bootf2: Estimate 90% Confidence Intervals of f2 with Bootstrap...
In bootf2: Simulation and Comparison of Dissolution Profiles
Description
Usage
Arguments
Details
Value
References
Examples
Description
Main function to estimate 90% confidence intervals of f2 using
bootstrap methodology.
Usage
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bootf2(test, ref, path.in, file.in, path.out, file.out,
n.boots = 10000L, seed = 306L, digits = 2L, alpha = 0.05,
regulation = c("EMA", "FDA", "WHO","Canada", "ANVISA"),
min.points = 1L, both.TR.85 = FALSE, print.report = TRUE,
report.style = c("concise", "intermediate", "detailed"),
f2.type = c("all", "est.f2", "exp.f2", "bc.f2",
"vc.exp.f2", "vc.bc.f2"),
ci.type = c("all", "normal", "basic", "percentile",
"bca.jackknife", "bca.boot"),
quantile.type = c("all", as.character(1:9), "boot"),
jackknife.type = c("all", "nt+nr", "nt*nr", "nt=nr"),
time.unit = c("min", "h"), output.to.screen = FALSE,
sim.data.out = FALSE)
Arguments
test, ref
Data frames of dissolution profiles of test and reference
product if path.in and file.in are not specified; otherwise, they
should be character strings indicating the worksheet names of the Excel
file where the dissolution data is saved. See Input/Output in Details.
path.in, file.in, path.out, file.out
Character strings of input and
output directories and file names. See Input/Output in Details.
n.boots
An integer indicating the number of bootstrap samples.
seed
Integer seed value for reproducibility. If missing, a random
seed will be generated for reproducibility purpose.
digits
An integer indicating the decimal points for the output.
alpha
A numeric value between 0 and 1 to estimate
(1 - 2*alpha)*100 confidence interval.
regulation
Character strings indicating regulatory guidelines.
@seealso calcf2() for details on regulation rules.
min.points
An integer indicating the minimum time points to be used
to calculate f2. For conventional f2 calculation, the
default is 3, however, for bootstrap f2, the value should be
lower as there might be less time points available in certain bootstrap
samples. The default is 1. @seealso calcf2().
both.TR.85
Logical. If TRUE, and if regulation = "FDA", all
measurements up to the time points at which both test and reference
products dissolve more than 85% will be used to calculate f2.
This is the conventional, but incorrect, interpretation of the US FDA rule.
Therefore, the argument should only be set to TRUE for validation purpose
such as comparing the results from old literature that use the wrong
interpretation to calculate f2. @seealso calcf2() for details
on regulation rules.
print.report
Logical. If TRUE, a plain text report will be
produced. See Input/Output in Details.
report.style
"concise" style produces the estimators and their
confidence intervals; "intermediate" style adds a list of individual
f2s for all bootstrap samples in the end of "concise" report;
"detailed" style further adds individual bootstrap samples along with
their f2s in the end of "intermediate" report. See
Input/Output in Details.
f2.type
Character strings indicating which type of f2
estimator should be calculated. See Types of estimators in Details.
ci.type
Character strings indicating which type of confidence
interval should be estimated. See Types of confidence intervals in
Details.
quantile.type
Character strings indicating the type of percentile.
jackknife.type
Character strings indicating the type of jackknife
method. See Details.
time.unit
Character strings indicating the unit of time. It should
be either "min" for minute or "h" for hour. It is mainly used for
checking CV rules and making plot. @seealso calcf2().
output.to.screen
Logical. If TRUE, a "concise" style summary
report will be printed on screen. See Input/Output in Details.
sim.data.out
Logical. If TRUE, all individual bootstrap data
sets will be included in the output.
Details
Minimum required arguments that must be provided by the user
Arguments test and ref must be provided by the user. They should be R
data frames, with time as the first column, and all individual profiles
profiles as the rest columns. The actual names of the columns do not matter
since they will be renamed internally.
