Basic Usage

Introduction

This vignette gives a minimal example of how to use poissonsuperlearner to fit piecewise-constant hazard models and combine them in a Poisson super learner. The package works by expanding subject-level time-to-event data to a long Poisson format on a grid of time intervals, fitting one or more base learners to the corresponding cause-specific hazards, and optionally combining them through a meta-learner.

The same workflow can be used both for a single fitted learner via fit_learner() and for an ensemble via Superlearner().

Generate synthetic Steno data

We first simulate a small synthetic data set with simulateStenoT1(). The simulator is inspired by the Steno Type-1 risk engine and generates correlated baseline covariates such as age, diabetes duration, LDL, systolic blood pressure, HbA1c, albuminuria, eGFR, smoking, and physical activity. Event times are then generated from Weibull proportional hazards models. In scenario "alpha", the event mechanism is linear in the covariates, and with competing_risks = TRUE the data contain two causes: cardiovascular disease (CVD) and death without prior CVD. In scenario "beta", the CVD hazard instead includes additional nonlinear hinge-squared effects of age and LDL.

Here we use the "alpha" scenario with competing risks to illustrate the cause-specific output of the package on a subset of the covariates.

set.seed(42)
d <- simulateStenoT1(
  n = 150,
  scenario = "alpha",
  competing_risks = TRUE
)

head(d[, .(id, time, event, age, diabetes_duration, value_LDL, sex)])
#>       id      time event      age diabetes_duration value_LDL    sex
#>    <int>     <num> <num>    <num>             <num>     <num> <fctr>
#> 1:     1 0.3390123     1 48.56530          22.40288 3.7434636      0
#> 2:     2 0.3576302     1 57.73618          25.73266 2.2979531      1
#> 3:     3 0.4172349     1 39.41783          16.74741 1.1053140      0
#> 4:     4 0.5742121     1 47.49727          23.21574 2.5886356      0
#> 5:     5 0.9066543     1 49.60508          23.06710 0.1462869      0
#> 6:     6 1.0303493     1 43.25154          17.76698 1.2642894      0

The observed follow-up time is stored in time and the event indicator in event. With competing risks, event = 0 denotes censoring, event = 1 corresponds to CVD, and event = 2 to death without prior CVD.

Define a small learner library

Each learner models the piecewise-constant hazard on a grid of time intervals. In the examples below, the grid is controlled by number_of_nodes = 5, which creates a quantile-based time grid used internally for the long Poisson representation.

We define two simple learners based on glmnet: one unpenalized Poisson model and one lasso-type learner.

lglmnet0 <- Learner_glmnet(
  covariates = c("sex", "diabetes_duration"),
  cross_validation = FALSE,
  lambda = 0,
  intercept = TRUE
)

lglmnet1 <- Learner_glmnet(
  covariates = c("value_Smoking", "value_LDL"),
  cross_validation = TRUE,
  alpha = 1,
  intercept = TRUE
)

learners_list <- list(
  glm = lglmnet0,
  lasso = lglmnet1
)

Alternative learner definitions and wrapper arguments

The package currently provides three learner classes: Learner_glmnet(), Learner_gam(), and Learner_hal(). The code below is shown for illustration only and is therefore not run. It highlights how learners are defined by initializing Reference Class objects and then passing them to fit_learner() or Superlearner().

l_glmnet <- Learner_glmnet(
  covariates = c("sex", "diabetes_duration", "value_LDL"),
  add_nodes = TRUE,
  cross_validation = TRUE,
  alpha = 1
)

l_gam <- Learner_gam(
  covariates = c("s(age)", "s(value_LDL)", "sex"),
  add_nodes = TRUE,
  method = "fREML",
  discrete = TRUE
)

l_hal <- Learner_hal(
  covariates = c("age", "diabetes_duration", "value_LDL"),
  add_nodes = TRUE,
  cross_validation = TRUE,
  num_knots = c(10L, 5L),
  max_degree = 2L
)

Some learner arguments are specific to the piecewise-constant hazard workflow implemented in poissonsuperlearner. In particular, covariates defines the terms used in the long-format hazard model, and add_nodes = TRUE adds the interval-specific node effects that represent the baseline hazard across the time grid. For the HAL learner, num_knots, max_degree, and maxit_prefit also control the package-specific basis construction and screening step used before the final penalized fit.

A useful feature of the package is that, except for HAL, the learners mainly wrap existing fitting routines. Learner_glmnet() forwards additional arguments in ... to glmnet::glmnet() or glmnet::cv.glmnet(), and Learner_gam() forwards them to mgcv::bam(). This means that most tuning can be done with the familiar arguments from the underlying packages rather than through a separate package-specific interface.

For GAMs, smooth terms are specified directly in the covariates vector using standard mgcv syntax. For example, if a spline effect of age is desired, one simply writes "s(age)"; tensor products or other mgcv terms can be passed in the same way.

The HAL learner is more specialized. It includes several parameters that are specific to the piecewise-constant hazard implementation, such as the number of basis cutpoints per interaction order (num_knots) and the maximum interaction degree (max_degree), while still relying on the underlying glmnet fitting routine for the penalized Poisson regression step. In other words, HAL combines a package-specific basis expansion with the familiar glmnet optimization controls available through ....

Fit an ensemble and individual learners

Superlearner() fits all learners, obtains cross-validated predictions for the meta-learning step, and then fits one cause-specific meta-learner per cause. For comparison, fit_learner() fits a single learner directly.

Superlearner() and fit_learner() can be supplied either with an explicit grid of time nodes (nodes) or with the number of nodes selected from the observed quantiles (number_of_nodes) used to construct that grid; nfolds specifies the number of folds used for internal cross-validation; if an id variable is provided it identifies which rows belong to the same individual, whereas if id is omitted each row is treated as a separate observation; the status variable must be coded as 0 for censoring and positive integers for the competing event types; and time_event is the event or follow-up time variable on which the model is built.

sl_model <- Superlearner(
  d,
  id = "id",
  status = "event",
  event_time = "time",
  learners = learners_list,
  number_of_nodes = 5,
  nfold = 3
)

l0_model <- fit_learner(
  d,
  id = "id",
  learner = lglmnet0,
  status = "event",
  event_time = "time",
  number_of_nodes = 5
)

l1_model <- fit_learner(
  d,
  id = "id",
  learner = lglmnet1,
  status = "event",
  event_time = "time",
  number_of_nodes = 5
)

Inspect the fitted objects

The fitted objects have print(), summary(), and coef() methods.

print() is useful for a quick look at the stored fitted object. For a fitted super learner, you can print the stacked meta-learner or one of the stored base learners.

