Package 'merlin'

Title: Mixed Effects Regression for Linear, Non-Linear and User-Defined Models
Description: Fits linear, non-linear, and user-defined mixed effects regression models following the framework developed by Crowther (2017) <arXiv:1710.02223>. 'merlin' can fit multivariate outcome models of any type, each of which could be repeatedly measured (longitudinal), with any number of levels, and with any number of random effects at each level. Standard distributions/models available include the Bernoulli, Gaussian, Poisson, beta, negative-binomial, and time-to-event/survival models include the exponential, Gompertz, Royston-Parmar, Weibull and general hazard model. 'merlin' provides a flexible predictor syntax, allowing the user to define variables, random effects, spline and fractional polynomial functions, functions of other outcome models, and any interaction between each of them. Non-linear and time-dependent effects are seamlessly incorporated into the predictor. 'merlin' allows multivariate normal random effects, which are integrated out using Gaussian quadrature or Monte-Carlo integration. Note, 'merlin' is based on the 'Stata' package of the same name, described in Crowther (2018) <arXiv:1806.01615>.
Authors: Emma Martin [aut], Alessandro Gasparini [aut], Michael Crowther [aut, cre]
Maintainer: Michael Crowther <[email protected]>
License: GPL (>= 3)
Version: 0.1.0
Built: 2024-11-22 08:31:05 UTC
Source: https://github.com/cranhaven/cranhaven.r-universe.dev

Help Index

Extract Model Coefficients

Description

coef extracts model coefficients from a merlin model fit. coefficients is an alias for it.

Usage

## S3 method for class 'merlin'
coef(object, ...)

## S3 method for class 'summary.merlin'
coef(object, ...)

Arguments

object

An object of class merlin or summary.merlin.
...

Not used.

Extract Model Coefficients

Description

coef extracts model coefficients from a mlrcs model fit. coefficients is an alias for it.

Usage

## S3 method for class 'mlrcs'
coef(object, ...)

## S3 method for class 'summary.mlrcs'
coef(object, ...)

Arguments

object

An object of class mlrcs or summary.mlrcs.
...

Not used.

Extract Model Coefficients

Description

coef extracts model coefficients from a mlsurv model fit. coefficients is an alias for it.

Usage

## S3 method for class 'mlsurv'
coef(object, ...)

## S3 method for class 'summary.mlsurv'
coef(object, ...)

Arguments

object

An object of class mlsurv or summary.mlsurv.
...

Not used.

Aortic valve replacement surgery data

Description

This is longitudinal data on an observational study on detecting effects of different heart valves, differing on type of tissue, implanted in the aortic position. The data consists of longitudinal measurements on three different heart function outcomes, after surgery occurred. There are several baseline covariates available, and also survival data.

Usage

data(heart.valve)

data(heart.valve.merlin)

Format

This is a data frame in the unbalanced format, that is, with one row per observation. The data consists in columns for patient identification, time of measurements, longitudinal multiple longitudinal measurements, baseline covariates, and survival data. The column names are identified as follows:

num

number for patient identification.

sex

gender of patient (0=Male and 1=Female).

age

age of patient at day of surgery (years).

time

observed time point, with surgery date as the time origin (years).

fuyrs

maximum follow up time, with surgery date as the time origin (years).

status

censoring indicator (1=died and 0=lost at follow up).

grad

valve gradient at follow-up visit.

log.grad

natural log transformation of grad.

lvmi

left ventricular mass index (standardised) at follow-up visit.

log.lvmi

natural log transformation of lvmi.

ef

ejection fraction at follow-up visit.

bsa

preoperative body surface area.

lvh

preoperative left ventricular hypertrophy.

prenyha

preoperative New York Heart Association (NYHA) classification (1=I/II and 3=III/IV).

redo

previous cardiac surgery.

size

size of the valve (millimetres).

con.cabg

concomitant coronary artery bypass graft.

creat

preoperative serum creatinine (μ\mumol/mL).

dm

preoperative diabetes.

acei

preoperative use of ace inhibitor.

lv

preoperative left ventricular ejection fraction (LVEF) (1=good, 2=moderate, and 3=poor).

emergenc

operative urgency (0=elective, 1=urgent, and 3=emergency).

hc

preoperative high cholesterol (0=absent, 1=present treated, and 2=present untreated).

sten.reg.mix

aortic valve haemodynamics (1=stenosis, 2=regurgitation, 3=mixed).

hs

implanted aortic prosthesis type (1=homograft and 0=stentless porcine tissue).

