From 7b7729694363515007193d1c3e29e9b76271abb3 Mon Sep 17 00:00:00 2001
From: Johannes Ranke <jranke@uni-bremen.de>
Date: Sat, 26 Oct 2019 20:50:09 +0200
Subject: parms and confint methods

The confint method can do profile likelihood based confidence intervals!
---
 R/confint.mkinfit.R | 139 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 139 insertions(+)
 create mode 100644 R/confint.mkinfit.R

(limited to 'R/confint.mkinfit.R')

diff --git a/R/confint.mkinfit.R b/R/confint.mkinfit.R
new file mode 100644
index 00000000..887adc9f
--- /dev/null
+++ b/R/confint.mkinfit.R
@@ -0,0 +1,139 @@
+#' Confidence intervals for parameters of mkinfit objects
+#'
+#' @param object An \code{\link{mkinfit}} object
+#' @param parm A vector of names of the parameters which are to be given
+#'   confidence intervals. If missing, all parameters are considered.
+#' @param level The confidence level required
+#' @param alpha The allowed error probability, overrides 'level' if specified.
+#' @param method The 'profile' method searches the parameter space for the
+#'   cutoff of the confidence intervals by means of a likelihood ratio test.
+#'   The 'quadratic' method approximates the likelihood function at the
+#'   optimised parameters using the second term of the Taylor expansion, using
+#'   a second derivative (hessian) contained in the object.
+#' @param transformed If the quadratic approximation is used, should it be
+#'   applied to the likelihood based on the transformed parameters?
+#' @param backtransform If we approximate the likelihood in terms of the
+#'   transformed parameters, should we backtransform the parameters with
+#'   their confidence intervals?
+#' @param distribution For the quadratic approximation, should we use
+#'   the student t distribution or assume normal distribution for
+#'   the parameter estimate
+#' @param quiet Should we suppress messages?
+#' @return A matrix with columns giving lower and upper confidence limits for
+#'   each parameter.
+#' @references Pawitan Y (2013) In all likelihood - Statistical modelling and
+#'   inference using likelihood. Clarendon Press, Oxford.
+#' @examples
+#' f <- mkinfit("SFO", FOCUS_2006_C, quiet = TRUE)
+#' confint(f, method = "quadratic")
+#' confint(f, method = "profile")
+#' @export
+confint.mkinfit <- function(object, parm,
+  level = 0.95, alpha = 1 - level,
+  method = c("profile", "quadratic"),
+  transformed = TRUE, backtransform = TRUE,
+  distribution = c("student_t", "normal"), quiet = FALSE, ...)
+{
+  tparms <- parms(object, transformed = TRUE)
+  bparms <- parms(object, transformed = FALSE)
+  tpnames <- names(tparms)
+  bpnames <- names(bparms)
+
+  return_pnames <- if (missing(parm)) {
+    if (backtransform) bpnames else tpnames
+  } else {
+    parm
+  }
+
+  p <- length(return_pnames)
+
+  method <- match.arg(method)
+
+  a <- c(alpha / 2, 1 - (alpha / 2))
+
+  if (method == "quadratic") {
+
+    distribution <- match.arg(distribution)
+
+    quantiles <- switch(distribution,
+      student_t = qt(a, object$df.residual),
+      normal = qnorm(a))
+
+    covar_pnames <- if (missing(parm)) {
+      if (transformed) tpnames else bpnames
+    } else {
+      parm
+    }
+
+    return_parms <- if (backtransform) bparms[return_pnames]
+      else tparms[return_pnames]
+
+    covar_parms <- if (transformed) tparms[covar_pnames]
+      else bparms[covar_pnames]
+
+    if (transformed) {
+      covar <- try(solve(object$hessian), silent = TRUE)
+    } else {
+      covar <- try(solve(object$hessian_notrans), silent = TRUE)
+    }
+
+    # If inverting the covariance matrix failed or produced NA values
+    if (!is.numeric(covar) | is.na(covar[1])) {
+      ses <- lci <- uci <- rep(NA, p)
+    } else {
+      ses     <- sqrt(diag(covar))[covar_pnames]
+      lci    <- covar_parms + quantiles[1] * ses
+      uci    <- covar_parms + quantiles[2] * ses
+      if (backtransform) {
+        lci_back <- backtransform_odeparms(lci,
+          object$mkinmod, object$transform_rates, object$transform_fractions)
+        lci <- c(lci_back, lci[names(object$errparms)])
+        uci_back <- backtransform_odeparms(uci,
+          object$mkinmod, object$transform_rates, object$transform_fractions)
+        uci <- c(uci_back, uci[names(object$errparms)])
+      }
+    }
+  }
+
+  if (method == "profile") {
+    message("Profiling the likelihood")
+    lci <- uci <- rep(NA, p)
+    names(lci) <- names(uci) <- return_pnames
+
+    profile_pnames <- if(missing(parm)) names(parms(object))
+      else parm
+
+    # We do two-sided intervals based on the likelihood ratio
+    cutoff <- 0.5 * qchisq(1 - (alpha / 2), 1)
+
+    all_parms <- parms(object)
+
+    for (pname in profile_pnames)
+    {
+      pnames_free <- setdiff(names(all_parms), pname)
+      profile_ll <- function(x)
+      {
+        pll_cost <- function(P) {
+          parms_cost <- all_parms
+          parms_cost[pnames_free] <- P[pnames_free]
+          parms_cost[pname] <- x
+          - object$ll(parms_cost)
+        }
+        - nlminb(all_parms[pnames_free], pll_cost)$objective
+      }
+
+      cost <- function(x) {
+        (cutoff - (object$logLik - profile_ll(x)))^2
+      }
+
+      lci[pname] <- optimize(cost, lower = 0, upper = all_parms[pname])$minimum
+      uci[pname] <- optimize(cost, lower = all_parms[pname], upper = 15 * all_parms[pname])$minimum
+    }
+  }
+
+  ci <- cbind(lower = lci, upper = uci)
+  colnames(ci) <- paste0(
+    format(100 * a, trim = TRUE, scientific = FALSE, digits = 3), "%")
+
+  return(ci)
+}
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