = "exponential")))
        betahat <- 1 / exp(-muu)
      } else {
        betahat <- beta0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(pexp(stimes, 1 / betahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    expRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rexp(n, mle), tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    beta <- ifelse(is.null(beta0), betaML, beta0)
    bts <- boot(data.frame(times, cens), expStat, R = BS, sim = "parametric",
                ran.gen = expRnd, mle = 1 / beta)
  }
  if (distr == "gumbel") {
    if (!is.null(mu0) && !is.null(beta0)) {
      hypo <- c(location = mu0, scale = beta0)
    }
    paramsML <- try(suppressMessages(fitdistcens(dd, "gumbel",
                                                 start = list(alpha = igumb[1],
                                                              scale = igumb[2]))),
                    silent = TRUE)
    if (attr(paramsML, "class") == "try-error") {
      stop("Function failed to estimate the parameters.\n
            Try with other initial values.")
    }
    muML <- unname(paramsML$estimate[1])
    betaML <- unname(paramsML$estimate[2])
    gumbStat <- function(dat) {
      if (is.null(mu0) || is.null(beta0)) {
        dd <- data.frame(left = as.vector(dat$times),
                         right = ifelse(dat$cens == 1, dat$times, NA))
        paramsBSML <- fitdistcens(dd, "gumbel", start = list(alpha = muML,
                                                             scale = betaML))
        muhat <- unname(paramsBSML$estimate[1])
        betahat <- unname(paramsBSML$estimate[2])
      } else {
        muhat <- mu0
        betahat <- beta0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(pgumbel(stimes, muhat, betahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    gumbRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rgumbel(n, mle[1], mle[2]), tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    if (is.null(mu0) || is.null(beta0)) {
      mu <- muML
      beta <- betaML
    } else {
      mu <- mu0
      beta <- beta0
    }
    bts <- boot(data.frame(times, cens), gumbStat, R = BS, sim = "parametric",
                ran.gen = gumbRnd, mle = c(mu, beta))
  }
  if (distr == "weibull") {
    if (!is.null(alpha0) && !is.null(beta0)) {
      hypo <- c(shape = alpha0, scale = beta0)
    }
    paramsML <- fitdistcens(dd, "weibull")
    alphaML <- unname(paramsML$estimate[1])
    betaML <- unname(paramsML$estimate[2])
    weiStat <- function(dat) {
      if (is.null(alpha0) || is.null(beta0)) {
        dd <- data.frame(left = as.vector(dat$times),
                         right = ifelse(dat$cens == 1, dat$times, NA))
        paramsBSML <- fitdistcens(dd, "weibull")
        alphahat <- unname(paramsBSML$estimate[1])
        betahat <- unname(paramsBSML$estimate[2])
      } else {
        alphahat <- alpha0
        betahat <- beta0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(pweibull(stimes, alphahat, betahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    weiRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rweibull(n, mle[1], mle[2]), tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    if (is.null(alpha0) || is.null(beta0)) {
      alpha <- alphaML
      beta <- betaML
    } else {
      alpha <- alpha0
      beta <- beta0
    }
    bts <- boot(data.frame(times, cens), weiStat, R = BS, sim = "parametric",
                ran.gen = weiRnd, mle = c(alpha, beta))
  }
  if (distr == "normal") {
    if (!is.null(mu0) && !is.null(beta0)) {
      hypo <- c(location = mu0, scale = beta0)
    }
    paramsML <- fitdistcens(dd, "norm")
    muML <- unname(paramsML$estimate[1])
    betaML <- unname(paramsML$estimate[2])
    normStat <- function(dat) {
      if (is.null(mu0) || is.null(beta0)) {
        dd <- data.frame(left = as.vector(dat$times),
                         right = ifelse(dat$cens == 1, dat$times, NA))
        paramsBSML <- fitdistcens(dd, "norm")
        muhat <- unname(paramsBSML$estimate[1])
        betahat <- unname(paramsBSML$estimate[2])
      } else {
        muhat <- mu0
        betahat <- beta0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(pnorm(stimes, muhat, betahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    normRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rnorm(n, mle[1], mle[2]), tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    if (is.null(mu0) || is.null(beta0)) {
      mu <- muML
      beta <- betaML
    } else {
      mu <- mu0
      beta <- beta0
    }
    bts <- boot(data.frame(times, cens), normStat, R = BS, sim = "parametric",