An object of class data.frame with 629 rows and 29 columns.

Note

heart.valve.merlin is a version of the heart.valve dataset in merlin format.

Source

Mr Eric Lim (http://www.drericlim.com)

References

Lim E, Ali A, Theodorou P, Sousa I, Ashrafian H, Chamageorgakis T, Duncan M, Diggle P, Pepper J. A longitudinal study of the profile and predictors of left ventricular mass regression after stentless aortic valve replacement. Ann Thorac Surg. 2008; 85(6): 2026-2029.

Extract Log-Likelihood

Description

Extract log-likelihood of a merlin model.

Usage

## S3 method for class 'merlin'
logLik(object, ...)

## S3 method for class 'summary.merlin'
logLik(object, ...)

Arguments

object

An object of class merlin or summary.merlin.
...

Not used.

Extract Log-Likelihood

Description

Extract log-likelihood of a mlrcs model.

Usage

## S3 method for class 'mlrcs'
logLik(object, ...)

## S3 method for class 'summary.mlrcs'
logLik(object, ...)

Arguments

object

An object of class mlrcs or summary.mlrcs.
...

Not used.

Extract Log-Likelihood

Description

Extract log-likelihood of a mlsurv model.

Usage

## S3 method for class 'mlsurv'
logLik(object, ...)

## S3 method for class 'summary.mlsurv'
logLik(object, ...)

Arguments

object

An object of class mlsurv or summary.mlsurv.
...

Not used.

merlin - Mixed Effects Regression for Linear, Nonlinear and User-defined models

Description

merlin fits linear, non-linear and user-defined mixed effects regression models. merlin can fit multivariate outcome models of any type, each of which could be repeatedly measured (longitudinal), with any number of levels, and with any number of random effects at each level. Standard distributions/models available include the Bernoulli, Gaussian, Poisson, beta, negative-binomial, and time-to-event/survival models include the exponential, Gompertz, Weibull, Royston-Parmar, and general hazard model. merlin provides a flexible predictor syntax, allowing the user to define variables, random effects, spline and fractional polynomial functions, functions of other outcome models, and any interaction between each of them. Non-linear and time-dependent effects are seamlessly incorporated into the predictor. merlin allows multivariate normal random effects, which are integrated out using Gaussian quadrature or Monte-Carlo integration. Relative survival (excess hazard) models are supported. Utility functions are provided to allow user-defined models to be specified, in conjunction with the complex predictor.

Usage

merlin(
  model,
  from = NULL,
  family = "gaussian",
  link = NULL,
  timevar = NULL,
  covariance = "diagonal",
  data,
  userf = NULL,
  sweights = NULL,
  levels = NULL,
  predict = FALSE,
  predtype = NULL,
  predmodel = NULL,
  causes = NULL,
  at = NULL,
  contrast = NULL,
  modelfit = NULL,
  control = list()
)

Arguments

model

specify the fixed and random elements for each model outcome. Where there are multiple outcomes, the models should be specified in a list. Each model should be specified as a formula (e.g. y~x). A number of different element types can be specified, including

  • varname - an independent variable from the data set

  • random-effects - a random-effect at the cluster level can be specified using M#[cluster level], for example M1[id] would define a random intercept at the ID level. Each independent random-effect should be given a unique name, if two random-effects are given the same name they will be treated as shared random-effects.

  • rcs() - restricted cubic spline terms, this option can be used to include a restricted cubic spline function, with the degrees of freedom (number of spline terms) specified using the df sub-option, with the boundary knots assumed to be at the minimum and maximum of the variable, with internal knots placed at equally spaced centiles. Other default options orthog = TRUE, which by default orthogonalises the splines, log = FALSE, which can be used to calculate splines of the log of the variable and event = F, which can be used to calculate the internal knots based only on observations that experienced the event of interest (for survival models).

  • srcs() is a shorthand element, equivalent to rcs(..., log = TRUE, event = TRUE), for use with survival models.

  • fp() - fractional polynomials of order 1 or 2 can be specified, the sub-option powers is used to specify the powers of the fp model.

