survHE: Survival Analysis in Health Economic Evaluation

Description

Contains a suite of functions for survival analysis in health economics. These can be used to run survival models under a frequentist (based on maximum likelihood) or a Bayesian approach (both based on Integrated Nested Laplace Approximation or Hamiltonian Monte Carlo). To run the Bayesian models, the user needs to install additional modules (packages), i.e. 'survHEinla' and 'survHEhmc'. These can be installed from https://giabaio.r-universe.dev/ using 'install.packages("survHEhmc", repos = c("https://giabaio.r-universe.dev", "https://cloud.r-project.org"))' and 'install.packages("survHEinla", repos = c("https://giabaio.r-universe.dev", "https://cloud.r-project.org"))' respectively. 'survHEinla' is based on the package INLA, which is available for download at https://inla.r-inla-download.org/R/stable/. The user can specify a set of parametric models using a common notation and select the preferred mode of inference. The results can also be post-processed to produce probabilistic sensitivity analysis and can be used to export the output to an Excel file (e.g. for a Markov model, as often done by modellers and practitioners). doi:10.18637/jss.v095.i14.

Author(s)

Maintainer: Gianluca Baio g.baio@ucl.ac.uk

Other contributors:

• Andrea Berardi and.be.like@gmail.com [contributor]

• Philip Cooney philip.cooney@hotmail.com [contributor]

• Andrew Jones andrew.r.johnson@postgrad.curtin.edu.au [contributor]

• Nathan Green n.green@ucl.ac.uk [contributor]

See Also

Useful links:

• https://github.com/giabaio/survHE

• https://gianluca.statistica.it/software/survhe/

• Report bugs at https://github.com/giabaio/survHE/issues

A fictional survival trial.

Description

A dataset containing fictional data from a trial, where the main outcome is in terms of time-to-event and censoring indicator and with additional covariates.

Usage

data

Format

A data frame with 367 rows and 8 variables:

ID_patient

The individual level identifier

time

The observed time at which the event happens

censored

An indicator to describe whether the event is fully observed or censored

arm

An indicator for the treatment arm, with 0 = control and 1 = active treatment

sex

An indicator for the individual's sex, with 0 = male and 1 = female

age

A numeric variable with the individual's age

imd

A categorical variable representing a measure of area-level social deprivation

ethnic

A categorical variable representing the individual's ethnic group, as measured from a Census

Format digitised data for use in survival analysis

Description

Produces txt files with Kaplan Meier and individual level survival data from digitised Kaplan Meier curves obtained by DigitizeIT

Usage

digitise(
  surv_inp,
  nrisk_inp,
  km_output = "KMdata.txt",
  ipd_output = "IPDdata.txt"
)

Arguments

Author(s)

Patricia Guyot and Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

Examples

## Not run: 
# Defines the txt files to be used as inputs
surv.inp <- system.file("extdata", "survival.txt", package = "survHE")
nrisk.inp <- system.file("extdata", "nrisk.txt", package = "survHE")
# Runs 'digitise' to create the relevant output files
digitise(surv.inp, nrisk.inp)

## End(Not run)

Fit parametric survival analysis for health economic evaluations

Description

Runs the survival analysis with several useful options, using either MLE (via flexsurv) or a Bayesian approach (via R-INLA or rstan)

Usage

fit.models(formula = NULL, data, distr = NULL, method = "mle", ...)

Arguments

Details

On object in the class survHE containing the following elements

Value

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

See Also

make.surv

Examples

## Not run: 
# Loads an example dataset from 'flexsurv'
data(bc)

# Fits the same model using the 3 inference methods
mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="mle")
inla = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="inla")
hmc = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="hmc")
    
# Prints the results in comparable fashion using the survHE method
print(mle)
print(inla)
print(hmc)

# Or visualises the results using the original packages methods
print(mle,original=TRUE)
print(inla,original=TRUE)
print(hmc,original=TRUE)

# Plots the survival curves and estimates
plot(mle)
plot(mle,inla,hmc,labs=c("MLE","INLA","HMC"),colors=c("black","red","blue"))

## End(Not run)

Create an individual level dataset from digitised data

Description

Piles in the simulated IPD resulting from running digitise for more than one treatment arm

Usage

make.ipd(ipd_files, ctr = 1, var.labs = c("time", "event", "arm"))

Arguments

Author(s)

Gianluca Baio

References

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See Also

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Examples

## Not run: 
# Defines the txt files to be used as inputs
surv.inp <- system.file("extdata", "survival.txt", package = "survHE")
nrisk.inp <- system.file("extdata", "nrisk.txt", package = "survHE")
# Runs 'digitise' to create the relevant output files
digitise(surv.inp, nrisk.inp, ipd_output = "IPD.txt")
# Now uses 'make.ipd' to create the pseudo-data
make.ipd("IPD.txt", ctr = 1, var.labs = c("time", "event", "arm"))

## End(Not run)

Engine for Probabilistic Sensitivity Analysis on the survival curves

Description

Creates the survival curves for the fitted model(s)

Usage

make.surv(fit, mod = 1, t = NULL, newdata = NULL, nsim = 1, ...)