print(sl_model, cause = 1)
#> 
#> Call:  (function (x, y, family = c("gaussian", "binomial", "poisson",      "multinomial", "cox", "mgaussian"), weights = NULL, offset = NULL,      alpha = 1, nlambda = 100, lambda.min.ratio = ifelse(nobs <          nvars, 0.01, 1e-04), lambda = NULL, standardize = TRUE,      intercept = TRUE, thresh = 1e-07, dfmax = nvars + 1, pmax = min(dfmax *          2 + 20, nvars), exclude = NULL, penalty.factor = rep(1,          nvars), lower.limits = -Inf, upper.limits = Inf, maxit = 1e+05,      type.gaussian = ifelse(nvars < 500, "covariance", "naive"),      type.logistic = c("Newton", "modified.Newton"), standardize.response = FALSE,      type.multinomial = c("ungrouped", "grouped"), relax = FALSE,      trace.it = 0, ...)  {     this.call = match.call()     np = dim(x)     if (is.null(np) | (np[2] <= 1))          stop("x should be a matrix with 2 or more columns")     nobs = as.integer(np[1])     nvars = as.integer(np[2])     if (any(is.na(x)))          stop("x has missing values; consider using makeX() to impute them")     if (is.null(weights))          weights = rep(1, nobs)     else if (length(weights) != nobs)          stop(paste("number of elements in weights (", length(weights),              ") not equal to the number of rows of x (", nobs,              ")", sep = ""))     if (is.function(exclude))          exclude <- check.exclude(exclude(x = x, y = y, weights = weights),              nvars)     if (length(penalty.factor) != nvars)          stop("the length of penalty.factor does not match the number of variables")     if (!is.character(family)) {         fit = glmnet.path(x, y, weights, lambda, nlambda, lambda.min.ratio,              alpha, offset, family, standardize, intercept, thresh = thresh,              maxit, penalty.factor, exclude, lower.limits, upper.limits,              trace.it = trace.it)         fit$call = this.call     }     else {         family = match.arg(family)         if (family == "cox" && use.cox.path(x, y)) {             fit <- cox.path(x, y, weights, offset, alpha, nlambda,                  lambda.min.ratio, lambda, standardize, thresh,                  exclude, penalty.factor, lower.limits, upper.limits,                  maxit, trace.it, ...)             fit$call <- this.call         }         else {             if (alpha > 1) {                 warning("alpha >1; set to 1")                 alpha = 1             }             if (alpha < 0) {                 warning("alpha<0; set to 0")                 alpha = 0             }             alpha = as.double(alpha)             nlam = as.integer(nlambda)             y = drop(y)             dimy = dim(y)             nrowy = ifelse(is.null(dimy), length(y), dimy[1])             if (nrowy != nobs)                  stop(paste("number of observations in y (", nrowy,                    ") not equal to the number of rows of x (",                    nobs, ")", sep = ""))             vnames = colnames(x)             if (is.null(vnames))                  vnames = paste("V", seq(nvars), sep = "")             ne = as.integer(dfmax)             nx = as.integer(pmax)             if (is.null(exclude))                  exclude = integer(0)             if (any(penalty.factor == Inf)) {                 exclude = c(exclude, seq(nvars)[penalty.factor ==                    Inf])                 exclude = sort(unique(exclude))             }             if (length(exclude) > 0) {                 jd = match(exclude, seq(nvars), 0)                 if (!all(jd > 0))                    stop("Some excluded variables out of range")                 penalty.factor[jd] = 1                 jd = as.integer(c(length(jd), jd))             }             else jd = as.integer(0)             vp = as.double(penalty.factor)             internal.parms = glmnet.control()             if (internal.parms$itrace)                  trace.it = 1             else {                 if (trace.it) {                   glmnet.control(itrace = 1)                   on.exit(glmnet.control(itrace = 0))                 }             }             if (any(lower.limits > 0)) {                 stop("Lower limits should be non-positive")             }             if (any(upper.limits < 0)) {                 stop("Upper limits should be non-negative")             }             lower.limits[lower.limits == -Inf] = -internal.parms$big             upper.limits[upper.limits == Inf] = internal.parms$big             if (length(lower.limits) < nvars) {                 if (length(lower.limits) == 1)                    lower.limits = rep(lower.limits, nvars)                 else stop("Require length 1 or nvars lower.limits")             }             else lower.limits = lower.limits[seq(nvars)]             if (length(upper.limits) < nvars) {                 if (length(upper.limits) == 1)                    upper.limits = rep(upper.limits, nvars)                 else stop("Require length 1 or nvars upper.limits")             }             else upper.limits = upper.limits[seq(nvars)]             cl = rbind(lower.limits, upper.limits)             if (any(cl == 0)) {                 fdev = glmnet.control()$fdev                 if (fdev != 0) {                   glmnet.control(fdev = 0)                   on.exit(glmnet.control(fdev = fdev))                 }             }             storage.mode(cl) = "double"             isd = as.integer(standardize)             intr = as.integer(intercept)             if (!missing(intercept) && family == "cox")                  warning("Cox model has no intercept")             jsd = as.integer(standardize.response)             thresh = as.double(thresh)             if (is.null(lambda)) {                 if (lambda.min.ratio >= 1)                    stop("lambda.min.ratio should be less than 1")                 flmin = as.double(lambda.min.ratio)                 ulam = double(1)             }             else {                 flmin = as.double(1)                 if (any(lambda < 0))                    stop("lambdas should be non-negative")                 ulam = as.double(rev(sort(lambda)))                 nlam = as.integer(length(lambda))             }             is.sparse = FALSE             if (inherits(x, "sparseMatrix")) {                 is.sparse = TRUE                 if (!inherits(x, "dgCMatrix"))                    x = as(as(as(x, "generalMatrix"), "CsparseMatrix"),                      "dMatrix")             }             else if (!inherits(x, "matrix")) {                 x <- data.matrix(x)             }             else {                 x <- x             }             if (!inherits(x, "sparseMatrix")) {                 storage.mode(x) <- "double"             }             if (trace.it) {                 if (relax)                    cat("Training Fit\n")                 pb <- createPB(min = 0, max = nlam, initial = 0,                    style = 3)             }             else {                 pb <- NULL             }             kopt = switch(match.arg(type.logistic), Newton = 0,                  modified.Newton = 1)             if (family == "multinomial") {                 type.multinomial = match.arg(type.multinomial)                 if (type.multinomial == "grouped")                    kopt = 2             }             kopt = as.integer(kopt)             fit = switch(family, gaussian = elnet(x, is.sparse,                  y, weights, offset, type.gaussian, alpha, nobs,                  nvars, jd, vp, cl, ne, nx, nlam, flmin, ulam,                  thresh, isd, intr, vnames, maxit, pb), poisson = fishnet(x,                  is.sparse, y, weights, offset, alpha, nobs, nvars,                  jd, vp, cl, ne, nx, nlam, flmin, ulam, thresh,                  isd, intr, vnames, maxit, pb), binomial = lognet(x,                  is.sparse, y, weights, offset, alpha, nobs, nvars,                  jd, vp, cl, ne, nx, nlam, flmin, ulam, thresh,                  isd, intr, vnames, maxit, kopt, family, pb),                  multinomial = lognet(x, is.sparse, y, weights,                    offset, alpha, nobs, nvars, jd, vp, cl, ne,                    nx, nlam, flmin, ulam, thresh, isd, intr, vnames,                    maxit, kopt, family, pb), cox = coxnet(x, is.sparse,                    y, weights, offset, alpha, nobs, nvars, jd,                    vp, cl, ne, nx, nlam, flmin, ulam, thresh,                    isd, vnames, maxit), mgaussian = mrelnet(x,                    is.sparse, y, weights, offset, alpha, nobs,                    nvars, jd, vp, cl, ne, nx, nlam, flmin, ulam,                    thresh, isd, jsd, intr, vnames, maxit, pb))             if (trace.it) {                 utils::setTxtProgressBar(pb, nlam)                 close(pb)             }             if (is.null(lambda))                  fit$lambda = fix.lam(fit$lambda)             fit$call = this.call             fit$nobs = nobs             class(fit) = c(class(fit), "glmnet")         }     }     if (relax)          relax.glmnet(fit, x = x, y = y, weights = weights, offset = offset,              lower.limits = lower.limits, upper.limits = upper.limits,              penalty.factor = penalty.factor, check.args = FALSE,              ...)     else fit })(x = new("dgCMatrix", i = c(0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L,  8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L,  21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L,  34L, 35L, 36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L,  47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L,  60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L, 71L, 72L,  73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L, 83L, 84L, 85L,  86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L, 97L, 98L,  99L, 100L, 101L, 102L, 103L, 104L, 105L, 106L, 107L, 108L, 109L,  110L, 111L, 112L, 113L, 114L, 115L, 116L, 117L, 118L, 119L, 120L,  121L, 122L, 123L, 124L, 125L, 126L, 127L, 128L, 129L, 130L, 131L,  132L, 133L, 134L, 135L, 136L, 137L, 138L, 139L, 140L, 141L, 142L,  143L, 144L, 145L, 146L, 147L, 148L, 149L, 150L, 151L, 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228L, 229L, 230L, 231L, 232L,  233L, 234L, 235L, 236L, 237L, 238L, 239L, 240L, 241L, 242L, 243L,  244L, 245L, 246L, 247L, 248L, 249L, 250L, 251L, 252L, 253L, 254L,  255L, 256L, 257L, 258L, 259L, 260L, 261L, 262L, 263L, 264L, 265L,  266L, 267L, 268L, 269L, 270L, 271L, 272L, 273L, 274L, 275L, 276L,  277L, 278L, 279L, 280L, 281L, 282L, 283L, 284L, 285L, 286L, 287L,  288L, 289L, 290L, 291L, 292L, 293L, 294L, 295L, 296L, 297L, 298L,  299L, 300L, 301L, 302L, 303L, 304L, 305L, 306L, 307L, 308L, 309L,  310L, 311L, 312L, 313L, 314L, 315L, 316L, 317L, 318L, 319L, 320L,  321L, 322L, 323L, 324L, 325L, 326L, 327L, 328L, 329L, 330L, 331L,  332L, 333L, 334L, 335L, 336L, 337L, 338L, 339L, 340L, 341L, 342L,  343L, 344L, 345L, 346L, 347L, 348L, 349L, 350L, 351L, 352L, 353L,  354L, 355L, 356L, 357L, 358L, 359L, 360L, 361L, 362L, 363L, 364L,  365L, 366L, 367L, 368L, 369L, 370L, 371L, 372L, 373L, 374L, 375L,  376L, 377L, 378L, 379L, 380L, 381L, 382L, 383L, 384L, 385L, 386L,  387L, 388L, 389L, 390L, 391L, 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-1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.42050901179438, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.44358739848253, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.44837738103435, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.48043338335665, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.69904441056629, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.90061226295242, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.95753338447636, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  2.10018312549547, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 2.27238716888237, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  2.44250995253019), lambda = 0, intercept = FALSE, penalise_nodes = TRUE) 