Input/Output
The dissolution data of test and reference product can either be provided as
data frames for test and ref, as explained above, or be read from an
Excel file with data of test and reference stored in separate worksheets.
In the latter case, the argument path.in, the directory where the Excel
file is, and file.in, the name of the Excel file including the file
extension .xls or .xlsx, must be provided. In such case, the argument
test and ref must be the names of the worksheets in quotation marks.
The first column of each Excel worksheet must be time, and the rest columns
are individual dissolution profiles. The first row should be column names,
such as time, unit01, unit02, ... The actual names of the columns do not
matter as they will be renamed internally.
Arguments path.out and file.out are the names of the output directory
and file. If they are not provided, but argument print.report is TRUE,
then a plain text report will be generated automatically in the current
working directory with file name test_vs_ref_TZ_YYYY-MM-DD_HHMMSS.txt,
where test and ref are data set names of test and reference, TZ is the
time zone such as CEST, YYYY-MM-DD is the numeric date format and
HHMMSS is the numeric time format for hour, minute, and second.
For a quick check, set argument output.to.screen = TRUE, a summary report
very similar to concise style report will be printed on screen.
Types of Estimators
According to Shah et al, the population f2 for the inference is
f2 = 100 - 25 log(1 + 1/P(∑(μ(Ti) - μ(Ri))^2)),
where P is the number of time points; μ(Ti)
and μ(Ri) are population mean of test and
reference product at time point i, respectively;
∑ is the summation from i = 1 to P.
Five estimators for f2 are included in the function:
The estimated f2, denoted by est.f2, is the
one written in various regulatory guidelines. It is expressed differently,
but mathematically equivalently, as
est.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2)),
where P is the number of time points;
X(Ti) and
X(Ri) are mean dissolution data at the
ith time point of random samples chosen from the test and the
reference population, respectively. Compared to the equation of population
f2 above, the only difference is that in the equation of
est.f2 the sample means of dissolution profiles replace
the population means for the approximation. In other words, a point
estimate is used for the statistical inference in practice.
The Bias-corrected f2, denoted by
bc.f2, was described in the article of
Shah et al, as
bc.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 - 1/n∑(S(Ti)^2 +
S(Ri)^2))),
where S(Ti)^2 and
S(Ri)^2 are unbiased estimates of variance at
the ith time points of random samples chosen from test and reference
population, respectively; and n is the sample size.
The variance- and bias-corrected f2, denoted by
vc.bc.f2, does not assume equal weight of
variance as bc.f2 does.
vc.bc.f2 = 100 -25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 - 1/n∑(w(Ti)
S(Ti)^2 + w(Ri)S(Ri)^2))),
where w(Ti) and w(Ri) are
weighting factors for variance of test and reference products,
respectively, which can be calculated as follows:
w(Ti) = 0.5 +
S(Ti)^2/(S(Ti)^2 + S(Ri)^2),
and
w(Ri) = 0.5 +
S(Ri)^2/(S(Ti)^2 + S(Ri)^2).
The expected f2, denoted by
exp.f2, is calculated based on the mathematical expectation of estimated
f2,
exp.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 + 1/n∑(
S(Ti)^2 + S(Ri)^2))),
using mean dissolution profiles and variance from samples for the
approximation of population values.
The variance-corrected expected f2, denoted by
vc.exp.f2, is calculated as
vc.exp.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 + 1/n∑(w(Ti)
S(Ti)^2 + w(Ri)S(Ri)^2))).