  • EV[depvar] - the expected value of the response of a submodel.

  • dEV[depvar] - the first derivative with respect to time of the expected value of the response of a submodel.

  • d2EV[depvar] - the second derivative with respect to time of the expected value of the response of a submodel.

  • iEV[depvar] - the integral with respect to time of the expected value of the response of a submodel.

  • XB[depvar] - the expected value of the complex predictor of a submodel.

  • dXB[depvar] - the first derivative with respect to time of the expected value of the complex predictor of a submodel.

  • d2XB[depvar] - the second derivative with respect to time of the expected value of the complex predictor of a submodel.

  • iXB[depvar] - the integral with respect to time of the expected value of the complex predictor of a submodel.

  • bhazard(varname) - invokes a relative survival (excess hazard) model. varname specifies the expected hazard rate at the event time.

  • exposure(varname) - include log(varname) in the linear predictor, with a coefficient of 1. For use with family = "poisson".

  • ap(#) - defines the number of ancillary parameters. Used with family="user".

from

this is an optional argument giving the initial values for the full parameter vector, for more details on how to specify the initial estimates see the vignette.
family

a vector of strings specifying the family for each outcome specified in model. The currently available models include,

  • gaussian - Gaussian distribution

  • bernoulli - Bernoulli distribution

  • poisson - Poisson distribution

  • beta - Beta distribution

  • negbinomial - Negative binomial distribution

with survival models including,

  • exponential - exponential distribution

  • weibull - Weibull distribution

  • gompertz - Gompertz distribution

  • rp - Royston-Parmar model (complex predictor on the log cumulative hazard scale)

  • loghazard - general log hazard model (complex predictor on the log hazard scale)

and user-defined,

  • user - fit a user-defined model, which should be written using merlin's utility functions. The name of your user-defined function should be passed through the userf option.

  • null - is a convenience tool to define additional complex predictors, that do not contribute to the log likelihood. For use with family = "user".

link

string vector defining the link functions for each model. Default is "identity" for all models. If specified, you must define a link function for all submodels. Options include "identity", "log" and "logit".
timevar

specifies the variable which represents time, this is necessary when a function of time is used in the linear predictor of a survival model as it may interact with other elements of the model.
covariance

the structure of the variance-covariance matrix can be varied, the default is diagonal where all diagonal elements of the variance-covariance matrix are estimated uniquely, identity assumes all diagonal elements are equal and unstructured estimates all elements of the variance-covariance matrix.
data

a data frame containing all variables required for fitting the model. Can be a tibble object.
userf

string vector defining the name of the user-written functions for each family="user". Each function must be in memory and should return the observation level contribution to the log-likelihood.
sweights

Not documented.
levels

if the model contains random-effects then a vector giving the order of levels must be specified, from the highest level to the lowest, e.g. levels=c("practice","id").
predict

Not documented.
predtype

Not documented.
predmodel

Not documented.
causes

Not documented.
at

Not documented.
contrast

Not documented.
modelfit

Not documented.
control

A list of parameters that control the estimation algorithm. Generally it should not be modified, unless there are convergence issues. Possible values are:

  • ip An optional vector of integers specifying the number of integration points to be used when integrating out the random effects. A different number of ip can be specified for each level (from highest to lowest level). If only a single number is given then merlin will assume that number of integration points at all levels. Default is ip = 7 for each level using Gauss-Hermite quadrature, or ip = 100 for each level using Monte-Carlo integration;

  • intmethod The method used for numerically integrating out the random-effects in order to calculate the likelihood for a mixed effects model which includes random effects. Options include ghermite for non-adaptive Gauss-Hermite quadrature, halton for Monte-Carlo integration using Halton sequences, sobol for Monte-Carlo integration using Sobol sequences, or mc for standard Monte-Carlo integration using normal draws. The default is ghermite. Level-specific integration techniques can be specified, for example, with a three level model, we may use Gauss-Hermite quadrature at the highest level, and Monte-Carlo integration with Halton sequences at level 2, using intmethod = c("ghermite","halton").

  • debug Not documented.

  • verbose Not documented.

  • optim.method The optim method to be used. Defaults to Nelder-Mead, see optim for available methods.

  • maxit The maximum number of iterations for the optimisation routine. Defaults to 5000.