#> 
#>   Df  %Dev Lambda
#> 1  2 81.25      0
print(sl_model, cause = 1, model = "glm")
#> 
#> Call:  (function (x, y, family = c("gaussian", "binomial", "poisson",      "multinomial", "cox", "mgaussian"), weights = NULL, offset = NULL,      alpha = 1, nlambda = 100, lambda.min.ratio = ifelse(nobs <          nvars, 0.01, 1e-04), lambda = NULL, standardize = TRUE,      intercept = TRUE, thresh = 1e-07, dfmax = nvars + 1, pmax = min(dfmax *          2 + 20, nvars), exclude = NULL, penalty.factor = rep(1,          nvars), lower.limits = -Inf, upper.limits = Inf, maxit = 1e+05,      type.gaussian = ifelse(nvars < 500, "covariance", "naive"),      type.logistic = c("Newton", "modified.Newton"), standardize.response = FALSE,      type.multinomial = c("ungrouped", "grouped"), relax = FALSE,      trace.it = 0, ...)  {     this.call = match.call()     np = dim(x)     if (is.null(np) | (np[2] <= 1))          stop("x should be a matrix with 2 or more columns")     nobs = as.integer(np[1])     nvars = as.integer(np[2])     if (any(is.na(x)))          stop("x has missing values; consider using makeX() to impute them")     if (is.null(weights))          weights = rep(1, nobs)     else if (length(weights) != nobs)          stop(paste("number of elements in weights (", length(weights),              ") not equal to the number of rows of x (", nobs,              ")", sep = ""))     if (is.function(exclude))          exclude <- check.exclude(exclude(x = x, y = y, weights = weights),              nvars)     if (length(penalty.factor) != nvars)          stop("the length of penalty.factor does not match the number of variables")     if (!is.character(family)) {         fit = glmnet.path(x, y, weights, lambda, nlambda, lambda.min.ratio,              alpha, offset, family, standardize, intercept, thresh = thresh,              maxit, penalty.factor, exclude, lower.limits, upper.limits,              trace.it = trace.it)         fit$call = this.call     }     else {         family = match.arg(family)         if (family == "cox" && use.cox.path(x, y)) {             fit <- cox.path(x, y, weights, offset, alpha, nlambda,                  lambda.min.ratio, lambda, standardize, thresh,                  exclude, penalty.factor, lower.limits, upper.limits,                  maxit, trace.it, ...)             fit$call <- this.call         }         else {             if (alpha > 1) {                 warning("alpha >1; set to 1")                 alpha = 1             }             if (alpha < 0) {                 warning("alpha<0; set to 0")                 alpha = 0             }             alpha = as.double(alpha)             nlam = as.integer(nlambda)             y = drop(y)             dimy = dim(y)             nrowy = ifelse(is.null(dimy), length(y), dimy[1])             if (nrowy != nobs)                  stop(paste("number of observations in y (", nrowy,                    ") not equal to the number of rows of x (",                    nobs, ")", sep = ""))             vnames = colnames(x)             if (is.null(vnames))                  vnames = paste("V", seq(nvars), sep = "")             ne = as.integer(dfmax)             nx = as.integer(pmax)             if (is.null(exclude))                  exclude = integer(0)             if (any(penalty.factor == Inf)) {                 exclude = c(exclude, seq(nvars)[penalty.factor ==                    Inf])                 exclude = sort(unique(exclude))             }             if (length(exclude) > 0) {                 jd = match(exclude, seq(nvars), 0)                 if (!all(jd > 0))                    stop("Some excluded variables out of range")                 penalty.factor[jd] = 1                 jd = as.integer(c(length(jd), jd))             }             else jd = as.integer(0)             vp = as.double(penalty.factor)             internal.parms = glmnet.control()             if (internal.parms$itrace)                  trace.it = 1             else {                 if (trace.it) {                   glmnet.control(itrace = 1)                   on.exit(glmnet.control(itrace = 0))                 }             }             if (any(lower.limits > 0)) {                 stop("Lower limits should be non-positive")             }             if (any(upper.limits < 0)) {                 stop("Upper limits should be non-negative")             }             lower.limits[lower.limits == -Inf] = -internal.parms$big             upper.limits[upper.limits == Inf] = internal.parms$big             if (length(lower.limits) < nvars) {                 if (length(lower.limits) == 1)                    lower.limits = rep(lower.limits, nvars)                 else stop("Require length 1 or nvars lower.limits")             }             else lower.limits = lower.limits[seq(nvars)]             if (length(upper.limits) < nvars) {                 if (length(upper.limits) == 1)                    upper.limits = rep(upper.limits, nvars)                 else stop("Require length 1 or nvars upper.limits")             }             else upper.limits = upper.limits[seq(nvars)]             cl = rbind(lower.limits, upper.limits)             if (any(cl == 0)) {                 fdev = glmnet.control()$fdev                 if (fdev != 0) {                   glmnet.control(fdev = 0)                   on.exit(glmnet.control(fdev = fdev))                 }             }             storage.mode(cl) = "double"             isd = as.integer(standardize)             intr = as.integer(intercept)             if (!missing(intercept) && family == "cox")                  warning("Cox model has no intercept")             jsd = as.integer(standardize.response)             thresh = as.double(thresh)             if (is.null(lambda)) {                 if (lambda.min.ratio >= 1)                    stop("lambda.min.ratio should be less than 1")                 flmin = as.double(lambda.min.ratio)                 ulam = double(1)             }             else {                 flmin = as.double(1)                 if (any(lambda < 0))                    stop("lambdas should be non-negative")                 ulam = as.double(rev(sort(lambda)))                 nlam = as.integer(length(lambda))             }             is.sparse = FALSE             if (inherits(x, "sparseMatrix")) {                 is.sparse = TRUE                 if (!inherits(x, "dgCMatrix"))                    x = as(as(as(x, "generalMatrix"), "CsparseMatrix"),                      "dMatrix")             }             else if (!inherits(x, "matrix")) {                 x <- data.matrix(x)             }             else {                 x <- x             }             if (!inherits(x, "sparseMatrix")) {                 storage.mode(x) <- "double"             }             if (trace.it) {                 if (relax)                    cat("Training Fit\n")                 pb <- createPB(min = 0, max = nlam, initial = 0,                    style = 3)             }             else {                 pb <- NULL             }             kopt = switch(match.arg(type.logistic), Newton = 0,                  modified.Newton = 1)             if (family == "multinomial") {                 type.multinomial = match.arg(type.multinomial)                 if (type.multinomial == "grouped")                    kopt = 2             }             kopt = as.integer(kopt)             fit = switch(family, gaussian = elnet(x, is.sparse,                  y, weights, offset, type.gaussian, alpha, nobs,                  nvars, jd, vp, cl, ne, nx, nlam, flmin, ulam,                  thresh, isd, intr, vnames, maxit, pb), poisson = fishnet(x,                  is.sparse, y, weights, offset, alpha, nobs, nvars,                  jd, vp, cl, ne, nx, nlam, flmin, ulam, thresh,                  isd, intr, vnames, maxit, pb), binomial = lognet(x,                  is.sparse, y, weights, offset, alpha, nobs, nvars,                  jd, vp, cl, ne, nx, nlam, flmin, ulam, thresh,                  isd, intr, vnames, maxit, kopt, family, pb),                  multinomial = lognet(x, is.sparse, y, weights,                    offset, alpha, nobs, nvars, jd, vp, cl, ne,                    nx, nlam, flmin, ulam, thresh, isd, intr, vnames,                    maxit, kopt, family, pb), cox = coxnet(x, is.sparse,                    y, weights, offset, alpha, nobs, nvars, jd,                    vp, cl, ne, nx, nlam, flmin, ulam, thresh,                    isd, vnames, maxit), mgaussian = mrelnet(x,                    is.sparse, y, weights, offset, alpha, nobs,                    nvars, jd, vp, cl, ne, nx, nlam, flmin, ulam,                    thresh, isd, jsd, intr, vnames, maxit, pb))             if (trace.it) {                 utils::setTxtProgressBar(pb, nlam)                 close(pb)             }             if (is.null(lambda))                  fit$lambda = fix.lam(fit$lambda)             fit$call = this.call             fit$nobs = nobs             class(fit) = c(class(fit), "glmnet")         }     }     if (relax)          relax.glmnet(fit, x = x, y = y, weights = weights, offset = offset,              lower.limits = lower.limits, upper.limits = upper.limits,              penalty.factor = penalty.factor, check.args = FALSE,              ...)     else fit })(x = new("dgCMatrix", i = c(1L, 2L, 15L, 16L, 23L, 24L, 27L,  28L, 29L, 30L, 33L, 34L, 35L, 36L, 37L, 38L, 62L, 63L, 64L, 74L,  75L, 76L, 83L, 84L, 85L, 89L, 90L, 91L, 101L, 102L, 103L, 110L,  111L, 112L, 113L, 114L, 115L, 131L, 132L, 133L, 140L, 141L, 142L,  149L, 150L, 151L, 152L, 161L, 162L, 163L, 164L, 169L, 170L, 171L,  172L, 173L, 174L, 175L, 176L, 177L, 178L, 179L, 180L, 181L, 182L,  183L, 184L, 189L, 190L, 191L, 192L, 209L, 210L, 211L, 212L, 213L,  214L, 215L, 216L, 217L, 218L, 219L, 220L, 221L, 222L, 223L, 224L,  225L, 226L, 227L, 228L, 229L, 230L, 231L, 232L, 261L, 262L, 263L,  264L, 293L, 294L, 295L, 296L, 297L, 298L, 299L, 300L, 301L, 302L,  313L, 314L, 315L, 316L, 317L, 323L, 324L, 325L, 326L, 327L, 333L,  334L, 335L, 336L, 337L, 343L, 344L, 345L, 346L, 347L, 378L, 379L,  380L, 381L, 382L, 383L, 384L, 385L, 386L, 387L, 393L, 394L, 395L,  396L, 397L, 408L, 409L, 410L, 411L, 412L, 413L, 414L, 415L, 416L,  417L, 418L, 419L, 420L, 421L, 422L, 423L, 436L, 437L, 438L, 439L,  440L, 441L, 442L, 443L, 444L, 445L, 446L, 447L, 448L, 449L, 450L,  451L, 452L, 453L, 460L, 461L, 462L, 463L, 464L, 465L, 472L, 473L,  474L, 475L, 476L, 477L, 478L, 479L, 480L, 481L, 482L, 483L, 490L,  491L, 492L, 493L, 494L, 495L, 496L, 497L, 498L, 499L, 500L, 501L,  508L, 509L, 510L, 511L, 512L, 513L, 514L, 515L, 516L, 517L, 518L,  519L, 532L, 533L, 534L, 535L, 536L, 537L, 538L, 539L, 540L, 541L,  542L, 543L, 550L, 551L, 552L, 553L, 554L, 555L, 556L, 557L, 558L,  559L, 560L, 561L, 568L, 569L, 570L, 571L, 572L, 573L, 580L, 581L,  582L, 583L, 584L, 585L, 586L, 587L, 588L, 589L, 590L, 591L, 592L,  593L, 594L, 595L, 596L, 597L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L,  8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L,  