Types of Confidence Interval
The following confidence intervals are included:
The Normal interval with bias correction, denoted by normal in the
function, is estimated according to Davison and Hinkley,
f2(L,U) = f2(S) - E(B) -/+
sqrt(V(B))Z(1-α)),
where f2(L,U) are the lower and upper
limit of the confidence interval estimated from bootstrap samples;
f2(S) denotes the estimators described
above; Z(1-α) represents the inverse of standard
normal cumulative distribution function with type I error α;
E(B) and V(B) are the resampling estimates of bias
and variance calculated as
E(B) = 1/B∑(f2(b)) - f2(S) = f2(b,m) - f2(S),
and
V(B) = 1/(B-1)∑(f2(b) - f2(b,m))^2,
where B is the number of bootstrap samples;
f2(b) is the f2 estimate with
bth bootstrap sample, and f2(b,m) is the
mean value.
The basic interval, denoted by basic in the function, is estimated
according to Davison and Hinkley,
f2(L) = 2*f2(S) -
f2((B+1)(1-α)),
and
f2(U) = 2*f2(S) - f2((B+1)α),
where f2((B+1)α) and
f2((B+1)(1-α)) are the
(B+1)αth and (B+1)(1-α)th ordered resampling
estimates of f2, respectively. When (B+1)α is not
an integer, the following equation is used for interpolation,
f2((B+1)α) = f2(k) +
(Φ^(-1)(α) - Φ^(-1)(k/(B+1)))/(Φ^(-1)((k+1)/(B+1)) -
Φ^(-1)(k/(B+1)))*(f2(k+1) - f2(k)),
where k is the integer part of (B+1)α,
f2(k+1) and
f2(k) are the (k+1)th and the kth ordered resampling
estimates of f2, respectively.
The percentile intervals, denoted by percentile in the function, are
estimated using nine different types of quantiles, Type 1 to Type 9, as
summarized in Hyndman and Fan's article and implemented in R's
quantile function. Using R's boot package, program bootf2BCA
outputs a percentile interval using the equation above for interpolation.
To be able to compare the results among different programs, the same
interval, denoted by Percentile (boot) in the function, is also
included in the function.
The bias-corrected and accelerated (BCa) intervals are estimated according
to Efron and Tibshirani,
f2(L) = f2(α1),
f2(L) = f2(α2),
where f2(α1) and
f2(α2) are the
100α1th and the 100α2th percentile of the
resampling estimates of f2, respectively. Type I errors
α1 and α2 are obtained as
α1 =
Φ(z0 + (z0 + za)/(1 - a(z0 + za))),
and
α2 = Φ(z0 +
(z0 + z(1-α))/(1 - a(z0 + z(1 - α)))),
where z0 and a are called
bias-correction and acceleration, respectively.
There are different methods to estimate z0 and
a. Shah et al. used jackknife technique, denoted by
bca.jackknife in the function,
z0 =
Φ^(-1)(N(f2(b) < f2(S))/B)
and
a = (∑(f2(m) - f2(i)))^3/(6(∑(f2(m) - f2(i))^2)^(3/2)),
where N(f2(b) < f2(S)) denotes the number of
element in the set, f2(i) is the ith
jackknife statistic, f2(m) is the mean of
the jackknife statistics, and ∑ is the summation from 1 to
sample size n.
Program bootf2BCA gives a slightly different BCa interval with R's
boot package. This approach, denoted by bca.boot in the function, is
also implemented in the function for estimating the interval.
Notes on the argument jackknife.type
For any sample with size n, the jackknife estimator is obtained by
estimating the parameter for each subsample omitting the ith
observation. However, when two samples (e.g., test and reference) are
involved, there are several possible ways to do it. Assuming sample size
of test and reference are nt and nr,
the following three possibility are considered:
Estimated by removing one observation from both test and reference samples.
In this case, the prerequisite is nt=nr,
denoted by nt=nr in the function. So if there are 12 units in test and
reference data sets, there will be 12 jackknife estimators.
Estimate the jackknife for test sample while keeping the reference data
unchanged; and then estimate jackknife for reference sample while keeping
the test sample unchanged. This is denoted by nt+nr in the function.
This is the default method. So if there are 12 units in test and reference
data sets, there will be 12 + 12 = 24 jackknife estimators.