Author(s)

Emma C. Martin, Alessandro Gasparini and Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear, non-linear and user-defined models.

See Also

predict.merlin

merlin_util_depvar, merlin_util_timevar, merlin_util_xzb, merlin_util_xzb_mod merlin_util_xzb_deriv, merlin_util_xzb_deriv_mod merlin_util_xzb_deriv2, merlin_util_xzb_deriv2_mod merlin_util_xzb_integ, merlin_util_xzb_integ_mod merlin_util_ev, merlin_util_ev_mod merlin_util_ev_deriv, merlin_util_ev_deriv_mod merlin_util_ev_deriv2, merlin_util_ev_deriv2_mod merlin_util_ev_integ, merlin_util_ev_integ_mod merlin_util_ap, merlin_util_ap_mod

Examples

## Not run: 
library(merlin)
data(pbc.merlin, package = "merlin")

# Linear fixed-effects model
merlin(logb ~ year,
       family = "gaussian",
       data = pbc.merlin)

# Linear mixed-effects model with random intercept and slope at ID level
merlin(logb ~ year + M1[id] * 1 + year:M2[id] * 1,
       family = "gaussian",
       levels = "id",
       data = pbc.merlin)

# Joint longitudinal and survival model with shared random effects
merlin(model = list(logb ~ year + M1[id] * 1,
                    Surv(stime, died) ~ trt + M1[id]),
       family = c("gaussian", "weibull"),
       levels = "id",
       data = pbc.merlin)

# Joint longitudinal and survival model with expected value
merlin(model = list(logb ~ year + M1[id] * 1,
                    Surv(stime, died) ~ trt + EV[logb]),
       family = c("gaussian", "weibull"),
       levels = "id",
       timevar = c("year","stime"),
       data = pbc.merlin)

# Gaussian distribution - implemented as a user-written family
logl_gaussian <- function(gml)
{
  y    <- merlin_util_depvar(gml)
  xzb  <- merlin_util_xzb(gml)
  se   <- exp(merlin_util_ap(gml,1))

  mu   <- (sweep(xzb,1,y,"-"))^2
  logl <- ((-0.5 * log(2*pi) - log(se)) - (mu/(2 * se^2)))
  return(logl)
}

merlin(logb ~ year + ap(1), family = "user", data = pbc.merlin,
                                  userf = "logl_gaussian")

# 3-level Weibull model
merlin(Surv(stime1,dead1) ~ age + M1[id1]*1 + M2[id2]*1,
       levels=c("id1","id2"), family="weibull", data=sim3)

## End(Not run)

merlin_util_ap - returns the current estimate of the ith ancillary parameter for the associated model

Description

merlin_util_ap - returns the current estimate of the ith ancillary parameter for the associated model

Usage

merlin_util_ap(gml, i)

Arguments

gml

merlin object - should not be edited
i

index for which ancillary parameter to extract

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ap_mod - returns the current estimate of the ith ancillary parameter for the specified model

Description

merlin_util_ap_mod - returns the current estimate of the ith ancillary parameter for the specified model

Usage

merlin_util_ap_mod(gml, m, i)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
i

index for which ancillary parameter to extract

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_depvar - returns the response variable(s)

Description

Utility function to extract the dependent variable(s) for the current model. If the model is a survival/time-to-event model, then it will contain the event times in the first column and the event indicator in the second.

Usage

merlin_util_depvar(gml)

Arguments

gml

merlin object - should not be edited

Author(s)

Emma C. Martin, Alessandro Gasparini and Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ev - returns the observation-level expected value of the outcome

Description

Utility function to extract the expected value of the outcome at the current parameter estimates for a particular model.

Usage

merlin_util_ev(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ev_deriv - returns the first derivative with respect to time of the observation-level expected value of the outcome

Description

Utility function to extract d/dt of the expected value of the outcome at the current parameter estimates for a particular model.

Usage

merlin_util_ev_deriv(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

Examples

library(merlin)
data(pbc.merlin, package = "merlin")

# Linear fixed-effects model
merlin(model = list(logb ~ year),
       family = "gaussian",
       data = pbc.merlin)

merlin_util_ev_deriv - returns the first derivative with respect to time of the observation-level expected value of the specified outcome

Description

Utility function to extract d/dt of the expected value of the outcome at the current parameter estimates for a specified model.

