Type: Package
Title: Group Sequential Designs with Negative Binomial Outcomes
Version: 0.1-4
Maintainer: Tobias Mütze <tobias.muetze@outlook.com>
Description: Design and analysis of group sequential designs for negative binomial outcomes, as described by T Mütze, E Glimm, H Schmidli, T Friede (2018) <doi:10.1177/0962280218773115>.
Depends: R (≥ 3.0.0)
Imports: stats, Rcpp(≥ 0.12.9)
Suggests: testthat, MASS, knitr, rmarkdown, dplyr, gsDesign, mvtnorm
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
NeedsCompilation: yes
URL: https://github.com/tobiasmuetze/gscounts
BugReports: https://github.com/tobiasmuetze/gscounts/issues
VignetteBuilder: knitr
LazyData: true
LinkingTo: Rcpp
Encoding: UTF-8
RoxygenNote: 7.1.2
Packaged: 2021-11-01 16:09:07 UTC; tobiasmuetze
Author: Tobias Mütze ORCID iD [aut, cre]
Repository: CRAN
Date/Publication: 2021-11-02 08:10:04 UTC

Maximum information

Description

Add maximum information and critical values to the object gsnb

Usage

add_maxinfo(x)

Calculate stopping probabilities

Description

Calculate analyses specific stopping probabilities and expected information level

Usage

add_stopping_prob(x)

Arguments

x

Object of class gsnb

Value

Object of class gsnb

Check object of class gsnb

Description

Performs validity checks of object of class gsnb

Usage

check_gsnb(x)

Arguments

x

object of class gsnb

Group sequential design with negative binomial outcomes

Description

Design a group sequential trial with negative binomial outcomes

Usage

design_gsnb(
  rate1,
  rate2,
  dispersion,
  ratio_H0 = 1,
  random_ratio = 1,
  power,
  sig_level,
  timing,
  esf = obrien,
  esf_futility = NULL,
  futility = NULL,
  t_recruit1 = NULL,
  t_recruit2 = NULL,
  study_period = NULL,
  accrual_period = NULL,
  followup_max = NULL,
  accrual_speed = 1,
  ...
)

Arguments

rate1

numeric; assumed rate of treatment group 1 in the alternative

rate2

numeric; assumed rate of treatment group 2 in the alternative

dispersion

numeric; dispersion (shape) parameter of negative binomial distribution

ratio_H0

numeric; positive number denoting the rate ratio \mu_1/\mu_2 under the null hypothesis, i.e. the non-inferiority or superiority margin

random_ratio

numeric; randomization ratio n1/n2

power

numeric; target power of group sequential design

sig_level

numeric; Type I error / significance level

timing

numeric vector; 0 < timing[1] < ... < timing[K] = 1 with K the number of analyses, i.e. (K-1) interim analyses and final analysis. When the timing of efficacy and futility analyses differ, timing should not be defined. Instead, the arguments timing_eff and timing_fut have to be used to specify the timing of the efficacy and futility analyses, respectively.

esf

function; error spending function

esf_futility

function; futility error spending function

futility

character; either "binding", "nonbinding", or NULL for binding, nonbinding, or no futility boundaries

t_recruit1

numeric vector; recruit (i.e. study entry) times in group 1

t_recruit2

numeric vector; recruit (i.e. study entry) times in group 2

study_period

numeric; study duration; to be set when follow-up times are not identical between subjects, NULL otherwise

accrual_period

numeric; accrual period

followup_max

numeric; maximum exposure time of a subject; to be set when follow-up times are to be equal for each subject, NULL otherwise

accrual_speed

numeric; determines accrual speed; values larger than 1 result in accrual slower than linear; values between 0 and 1 result in accrual faster than linear.

...

further arguments. Will be passed to the error spending function.

Details

Denote \mu_1 and \mu_2 the event rates in treatment groups 1 and 2. This function considers smaller event rates to be better. The statistical hypothesis testing problem of interest is

H_0: \frac{\mu_1}{\mu_2} \ge \delta vs. H_1: \frac{\mu_1}{\mu_2} < \delta,

with \delta=ratio_H0. Non-inferiority of treatment group 1 compared to treatment group 2 is tested for \delta\in (1,\infty). Superiority of treatment group 1 over treatment group 2 is tested for \delta \in (0,1]. The calculation of the efficacy and (non-)binding futility boundaries are performed under the hypothesis H_0: \frac{\mu_1}{\mu_2}= \delta and under the alternative H_1: \frac{\mu_1}{\mu_2} = rate1 / rate2.

The argument 'accrual_speed' is used to adjust the accrual speed. Number of subjects in the study at study time t is given by f(t)=a * t^b with a = n / accrual_period and b=accrual_speed For linear recruitment, b=1. b > 1 results is slower than linear recruitment for t < accrual_period and faster than linear recruitment for t > accrual_period. Vice verse for b < 1.