For each observation deleted from test sample, estimate jackknife for
reference sample. This is denoted by nt*nr in the function. So if there
are 12 units in test and reference data sets, there will be 12*12 = 144 jackknife estimators.
Value
A list of 3 or 5 components.
-
boot.ci: A data frame of bootstrap f2 confidence intervals.
-
boot.f2: A data frame of all individual f2 values for all
bootstrap data set.
-
boot.info: A data frame with detailed information of bootstrap for
reproducibility purpose, such as all arguments used in the function, time
points used for calculation of f2, and the number of NAs.
-
boot.summary: A data frame with descriptive statistics of the
bootstrap f2.
-
boot.t and boot.r: Lists of individual bootstrap samples for test
and reference product if sim.data.out = TRUE.
References
Shah, V. P.; Tsong, Y.; Sathe, P.; Liu, J.-P. In Vitro
Dissolution Profile Comparison—Statistics and Analysis of the
Similarity Factor, f2. Pharmaceutical Research 1998,
15 (6), 889–896. DOI: 10.1023/A:1011976615750.
Davison, A. C.; Hinkley, D. V. Bootstrap Methods and Their
Application. Cambridge University Press, 1997.
Hyndman, R. J.; Fan, Y. Sample Quantiles in Statistical Packages.
The American Statistician 1996, 50 (4), 361–365. DOI:
/10.1080/00031305.1996.10473566.
Efron, B.; Tibshirani, R. An Introduction to the Bootstrap.
Chapman & Hall, 1993.
Examples
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# time points
tp <- c(5, 10, 15, 20, 30, 45, 60)
# model.par for reference with low variability
par.r <- list(fmax = 100, fmax.cv = 3, mdt = 15, mdt.cv = 14,
tlag = 0, tlag.cv = 0, beta = 1.5, beta.cv = 8)
# simulate reference data
dr <- sim.dp(tp, model.par = par.r, seed = 100, plot = FALSE)
# model.par for test
par.t <- list(fmax = 100, fmax.cv = 3, mdt = 12.29, mdt.cv = 12,
tlag = 0, tlag.cv = 0, beta = 1.727, beta.cv = 9)
# simulate test data with low variability
dt <- sim.dp(tp, model.par = par.t, seed = 100, plot = FALSE)
# bootstrap. to reduce test run time, n.boots of 100 was used in the example.
# In practice, it is recommended to use n.boots of 5000--10000.
# Set `output.to.screen = TRUE` to view the result on screen
d <- bootf2(dt$sim.disso, dr$sim.disso, n.boots = 100, print.report = FALSE)
bootf2 documentation built on Aug. 25, 2021, 5:07 p.m.
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Description Usage Arguments Details Value References Examples
Description
Main function to estimate 90% confidence intervals of f2 using bootstrap methodology.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 | bootf2(test, ref, path.in, file.in, path.out, file.out,
n.boots = 10000L, seed = 306L, digits = 2L, alpha = 0.05,
regulation = c("EMA", "FDA", "WHO","Canada", "ANVISA"),
min.points = 1L, both.TR.85 = FALSE, print.report = TRUE,
report.style = c("concise", "intermediate", "detailed"),
f2.type = c("all", "est.f2", "exp.f2", "bc.f2",
"vc.exp.f2", "vc.bc.f2"),
ci.type = c("all", "normal", "basic", "percentile",
"bca.jackknife", "bca.boot"),
quantile.type = c("all", as.character(1:9), "boot"),
jackknife.type = c("all", "nt+nr", "nt*nr", "nt=nr"),
time.unit = c("min", "h"), output.to.screen = FALSE,
sim.data.out = FALSE)
|
Arguments
test, ref |
Data frames of dissolution profiles of test and reference
product if |
path.in, file.in, path.out, file.out |
Character strings of input and output directories and file names. See Input/Output in Details. |
n.boots |
An integer indicating the number of bootstrap samples. |
seed |
Integer seed value for reproducibility. If missing, a random seed will be generated for reproducibility purpose. |
digits |
An integer indicating the decimal points for the output. |
alpha |
A numeric value between 0 and 1 to estimate (1 - 2*alpha)*100 confidence interval. |
regulation |
Character strings indicating regulatory guidelines.