Usage

merlin_util_ev_deriv_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ev_deriv2 - returns the second derivative with respect to time of the observation-level expected value of the outcome

Description

merlin_util_ev_deriv2 - returns the second derivative with respect to time of the observation-level expected value of the outcome

Usage

merlin_util_ev_deriv2(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ev_deriv2_mod - returns the second derivative with respect to time of the observation-level expected value of the specified outcome

Description

merlin_util_ev_deriv2_mod - returns the second derivative with respect to time of the observation-level expected value of the specified outcome

Usage

merlin_util_ev_deriv2_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ev_integ - returns the integral with respect to time of the observation-level expected value of the outcome

Description

merlin_util_ev_integ - returns the integral with respect to time of the observation-level expected value of the outcome

Usage

merlin_util_ev_integ(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ev_integ_mod - returns the integral with respect to time of the observation-level expected value of the specified outcome

Description

merlin_util_ev_integ_mod - returns the integral with respect to time of the observation-level expected value of the specified outcome

Usage

merlin_util_ev_integ_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_ev_mod - returns the observation-level expected value of the outcome for a specified model

Description

Utility function to extract the expected value of the outcome at the current parameter estimates for a specified model.

Usage

merlin_util_ev_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the model
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_timevar - returns the time variable

Description

Utility function to extract the time variable(s) for the current model.

Usage

merlin_util_timevar(gml)

Arguments

gml

merlin object - should not be edited

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_xzb - returns the observation-level complex predictor

Description

Utility function to extract the complex predictor evaluated at the current parameter estimates for a particular model.

Usage

merlin_util_xzb(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Emma C. Martin, Alessandro Gasparini and Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

Examples

library(merlin)
data(pbc.merlin, package = "merlin")

# Linear fixed-effects model
merlin(model = list(logb ~ year),
       family = "gaussian",
       data = pbc.merlin)

merlin_util_xzb_deriv - returns the first derivative with respect to time of the observation-level complex predictor

Description

Utility function to extract d/dt of the complex predictor evaluated at the current parameter estimates for a particular model.

Usage

merlin_util_xzb_deriv(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

Examples

library(merlin)
data(pbc.merlin, package = "merlin")

# Linear fixed-effects model
merlin(model = list(logb ~ year),
       family = "gaussian",
       data = pbc.merlin)

merlin_util_xzb_deriv_mod - returns the first derivative with respect to time of the observation-level complex predictor of a specified model

Description

merlin_util_xzb_deriv_mod - returns the first derivative with respect to time of the observation-level complex predictor of a specified model

Usage

merlin_util_xzb_deriv_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_xzb_deriv2 - returns the second derivative with respect to time of the observation-level complex predictor

Description

merlin_util_xzb_deriv2 - returns the second derivative with respect to time of the observation-level complex predictor

Usage

merlin_util_xzb_deriv2(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_xzb_deriv2_mod - returns the second derivative with respect to time of the observation-level complex predictor of the specified model

Description

merlin_util_xzb_deriv2_mod - returns the second derivative with respect to time of the observation-level complex predictor of the specified model

Usage

merlin_util_xzb_deriv2_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_xzb_integ - returns the integral with respect to time of the observation-level complex predictor

Description

merlin_util_xzb_integ - returns the integral with respect to time of the observation-level complex predictor

Usage

merlin_util_xzb_integ(gml, t = NULL)

Arguments

gml

merlin object - should not be edited
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_xzb_integ_mod - returns the integral with respect to time of the observation-level complex predictor of the specified model

Description

merlin_util_xzb_integ_mod - returns the integral with respect to time of the observation-level complex predictor of the specified model

Usage

merlin_util_xzb_integ_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

merlin_util_xzb_mod - returns the observation-level complex predictor of the specified model

Description

Utility function to extract the complex predictor evaluated at the current parameter estimates for a particular model.

Usage

merlin_util_xzb_mod(gml, m, t = NULL)

Arguments

gml

merlin object - should not be edited
m

specifies the merlin submodel
t

specifies the variable which represents time

Author(s)

Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear and non-linear models.

Fit multi-level restricted cubic spline model

Description

Fit multi-level restricted cubic spline model

Usage

mlrcs(formula, random = NULL, data, ...)