21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L,  34L, 35L, 36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L,  47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L,  60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L, 71L, 72L,  73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L, 83L, 84L, 85L,  86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L, 97L, 98L,  99L, 100L, 101L, 102L, 103L, 104L, 105L, 106L, 107L, 108L, 109L,  110L, 111L, 112L, 113L, 114L, 115L, 116L, 117L, 118L, 119L, 120L,  121L, 122L, 123L, 124L, 125L, 126L, 127L, 128L, 129L, 130L, 131L,  132L, 133L, 134L, 135L, 136L, 137L, 138L, 139L, 140L, 141L, 142L,  143L, 144L, 145L, 146L, 147L, 148L, 149L, 150L, 151L, 152L, 153L,  154L, 155L, 156L, 157L, 158L, 159L, 160L, 161L, 162L, 163L, 164L,  165L, 166L, 167L, 168L, 169L, 170L, 171L, 172L, 173L, 174L, 175L,  176L, 177L, 178L, 179L, 180L, 181L, 182L, 183L, 184L, 185L, 186L,  187L, 188L, 189L, 190L, 191L, 192L, 193L, 194L, 195L, 196L, 197L,  198L, 199L, 200L, 201L, 202L, 203L, 204L, 205L, 206L, 207L, 208L,  209L, 210L, 211L, 212L, 213L, 214L, 215L, 216L, 217L, 218L, 219L,  220L, 221L, 222L, 223L, 224L, 225L, 226L, 227L, 228L, 229L, 230L,  231L, 232L, 233L, 234L, 235L, 236L, 237L, 238L, 239L, 240L, 241L,  242L, 243L, 244L, 245L, 246L, 247L, 248L, 249L, 250L, 251L, 252L,  253L, 254L, 255L, 256L, 257L, 258L, 259L, 260L, 261L, 262L, 263L,  264L, 265L, 266L, 267L, 268L, 269L, 270L, 271L, 272L, 273L, 274L,  275L, 276L, 277L, 278L, 279L, 280L, 281L, 282L, 283L, 284L, 285L,  286L, 287L, 288L, 289L, 290L, 291L, 292L, 293L, 294L, 295L, 296L,  297L, 298L, 299L, 300L, 301L, 302L, 303L, 304L, 305L, 306L, 307L,  308L, 309L, 310L, 311L, 312L, 313L, 314L, 315L, 316L, 317L, 318L,  319L, 320L, 321L, 322L, 323L, 324L, 325L, 326L, 327L, 328L, 329L,  330L, 331L, 332L, 333L, 334L, 335L, 336L, 337L, 338L, 339L, 340L,  341L, 342L, 343L, 344L, 345L, 346L, 347L, 348L, 349L, 350L, 351L,  352L, 353L, 354L, 355L, 356L, 357L, 358L, 359L, 360L, 361L, 362L,  363L, 364L, 365L, 366L, 367L, 368L, 369L, 370L, 371L, 372L, 373L,  374L, 375L, 376L, 377L, 378L, 379L, 380L, 381L, 382L, 383L, 384L,  385L, 386L, 387L, 388L, 389L, 390L, 391L, 392L, 393L, 394L, 395L,  396L, 397L, 398L, 399L, 400L, 401L, 402L, 403L, 404L, 405L, 406L,  407L, 408L, 409L, 410L, 411L, 412L, 413L, 414L, 415L, 416L, 417L,  418L, 419L, 420L, 421L, 422L, 423L, 424L, 425L, 426L, 427L, 428L,  429L, 430L, 431L, 432L, 433L, 434L, 435L, 436L, 437L, 438L, 439L,  440L, 441L, 442L, 443L, 444L, 445L, 446L, 447L, 448L, 449L, 450L,  451L, 452L, 453L, 454L, 455L, 456L, 457L, 458L, 459L, 460L, 461L,  462L, 463L, 464L, 465L, 466L, 467L, 468L, 469L, 470L, 471L, 472L,  473L, 474L, 475L, 476L, 477L, 478L, 479L, 480L, 481L, 482L, 483L,  484L, 485L, 486L, 487L, 488L, 489L, 490L, 491L, 492L, 493L, 494L,  495L, 496L, 497L, 498L, 499L, 500L, 501L, 502L, 503L, 504L, 505L,  506L, 507L, 508L, 509L, 510L, 511L, 512L, 513L, 514L, 515L, 516L,  517L, 518L, 519L, 520L, 521L, 522L, 523L, 524L, 525L, 526L, 527L,  528L, 529L, 530L, 531L, 532L, 533L, 534L, 535L, 536L, 537L, 538L,  539L, 540L, 541L, 542L, 543L, 544L, 545L, 546L, 547L, 548L, 549L,  550L, 551L, 552L, 553L, 554L, 555L, 556L, 557L, 558L, 559L, 560L,  561L, 562L, 563L, 564L, 565L, 566L, 567L, 568L, 569L, 570L, 571L,  572L, 573L, 574L, 575L, 576L, 577L, 578L, 579L, 580L, 581L, 582L,  583L, 584L, 585L, 586L, 587L, 588L, 589L, 590L, 591L, 592L, 593L,  594L, 595L, 596L, 597L, 0L, 1L, 3L, 5L, 7L, 9L, 11L, 13L, 15L,  17L, 19L, 21L, 23L, 25L, 27L, 29L, 31L, 33L, 35L, 37L, 39L, 41L,  43L, 45L, 47L, 49L, 51L, 53L, 55L, 57L, 59L, 62L, 65L, 68L, 71L,  74L, 77L, 80L, 83L, 86L, 89L, 92L, 95L, 98L, 101L, 104L, 107L,  110L, 113L, 116L, 119L, 122L, 125L, 128L, 131L, 134L, 137L, 140L,  143L, 146L, 149L, 153L, 157L, 161L, 165L, 169L, 173L, 177L, 181L,  185L, 189L, 193L, 197L, 201L, 205L, 209L, 213L, 217L, 221L, 225L,  229L, 233L, 237L, 241L, 245L, 249L, 253L, 257L, 261L, 265L, 269L,  273L, 278L, 283L, 288L, 293L, 298L, 303L, 308L, 313L, 318L, 323L,  328L, 333L, 338L, 343L, 348L, 353L, 358L, 363L, 368L, 373L, 378L,  383L, 388L, 393L, 398L, 403L, 408L, 413L, 418L, 424L, 430L, 436L,  442L, 448L, 454L, 460L, 466L, 472L, 478L, 484L, 490L, 496L, 502L,  508L, 514L, 520L, 526L, 532L, 538L, 544L, 550L, 556L, 562L, 568L,  574L, 580L, 586L, 592L, 2L, 4L, 6L, 8L, 10L, 12L, 14L, 16L, 18L,  20L, 22L, 24L, 26L, 28L, 30L, 32L, 34L, 36L, 38L, 40L, 42L, 44L,  46L, 48L, 50L, 52L, 54L, 56L, 58L, 60L, 63L, 66L, 69L, 72L, 75L,  78L, 81L, 84L, 87L, 90L, 93L, 96L, 99L, 102L, 105L, 108L, 111L,  114L, 117L, 120L, 123L, 126L, 129L, 132L, 135L, 138L, 141L, 144L,  147L, 150L, 154L, 158L, 162L, 166L, 170L, 174L, 178L, 182L, 186L,  190L, 194L, 198L, 202L, 206L, 210L, 214L, 218L, 222L, 226L, 230L,  234L, 238L, 242L, 246L, 250L, 254L, 258L, 262L, 266L, 270L, 274L,  279L, 284L, 289L, 294L, 299L, 304L, 309L, 314L, 319L, 324L, 329L,  334L, 339L, 344L, 349L, 354L, 359L, 364L, 369L, 374L, 379L, 384L,  389L, 394L, 399L, 404L, 409L, 414L, 419L, 425L, 431L, 437L, 443L,  449L, 455L, 461L, 467L, 473L, 479L, 485L, 491L, 497L, 503L, 509L,  515L, 521L, 527L, 533L, 539L, 545L, 551L, 557L, 563L, 569L, 575L,  581L, 587L, 593L, 61L, 64L, 67L, 70L, 73L, 76L, 79L, 82L, 85L,  88L, 91L, 94L, 97L, 100L, 103L, 106L, 109L, 112L, 115L, 118L,  121L, 124L, 127L, 130L, 133L, 136L, 139L, 142L, 145L, 148L, 151L,  155L, 159L, 163L, 167L, 171L, 175L, 179L, 183L, 187L, 191L, 195L,  199L, 203L, 207L, 211L, 215L, 219L, 223L, 227L, 231L, 235L, 239L,  243L, 247L, 251L, 255L, 259L, 263L, 267L, 271L, 275L, 280L, 285L,  290L, 295L, 300L, 305L, 310L, 315L, 320L, 325L, 330L, 335L, 340L,  345L, 350L, 355L, 360L, 365L, 370L, 375L, 380L, 385L, 390L, 395L,  400L, 405L, 410L, 415L, 420L, 426L, 432L, 438L, 444L, 450L, 456L,  462L, 468L, 474L, 480L, 486L, 492L, 498L, 504L, 510L, 516L, 522L,  528L, 534L, 540L, 546L, 552L, 558L, 564L, 570L, 576L, 582L, 588L,  594L, 152L, 156L, 160L, 164L, 168L, 172L, 176L, 180L, 184L, 188L,  192L, 196L, 200L, 204L, 208L, 212L, 216L, 220L, 224L, 228L, 232L,  236L, 240L, 244L, 248L, 252L, 256L, 260L, 264L, 268L, 272L, 276L,  281L, 286L, 291L, 296L, 301L, 306L, 311L, 316L, 321L, 326L, 331L,  336L, 341L, 346L, 351L, 356L, 361L, 366L, 371L, 376L, 381L, 386L,  391L, 396L, 401L, 406L, 411L, 416L, 421L, 427L, 433L, 439L, 445L,  451L, 457L, 463L, 469L, 475L, 481L, 487L, 493L, 499L, 505L, 511L,  517L, 523L, 529L, 535L, 541L, 547L, 553L, 559L, 565L, 571L, 577L,  583L, 589L, 595L, 277L, 282L, 287L, 292L, 297L, 302L, 307L, 312L,  317L, 322L, 327L, 332L, 337L, 342L, 347L, 352L, 357L, 362L, 367L,  372L, 377L, 382L, 387L, 392L, 397L, 402L, 407L, 412L, 417L, 422L,  428L, 434L, 440L, 446L, 452L, 458L, 464L, 470L, 476L, 482L, 488L,  494L, 500L, 506L, 512L, 518L, 524L, 530L, 536L, 542L, 548L, 554L,  560L, 566L, 572L, 578L, 584L, 590L, 596L), p = c(0L, 268L, 866L,  1016L, 1165L, 1285L, 1375L, 1434L), Dim = c(598L, 7L), Dimnames = list(     c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11",      "12", "13", "14", "15", "16", "17", "18", "19", "20", "21",      "22", "23", "24", "25", "26", "27", "28", "29", "30", "31",      "32", "33", "34", "35", "36", 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-1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  -3.87590563548892, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, -0.960803578315031, -1.08171900457779, 0.705061850648697,  0.986638937859699, 0.97534120439782, -0.939246945477888, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, -0.855666642180885,  -1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  -0.826348339680731, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, -0.744613432969816, -1.08171900457779, 0.705061850648697,  0.986638937859699, 0.97534120439782, -0.668045852159904, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, -0.30687704291588,  -1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  -0.292498433729975, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 0.0408417629874603, -1.08171900457779, 0.705061850648697,  0.986638937859699, 0.97534120439782, 0.374795478676572, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 0.420735075180996,  -1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  0.42576039034331, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 0.629860125184907, -1.08171900457779, 0.705061850648697,  0.986638937859699, 0.97534120439782, 0.674159248170935, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 0.675255755796282,  -1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  0.708305381171109, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 0.747272996818123, -1.08171900457779, 0.705061850648697,  0.986638937859699, 0.97534120439782, 0.781705794781599, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 0.860177747237857,  -1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  0.942039065009092, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 0.966983464962776, -1.08171900457779, 0.705061850648697,  0.986638937859699, 0.97534120439782, 1.09096172472184, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.10192644115082,  -1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  1.12038105211889, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.17413918543708, -1.08171900457779, 0.705061850648697,  0.986638937859699, 0.97534120439782, 1.1905192855779, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.2581531005798,  -1.08171900457779, 0.705061850648697, 0.986638937859699, 0.97534120439782,  1.26204845982929, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, -3.00177325373065, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  -0.702360797255323, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, -0.625139579266844, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  -0.1149790271379, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, -0.0284201775069216, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  0.0564614397773887, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 0.0860652981735748, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  0.19220353234205, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 0.33938818204814, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  0.573777806810113, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 0.605696630355483, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  0.660068816121792, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 0.707690559456427, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  0.748621191752101, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 0.829528177437931, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  0.85910237328832, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 0.891199114751497, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.0777340923896, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.27624304344664, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.30195447252204, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.42050901179438, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.44358739848253, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.44837738103435, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.48043338335665, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.69904441056629, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  1.90061226295242, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 1.95753338447636, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  2.10018312549547, -1.08171900457779, 0.705061850648697, 0.986638937859699,  0.97534120439782, 1.26204845982929, 2.27238716888237, -1.08171900457779,  0.705061850648697, 0.986638937859699, 0.97534120439782, 1.26204845982929,  2.44250995253019), lambda = 0, intercept = TRUE) 