Arguments

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

See Also

fit.models, psa.plot, write.surv

Examples

## Not run:  
# Loads an example dataset from 'flexsurv'
data(bc)

# Fits the same model using the 3 inference methods
mle <- fit.models(formula=Surv(recyrs,censrec) ~ group, data=bc,
                  distr="exp", method="mle")
p.mle <- make.surv(mle)
psa.plot(p.mle)

# Can also use the main 'plot' function to visualise the survival curves
# and include uncertainty by using a number 'nsim' of simulations
plot(mle, nsim=10)

## End(Not run)

make.transition.probs

Description

Computes the transition probabilities (to be passed to a Markov model) from the cumulative hazard curves obtained using fit.models, using the formula p(t)=1-exp(H(t-k)/H(t)), where k is the Markov model cycle length (or the difference across two consecutive times) and t is a generic time

Usage

make.transition.probs(fit, labs = NULL, ...)

Arguments

Value

A tibble 'lambda' with an indicator for the treatment arm, the times at which the probabilities have been computed and nsim columns each with a simulation of the transition probabilities for all the times specified by the user

Note

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Author(s)

Gianluca Baio

References

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See Also

make.surv

Examples

## Not run: 
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## End(Not run)

make_data_multi_state

Description

Takes as input an individual-level dataset including data on both progression and death time (jointly) and manipulates it using dplyr functions to create a full "multi-state" dataset, in which all the transitions are tracked. This can then be used to fit survival models and compute all the estimates for the whole set of transition probabilities

Usage

make_data_multi_state(
  data,
  id = "id",
  prog = "prog",
  death = "death",
  prog_t = "prog_t",
  death_t = "death_t",
  keep = NULL,
  ...
)

Arguments

Value

A tibble containing the event history for each individual and with the following variables: id = Patients ID; from = Initial state (1=Pre-progression, 2=Progression, 3=Death); to = End state (1=Pre-progression, 2=Progression, 3=Death); trans = Transition ID: 1=Pre-progression -> Progression; 2=Pre-Progression -> Death; 3=Progression -> Death; Tstart = Entry time (either entry or progression); Tstop = Exit time (time of event or censoring time); status = Event indicator (1=yes, 0=censored), for the specific event under consideration; treat = Treatment indicator All the other original variables are appended to these, but can be removed

Note

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Author(s)

Gianluca Baio

References

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See Also

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Examples

## Not run: 
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## End(Not run)

Creates a 'newdata' list to modify the plots for specific individual profiles (with respect to the covariates)

Description

Creates a 'newdata' list to modify the plots for specific individual profiles (with respect to the covariates)

Usage

make_newdata(data, vars, conts = NULL)

Arguments

Value

Note

Something will go here

Author(s)

Gianluca Baio

Examples

## Not run: 
data(bc)

# Fits a model using the 'bc' data
mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="mle")
# Now makes the default plot
plot(mle)
# Now creates a 'newdata' list to modify the plot for selected profiles
newdata=make_newdata(data=bc,vars="group")
# And can plot, say, only two of the three treatment arms
plot(mle,newdata=newdata$newdata[c(1,3)],lab.profile=newdata$labs[c(1,3)])

## End(Not run)

Markov trace

Description

Plots the Markov Trace from an object generated using three_state_mm

Usage

markov_trace(mm, interventions = NULL, ...)

Arguments

Value

Plot

Note

Something will go here

Author(s)

Gianluca Baio

References

Something will go here

See Also

make.surv, three_state_mm

Examples

## Not run: 
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## End(Not run)

Graphical representation of the measures of model fitting based on Information Criteria

Description

Plots a summary of the model fit for all the models fitted

Usage

model.fit.plot(..., type = "aic", scale = "absolute", stacked = FALSE)

Arguments

Details

Something will go here

Value

A plot with the relevant model fitting statistics

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

See Also

fit.models

Examples

## Not run:  
data(bc)

mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr=c("exp","wei","lno"),method="mle")
model.fit.plot(mle)

## End(Not run)

NICE TA174 dataset in multi-state format.