Arguments

formula

A model formula for the fixed-effects in the model. Must include one restricted cubic spline term, specified as rcs(variable, df = #).
random

A formula for the random-effects in the model. Random-effects should be specified as a one-sided formula, e.g. ~ 1 + trt | id for random effect on the intercept and treatment at the id level. Random-effects can be estimated at any number of nested random-effect levels by providing a list of one-sided formulas. When specifying random-effect at multiple levels. The one-sided formula should be given in order, starting with the highest level. Only required when rcs = TRUE.
data

A data frame containing all variables required for fitting the model.
...

Further arguments passed to merlin.

Value

An object of class mlrcs.

Examples

## Not run: 
# Two-level model
data("pbc.merlin", package = "merlin")
fit <- mlrcs(formula = logp ~ 1 + rcs(year, df = 4) + age + trt,
             random  = ~ 1 + trt | id,
             data = pbc.merlin
)
summary(fit)

# Three-level model
fit <- mlrcs(formula = logp ~ 1 + rcs(year, df = 4) + age + trt,
             random  = list(~ 1 | region,
                            ~ 1 + trt | id),
             data = pbc.merlin
)
summary(fit)

## End(Not run)

Fit proportional hazards survival models

Description

Fit proportional hazards survival models

Usage

mlsurv(
  formula,
  distribution,
  df = NULL,
  powers = NULL,
  rcs = TRUE,
  data,
  from.null = NULL,
  ...
)

Arguments

formula

A model formula, where the left-hand side is a Surv object.
distribution

A parametric distribution for the baseline hazard. Possible values are exponential, weibull, gompertz, rp, logchazard, and loghazard. rp is equivalent to a logchazard model with restricted cubic splines (argument rcs = TRUE).
df

Represents the number of degrees of freedom used for the restricted cubic splines when flexibly modelling the baseline hazard. Only required when rcs = TRUE.
powers

A vector representing the degree of the fractional polynomials used to model the baseline hazard (with a maximum degree of 2). Only required when rcs = FALSE.
rcs

Use restricted cubic splines when flexibly modelling the baseline hazard? Defaults to TRUE, and the alternative is using fractional polynomials.
data

A data frame containing all variables required for fitting the model. Can be a tibble object.
from.null

A vector of starting values for the null model (used to get improved starting values). This is mostly useful when experiencing issues with default starting values or convergence issues.
...

Further arguments passed to merlin.

Value

An object of class mlsurv.

Examples

# Weibull model
library(survival)
data("pbc.merlin", package = "merlin")
fit <- mlsurv(
  formula = Surv(stime, died) ~ trt,
  distribution = "weibull",
  data = pbc.merlin
)
summary(fit)

# Royston-Parmar model with 3 degrees of freedom
fit <- mlsurv(
  formula = Surv(stime, died) ~ trt,
  distribution = "rp",
  df = 3,
  data = pbc.merlin
)
summary(fit)

## Not run: 
# Flexible parametric model on the log-hazard scale with fractional polynomials
fit <- mlsurv(
  formula = Surv(stime, died) ~ trt,
  distribution = "loghazard",
  powers = c(0, 1),
  rcs = FALSE,
  data = pbc.merlin
)
summary(fit)

## End(Not run)

Mayo Clinic primary biliary cirrhosis data

Description

This data is from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver conducted between 1974 and 1984. A total of 424 PBC patients, referred to Mayo Clinic during that ten-year interval met eligibility criteria for the randomized placebo controlled trial of the drug D-penicillamine, but only the first 312 cases in the data set participated in the randomized trial. Therefore, the data here are for the 312 patients with largely complete data.

Usage

data(pbc)

data(pbc.merlin)

Format

A data frame with 1945 observations on the following 20 variables:

id

patients identifier; in total there are 312 patients.

years

number of years between registration and the earlier of death, transplantation, or study analysis time.

status

a factor with levels alive, transplanted and dead.

drug

a factor with levels placebo and D-penicil.

age

at registration in years.

sex

a factor with levels male and female.

year

number of years between enrollment and this visit date, remaining values on the line of data refer to this visit.

ascites

a factor with levels No and Yes.

hepatomegaly

a factor with levels No and Yes.

spiders

a factor with levels No and Yes.

edema

a factor with levels No edema (i.e. no edema and no diuretic therapy for edema), edema no diuretics (i.e. edema present without diuretics, or edema resolved by diuretics), and edema despite diuretics (i.e. edema despite diuretic therapy).

serBilir

serum bilirubin in mg/dl.

serChol

serum cholesterol in mg/dl.

albumin

albumin in mg/dl.

alkaline

alkaline phosphatase in U/liter.