#> 
#>   Df %Dev Lambda
#> 1  7 10.8      0
print(l0_model, cause = 1)
#> 
#> Call:  (function (x, y, family = c("gaussian", "binomial", "poisson",      "multinomial", "cox", "mgaussian"), weights = NULL, offset = NULL,      alpha = 1, nlambda = 100, lambda.min.ratio = ifelse(nobs <          nvars, 0.01, 1e-04), lambda = NULL, standardize = TRUE,      intercept = TRUE, thresh = 1e-07, dfmax = nvars + 1, pmax = min(dfmax *          2 + 20, nvars), exclude = NULL, penalty.factor = rep(1,          nvars), lower.limits = -Inf, upper.limits = Inf, maxit = 1e+05,      type.gaussian = ifelse(nvars < 500, "covariance", "naive"),      type.logistic = c("Newton", "modified.Newton"), standardize.response = FALSE,      type.multinomial = c("ungrouped", "grouped"), relax = FALSE,      trace.it = 0, ...)  {     this.call = match.call()     np = dim(x)     if (is.null(np) | (np[2] <= 1))          stop("x should be a matrix with 2 or more columns")     nobs = as.integer(np[1])     nvars = as.integer(np[2])     if (any(is.na(x)))          stop("x has missing values; consider using makeX() to impute them")     if (is.null(weights))          weights = rep(1, nobs)     else if (length(weights) != nobs)          stop(paste("number of elements in weights (", length(weights),              ") not equal to the number of rows of x (", nobs,              ")", sep = ""))     if (is.function(exclude))          exclude <- check.exclude(exclude(x = x, y = y, weights = weights),              nvars)     if (length(penalty.factor) != nvars)          stop("the length of penalty.factor does not match the number of variables")     if (!is.character(family)) {         fit = glmnet.path(x, y, weights, lambda, nlambda, lambda.min.ratio,              alpha, offset, family, standardize, intercept, thresh = thresh,              maxit, penalty.factor, exclude, lower.limits, upper.limits,              trace.it = trace.it)         fit$call = this.call     }     else {         family = match.arg(family)         if (family == "cox" && use.cox.path(x, y)) {             fit <- cox.path(x, y, weights, offset, alpha, nlambda,                  lambda.min.ratio, lambda, standardize, thresh,                  exclude, penalty.factor, lower.limits, upper.limits,                  maxit, trace.it, ...)             fit$call <- this.call         }         else {             if (alpha > 1) {                 warning("alpha >1; set to 1")                 alpha = 1             }             if (alpha < 0) {                 warning("alpha<0; set to 0")                 alpha = 0             }             alpha = as.double(alpha)             nlam = as.integer(nlambda)             y = drop(y)             dimy = dim(y)             nrowy = ifelse(is.null(dimy), length(y), dimy[1])             if (nrowy != nobs)                  stop(paste("number of observations in y (", nrowy,                    ") not equal to the number of rows of x (",                    nobs, ")", sep = ""))             vnames = colnames(x)             if (is.null(vnames))                  vnames = paste("V", seq(nvars), sep = "")             ne = as.integer(dfmax)             nx = as.integer(pmax)             if (is.null(exclude))                  exclude = integer(0)             if (any(penalty.factor == Inf)) {                 exclude = c(exclude, seq(nvars)[penalty.factor ==                    Inf])                 exclude = sort(unique(exclude))             }             if (length(exclude) > 0) {                 jd = match(exclude, seq(nvars), 0)                 if (!all(jd > 0))                    stop("Some excluded variables out of range")                 penalty.factor[jd] = 1                 jd = as.integer(c(length(jd), jd))             }             else jd = as.integer(0)             vp = as.double(penalty.factor)             internal.parms = glmnet.control()             if (internal.parms$itrace)                  trace.it = 1             else {                 if (trace.it) {                   glmnet.control(itrace = 1)                   on.exit(glmnet.control(itrace = 0))                 }             }             if (any(lower.limits > 0)) {                 stop("Lower limits should be non-positive")             }             if (any(upper.limits < 0)) {                 stop("Upper limits should be non-negative")             }             lower.limits[lower.limits == -Inf] = -internal.parms$big             upper.limits[upper.limits == Inf] = internal.parms$big             if (length(lower.limits) < nvars) {                 if (length(lower.limits) == 1)                    lower.limits = rep(lower.limits, nvars)                 else stop("Require length 1 or nvars lower.limits")             }             else lower.limits = lower.limits[seq(nvars)]             if (length(upper.limits) < nvars) {                 if (length(upper.limits) == 1)                    upper.limits = rep(upper.limits, nvars)                 else stop("Require length 1 or nvars upper.limits")             }             else upper.limits = upper.limits[seq(nvars)]             cl = rbind(lower.limits, upper.limits)             if (any(cl == 0)) {                 fdev = glmnet.control()$fdev                 if (fdev != 0) {                   glmnet.control(fdev = 0)                   on.exit(glmnet.control(fdev = fdev))                 }             }             storage.mode(cl) = "double"             isd = as.integer(standardize)             intr = as.integer(intercept)             if (!missing(intercept) && family == "cox")                  warning("Cox model has no intercept")             jsd = as.integer(standardize.response)             thresh = as.double(thresh)             if (is.null(lambda)) {                 if (lambda.min.ratio >= 1)                    stop("lambda.min.ratio should be less than 1")                 flmin = as.double(lambda.min.ratio)                 ulam = double(1)             }             else {                 flmin = as.double(1)                 if (any(lambda < 0))                    stop("lambdas should be non-negative")                 ulam = as.double(rev(sort(lambda)))                 nlam = as.integer(length(lambda))             }             is.sparse = FALSE             if (inherits(x, "sparseMatrix")) {                 is.sparse = TRUE                 if (!inherits(x, "dgCMatrix"))                    x = as(as(as(x, "generalMatrix"), "CsparseMatrix"),                      "dMatrix")             }             else if (!inherits(x, "matrix")) {                 x <- data.matrix(x)             }             else {                 x <- x             }             if (!inherits(x, "sparseMatrix")) {                 storage.mode(x) <- "double"             }             if (trace.it) {                 if (relax)                    cat("Training Fit\n")                 pb <- createPB(min = 0, max = nlam, initial = 0,                    style = 3)             }             else {                 pb <- NULL             }             kopt = switch(match.arg(type.logistic), Newton = 0,                  modified.Newton = 1)             if (family == "multinomial") {                 type.multinomial = match.arg(type.multinomial)                 if (type.multinomial == "grouped")                    kopt = 2             }             kopt = as.integer(kopt)             fit = switch(family, gaussian = elnet(x, is.sparse,                  y, weights, offset, type.gaussian, alpha, nobs,                  nvars, jd, vp, cl, ne, nx, nlam, flmin, ulam,                  thresh, isd, intr, vnames, maxit, pb), poisson = fishnet(x,                  is.sparse, y, weights, offset, alpha, nobs, nvars,                  jd, vp, cl, ne, nx, nlam, flmin, ulam, thresh,                  isd, intr, vnames, maxit, pb), binomial = lognet(x,                  is.sparse, y, weights, offset, alpha, nobs, nvars,                  jd, vp, cl, ne, nx, nlam, flmin, ulam, thresh,                  isd, intr, vnames, maxit, kopt, family, pb),                  multinomial = lognet(x, is.sparse, y, weights,                    offset, alpha, nobs, nvars, jd, vp, cl, ne,                    nx, nlam, flmin, ulam, thresh, isd, intr, vnames,                    maxit, kopt, family, pb), cox = coxnet(x, is.sparse,                    y, weights, offset, alpha, nobs, nvars, jd,                    vp, cl, ne, nx, nlam, flmin, ulam, thresh,                    isd, vnames, maxit), mgaussian = mrelnet(x,                    is.sparse, y, weights, offset, alpha, nobs,                    nvars, jd, vp, cl, ne, nx, nlam, flmin, ulam,                    thresh, isd, jsd, intr, vnames, maxit, pb))             if (trace.it) {                 utils::setTxtProgressBar(pb, nlam)                 close(pb)             }             if (is.null(lambda))                  fit$lambda = fix.lam(fit$lambda)             fit$call = this.call             fit$nobs = nobs             class(fit) = c(class(fit), "glmnet")         }     }     if (relax)          relax.glmnet(fit, x = x, y = y, weights = weights, offset = offset,              lower.limits = lower.limits, upper.limits = upper.limits,              penalty.factor = penalty.factor, check.args = FALSE,              ...)     else fit })(x = new("dgCMatrix", i = c(1L, 2L, 15L, 16L, 23L, 24L, 27L,  28L, 29L, 30L, 33L, 34L, 35L, 36L, 37L, 38L, 62L, 63L, 64L, 74L,  75L, 76L, 83L, 84L, 85L, 89L, 90L, 91L, 101L, 102L, 103L, 110L,  111L, 112L, 113L, 114L, 115L, 131L, 132L, 133L, 140L, 141L, 142L,  149L, 150L, 151L, 152L, 161L, 162L, 163L, 164L, 169L, 170L, 171L,  172L, 173L, 174L, 175L, 176L, 177L, 178L, 179L, 180L, 181L, 182L,  183L, 184L, 189L, 190L, 191L, 192L, 209L, 210L, 211L, 212L, 213L,  214L, 215L, 216L, 217L, 218L, 219L, 220L, 221L, 222L, 223L, 224L,  225L, 226L, 227L, 228L, 229L, 230L, 231L, 232L, 261L, 262L, 263L,  264L, 293L, 294L, 295L, 296L, 297L, 298L, 299L, 300L, 301L, 302L,  313L, 314L, 315L, 316L, 317L, 323L, 324L, 325L, 326L, 327L, 333L,  334L, 335L, 336L, 337L, 343L, 344L, 345L, 346L, 347L, 378L, 379L,  380L, 381L, 382L, 383L, 384L, 385L, 386L, 387L, 393L, 394L, 395L,  396L, 397L, 408L, 409L, 410L, 411L, 412L, 413L, 414L, 415L, 416L,  417L, 418L, 419L, 420L, 421L, 422L, 423L, 436L, 437L, 438L, 439L,  440L, 441L, 442L, 443L, 444L, 445L, 446L, 447L, 448L, 449L, 450L,  451L, 452L, 453L, 460L, 461L, 462L, 463L, 464L, 465L, 472L, 473L,  474L, 475L, 476L, 477L, 478L, 479L, 480L, 481L, 482L, 483L, 490L,  491L, 492L, 493L, 494L, 495L, 496L, 497L, 498L, 499L, 500L, 501L,  508L, 509L, 510L, 511L, 512L, 513L, 514L, 515L, 516L, 517L, 518L,  519L, 532L, 533L, 534L, 535L, 536L, 537L, 538L, 539L, 540L, 541L,  542L, 543L, 550L, 551L, 552L, 553L, 554L, 555L, 556L, 557L, 558L,  559L, 560L, 561L, 568L, 569L, 570L, 571L, 572L, 573L, 580L, 581L,  582L, 583L, 584L, 585L, 586L, 587L, 588L, 589L, 590L, 591L, 592L,  593L, 594L, 595L, 596L, 597L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L,  8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L,  21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L,  34L, 35L, 36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L,  47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L,  