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diff --git a/R/saem.R b/R/saem.R new file mode 100644 index 00000000..6f28a47a --- /dev/null +++ b/R/saem.R @@ -0,0 +1,537 @@ +utils::globalVariables(c("predicted", "std")) + +#' Fit nonlinear mixed models with SAEM +#' +#' This function uses [saemix::saemix()] as a backend for fitting nonlinear mixed +#' effects models created from [mmkin] row objects using the Stochastic Approximation +#' Expectation Maximisation algorithm (SAEM). +#' +#' An mmkin row object is essentially a list of mkinfit objects that have been +#' obtained by fitting the same model to a list of datasets using [mkinfit]. +#' +#' Starting values for the fixed effects (population mean parameters, argument +#' psi0 of [saemix::saemixModel()] are the mean values of the parameters found +#' using [mmkin]. +#' +#' @param object An [mmkin] row object containing several fits of the same +#' [mkinmod] model to different datasets +#' @param verbose Should we print information about created objects of +#' type [saemix::SaemixModel] and [saemix::SaemixData]? +#' @param transformations Per default, all parameter transformations are done +#' in mkin. If this argument is set to 'saemix', parameter transformations +#' are done in 'saemix' for the supported cases. Currently this is only +#' supported in cases where the initial concentration of the parent is not fixed, +#' SFO or DFOP is used for the parent and there is either no metabolite or one. +#' @param degparms_start Parameter values given as a named numeric vector will +#' be used to override the starting values obtained from the 'mmkin' object. +#' @param test_log_parms If TRUE, an attempt is made to use more robust starting +#' values for population parameters fitted as log parameters in mkin (like +#' rate constants) by only considering rate constants that pass the t-test +#' when calculating mean degradation parameters using [mean_degparms]. +#' @param conf.level Possibility to adjust the required confidence level +#' for parameter that are tested if requested by 'test_log_parms'. +#' @param solution_type Possibility to specify the solution type in case the +#' automatic choice is not desired +#' @param fail_with_errors Should a failure to compute standard errors +#' from the inverse of the Fisher Information Matrix be a failure? +#' @param quiet Should we suppress the messages saemix prints at the beginning +#' and the end of the optimisation process? +#' @param nbiter.saemix Convenience option to increase the number of +#' iterations +#' @param control Passed to [saemix::saemix]. +#' @param \dots Further parameters passed to [saemix::saemixModel]. +#' @return An S3 object of class 'saem.mmkin', containing the fitted +#' [saemix::SaemixObject] as a list component named 'so'. The +#' object also inherits from 'mixed.mmkin'. +#' @seealso [summary.saem.mmkin] [plot.mixed.mmkin] +#' @examples +#' \dontrun{ +#' ds <- lapply(experimental_data_for_UBA_2019[6:10], +#' function(x) subset(x$data[c("name", "time", "value")])) +#' names(ds) <- paste("Dataset", 6:10) +#' f_mmkin_parent_p0_fixed <- mmkin("FOMC", ds, +#' state.ini = c(parent = 100), fixed_initials = "parent", quiet = TRUE) +#' f_saem_p0_fixed <- saem(f_mmkin_parent_p0_fixed) +#' +#' f_mmkin_parent <- mmkin(c("SFO", "FOMC", "DFOP"), ds, quiet = TRUE) +#' f_saem_sfo <- saem(f_mmkin_parent["SFO", ]) +#' f_saem_fomc <- saem(f_mmkin_parent["FOMC", ]) +#' f_saem_dfop <- saem(f_mmkin_parent["DFOP", ]) +#' +#' # The returned saem.mmkin object contains an SaemixObject, therefore we can use +#' # functions from saemix +#' library(saemix) +#' compare.saemix(f_saem_sfo$so, f_saem_fomc$so, f_saem_dfop$so) +#' plot(f_saem_fomc$so, plot.type = "convergence") +#' plot(f_saem_fomc$so, plot.type = "individual.fit") +#' plot(f_saem_fomc$so, plot.type = "npde") +#' plot(f_saem_fomc$so, plot.type = "vpc") +#' +#' f_mmkin_parent_tc <- update(f_mmkin_parent, error_model = "tc") +#' f_saem_fomc_tc <- saem(f_mmkin_parent_tc["FOMC", ]) +#' compare.saemix(f_saem_fomc$so, f_saem_fomc_tc$so) +#' +#' sfo_sfo <- mkinmod(parent = mkinsub("SFO", "A1"), +#' A1 = mkinsub("SFO")) +#' fomc_sfo <- mkinmod(parent = mkinsub("FOMC", "A1"), +#' A1 = mkinsub("SFO")) +#' dfop_sfo <- mkinmod(parent = mkinsub("DFOP", "A1"), +#' A1 = mkinsub("SFO")) +#' # The following fit uses analytical solutions for SFO-SFO and DFOP-SFO, +#' # and compiled ODEs for FOMC that are much slower +#' f_mmkin <- mmkin(list( +#' "SFO-SFO" = sfo_sfo, "FOMC-SFO" = fomc_sfo, "DFOP-SFO" = dfop_sfo), +#' ds, quiet = TRUE) +#' # saem fits of SFO-SFO and DFOP-SFO to these data take about five seconds +#' # each on this system, as we use analytical solutions written for saemix. +#' # When using the analytical solutions written for mkin this took around +#' # four minutes +#' f_saem_sfo_sfo <- saem(f_mmkin["SFO-SFO", ]) +#' f_saem_dfop_sfo <- saem(f_mmkin["DFOP-SFO", ]) +#' # We can use print, plot and summary methods to check the results +#' print(f_saem_dfop_sfo) +#' plot(f_saem_dfop_sfo) +#' summary(f_saem_dfop_sfo, data = TRUE) +#' +#' # The following takes about 6 minutes +#' #f_saem_dfop_sfo_deSolve <- saem(f_mmkin["DFOP-SFO", ], solution_type = "deSolve", +#' # control = list(nbiter.saemix = c(200, 80), nbdisplay = 10)) +#' +#' #saemix::compare.saemix(list( +#' # f_saem_dfop_sfo$so, +#' # f_saem_dfop_sfo_deSolve$so)) +#' +#' # If the model supports it, we can also use eigenvalue based solutions, which +#' # take a similar amount of time +#' #f_saem_sfo_sfo_eigen <- saem(f_mmkin["SFO-SFO", ], solution_type = "eigen", +#' # control = list(nbiter.saemix = c(200, 80), nbdisplay = 10)) +#' } +#' @export +saem <- function(object, ...) UseMethod("saem") + +#' @rdname saem +#' @export +saem.mmkin <- function(object, + transformations = c("mkin", "saemix"), + degparms_start = numeric(), + test_log_parms = FALSE, + conf.level = 0.6, + solution_type = "auto", + nbiter.saemix = c(300, 100), + control = list(displayProgress = FALSE, print = FALSE, + nbiter.saemix = nbiter.saemix, + save = FALSE, save.graphs = FALSE), + fail_with_errors = TRUE, + verbose = FALSE, quiet = FALSE, ...) +{ + transformations <- match.arg(transformations) + m_saemix <- saemix_model(object, verbose = verbose, + degparms_start = degparms_start, + test_log_parms = test_log_parms, conf.level = conf.level, + solution_type = solution_type, + transformations = transformations, ...) + d_saemix <- saemix_data(object, verbose = verbose) + + fit_time <- system.time({ + utils::capture.output(f_saemix <- saemix::saemix(m_saemix, d_saemix, control), split = !quiet) + FIM_failed <- NULL + if (any(is.na(f_saemix@results@se.fixed))) FIM_failed <- c(FIM_failed, "fixed effects") + if (any(is.na(c(f_saemix@results@se.omega, f_saemix@results@se.respar)))) { + FIM_failed <- c(FIM_failed, "random effects and residual error parameters") + } + if (!is.null(FIM_failed) & fail_with_errors) { + stop("Could not invert FIM for ", paste(FIM_failed, collapse = " and ")) + } + }) + + transparms_optim <- f_saemix@results@fixed.effects + names(transparms_optim) <- f_saemix@results@name.fixed + + if (transformations == "mkin") { + bparms_optim <- backtransform_odeparms(transparms_optim, + object[[1]]$mkinmod, + object[[1]]$transform_rates, + object[[1]]$transform_fractions) + } else { + bparms_optim <- transparms_optim + } + + return_data <- nlme_data(object) + + return_data$predicted <- f_saemix@model@model( + psi = saemix::psi(f_saemix), + id = as.numeric(return_data$ds), + xidep = return_data[c("time", "name")]) + + return_data <- transform(return_data, + residual = value - predicted, + std = sigma_twocomp(predicted, + f_saemix@results@respar[1], f_saemix@results@respar[2])) + return_data <- transform(return_data, + standardized = residual / std) + + result <- list( + mkinmod = object[[1]]$mkinmod, + mmkin = object, + solution_type = object[[1]]$solution_type, + transformations = transformations, + transform_rates = object[[1]]$transform_rates, + transform_fractions = object[[1]]$transform_fractions, + so = f_saemix, + time = fit_time, + mean_dp_start = attr(m_saemix, "mean_dp_start"), + bparms.optim = bparms_optim, + bparms.fixed = object[[1]]$bparms.fixed, + data = return_data, + err_mod = object[[1]]$err_mod, + date.fit = date(), + saemixversion = as.character(utils::packageVersion("saemix")), + mkinversion = as.character(utils::packageVersion("mkin")), + Rversion = paste(R.version$major, R.version$minor, sep=".") + ) + + class(result) <- c("saem.mmkin", "mixed.mmkin") + return(result) +} + +#' @export +#' @rdname saem +#' @param x An saem.mmkin object to print +#' @param digits Number of digits to use for printing +print.saem.mmkin <- function(x, digits = max(3, getOption("digits") - 3), ...) { + cat( "Kinetic nonlinear mixed-effects model fit by SAEM" ) + cat("\nStructural model:\n") + diffs <- x$mmkin[[1]]$mkinmod$diffs + nice_diffs <- gsub("^(d.*) =", "\\1/dt =", diffs) + writeLines(strwrap(nice_diffs, exdent = 11)) + cat("\nData:\n") + cat(nrow(x$data), "observations of", + length(unique(x$data$name)), "variable(s) grouped in", + length(unique(x$data$ds)), "datasets\n") + + cat("\nLikelihood computed by importance sampling\n") + print(data.frame( + AIC = AIC(x$so, type = "is"), + BIC = BIC(x$so, type = "is"), + logLik = logLik(x$so, type = "is"), + row.names = " "), digits = digits) + + cat("\nFitted parameters:\n") + conf.int <- x$so@results@conf.int[c("estimate", "lower", "upper")] + rownames(conf.int) <- x$so@results@conf.int[["name"]] + print(conf.int, digits = digits) + + invisible(x) +} + +#' @rdname saem +#' @return An [saemix::SaemixModel] object. +#' @export +saemix_model <- function(object, solution_type = "auto", transformations = c("mkin", "saemix"), + degparms_start = numeric(), test_log_parms = FALSE, verbose = FALSE, ...) +{ + if (nrow(object) > 1) stop("Only row objects allowed") + + mkin_model <- object[[1]]$mkinmod + + degparms_optim <- mean_degparms(object, test_log_parms = test_log_parms) + if (transformations == "saemix") { + degparms_optim <- backtransform_odeparms(degparms_optim, + object[[1]]$mkinmod, + object[[1]]$transform_rates, + object[[1]]$transform_fractions) + } + degparms_fixed <- object[[1]]$bparms.fixed + + # Transformations are done in the degradation function + transform.par = rep(0, length(degparms_optim)) + + odeini_optim_parm_names <- grep('_0$', names(degparms_optim), value = TRUE) + odeini_fixed_parm_names <- grep('_0$', names(degparms_fixed), value = TRUE) + + odeparms_fixed_names <- setdiff(names(degparms_fixed), odeini_fixed_parm_names) + odeparms_fixed <- degparms_fixed[odeparms_fixed_names] + + odeini_fixed <- degparms_fixed[odeini_fixed_parm_names] + names(odeini_fixed) <- gsub('_0$', '', odeini_fixed_parm_names) + + model_function <- FALSE + + # Model functions with analytical solutions + # Fixed parameters, use_of_ff = "min" and turning off sinks currently not supported here + # In general, we need to consider exactly how the parameters in mkinfit were specified, + # as the parameters are currently mapped by position in these solutions + sinks <- sapply(mkin_model$spec, function(x) x$sink) + if (length(odeparms_fixed) == 0 & mkin_model$use_of_ff == "max" & all(sinks)) { + # Parent only + if (length(mkin_model$spec) == 1) { + parent_type <- mkin_model$spec[[1]]$type + if (length(odeini_fixed) == 1) { + if (parent_type == "SFO") { + stop("saemix needs at least two parameters to work on.") + } + if (parent_type == "FOMC") { + model_function <- function(psi, id, xidep) { + odeini_fixed / (xidep[, "time"]/exp(psi[id, 2]) + 1)^exp(psi[id, 1]) + } + } + if (parent_type == "DFOP") { + model_function <- function(psi, id, xidep) { + g <- plogis(psi[id, 3]) + t <- xidep[, "time"] + odeini_fixed * (g * exp(- exp(psi[id, 1]) * t) + + (1 - g) * exp(- exp(psi[id, 2]) * t)) + } + } + if (parent_type == "HS") { + model_function <- function(psi, id, xidep) { + tb <- exp(psi[id, 3]) + t <- xidep[, "time"] + k1 = exp(psi[id, 1]) + odeini_fixed * ifelse(t <= tb, + exp(- k1 * t), + exp(- k1 * tb) * exp(- exp(psi[id, 2]) * (t - tb))) + } + } + } else { + if (parent_type == "SFO") { + if (transformations == "mkin") { + model_function <- function(psi, id, xidep) { + psi[id, 1] * exp( - exp(psi[id, 2]) * xidep[, "time"]) + } + } else { + model_function <- function(psi, id, xidep) { + psi[id, 1] * exp( - psi[id, 2] * xidep[, "time"]) + } + transform.par = c(0, 1) + } + } + if (parent_type == "FOMC") { + model_function <- function(psi, id, xidep) { + psi[id, 1] / (xidep[, "time"]/exp(psi[id, 3]) + 1)^exp(psi[id, 2]) + } + } + if (parent_type == "DFOP") { + if (transformations == "mkin") { + model_function <- function(psi, id, xidep) { + g <- plogis(psi[id, 4]) + t <- xidep[, "time"] + psi[id, 1] * (g * exp(- exp(psi[id, 2]) * t) + + (1 - g) * exp(- exp(psi[id, 3]) * t)) + } + } else { + model_function <- function(psi, id, xidep) { + g <- psi[id, 4] + t <- xidep[, "time"] + psi[id, 1] * (g * exp(- psi[id, 2] * t) + + (1 - g) * exp(- psi[id, 3] * t)) + } + transform.par = c(0, 1, 1, 3) + } + } + if (parent_type == "HS") { + model_function <- function(psi, id, xidep) { + tb <- exp(psi[id, 4]) + t <- xidep[, "time"] + k1 = exp(psi[id, 2]) + psi[id, 1] * ifelse(t <= tb, + exp(- k1 * t), + exp(- k1 * tb) * exp(- exp(psi[id, 3]) * (t - tb))) + } + } + } + } + + # Parent with one metabolite + # Parameter names used in the model functions are as in + # https://nbviewer.jupyter.org/urls/jrwb.de/nb/Symbolic%20ODE%20solutions%20for%20mkin.ipynb + types <- unname(sapply(mkin_model$spec, function(x) x$type)) + if (length(mkin_model$spec) == 2 &! "SFORB" %in% types ) { + # Initial value for the metabolite (n20) must be fixed + if (names(odeini_fixed) == names(mkin_model$spec)[2]) { + n20 <- odeini_fixed + parent_name <- names(mkin_model$spec)[1] + if (identical(types, c("SFO", "SFO"))) { + if (transformations == "mkin") { + model_function <- function(psi, id, xidep) { + t <- xidep[, "time"] + n10 <- psi[id, 1] + k1 <- exp(psi[id, 2]) + k2 <- exp(psi[id, 3]) + f12 <- plogis(psi[id, 4]) + ifelse(xidep[, "name"] == parent_name, + n10 * exp(- k1 * t), + (((k2 - k1) * n20 - f12 * k1 * n10) * exp(- k2 * t)) / (k2 - k1) + + (f12 * k1 * n10 * exp(- k1 * t)) / (k2 - k1) + ) + } + } else { + model_function <- function(psi, id, xidep) { + t <- xidep[, "time"] + n10 <- psi[id, 1] + k1 <- psi[id, 2] + k2 <- psi[id, 3] + f12 <- psi[id, 4] + ifelse(xidep[, "name"] == parent_name, + n10 * exp(- k1 * t), + (((k2 - k1) * n20 - f12 * k1 * n10) * exp(- k2 * t)) / (k2 - k1) + + (f12 * k1 * n10 * exp(- k1 * t)) / (k2 - k1) + ) + } + transform.par = c(0, 1, 1, 3) + } + } + if (identical(types, c("DFOP", "SFO"))) { + if (transformations == "mkin") { + model_function <- function(psi, id, xidep) { + t <- xidep[, "time"] + n10 <- psi[id, 1] + k2 <- exp(psi[id, 2]) + f12 <- plogis(psi[id, 3]) + l1 <- exp(psi[id, 4]) + l2 <- exp(psi[id, 5]) + g <- plogis(psi[id, 6]) + ifelse(xidep[, "name"] == parent_name, + n10 * (g * exp(- l1 * t) + (1 - g) * exp(- l2 * t)), + ((f12 * g - f12) * l2 * n10 * exp(- l2 * t)) / (l2 - k2) - + (f12 * g * l1 * n10 * exp(- l1 * t)) / (l1 - k2) + + ((((l1 - k2) * l2 - k2 * l1 + k2^2) * n20 + + ((f12 * l1 + (f12 * g - f12) * k2) * l2 - + f12 * g * k2 * l1) * n10) * exp( - k2 * t)) / + ((l1 - k2) * l2 - k2 * l1 + k2^2) + ) + } + } else { + model_function <- function(psi, id, xidep) { + t <- xidep[, "time"] + n10 <- psi[id, 1] + k2 <- psi[id, 2] + f12 <- psi[id, 3] + l1 <- psi[id, 4] + l2 <- psi[id, 5] + g <- psi[id, 6] + ifelse(xidep[, "name"] == parent_name, + n10 * (g * exp(- l1 * t) + (1 - g) * exp(- l2 * t)), + ((f12 * g - f12) * l2 * n10 * exp(- l2 * t)) / (l2 - k2) - + (f12 * g * l1 * n10 * exp(- l1 * t)) / (l1 - k2) + + ((((l1 - k2) * l2 - k2 * l1 + k2^2) * n20 + + ((f12 * l1 + (f12 * g - f12) * k2) * l2 - + f12 * g * k2 * l1) * n10) * exp( - k2 * t)) / + ((l1 - k2) * l2 - k2 * l1 + k2^2) + ) + } + transform.par = c(0, 1, 3, 1, 1, 3) + } + } + } + } + } + + if (is.function(model_function) & solution_type == "auto") { + solution_type = "analytical saemix" + } else { + + if (solution_type == "auto") + solution_type <- object[[1]]$solution_type + + model_function <- function(psi, id, xidep) { + + uid <- unique(id) + + res_list <- lapply(uid, function(i) { + + transparms_optim <- as.numeric(psi[i, ]) # psi[i, ] is a dataframe when called in saemix.predict + names(transparms_optim) <- names(degparms_optim) + + odeini_optim <- transparms_optim[odeini_optim_parm_names] + names(odeini_optim) <- gsub('_0$', '', odeini_optim_parm_names) + + odeini <- c(odeini_optim, odeini_fixed)[names(mkin_model$diffs)] + + ode_transparms_optim_names <- setdiff(names(transparms_optim), odeini_optim_parm_names) + odeparms_optim <- backtransform_odeparms(transparms_optim[ode_transparms_optim_names], mkin_model, + transform_rates = object[[1]]$transform_rates, + transform_fractions = object[[1]]$transform_fractions) + odeparms <- c(odeparms_optim, odeparms_fixed) + + xidep_i <- subset(xidep, id == i) + + if (solution_type == "analytical") { + out_values <- mkin_model$deg_func(xidep_i, odeini, odeparms) + } else { + + i_time <- xidep_i$time + i_name <- xidep_i$name + + out_wide <- mkinpredict(mkin_model, + odeparms = odeparms, odeini = odeini, + solution_type = solution_type, + outtimes = sort(unique(i_time)), + na_stop = FALSE + ) + + out_index <- cbind(as.character(i_time), as.character(i_name)) + out_values <- out_wide[out_index] + } + return(out_values) + }) + res <- unlist(res_list) + return(res) + } + } + + error.model <- switch(object[[1]]$err_mod, + const = "constant", + tc = "combined", + obs = "constant") + + if (object[[1]]$err_mod == "obs") { + warning("The error model 'obs' (variance by variable) can currently not be transferred to an saemix model") + } + + error.init <- switch(object[[1]]$err_mod, + const = c(a = mean(sapply(object, function(x) x$errparms)), b = 1), + tc = c(a = mean(sapply(object, function(x) x$errparms[1])), + b = mean(sapply(object, function(x) x$errparms[2]))), + obs = c(a = mean(sapply(object, function(x) x$errparms)), b = 1)) + + degparms_psi0 <- degparms_optim + degparms_psi0[names(degparms_start)] <- degparms_start + psi0_matrix <- matrix(degparms_psi0, nrow = 1) + colnames(psi0_matrix) <- names(degparms_psi0) + + res <- saemix::saemixModel(model_function, + psi0 = psi0_matrix, + "Mixed model generated from mmkin object", + transform.par = transform.par, + error.model = error.model, + verbose = verbose + ) + attr(res, "mean_dp_start") <- degparms_optim + return(res) +} + +#' @rdname saem +#' @return An [saemix::SaemixData] object. +#' @export +saemix_data <- function(object, verbose = FALSE, ...) { + if (nrow(object) > 1) stop("Only row objects allowed") + ds_names <- colnames(object) + + ds_list <- lapply(object, function(x) x$data[c("time", "variable", "observed")]) + names(ds_list) <- ds_names + ds_saemix_all <- purrr::map_dfr(ds_list, function(x) x, .id = "ds") + ds_saemix <- data.frame(ds = ds_saemix_all$ds, + name = as.character(ds_saemix_all$variable), + time = ds_saemix_all$time, + value = ds_saemix_all$observed, + stringsAsFactors = FALSE) + + res <- saemix::saemixData(ds_saemix, + name.group = "ds", + name.predictors = c("time", "name"), + name.response = "value", + verbose = verbose, + ...) + return(res) +} |