Description

These are the same data contained in NICE TA174, as made publicly available as part of the supplementary material for Williams et al (2017). Medical Decision Making, 37;427-439. However, the data have been restructured (by using the function make_data_multi_state()) to be used for multi-state analysis

Usage

msmdata

Format

A tibble with 1868 rows and 16 variables:

id

A numeric patient identifier

from

An indicator of the starting state. 1=Pre-progression; 2=Progression; 3=Death

to

An indicator for the arriving state

trans

A code for the actual transition considered. 1=Pre-progression -> Progression; 2=Pre-progression -> Death; 3=Progression -> Death

Tstart

The time of entry into the observation

Tstop

The time of exit from observation

time

The observed time until even (progression or death), or censoring occurs

status

The event indicator; takes value 1 if the underlying event (which varies depending on which transition is being considered) happens and 0 otherwise

treat

The treatment indicator. 1=rituximab in combination with fludarabine andcyclophosphamide (RFC); 0=fludarabine and cyclo-phosphamide alone (FC)

patid

The original numeric patient identifier

prog

The original indicator to describe whether the patient has experience a progression

death

The original indicator to describe whether the patient has experience death

prog_t

The original observed time at progression, or the time at which the patient has been censored; measured in months

death_t

The original observed time at death, or the time at which the patient has been censored; measured in months

prog_ty

The original observed time at progression, or the time at which the patient has been censored; measured in years

death_ty

The original observed time at death, or the time at which the patient has been censored; measured in years

Plot survival curves for the models fitted using fit.models

Description

Plots the results of model fit.

Usage

## S3 method for class 'survHE'
plot(...)

Arguments

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

See Also

fit.models, write.surv

Examples

## Not run: 
data(bc)

mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="mle")
inla = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="inla")
plot(MLE=mle,INLA=inla)

## End(Not run)

Plot to assess suitability of parametric model

Description

Perform an exploratory investigation for linearity of transformed survival models.

Usage

plot_transformed_km(fit, mod = 1, add_legend = FALSE, graph = "base", ...)

Arguments

Details

For the Weibull, twice taking logs of the survivor function

log(-log S(t)) = log \lambda + \gamma log t

A plot of log(-log S(t)) against log(t) would give an approximately straight line if the Weibull assumption is reasonable. The plot could also be used to give a rough estimate of the parameters.

Similarly, for the log-logistic distribution

logS(t)/(1 - S(t)) = \theta - \kappa log t

For the log-normal distribution

\Phi^{-1} (1 - S(t)) = (log t - \mu) / \sigma

We can also check the assumption made with using the Cox regression model of proportional hazards by inspecting the log-cumulative hazard plot.

log H_i(t) = \beta x_i + log H_0(t)

The transformed curves for different values of the explanatory variables will be parallel if PH holds.

Value

Diagnostic plot

Author(s)

William Browne, Nathan Green

References

Collett (2015) Modelling Survival Data in Medical Research, CRC Press

Examples

data(bc)
form <- formula("Surv(recyrs, censrec) ~ group")

# exponential distribution
fit_exp <- fit.models(form, data = bc,
                  distr = "exp", method = "mle")
plot_transformed_km(fit_exp)
plot_transformed_km(fit_exp, graph = "ggplot2")
                 
# weibull distribution
fit_wei <- fit.models(form, data = bc,
                  distr = "weibull", method = "mle")
plot_transformed_km(fit_wei)
plot_transformed_km(fit_wei, graph = "ggplot2")
                 
# loglogistic distribution
fit_llog <- fit.models(form, data = bc,
                  distr = "loglogistic", method = "mle")
plot_transformed_km(fit_llog)
plot_transformed_km(fit_llog, graph = "ggplot2")
                 
# lognormal distribution
fit_lnorm <- fit.models(form, data = bc,
                  distr = "lognormal", method = "mle")
plot_transformed_km(fit_lnorm)
plot_transformed_km(fit_lnorm, graph = "ggplot2")

## for only one group
form <- formula("Surv(recyrs, censrec) ~ 1")

fit_exp <- fit.models(form, data = bc,
                  distr = "exp", method = "mle")
plot_transformed_km(fit_exp)
plot_transformed_km(fit_exp, graph = "ggplot2")

Print a summary of the survival model(s) fitted by fit.models

Description

Prints the summary table for the model(s) fitted, with the estimate of the parameters

Usage

## S3 method for class 'survHE'
print(x, mod = 1, ...)

Arguments

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

Examples

## Not run:  
data(bc)

mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="mle")
print(mle)

## End(Not run)

Graphical depiction of the probabilistic sensitivity analysis for the survival curves

Description

Plots the survival curves for all the PSA simulations. The function is actually deprecated - similar graphs can be obtained directly using the plot method (with options), which allows a finer depiction of the results.