60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L, 71L, 72L,  73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L, 83L, 84L, 85L,  86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L, 97L, 98L,  99L, 100L, 101L, 102L, 103L, 104L, 105L, 106L, 107L, 108L, 109L,  110L, 111L, 112L, 113L, 114L, 115L, 116L, 117L, 118L, 119L, 120L,  121L, 122L, 123L, 124L, 125L, 126L, 127L, 128L, 129L, 130L, 131L,  132L, 133L, 134L, 135L, 136L, 137L, 138L, 139L, 140L, 141L, 142L,  143L, 144L, 145L, 146L, 147L, 148L, 149L, 150L, 151L, 152L, 153L,  154L, 155L, 156L, 157L, 158L, 159L, 160L, 161L, 162L, 163L, 164L,  165L, 166L, 167L, 168L, 169L, 170L, 171L, 172L, 173L, 174L, 175L,  176L, 177L, 178L, 179L, 180L, 181L, 182L, 183L, 184L, 185L, 186L,  187L, 188L, 189L, 190L, 191L, 192L, 193L, 194L, 195L, 196L, 197L,  198L, 199L, 200L, 201L, 202L, 203L, 204L, 205L, 206L, 207L, 208L,  209L, 210L, 211L, 212L, 213L, 214L, 215L, 216L, 217L, 218L, 219L,  220L, 221L, 222L, 223L, 224L, 225L, 226L, 227L, 228L, 229L, 230L,  231L, 232L, 233L, 234L, 235L, 236L, 237L, 238L, 239L, 240L, 241L,  242L, 243L, 244L, 245L, 246L, 247L, 248L, 249L, 250L, 251L, 252L,  253L, 254L, 255L, 256L, 257L, 258L, 259L, 260L, 261L, 262L, 263L,  264L, 265L, 266L, 267L, 268L, 269L, 270L, 271L, 272L, 273L, 274L,  275L, 276L, 277L, 278L, 279L, 280L, 281L, 282L, 283L, 284L, 285L,  286L, 287L, 288L, 289L, 290L, 291L, 292L, 293L, 294L, 295L, 296L,  297L, 298L, 299L, 300L, 301L, 302L, 303L, 304L, 305L, 306L, 307L,  308L, 309L, 310L, 311L, 312L, 313L, 314L, 315L, 316L, 317L, 318L,  319L, 320L, 321L, 322L, 323L, 324L, 325L, 326L, 327L, 328L, 329L,  330L, 331L, 332L, 333L, 334L, 335L, 336L, 337L, 338L, 339L, 340L,  341L, 342L, 343L, 344L, 345L, 346L, 347L, 348L, 349L, 350L, 351L,  352L, 353L, 354L, 355L, 356L, 357L, 358L, 359L, 360L, 361L, 362L,  363L, 364L, 365L, 366L, 367L, 368L, 369L, 370L, 371L, 372L, 373L,  374L, 375L, 376L, 377L, 378L, 379L, 380L, 381L, 382L, 383L, 384L,  385L, 386L, 387L, 388L, 389L, 390L, 391L, 392L, 393L, 394L, 395L,  396L, 397L, 398L, 399L, 400L, 401L, 402L, 403L, 404L, 405L, 406L,  407L, 408L, 409L, 410L, 411L, 412L, 413L, 414L, 415L, 416L, 417L,  418L, 419L, 420L, 421L, 422L, 423L, 424L, 425L, 426L, 427L, 428L,  429L, 430L, 431L, 432L, 433L, 434L, 435L, 436L, 437L, 438L, 439L,  440L, 441L, 442L, 443L, 444L, 445L, 446L, 447L, 448L, 449L, 450L,  451L, 452L, 453L, 454L, 455L, 456L, 457L, 458L, 459L, 460L, 461L,  462L, 463L, 464L, 465L, 466L, 467L, 468L, 469L, 470L, 471L, 472L,  473L, 474L, 475L, 476L, 477L, 478L, 479L, 480L, 481L, 482L, 483L,  484L, 485L, 486L, 487L, 488L, 489L, 490L, 491L, 492L, 493L, 494L,  495L, 496L, 497L, 498L, 499L, 500L, 501L, 502L, 503L, 504L, 505L,  506L, 507L, 508L, 509L, 510L, 511L, 512L, 513L, 514L, 515L, 516L,  517L, 518L, 519L, 520L, 521L, 522L, 523L, 524L, 525L, 526L, 527L,  528L, 529L, 530L, 531L, 532L, 533L, 534L, 535L, 536L, 537L, 538L,  539L, 540L, 541L, 542L, 543L, 544L, 545L, 546L, 547L, 548L, 549L,  550L, 551L, 552L, 553L, 554L, 555L, 556L, 557L, 558L, 559L, 560L,  561L, 562L, 563L, 564L, 565L, 566L, 567L, 568L, 569L, 570L, 571L,  572L, 573L, 574L, 575L, 576L, 577L, 578L, 579L, 580L, 581L, 582L,  583L, 584L, 585L, 586L, 587L, 588L, 589L, 590L, 591L, 592L, 593L,  594L, 595L, 596L, 597L, 0L, 1L, 3L, 5L, 7L, 9L, 11L, 13L, 15L,  17L, 19L, 21L, 23L, 25L, 27L, 29L, 31L, 33L, 35L, 37L, 39L, 41L,  43L, 45L, 47L, 49L, 51L, 53L, 55L, 57L, 59L, 62L, 65L, 68L, 71L,  74L, 77L, 80L, 83L, 86L, 89L, 92L, 95L, 98L, 101L, 104L, 107L,  110L, 113L, 116L, 119L, 122L, 125L, 128L, 131L, 134L, 137L, 140L,  143L, 146L, 149L, 153L, 157L, 161L, 165L, 169L, 173L, 177L, 181L,  185L, 189L, 193L, 197L, 201L, 205L, 209L, 213L, 217L, 221L, 225L,  229L, 233L, 237L, 241L, 245L, 249L, 253L, 257L, 261L, 265L, 269L,  273L, 278L, 283L, 288L, 293L, 298L, 303L, 308L, 313L, 318L, 323L,  328L, 333L, 338L, 343L, 348L, 353L, 358L, 363L, 368L, 373L, 378L,  383L, 388L, 393L, 398L, 403L, 408L, 413L, 418L, 424L, 430L, 436L,  442L, 448L, 454L, 460L, 466L, 472L, 478L, 484L, 490L, 496L, 502L,  508L, 514L, 520L, 526L, 532L, 538L, 544L, 550L, 556L, 562L, 568L,  574L, 580L, 586L, 592L, 2L, 4L, 6L, 8L, 10L, 12L, 14L, 16L, 18L,  20L, 22L, 24L, 26L, 28L, 30L, 32L, 34L, 36L, 38L, 40L, 42L, 44L,  46L, 48L, 50L, 52L, 54L, 56L, 58L, 60L, 63L, 66L, 69L, 72L, 75L,  78L, 81L, 84L, 87L, 90L, 93L, 96L, 99L, 102L, 105L, 108L, 111L,  114L, 117L, 120L, 123L, 126L, 129L, 132L, 135L, 138L, 141L, 144L,  147L, 150L, 154L, 158L, 162L, 166L, 170L, 174L, 178L, 182L, 186L,  190L, 194L, 198L, 202L, 206L, 210L, 214L, 218L, 222L, 226L, 230L,  234L, 238L, 242L, 246L, 250L, 254L, 258L, 262L, 266L, 270L, 274L,  279L, 284L, 289L, 294L, 299L, 304L, 309L, 314L, 319L, 324L, 329L,  334L, 339L, 344L, 349L, 354L, 359L, 364L, 369L, 374L, 379L, 384L,  389L, 394L, 399L, 404L, 409L, 414L, 419L, 425L, 431L, 437L, 443L,  449L, 455L, 461L, 467L, 473L, 479L, 485L, 491L, 497L, 503L, 509L,  515L, 521L, 527L, 533L, 539L, 545L, 551L, 557L, 563L, 569L, 575L,  581L, 587L, 593L, 61L, 64L, 67L, 70L, 73L, 76L, 79L, 82L, 85L,  88L, 91L, 94L, 97L, 100L, 103L, 106L, 109L, 112L, 115L, 118L,  121L, 124L, 127L, 130L, 133L, 136L, 139L, 142L, 145L, 148L, 151L,  155L, 159L, 163L, 167L, 171L, 175L, 179L, 183L, 187L, 191L, 195L,  199L, 203L, 207L, 211L, 215L, 219L, 223L, 227L, 231L, 235L, 239L,  243L, 247L, 251L, 255L, 259L, 263L, 267L, 271L, 275L, 280L, 285L,  290L, 295L, 300L, 305L, 310L, 315L, 320L, 325L, 330L, 335L, 340L,  345L, 350L, 355L, 360L, 365L, 370L, 375L, 380L, 385L, 390L, 395L,  400L, 405L, 410L, 415L, 420L, 426L, 432L, 438L, 444L, 450L, 456L,  462L, 468L, 474L, 480L, 486L, 492L, 498L, 504L, 510L, 516L, 522L,  528L, 534L, 540L, 546L, 552L, 558L, 564L, 570L, 576L, 582L, 588L,  594L, 152L, 156L, 160L, 164L, 168L, 172L, 176L, 180L, 184L, 188L,  192L, 196L, 200L, 204L, 208L, 212L, 216L, 220L, 224L, 228L, 232L,  236L, 240L, 244L, 248L, 252L, 256L, 260L, 264L, 268L, 272L, 276L,  281L, 286L, 291L, 296L, 301L, 306L, 311L, 316L, 321L, 326L, 331L,  336L, 341L, 346L, 351L, 356L, 361L, 366L, 371L, 376L, 381L, 386L,  391L, 396L, 401L, 406L, 411L, 416L, 421L, 427L, 433L, 439L, 445L,  451L, 457L, 463L, 469L, 475L, 481L, 487L, 493L, 499L, 505L, 511L,  517L, 523L, 529L, 535L, 541L, 547L, 553L, 559L, 565L, 571L, 577L,  583L, 589L, 595L, 277L, 282L, 287L, 292L, 297L, 302L, 307L, 312L,  317L, 322L, 327L, 332L, 337L, 342L, 347L, 352L, 357L, 362L, 367L,  372L, 377L, 382L, 387L, 392L, 397L, 402L, 407L, 412L, 417L, 422L,  428L, 434L, 440L, 446L, 452L, 458L, 464L, 470L, 476L, 482L, 488L,  494L, 500L, 506L, 512L, 518L, 524L, 530L, 536L, 542L, 548L, 554L,  560L, 566L, 572L, 578L, 584L, 590L, 596L), p = c(0L, 268L, 866L,  1016L, 1165L, 1285L, 1375L, 1434L), Dim = c(598L, 7L), Dimnames = list(     c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11",      "12", "13", "14", "15", "16", "17", "18", "19", "20", "21",      "22", "23", "24", "25", "26", "27", "28", "29", "30", "31",      "32", "33", "34", "35", "36", "37", "38", "39", "40", "41",      "42", "43", "44", "45", "46", "47", "48", "49", "50", "51",      "52", "53", "54", "55", "56", "57", "58", "59", "60", "61",      "62", "63", "64", "65", "66", "67", "68", "69", "70", "71",      "72", "73", "74", "75", "76", "77", "78", "79", "80", "81",      "82", "83", "84", "85", "86", "87", "88", "89", "90", "91",      "92", "93", "94", "95", "96", "97", "98", "99", "100", "101",      "102", "103", "104", "105", "106", "107", "108", "109", "110",      "111", "112", "113", "114", "115", "116", "117", "118", "119",      "120", "121", "122", "123", "124", "125", "126", "127", "128",      "129", "130", "131", "132", "133", "134", "135", "136", "137",      "138", "139", "140", "141", "142", "143", "144", "145", "146",      "147", "148", "149", "150", "151", "152", "153", "154", "155",      "156", "157", "158", "159", "160", "161", "162", "163", "164",      "165", "166", "167", "168", "169", "170", "171", "172", "173",      "174", "175", "176", "177", "178", "179", "180", "181", "182",      "183", "184", "185", "186", "187", "188", "189", "190", "191",      "192", "193", "194", "195", "196", "197", "198", "199", "200",      "201", "202", "203", "204", "205", "206", "207", "208", "209",      "210", "211", "212", "213", "214", "215", "216", "217", "218",      "219", "220", "221", "222", "223", "224", "225", "226", "227",      "228", "229", "230", "231", "232", "233", "234", "235", "236",      "237", "238", "239", "240", "241", "242", "243", "244", "245",      "246", "247", "248", "249", "250", "251", "252", "253", "254",      "255", "256", "257", "258", "259", "260", "261", "262", "263",      "264", "265", "266", "267", "268", "269", "270", "271", "272",      "273", "274", "275", "276", "277", "278", "279", "280", "281",      "282", "283", "284", "285", "286", "287", "288", "289", "290",      "291", "292", "293", "294", "295", "296", "297", "298", "299",      "300", "301", "302", "303", "304", "305", "306", "307", "308",      "309", "310", "311", "312", "313", "314", "315", "316", "317",      "318", "319", "320", "321", "322", "323", "324", "325", "326",      "327", "328", "329", "330", "331", "332", "333", "334", "335",      "336", "337", "338", "339", "340", "341", "342", "343", "344",      "345", "346", "347", "348", "349", "350", "351", "352", "353",      "354", "355", "356", "357", "358", "359", "360", "361", "362",      "363", "364", "365", "366", "367", "368", "369", "370", "371",      "372", "373", "374", "375", "376", "377", "378", "379", "380",      "381", "382", "383", "384", "385", "386", "387", "388", "389",      "390", "391", "392", "393", "394", "395", "396", "397", "398",      "399", "400", "401", "402", "403", "404", "405", "406", "407",      "408", "409", "410", "411", "412", "413", "414", "415", "416",      "417", "418", "419", "420", "421", "422", "423", "424", "425",      "426", "427", "428", "429", "430", "431", "432", "433", "434",      "435", "436", "437", "438", "439", "440", "441", "442", "443",      "444", "445", "446", "447", "448", "449", "450", "451", "452",      "453", "454", "455", "456", "457", "458", "459", "460", "461",      "462", "463", "464", "465", "466", "467", "468", "469", "470",      "471", "472", "473", "474", "475", "476", "477", "478", "479",      "480", "481", "482", "483", "484", "485", "486", "487", "488",      "489", "490", "491", "492", "493", "494", "495", "496", "497",      "498", "499", "500", "501", "502", "503", "504", "505", "506",      "507", "508", "509", "510", "511", "512", "513", "514", "515",      "516", "517", "518", "519", "520", "521", "522", "523", "524",      "525", "526", "527", "528", "529", "530", "531", "532", "533",      "534", "535", "536", "537", "538", "539", "540", "541", "542",      "543", "544", "545", "546", "547", "548", "549", "550", "551",      "552", "553", "554", "555", "556", "557", "558", "559", "560",      "561", "562", "563", "564", "565", "566", "567", "568", "569",      "570", "571", "572", "573", "574", "575", "576", "577", "578",      "579", "580", "581", "582", "583", "584", "585", "586", "587",      "588", "589", "590", "591", "592", "593", "594", "595", "596",      "597", "598"), c("sex1", "diabetes_duration", "node0", "node0.339012260842819",      "node2.36298412586669", "node5.04518837599029", "node7.69726033122722"     )), x = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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#> 
#>   Df %Dev Lambda
#> 1  7 10.8      0