                ran.gen = normRnd, mle = c(mu, beta))
  }
  if (distr == "lognormal") {
    if (!is.null(mu0) && !is.null(beta0)) {
      hypo <- c(location = mu0, scale = beta0)
    }
    paramsML <- fitdistcens(dd, "lnorm")
    muML <- unname(paramsML$estimate[1])
    betaML <- unname(paramsML$estimate[2])
    lnormStat <- function(dat) {
      if (is.null(mu0) || is.null(beta0)) {
        dd <- data.frame(left = as.vector(dat$times),
                         right = ifelse(dat$cens == 1, dat$times, NA))
        paramsBSML <- fitdistcens(dd, "lnorm")
        muhat <- unname(paramsBSML$estimate[1])
        betahat <- unname(paramsBSML$estimate[2])
      } else {
        muhat <- mu0
        betahat <- beta0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(plnorm(stimes, muhat, betahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    lnormRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rlnorm(n, mle[1], mle[2]), tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    if (is.null(mu0) || is.null(beta0)) {
      mu <- muML
      beta <- betaML
    } else {
      mu <- mu0
      beta <- beta0
    }
    bts <- boot(data.frame(times, cens), lnormStat, R = BS, sim = "parametric",
                ran.gen = lnormRnd, mle = c(mu, beta))
  }
  if (distr == "logistic") {
    if (!is.null(mu0) && !is.null(beta0)) {
      hypo <- c(location = mu0, scale = beta0)
    }
    paramsML <- fitdistcens(dd, "logis")
    muML <- unname(paramsML$estimate[1])
    betaML <- unname(paramsML$estimate[2])
    logiStat <- function(dat) {
      if (is.null(mu0) || is.null(beta0)) {
        dd <- data.frame(left = as.vector(dat$times),
                         right = ifelse(dat$cens == 1, dat$times, NA))
        paramsBSML <- fitdistcens(dd, "logis")
        muhat <- unname(paramsBSML$estimate[1])
        betahat <- unname(paramsBSML$estimate[2])
      } else {
        muhat <- mu0
        betahat <- beta0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(plogis(stimes, muhat, betahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    logiRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rlogis(n, mle[1], mle[2]), tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    if (is.null(mu0) || is.null(beta0)) {
      mu <- muML
      beta <- betaML
    } else {
      mu <- mu0
      beta <- beta0
    }
    bts <- boot(data.frame(times, cens), logiStat, R = BS, sim = "parametric",
                ran.gen = logiRnd, mle = c(mu, beta))
  }
  if (distr == "loglogistic") {
    if (!is.null(alpha0) && !is.null(beta0)) {
      hypo <- c(shape = alpha0, scale = beta0)
    }
    paramsML <- unname(survreg(Surv(times, cens) ~ 1,
                               dist = "loglogistic")$icoef)
    alphaML <- 1 / exp(paramsML[2])
    betaML <- exp(paramsML[1])
    llogiStat <- function(dat) {
      if (is.null(alpha0) || is.null(beta0)) {
        paramsBSML <- unname(survreg(Surv(dat$times, dat$cens) ~ 1,
                                     dist = "loglogistic")$icoef)
        alphahat <- 1 / exp(paramsBSML[2])
        betahat <- exp(paramsBSML[1])
      } else {
        alphahat <- alpha0
        betahat <- beta0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(pllogis(stimes, alphahat, scale = betahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    llogiRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rllogis(n, mle[1], scale = mle[2]), tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    if (is.null(alpha0) || is.null(beta0)) {
      alpha <- alphaML
      beta <- betaML
    } else {
      alpha <- alpha0
      beta <- beta0
    }
    bts <- boot(data.frame(times, cens), llogiStat, R = BS, sim = "parametric",
                ran.gen = llogiRnd, mle = c(alpha, beta))
  }
  if (distr == "beta") {
    if (!is.null(alpha0) && !is.null(gamma0)) {
      hypo <- c(shape = alpha0, shape2 = gamma0)
    }
    aBeta <- betaLimits[1]
    bBeta <- betaLimits[2]
    paramsML <- fitdistcens((dd - aBeta) / (bBeta - aBeta), "beta")
    alphaML <- unname(paramsML$estimate[1])
    gammaML <- unname(paramsML$estimate[2])
    betaStat <- function(dat) {
      if (is.null(alpha0) || is.null(gamma0)) {
        dd <- data.frame(left = as.vector(dat$times),
                         right = ifelse(dat$cens == 1, dat$times, NA))
        paramsBSML <- fitdistcens((dd - aBeta) / (bBeta - aBeta), "beta")
        alphahat <- unname(paramsBSML$estimate[1])
        gammahat <- unname(paramsBSML$estimate[2])
      } else {
        alphahat <- alpha0
        gammahat <- gamma0
      }
      stimes <- sort(unique(dat$times[dat$cens == 1]))
      KM <- summary(survfit(Surv(dat$times, dat$cens) ~ 1))$surv