Usage

psa.plot(psa, ...)

Arguments

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

See Also

make.surv, write.surv

Examples

## Not run:  
data(bc)

# Fits the same model using the 3 inference methods
mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="mle")
p.mle = make.surv(mle,nsim=100)
psa.plot(p.mle)

## End(Not run)

Prints a summary table for the distribution the mean survival time for a given model and data

Description

Calculates the mean survival time as the area under the survival curve

Usage

## S3 method for class 'survHE'
summary(object, mod = 1, t = NULL, nsim = 1000, ...)

Arguments

Details

A list comprising of the following elements

Value

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

See Also

fit.models, make.surv

Examples

## Not run: 
data(bc)

mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="mle")
summary(mle,nsim=100)

## End(Not run)

NICE TA174 dataset.

Description

A dataset containing the data used for NICE TA174, as made publicly available as part of the supplementary material for Williams et al (2017). Medical Decision Making, 37;427-439.

Usage

ta174

Format

A tibble with 810 rows and 8 variables:

patid

A numeric patient identifier

treat

The treatment indicator. 1=rituximab in combination with fludarabine andcyclophosphamide (RFC); 0=fludarabine and cyclo-phosphamide alone (FC)

prog

An indicator to describe whether the patient has experience a progression

death

An indicator to describe whether the patient has experience death

prog_t

The observed time at progression, or the time at which the patient has been censored; measured in months

death_t

The observed time at death, or the time at which the patient has been censored; measured in months

prog_ty

The observed time at progression, or the time at which the patient has been censored; measured in years

death_ty

The observed time at death, or the time at which the patient has been censored; measured in years

A Custom ggplot2 Theme for Survival Plots

Description

This theme is designed for use with survival analysis plots, particularly those created using the survHE package. It builds on theme_bw() and customizes axis text, titles, plot background, and legend styling.

Usage

theme_survHE()

Details

Note: To position the legend inside the plot, use an additional call to theme(legend.position = c(x, y), legend.justification = c("left", "top")).

Value

A ggplot2 theme object that can be added to a ggplot.

Examples

library(ggplot2)
library(survHE)
ggplot(mtcars, aes(wt, mpg)) +
 geom_point() +
 theme_survHE() +
 theme(legend.position = c(0.6, 0.8), legend.justification = c("left", "top"))

three_state_mm

Description

General purpose function to run a standard three-state Markov model (typically used in cancer modelling). The states are typically 'Pre-progression', 'Progressed' and 'Death'. No backward transition from 'Progressed' to 'Pre-progression' is allowed and 'Death' is obviously an absorbing state. All other transitions are possible. The crucial assumption is that individual-level data are available recording an indicator and the time of progression and death for each individual. The function returns the full transition matrix

Usage

three_state_mm(
  m_12,
  m_13,
  m_23,
  nsim = 1,
  start = c(1000, 0, 0),
  basecase = FALSE,
  ...
)

Arguments

Value

A list including the state occupancy simulations in an object 'm'. This is a tibble with the number of individuals in each of the 3 states at each of the times specified by the user. If nsim>1, then the tibble also contains a simulation index to keep track of that. The list also includes the computation time to obtain the state occupancy tibble (in the object 'running_time'). If basecase==TRUE, then the function also computes the "base case scenario" (based on 1 simulation from of the underlying survival curves, i.e. the point estimate of the model parameters) and stores it in the object 'base_case'

Note

Something will go here

Author(s)

Gianluca Baio

References

Something will go here

See Also

make.transition.probs make_data_multi_state

Examples

## Not run: 
# Something will go here

## End(Not run)

write.surv

Description

Writes the survival summary to an excel file (helpful to then call the values in the Markov model)

Usage

write.surv(object, file, sheet = NULL, what = "surv")

Arguments

Details

Something will go here

Value

A spreadsheet file with the simulation(s) of the relevant quantity

Author(s)

Gianluca Baio

References

G Baio (2019). survHE: Survival analysis for health economic evaluation and cost-effectiveness modelling. Journal of Statistical Software (2020). vol 95, 14, 1-47. doi:10.18637/jss.v095.i14

See Also

make.surv

Examples

## Not run: 
# Loads an example dataset from 'flexsurv'
data(bc)

# Fits the same model using the 3 inference methods
mle = fit.models(formula=Surv(recyrs,censrec)~group,data=bc,
    distr="exp",method="mle")
p.mle = make.surv(mle)
write.surv(p.mle,file="test.xlsx")

## End(Not run)