@seealso |
min.points |
An integer indicating the minimum time points to be used
to calculate f2. For conventional f2 calculation, the
default is 3, however, for bootstrap f2, the value should be
lower as there might be less time points available in certain bootstrap
samples. The default is 1. @seealso |
both.TR.85 |
Logical. If |
print.report |
Logical. If |
report.style |
|
f2.type |
Character strings indicating which type of f2 estimator should be calculated. See Types of estimators in Details. |
ci.type |
Character strings indicating which type of confidence interval should be estimated. See Types of confidence intervals in Details. |
quantile.type |
Character strings indicating the type of percentile. |
jackknife.type |
Character strings indicating the type of jackknife method. See Details. |
time.unit |
Character strings indicating the unit of time. It should
be either |
output.to.screen |
Logical. If |
sim.data.out |
Logical. If |
Details
Minimum required arguments that must be provided by the user
Arguments test and ref must be provided by the user. They should be R
data frames, with time as the first column, and all individual profiles
profiles as the rest columns. The actual names of the columns do not matter
since they will be renamed internally.
Input/Output
The dissolution data of test and reference product can either be provided as
data frames for test and ref, as explained above, or be read from an
Excel file with data of test and reference stored in separate worksheets.
In the latter case, the argument path.in, the directory where the Excel
file is, and file.in, the name of the Excel file including the file
extension .xls or .xlsx, must be provided. In such case, the argument
test and ref must be the names of the worksheets in quotation marks.
The first column of each Excel worksheet must be time, and the rest columns
are individual dissolution profiles. The first row should be column names,
such as time, unit01, unit02, ... The actual names of the columns do not
matter as they will be renamed internally.
Arguments path.out and file.out are the names of the output directory
and file. If they are not provided, but argument print.report is TRUE,
then a plain text report will be generated automatically in the current
working directory with file name test_vs_ref_TZ_YYYY-MM-DD_HHMMSS.txt,
where test and ref are data set names of test and reference, TZ is the
time zone such as CEST, YYYY-MM-DD is the numeric date format and
HHMMSS is the numeric time format for hour, minute, and second.
For a quick check, set argument output.to.screen = TRUE, a summary report
very similar to concise style report will be printed on screen.
Types of Estimators
According to Shah et al, the population f2 for the inference is
f2 = 100 - 25 log(1 + 1/P(∑(μ(Ti) - μ(Ri))^2)),
where P is the number of time points; μ(Ti) and μ(Ri) are population mean of test and reference product at time point i, respectively; ∑ is the summation from i = 1 to P.
Five estimators for f2 are included in the function:
The estimated f2, denoted by est.f2, is the one written in various regulatory guidelines. It is expressed differently, but mathematically equivalently, as
est.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2)),
where P is the number of time points; X(Ti) and X(Ri) are mean dissolution data at the ith time point of random samples chosen from the test and the reference population, respectively. Compared to the equation of population f2 above, the only difference is that in the equation of est.f2 the sample means of dissolution profiles replace the population means for the approximation. In other words, a point estimate is used for the statistical inference in practice.
The Bias-corrected f2, denoted by bc.f2, was described in the article of Shah et al, as
bc.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 - 1/n∑(S(Ti)^2 + S(Ri)^2))),
where S(Ti)^2 and S(Ri)^2 are unbiased estimates of variance at the ith time points of random samples chosen from test and reference population, respectively; and n is the sample size.