      nc <- length(KM)
      Fn <- c(1 - KM, NA)
      y0 <- c(pbeta((stimes - aBeta) / (bBeta - aBeta), alphahat, gammahat), 1)
      CvM <- nc * (sum(Fn[-(nc + 1)] * (y0[-1] - y0[-(nc + 1)]) *
                         (Fn[-(nc + 1)] - (y0[-1] + y0[-(nc + 1)]))) + 1 / 3)
      return(CvM)
    }
    betaRnd <- function(dat, mle) {
      out <- dat
      n <- nrow(dat)
      unifn <- runif(n)
      survtimes <- round(pmax(rbeta(n, mle[1], mle[2]) * (bBeta - aBeta) + aBeta,
                              tol), rnd)
      censtimes <- as.vector(quantile(censKM, unifn)$quantile)
      censtimes[is.na(censtimes)] <- Inf
      out$times <- pmin(survtimes, censtimes)
      out$cens <- as.numeric(survtimes < censtimes)
      out
    }
    if (is.null(alpha0) || is.null(gamma0)) {
      alpha <- alphaML
      gamma <- gammaML
    } else {
      alpha <- alpha0
      gamma <- gamma0
    }
    bts <- boot(data.frame(times, cens), betaStat, R = BS, sim = "parametric",
                ran.gen = betaRnd, mle = c(alpha, gamma))
  }
  CvM <- bts$t0
  pval <- (sum(bts$t[, 1] > bts$t0[1]) + 1) / (bts$R + 1)
  if (all(sapply(params0, is.null))) {
    output <- list(Distribution = distr,
                   Test = round(c(CvM = CvM, "p-value" = pval), degs),
                   Estimates = round(c(shape = alphaML, shape2 = gammaML,
                                       location = muML, scale = betaML), degs))
  } else {
    output <- list(Distribution = distr,
                   Hypothesis = hypo,
                   Test = round(c(CvM = CvM, "p-value" = pval), degs),
                   Estimates = round(c(shape = alphaML, shape2 = gammaML,
                                       location = muML, scale = betaML), degs))
  }
  if (prnt) {
    if (outp == "table") {
      cat("Distribution:", output$Distribution, "\n")
      if (!all(sapply(params0, is.null))) {
        cat("\nNull hypothesis:\n")
        header1 <- c("Parameter", "Value")
        max_col_width1 <- max(nchar(header1), nchar(names(output$Hypothesis)))
        cat(sprintf("%s | %s\n", strrep("-", max_col_width1),
                    strrep("-", max_col_width1)))
        cat(sprintf("%-*s | %-*s\n", max_col_width1, header1[1],
                    max_col_width1, header1[2]))
        cat(sprintf("%s | %s\n", strrep("-", max_col_width1),
                    strrep("-", max_col_width1)))
        for (i in 1:length(output$Hypothesis)) {
          cat(sprintf("%-*s | %-*s\n", max_col_width1, names(output$Hypothesis)[i],
                      max_col_width1, unname(output$Hypothesis)[i]))
        }
        cat(sprintf("%s | %s\n", strrep("-", max_col_width1),
                    strrep("-", max_col_width1)))
      }
      cat("\nCvM Test results:\n")
      header <- c("Metric", "Value")
      max_col_width <- max(nchar(header), nchar(names(output$Test)))
      cat(sprintf("%s | %s\n", strrep("-", max_col_width),
                  strrep("-", max_col_width)))
      cat(sprintf("%-*s | %-*s\n", max_col_width, header[1],
                  max_col_width, header[2]))
      cat(sprintf("%s | %s\n", strrep("-", max_col_width),
                  strrep("-", max_col_width)))
      for (i in 1:length(output$Test)) {
        cat(sprintf("%-*s | %-*s\n", max_col_width, names(output$Test)[i],
                    max_col_width, unname(output$Test)[i]))
      }
      cat(sprintf("%s | %s\n", strrep("-", max_col_width),
                  strrep("-", max_col_width)))
      cat("\nParameter estimates:\n")
      header1 <- c("Parameter", "Value")
      max_col_width1 <- max(nchar(header1), nchar(names(output$Estimates)))
      cat(sprintf("%s | %s\n", strrep("-", max_col_width1),
                  strrep("-", max_col_width1)))
      cat(sprintf("%-*s | %-*s\n", max_col_width1, header1[1],
                  max_col_width1, header1[2]))
      cat(sprintf("%s | %s\n", strrep("-", max_col_width1),
                  strrep("-", max_col_width1)))
      for (i in 1:length(output$Estimates)) {
        cat(sprintf("%-*s | %-*s\n", max_col_width1, names(output$Estimates)[i],
                    max_col_width1, unname(output$Estimates)[i]))
      }
      cat(sprintf("%s | %s\n", strrep("-", max_col_width1),
                  strrep("-", max_col_width1)))
      invisible(output)
    } else {
      cat("Distribution:", output$Distribution, "\n")
      if (!all(sapply(params0, is.null))) {
        cat("\nNull hypothesis:\n")
        print(output$Hypothesis)
      }
      cat("\nCvM Test results:\n")
      print(output$Test)
      cat("\nParameter estimates:\n")
      print(output$Estimates)
      invisible(output)
    }
  } else {
    invisible(output)
  }
}