summary() provides a more informative overview. For a fitted super learner, it prints a compact description of the ensemble, the number of causes, learners, folds and nodes, the cross-validated Poisson deviance used to compare the base learners, and the cause-specific meta-learner coefficients. These coefficients show how the ensemble combines the learners for each cause.

summary(sl_model)
#> Call:
#>   Superlearner(..., learners = c(glm, lasso), metalearner = Learner_glmnet)
#> 
#> Fitted object:
#>   Class: poisson_superlearner
#>   Number of competing risks: 2 
#>   Number of learners: 2 
#>   Learners: glm, lasso 
#>   Number of folds: 3 
#>   Maximum follow-up: 22.73178 
#>   Number of nodes: 6 
#> 
#> Cross-validation deviance (Average across V-Folds):
#>    learner deviance
#>     <char>    <num>
#> 1:     glm 171.4138
#> 2:   lasso 178.9889
#> 
#> Meta-learner coefficients:
#>   k = 1:
#> (Intercept)         glm       lasso 
#>   0.0000000   0.7280179   0.2479293 
#> 
#>   k = 2:
#> (Intercept)         glm       lasso 
#>   0.0000000   0.5989187   0.3458754

You can also summarize one of the base learners stored inside the ensemble, or a learner fitted directly with fit_learner().