Value

A list with class "gsnb" containing the following components:

rate1

as input

rate2

as input

dispersion

as input

power

as input

timing

as input

ratio_H0

as input

ratio_H1

ratio rate1/rate2

sig_level

as input

random_ratio

as input

power_fix

power of fixed design

expected_info

list; expected information under ratio_H0 and ratio_H1

efficacy

list; contains the elements esf (type I error spending function), spend (type I error spend at each look), and critical (critical value for efficacy testing)

futility

list; only part of the output if argument futility is defined in the input. Contains the elements futility (input argument futility), esf (type II error spending function), spend (type II error spend at each look), and critical (critical value for futility testing)

stop_prob

list; contains the element efficacy with the probabilities for stopping for efficacy and, if futility bounds are calculated, the element futility with the probabilities for stopping for futility

t_recruit1

as input

t_recruit2

as input

study_period

as input

followup_max

as input

max_info

maximum information

calendar

calendar times of data looks; only calculated when exposure times are not identical

References

Mütze, T., Glimm, E., Schmidli, H., & Friede, T. (2018). Group sequential designs for negative binomial outcomes. Statistical Methods in Medical Research, <doi:10.1177/0962280218773115>.

Examples

# Calculate the sample sizes for a given accrual period and study period (without futility)
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025,
                   study_period = 3.5, accrual_period = 1.25, random_ratio = 1)
out

# Calculate the sample sizes for a given accrual period and study period with binding futility
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025, study_period = 3.5, 
                   accrual_period = 1.25, random_ratio = 1, futility = "binding", 
                   esf_futility = obrien)
out


# Calculate study period for given recruitment times
expose <- seq(0, 1.25, length.out = 1042)
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025, t_recruit1 = expose, 
                   t_recruit2 = expose, random_ratio = 1)
out

# Calculate sample size for a fixed exposure time
out <- design_gsnb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, 
                   power = 0.8, timing = c(0.5, 1), esf = obrien,
                   ratio_H0 = 1, sig_level = 0.025,
                   followup_max = 0.5, random_ratio = 1)
                   
# Different timing for efficacy and futility analyses
 design_gsnb(rate1 = 1, rate2 = 2, dispersion = 5,
             power = 0.8, esf = obrien,
             ratio_H0 = 1, sig_level = 0.025, study_period = 3.5,
             accrual_period = 1.25, random_ratio = 1, futility = "binding",
             esf_futility = pocock, 
             timing_eff = c(0.8, 1),
             timing_fut = c(0.2, 0.5, 1))

Clinical trials with negative binomial outcomes

Description

Design a clinical trial with negative binomial outcomes

Usage

design_nb(
  rate1,
  rate2,
  dispersion,
  power,
  ratio_H0 = 1,
  sig_level,
  random_ratio = 1,
  t_recruit1 = NULL,
  t_recruit2 = NULL,
  study_period = NULL,
  accrual_period = NULL,
  followup_max = NULL,
  accrual_speed = 1
)

Arguments

rate1

numeric; assumed rate of treatment group 1 in the alternative

rate2

numeric; assumed rate of treatment group 2 in the alternative

dispersion

numeric; dispersion (shape) parameter of negative binomial distribution

power

numeric; target power

ratio_H0

numeric; positive number denoting the rate ratio rate_1/rate_2 under the null hypothesis, i.e. the non-inferiority or superiority margin

sig_level

numeric; Type I error / significance level

random_ratio

numeric; randomization ratio n1/n2

t_recruit1

numeric vector; recruit (i.e. study entry) times in group 1

t_recruit2

numeric vector; recruit (i.e. study entry) times in group 2

study_period

numeric; study duration

accrual_period

numeric; accrual period

followup_max

numeric; maximum exposure time of a patient

accrual_speed

numeric; determines accrual speed; values larger than 1 result in accrual slower than linear; values between 0 and 1 result in accrual faster than linear.

Value

A list containing the following components:

rate1

as input

rate2

as input

dispersion

as input

power

as input

ratio_H0

as input

ratio_H1

ratio rate1/rate2

sig_level

as input

random_ratio

as input

t_recruit1

as input

t_recruit2

as input

study_period

as input

followup_max

as input

max_info

maximum information

Examples

# Calculate sample size for given accrual period and study duration assuming uniformal accrual
out <- design_nb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, power = 0.8,
                 ratio_H0 = 1, sig_level = 0.025,
                 study_period = 4, accrual_period = 1, random_ratio = 2)
out

# Calculate sample size for a fixed exposure time of 0.5 years
out <- design_nb(rate1 = 4.2, rate2 = 8.4, dispersion = 3, power = 0.8,
                 ratio_H0 = 1, sig_level = 0.025,
                 followup_max = 0.5, random_ratio = 2)
out

# Calculate study period for given recruitment time
t_recruit1 <- seq(0, 1.25, length.out = 1200)
t_recruit2 <- seq(0, 1.25, length.out = 800)
out <- design_nb(rate1 = 0.0875, rate2 = 0.125, dispersion = 5, power = 0.8,
                 ratio_H0 = 1, sig_level = 0.025,
                 t_recruit1 = t_recruit1, t_recruit2 = t_recruit2)

Calendar time of data looks

Description

Calculate the calendar time of looks given the information time

Usage

get_calendartime_gsnb(
  rate1,
  rate2,
  dispersion,
  t_recruit1,
  t_recruit2,
  timing,
  followup1,
  followup2
)