The variance- and bias-corrected f2, denoted by vc.bc.f2, does not assume equal weight of variance as bc.f2 does.
vc.bc.f2 = 100 -25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 - 1/n∑(w(Ti) S(Ti)^2 + w(Ri)S(Ri)^2))),
where w(Ti) and w(Ri) are weighting factors for variance of test and reference products, respectively, which can be calculated as follows:
w(Ti) = 0.5 + S(Ti)^2/(S(Ti)^2 + S(Ri)^2),
and
w(Ri) = 0.5 + S(Ri)^2/(S(Ti)^2 + S(Ri)^2).
The expected f2, denoted by exp.f2, is calculated based on the mathematical expectation of estimated f2,
exp.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 + 1/n∑( S(Ti)^2 + S(Ri)^2))),
using mean dissolution profiles and variance from samples for the approximation of population values.
The variance-corrected expected f2, denoted by vc.exp.f2, is calculated as
vc.exp.f2 = 100 - 25 log(1 + 1/P(∑(X(Ti) - X(Ri))^2 + 1/n∑(w(Ti) S(Ti)^2 + w(Ri)S(Ri)^2))).
Types of Confidence Interval
The following confidence intervals are included:
The Normal interval with bias correction, denoted by
normalin the function, is estimated according to Davison and Hinkley,f2(L,U) = f2(S) - E(B) -/+ sqrt(V(B))Z(1-α)),
where f2(L,U) are the lower and upper limit of the confidence interval estimated from bootstrap samples; f2(S) denotes the estimators described above; Z(1-α) represents the inverse of standard normal cumulative distribution function with type I error α; E(B) and V(B) are the resampling estimates of bias and variance calculated as
E(B) = 1/B∑(f2(b)) - f2(S) = f2(b,m) - f2(S),
and
V(B) = 1/(B-1)∑(f2(b) - f2(b,m))^2,
where B is the number of bootstrap samples; f2(b) is the f2 estimate with bth bootstrap sample, and f2(b,m) is the mean value.
The basic interval, denoted by
basicin the function, is estimated according to Davison and Hinkley,f2(L) = 2*f2(S) - f2((B+1)(1-α)),
and
f2(U) = 2*f2(S) - f2((B+1)α),
where f2((B+1)α) and f2((B+1)(1-α)) are the (B+1)αth and (B+1)(1-α)th ordered resampling estimates of f2, respectively. When (B+1)α is not an integer, the following equation is used for interpolation,
f2((B+1)α) = f2(k) + (Φ^(-1)(α) - Φ^(-1)(k/(B+1)))/(Φ^(-1)((k+1)/(B+1)) - Φ^(-1)(k/(B+1)))*(f2(k+1) - f2(k)),
where k is the integer part of (B+1)α, f2(k+1) and f2(k) are the (k+1)th and the kth ordered resampling estimates of f2, respectively.
The percentile intervals, denoted by
percentilein the function, are estimated using nine different types of quantiles, Type 1 to Type 9, as summarized in Hyndman and Fan's article and implemented inR'squantilefunction. UsingR'sbootpackage, programbootf2BCAoutputs a percentile interval using the equation above for interpolation. To be able to compare the results among different programs, the same interval, denoted byPercentile (boot)in the function, is also included in the function.The bias-corrected and accelerated (BCa) intervals are estimated according to Efron and Tibshirani,
f2(L) = f2(α1),
f2(L) = f2(α2),
where f2(α1) and f2(α2) are the 100α1th and the 100α2th percentile of the resampling estimates of f2, respectively. Type I errors α1 and α2 are obtained as
α1 = Φ(z0 + (z0 + za)/(1 - a(z0 + za))),
and
α2 = Φ(z0 + (z0 + z(1-α))/(1 - a(z0 + z(1 - α)))),
where z0 and a are called bias-correction and acceleration, respectively.