summary(sl_model, cause = 1, model = "glm")
#>           Length Class     Mode   
#> a0        1      -none-    numeric
#> beta      7      dgCMatrix S4     
#> df        1      -none-    numeric
#> dim       2      -none-    numeric
#> lambda    1      -none-    numeric
#> dev.ratio 1      -none-    numeric
#> nulldev   1      -none-    numeric
#> npasses   1      -none-    numeric
#> jerr      1      -none-    numeric
#> offset    1      -none-    logical
#> call      7      -none-    call   
#> nobs      1      -none-    numeric
summary(l0_model, cause = 1)
#>           Length Class     Mode   
#> a0        1      -none-    numeric
#> beta      7      dgCMatrix S4     
#> df        1      -none-    numeric
#> dim       2      -none-    numeric
#> lambda    1      -none-    numeric
#> dev.ratio 1      -none-    numeric
#> nulldev   1      -none-    numeric
#> npasses   1      -none-    numeric
#> jerr      1      -none-    numeric
#> offset    1      -none-    logical
#> call      7      -none-    call   
#> nobs      1      -none-    numeric

coef() extracts model coefficients. For a fitted super learner, coef() returns the meta-learner coefficients by default, while the model argument can be used to extract coefficients from one of the stored base learners.

coef(sl_model, cause = 1)
#> 3 x 1 sparse Matrix of class "dgCMatrix"
#>                    s0
#> (Intercept) .        
#> Z1          0.7280179
#> Z2          0.2479293
coef(sl_model, cause = 1, model = "glm")
#> 8 x 1 sparse Matrix of class "dgCMatrix"
#>                                s0
#> (Intercept)           -7.36035683
#> sex1                  -1.05713940
#> diabetes_duration      0.26272645
#> node0                 -1.61251128
#> node0.339012260842819 -0.04862647
#> node2.36298412586669  -0.09245152
#> node5.04518837599029   0.06596544
#> node7.69726033122722  -0.45621644
coef(l0_model, cause = 1)
#> 8 x 1 sparse Matrix of class "dgCMatrix"
#>                                s0
#> (Intercept)           -7.36035683
#> sex1                  -1.05713940
#> diabetes_duration      0.26272645
#> node0                 -1.61251128
#> node0.339012260842819 -0.04862647
#> node2.36298412586669  -0.09245152
#> node5.04518837599029   0.06596544
#> node7.69726033122722  -0.45621644

Predict hazards, survival, and absolute risk

The low-level predict() method returns a data set with one row per requested prediction time. In addition to the original covariates, it includes the predicted cause-specific piecewise hazards (pwch_1, pwch_2, …), the predicted survival function, and the absolute risk for the chosen cause.

pred_sl <- predict(
  sl_model,
  newdata = d[1:2],
  times = c(2, 5),
  cause = 1
)

pred_sl
#>       sex      age diabetes_duration value_SBP value_LDL value_HBA1C
#>    <fctr>    <num>             <num>     <num>     <num>       <num>
#> 1:      0 48.56530          22.40288  137.5896  3.743464    67.12621
#> 2:      0 48.56530          22.40288  137.5896  3.743464    67.12621
#> 3:      1 57.73618          25.73266  136.8310  2.297953    64.23921
#> 4:      1 57.73618          25.73266  136.8310  2.297953    64.23921
#>    value_Smoking value_Motion value_Albuminuria     eGFR time.event.1
#>           <fctr>       <fctr>            <fctr>    <num>        <num>
#> 1:             0            1            Normal 3.893651    0.3390123
#> 2:             0            1            Normal 3.893651    0.3390123
#> 3:             0            1            Normal 0.356103    0.3576302
#> 4:             0            1            Normal 0.356103    0.3576302
#>    time.event.0 time.event.2  time_cvd status_cvd uncensored_time_cvd
#>           <num>        <num>     <num>      <num>               <num>
#> 1:    10.484410     10.40121 0.3390123          1           0.3390123
#> 2:    10.484410     10.40121 0.3390123          1           0.3390123
#> 3:     3.945603     42.93017 0.3576302          1           0.3576302
#> 4:     3.945603     42.93017 0.3576302          1           0.3576302
#>    uncensored_status_cvd  time event uncensored_time uncensored_event    pwch_1
#>                    <num> <num> <num>           <num>            <num>     <num>
#> 1:                     1     2     0       0.3390123                1 0.1787839
#> 2:                     1     5     0       0.3390123                1 0.1647861
#> 3:                     1     2     0       0.3576302                1 0.1565612
#> 4:                     1     5     0       0.3576302                1 0.1443033
#>        pwch_2 survival_function absolute_risk    id
#>         <num>             <num>         <num> <int>
#> 1: 0.02441779         0.7039082     0.2620830     1
#> 2: 0.03291557         0.3882101     0.5275388     1
#> 3: 0.01832687         0.7390550     0.2348009     2
#> 4: 0.02470491         0.4441727     0.4884598     2

For interoperability with riskRegression, the package also provides predictRisk(). This returns a matrix with one column per requested time.

Risk predictions can be obtained directly from a learner fitted with fit_learner():

cbind(
  glm_direct = predictRisk(l0_model, newdata = d[1, ], times = 5, cause = 1),
  lasso_direct = predictRisk(l1_model, newdata = d[1, ], times = 5, cause = 1)
)
#>           [,1]      [,2]
#> [1,] 0.5996443 0.2952072

The same is possible from the fitted super learner object. Setting model = "sl" uses the ensemble prediction, while setting model equal to a learner label such as "glm" or "lasso" uses the corresponding stored base learner from the fitted ensemble.

cbind(
  sl = predictRisk(sl_model, newdata = d[1, ], times = 5, cause = 1, model = "sl"),
  glm_from_ensemble = predictRisk(sl_model, newdata = d[1, ], times = 5, cause = 1, model = "glm"),
  lasso_from_ensemble = predictRisk(sl_model, newdata = d[1, ], times = 5, cause = 1, model = "lasso")
)
#>           [,1]      [,2]      [,3]
#> [1,] 0.5275388 0.5996443 0.2952072

This illustrates the two main prediction workflows supported by the package: using a single fitted learner with fit_learner() or using the fitted ensemble returned by Superlearner().