SGOT

SGOT in U/ml.

platelets

platelets per cubic ml/1000.

prothrombin

prothrombin time in seconds.

histologic

histologic stage of disease.

status2

a numeric vector with the value 1 denoting if the patient was dead, and 0 if the patient was alive or transplanted.

An object of class data.frame with 1945 rows and 25 columns.

Note

pbc.merlin is a version of the pbc dataset in merlin format.

Source

pbc.

References

Fleming T, Harrington D. Counting Processes and Survival Analysis. 1991; New York: Wiley.

Therneau T, Grambsch P. Modeling Survival Data: Extending the Cox Model. 2000; New York: Springer-Verlag.

predict.merlin - post-estimation tools for merlin

Description

predictions following the fit of a merlin model

Usage

## S3 method for class 'merlin'
predict(
  object,
  stat = "eta",
  type = "fixedonly",
  predmodel = 1,
  causes = NULL,
  at = NULL,
  contrast = NULL,
  ...
)

Arguments

object

merlin model object
stat

specifies which prediction, which can be one of:

  • eta the expected value of the complex predictor

  • mu the expected value of the response variable

  • hazard the hazard function

  • chazard the cumulative hazard function

  • logchazard the log cumulative hazard function

  • survival the survival function

  • cif the cumulative incidence function

  • rmst calculates the restricted mean survival time, which is the integral of the survival function within the interval (0,t], where t is the time at which predictions are made. If multiple survival models have been specified in your merlin model, then it will assume all of them are cause-specific competing risks models, and include them in the calculation. If this is not the case, you can override which models are included by using the causes option. rmst = t - totaltimelost.

  • timelost calculates the time lost due to a particular event occurring, within the interval (0,t]. In a single event survival model, this is the integral of the cif between (0,t]. If multiple survival models are specified in the merlin model then by default all are assumed to be cause-specific event time models contributing to the calculation. This can be overridden using the causes option.

  • totaltimelost total time lost due to all competing events, within (0,t]. If multiple survival models are specified in the merlin model then by default all are assumed to be cause-specific event time models contributing to the calculation. This can be overridden using the causes option. totaltimelost is the sum of the timelost due to all causes.

  • cifdifference calculates the difference in cif predictions between values of a covariate specified using the contrast option.

  • hdifference calculates the difference in hazard predictions between values of a covariate specified using the contrast option.

  • rmstdifference calculates the difference in rmst predictions between values of a covariate specified using the contrast option.

  • mudifference calculates the difference in mu predictions between values of a covariate specified using the contrast option.

  • etadifference calculates the difference in eta predictions between values of a covariate specified using the contrast option.

type

the type of prediction, either:

  • fixedonly prediction calculated based only on the fixed effects; the default.

  • marginal prediction calculated marginally with respect to the latent variables. the stat is calculated by integrating the prediction function with respect to all the latent variables over their entire support.

predmodel

specifies which model to obtain predictions from; default is predmodel=1
causes

is for use when calculating predictions from a competing risks merlin model. By default, cif, rmst, timelost and totaltimelost assume that all survival models included in the merlin model are cause-specific hazard models contributing to the calculation. If this is not the case, then you can specify which models (indexed using the order they appear in your merlin model by using the causes option, e.g. causes=c(1,2).
at

specify covariate values for prediction. Fixed values of covariates should be specified in a list e.g. at = c("trt" = 1, "age" = 50).
contrast

specifies the values of a covariate to be used when comparing statistics, such as when using the cifdifference option to compare cumulative incidence functions, e.g. contrast = c("trt" = 0, "trt" = 1).
...

other options

Author(s)

Emma C. Martin, Alessandro Gasparini and Michael J. Crowther

References

Crowther MJ. Extended multivariate generalised linear and non-linear mixed effects models. https://arxiv.org/abs/1710.02223

Crowther MJ. merlin - a unified framework for data analysis and methods development in Stata. https://arxiv.org/abs/1806.01615

Martin EC, Gasparini A, Crowther MJ. merlin - an R package for mixed effects regression of linear, non-linear and user-defined models.