Arguments

rate1

numeric; rate in treatment group 1

rate2

numeric; rate in treatment group 2

dispersion

numeric; dispersion (shape) parameter of negative binomial distribution

t_recruit1

numeric vector; recruit (i.e. study entry) times in group 1

t_recruit2

numeric vector; recruit (i.e. study entry) times in group 2

timing

numeric vector with entries in (0,1]; information times of data looks

followup1

numeric vector; final individual follow-up times in treatment group 1

followup2

numeric vector; final individual follow-up times in treatment group 2

Value

numeric; vector with calendar time of data looks

Examples

# Calendar time at which 50%, 75%, and 100% of the maximum information is attained
# 100 subjects in each group are recruited uniformly over 1.5 years
# Study ends after two years, i.e. follow-up times vary between 2 and 0.5 years 
get_calendartime_gsnb(rate1 = 0.1, 
                      rate2 = 0.125, 
                      dispersion = 5, 
                      t_recruit1 = seq(0, 1.5, length.out = 100), 
                      t_recruit2 = seq(0, 1.5, length.out = 100),
                      timing = c(0.5, 0.75, 1),
                      followup1 = seq(2, 0.5, length.out = 100),
                      followup2 = seq(2, 0.5, length.out = 100))

get_covar

Description

Get canonical form covariance matrix

Usage

get_covar(timing)

Arguments

timing

numeric vector; 0 < timing[1] < ... < timing[k]

Information level for log rate ratio

Description

Calculates the information level for the log rate ratio of the negative binomial model

Usage

get_info_gsnb(rate1, rate2, dispersion, followup1, followup2)

Arguments

rate1

numeric; rate in treatment group 1

rate2

numeric; rate in treatment group 2

dispersion

numeric; dispersion (shape) parameter of negative binomial distribution

followup1

numeric vector; individual follow-up times in treatment group 1

followup2

numeric vector; individual follow-up times in treatment group 2

Value

numeric; information level

Examples

# Calculates information level for case of 10 subjects per group
# Follow-up times of subjects in each group range from 1 to 3
get_info_gsnb(rate1 = 0.1,
              rate2 = 0.125,
              dispersion = 4, 
              followup1 = seq(1, 3, length.out = 10), 
              followup2 = seq(1, 3, length.out = 10))

get_recruittimes

Description

Calculate the times subjects enter the study

Usage

get_recruittimes(accrual_period, n, accrual_exponent)

Arguments

accrual_period

numeric; duration of accrual period. Must be positive.

n

numeric; number of subjects recruited at end of accrual period.

accrual_exponent

numeric; exponent in sample size function f(t).

Details

Number of subjects in the study at study time t is given by f(t)=a * t^b with a = n / accrual_period. For linear recruitment, b=1. b > 1 results is slower than linear recruitment for t < accrual_period and faster than linear recruitment for t > accrual_period. b < 1 vice versa.

gscounts

Description

Design and monitoring of group sequential designs with negative binomial data.

Author(s)

Tobias Muetze <tobias.muetze@outlook.com>

Hospitalizations

Description

A dataset containing the hospitalization times of 1980 patients:

Usage

data(hospitalizations)

Format

A data frame with 2323 rows and 4 variables

Details

obrien

Description

Error spending function mimicking O'Brien & Fleming critical values

Usage

obrien(t, sig_level, ...)

Arguments

t

numeric; Non-negative information ratio

sig_level

numeric; significance level

...

optional arguments

Value

numeric

Examples

# O'Brien-Fleming-type error spending function
obrien(t = c(0.5, 1), sig_level = 0.025)

pocock

Description

Error spending function mimicking Pococks critical values

Usage

pocock(t, sig_level, ...)

Arguments

t

numeric; Non-negative information ratio

sig_level

numeric; significance level

...

optional arguments

Value

numeric

Examples

# Pocock-type error spending function
pocock(t = c(0.5, 1), sig_level = 0.025)

print.gsnb

Description

print method for instance of class gsnb

Usage

## S3 method for class 'gsnb'
print(x, ...)

Arguments

x

an object of class gsnb

...

optional arguments to print or plot methods

print.nb

Description

print method for instance of class nb

Usage

## S3 method for class 'nb'
print(x, ...)

Arguments

x

an object of class nb

...

optional arguments to print or plot methods

samplesize_from_followup

Description

Determine the sample size from a given follow-up time

Usage

samplesize_from_followup(
  max_info,
  random_ratio,
  rate1,
  rate2,
  shape,
  followup_max
)

samplesize_from_periods

Description

Determine the total sample size for given accrual and study period

Usage

samplesize_from_periods(
  max_info,
  accrual_period,
  study_period,
  random_ratio,
  rate1,
  rate2,
  shape,
  accrual_speed
)

studyperiod_from_recruit

Description

Determine the study period for given recruitment times

Usage

studyperiod_from_recruit(
  max_info,
  random_ratio,
  rate1,
  rate2,
  shape,
  t_recruit1,
  t_recruit2
)

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