There are different methods to estimate z0 and a. Shah et al. used jackknife technique, denoted by
bca.jackknifein the function,z0 = Φ^(-1)(N(f2(b) < f2(S))/B)
and
a = (∑(f2(m) - f2(i)))^3/(6(∑(f2(m) - f2(i))^2)^(3/2)),
where N(f2(b) < f2(S)) denotes the number of element in the set, f2(i) is the ith jackknife statistic, f2(m) is the mean of the jackknife statistics, and ∑ is the summation from 1 to sample size n.
Program
bootf2BCAgives a slightly different BCa interval withR'sbootpackage. This approach, denoted bybca.bootin the function, is also implemented in the function for estimating the interval.
Notes on the argument jackknife.type
For any sample with size n, the jackknife estimator is obtained by estimating the parameter for each subsample omitting the ith observation. However, when two samples (e.g., test and reference) are involved, there are several possible ways to do it. Assuming sample size of test and reference are nt and nr, the following three possibility are considered:
Estimated by removing one observation from both test and reference samples. In this case, the prerequisite is nt=nr, denoted by
nt=nrin the function. So if there are 12 units in test and reference data sets, there will be 12 jackknife estimators.Estimate the jackknife for test sample while keeping the reference data unchanged; and then estimate jackknife for reference sample while keeping the test sample unchanged. This is denoted by
nt+nrin the function. This is the default method. So if there are 12 units in test and reference data sets, there will be 12 + 12 = 24 jackknife estimators.For each observation deleted from test sample, estimate jackknife for reference sample. This is denoted by
nt*nrin the function. So if there are 12 units in test and reference data sets, there will be 12*12 = 144 jackknife estimators.
Value
A list of 3 or 5 components.
-
boot.ci: A data frame of bootstrap f2 confidence intervals. -
boot.f2: A data frame of all individual f2 values for all bootstrap data set. -
boot.info: A data frame with detailed information of bootstrap for reproducibility purpose, such as all arguments used in the function, time points used for calculation of f2, and the number ofNAs. -
boot.summary: A data frame with descriptive statistics of the bootstrap f2. -
boot.tandboot.r: Lists of individual bootstrap samples for test and reference product ifsim.data.out = TRUE.
References
Shah, V. P.; Tsong, Y.; Sathe, P.; Liu, J.-P. In Vitro Dissolution Profile Comparison—Statistics and Analysis of the Similarity Factor, f2. Pharmaceutical Research 1998, 15 (6), 889–896. DOI: 10.1023/A:1011976615750.
Davison, A. C.; Hinkley, D. V. Bootstrap Methods and Their Application. Cambridge University Press, 1997.
Hyndman, R. J.; Fan, Y. Sample Quantiles in Statistical Packages. The American Statistician 1996, 50 (4), 361–365. DOI: /10.1080/00031305.1996.10473566.
Efron, B.; Tibshirani, R. An Introduction to the Bootstrap. Chapman & Hall, 1993.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | # time points
tp <- c(5, 10, 15, 20, 30, 45, 60)
# model.par for reference with low variability
par.r <- list(fmax = 100, fmax.cv = 3, mdt = 15, mdt.cv = 14,
tlag = 0, tlag.cv = 0, beta = 1.5, beta.cv = 8)
# simulate reference data
dr <- sim.dp(tp, model.par = par.r, seed = 100, plot = FALSE)
# model.par for test
par.t <- list(fmax = 100, fmax.cv = 3, mdt = 12.29, mdt.cv = 12,
tlag = 0, tlag.cv = 0, beta = 1.727, beta.cv = 9)
# simulate test data with low variability
dt <- sim.dp(tp, model.par = par.t, seed = 100, plot = FALSE)
# bootstrap. to reduce test run time, n.boots of 100 was used in the example.
# In practice, it is recommended to use n.boots of 5000--10000.
# Set `output.to.screen = TRUE` to view the result on screen
d <- bootf2(dt$sim.disso, dr$sim.disso, n.boots = 100, print.report = FALSE)
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