See Also

merlin

Examples

library(merlin)
data(pbc.merlin, package = "merlin")

# Linear fixed-effects model
mod <-merlin(model = list(logb ~ year),
             family = "gaussian",
             data = pbc.merlin)
predict(mod,stat="eta",type="fixedonly")

Print merlin Fits

Description

Print the coefficients from a merlin fit.

Usage

## S3 method for class 'merlin'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

An object of class merlin.
digits

The number of significant digits to use when printing.
...

Not used.

Print mlrcs Fits

Description

Print the coefficients from a mlrsc fit.

Usage

## S3 method for class 'mlrcs'
print(x, digits = max(3L, getOption("digits") - 3L), simplify = TRUE, ...)

Arguments

x

An object of class mlrcs.
digits

The number of significant digits to use when printing.
simplify

Should non-interpretable coefficients be hidden (e.g. splines and flexible polynomials terms)? Defaults to TRUE.
...

Not used.

Print mlsurv Fits

Description

Print the coefficients from a mlsurv fit.

Usage

## S3 method for class 'mlsurv'
print(x, digits = max(3L, getOption("digits") - 3L), simplify = TRUE, ...)

Arguments

x

An object of class mlsurv.
digits

The number of significant digits to use when printing.
simplify

Should non-interpretable coefficients be hidden (e.g. splines and flexible polynomials terms)? Defaults to TRUE.
...

Not used.

Simulated 3-level survival data

Description

Simulated 3-level survival data

Usage

data(sim3)

Format

A data frame...

Summarizing merlin Fits

Description

These functions are all methods for class merlin or summary.merlin objects.

Usage

## S3 method for class 'merlin'
summary(object, sig = 0.95, ...)

## S3 method for class 'summary.merlin'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

object

An object of class merlin
sig

Significancy level for confidence intervals. Defaults to 0.95.
...

Not used.
x

An object of class summary.merlin
digits

The number of significant digits to use when printing.

Summarizing mlrcs Fits

Description

These functions are all methods for class mlrcs or summary.mlrcs objects.

Usage

## S3 method for class 'mlrcs'
summary(object, sig = 0.95, ...)

## S3 method for class 'summary.mlrcs'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

object

An object of class mlrcs
sig

Significancy level for confidence intervals. Defaults to 0.95.
...

Not used.
x

An object of class summary.mlrcs
digits

The number of significant digits to use when printing.

Summarizing mlsurv Fits

Description

These functions are all methods for class mlsurv or summary.mlsurv objects.

Usage

## S3 method for class 'mlsurv'
summary(object, sig = 0.95, ...)

## S3 method for class 'summary.mlsurv'
print(x, digits = max(3, getOption("digits") - 3), simplify = TRUE, ...)

Arguments

object

An object of class mlsurv
sig

Significancy level for confidence intervals. Defaults to 0.95.
...

Not used.
x

An object of class summary.mlsurv
digits

The number of significant digits to use when printing.
simplify

Should non-interpretable coefficients be hidden (e.g. splines and flexible polynomials terms)? Defaults to TRUE.

Calculate Variance-Covariance Matrix for a merlin Model Object

Description

Returns the variance-covariance matrix of all estimated parameters of a fitted merlin model.

Usage

## S3 method for class 'merlin'
vcov(object, ...)

## S3 method for class 'summary.merlin'
vcov(object, ...)

Arguments

object

An object of class merlin or summary.merlin.
...

Not used.

Calculate Variance-Covariance Matrix for a mlrcs Model Object

Description

Returns the variance-covariance matrix of all estimated parameters of a fitted mlrcs model.

Usage

## S3 method for class 'mlrcs'
vcov(object, ...)

## S3 method for class 'summary.mlrcs'
vcov(object, ...)

Arguments

object

An object of class mlrcs or summary.mlrcs.
...

Not used.

Calculate Variance-Covariance Matrix for a mlsurv Model Object

Description

Returns the variance-covariance matrix of all estimated parameters of a fitted mlsurv model.

Usage

## S3 method for class 'mlsurv'
vcov(object, ...)

## S3 method for class 'summary.mlsurv'
vcov(object, ...)

Arguments

object

An object of class mlsurv or summary.mlsurv.
...

Not used.