VERSION 0.2.0 INCOMATIBLE WITH 0.1.x
Clinical trial related calculation: descriptive statistics, power and sample size calculation, power simulations, confidence interval, pharmacokinetics/pharmacodynamics parameters calculation.
The package is designed to perform calculations related to the planning and analysis of the results of clinical trials. The package includes the basic functions described below, as well as a few modules to perform specific calculations.
- Installation
- Basic functions
- Usage
- Submodules
- Types
- Examples
- Other
- Dependencies
- Copyrights&References
using Pkg; Pkg.add("ClinicalTrialUtilities");
or
using Pkg; Pkg.clone("https://github.com/PharmCat/ClinicalTrialUtilities.jl.git");
And then to perform tests:
Pkg.test("ClinicalTrialUtilities");
NB! Hypothesis types:
- :ea - Equality: two-sided;
- :ei - Equivalencens: two one-sided hypothesis;
- :ns - Non-Inferiority / Superiority: one-sided hypothesis, for some cases you should use two-sided hypothesis for Non-Inferiority/Superiority, you can use alpha/2 for this;
Descriptive statistics.
descriptives(data::DataFrame; sort = NaN, vars = NaN, stats = [:n, :mean, :sd, :sem, :uq, :median, :lq])::DataFrame
Sample size estimation for clinical trial.
ctsamplen(;param=:notdef, type=:notdef, group=:notdef, alpha=0.05, beta=0.2, diff=0, sd=0, a=0, b=0, k=1, logscale=false)
param (Parameter type):
- :mean - Means;
- :prop - Proportions;
- :or - Odd Ratio;
type (Hypothesis type):
- :ea - Equality;
- :ei - Equivalencens;
- :ns - Non-Inferiority / Superiority (!one-sided hypothesis!);
- :mcnm - McNemar's Equality test;
group (group num):
- :one - One sample;
- :two - Two sample, result is for one group, second group size = n * k;
alpha - Alpha (o < α < 1) (default=0.05);
beta - Beta (o < β < 1) (default=0.2); power = 1 - β;
diff - difference/equivalence margin/non-inferiority/superiority margin;
sd - Standard deviation (σ, for Means only);
a - Group A (μ₀/p₀) - Test group;
b - Group B (μ₁/p₁) - Reference group or reference value;
k - Na/Nb (after sample size estimation second group size: Na=k*Nb, only for two sample design) (default=1);
logscale - diff is log transformed for OR:
- true - diff is already in log-scale, no transformation required (default);
- false - diff is not in log-scale, will be transformed;
Power estimation for clinical trials.
ctpower(;param=:notdef, type=:notdef, group=:notdef, alpha=0.05, logdiff=false, diff=0, sd=0, a=0, b=0, n=0, k=1)
param (Parameter type):
- :mean - Means;
- :prop - Proportions;
- :or - Odd Ratio;
type (Hypothesis type):
- :ea - Equality;
- :ei - Equivalence;
- :ns - Non-Inferiority / Superiority;
- :mcnm - McNemar's Equality test;
group (group num):
- :one - one sample;
- :two - Two sample;
alpha - Alpha (0 < α < 1) (default=0.05);
n - Subjects number;
diff - difference/equivalence margin/non-inferiority/superiority margin;
sd - Standard deviation (σ, for Means only);
a - Group A (μ₀/p₀) - Test group;
b - Group B (μ₁/p₁) - Reference group or reference value;
k - Na/Nb (after sample size estimation second group size: Na=k*Nb, only for two sample design) (default=1);
logscale - diff is log transformed for OR:
- true - diff is already in log-scale, no transformation required (default);
- false - diff is not in log-scale, will be transformed;
Sample size estimation for bioequivalence study (iterative procedure).
besamplen(;alpha=0.05, beta=0.2, theta0=0.95, theta1=0.8, theta2=1.25, cv=0.0, logscale=true, design=:d2x2, method=:owenq)
alpha - Alpha (o < α < 1) (default=0.05);
beta - Beta (o < β < 1) (default=0.2); power = 1 - β;
theta0 - T/R Ratio (default=0.95);
theta1 - Lower Level (default=0.8);
theta2 - Upper level (default=1.25);
cv - coefficient of variation;
logscale - theta1, theta2, theta0: if true - make log transformation (default true);
design - trial design;
- :parallel
- :d2x2 (default)
- :d2x2x4
- :d2x4x4
- :d2x3x3
- :d2x4x2
- :d3x3
- :d3x6x3
method - calculating method: Owen's Q Function | NonCentral T | Shifted;
- :owenq (default)
- :nct
- :shifted
Power estimation for bioequivalence trials.
bepower(;alpha=0.05, theta1=0.8, theta2=1.25, theta0=0.95, cv=0.0, n=0, logscale=true, design=:d2x2, method=:owenq)
alpha - Alpha (0 < α < 1) (default=0.05);
theta1 - Lower Level (default=0.8);
theta2 - Upper level (default=1.25);
theta0 - T/R Ratio (default=0.95);
cv - coefficient of variation;
n - subject number;
logscale - theta1, theta2, theta0: if true - make log transformation (default true);
design - trial design;
- :parallel
- :d2x2 (default)
- :d2x2x4
- :d2x4x4
- :d2x3x3
- :d2x4x2
- :d3x3
- :d3x6x3
method - calculating method: Owen's Q Function | NonCentral T, Shifted;
- :owenq (default)
- :nct
- :shifted
Take CV from known CI and subject number.
cvfromci(;alpha = 0.05, theta1 = 0.8, theta2 = 1.25, n, design=:d2x2, mso=false, cvms=false)
alpha - Alpha (o < alpha < 1) (default=0.05);
beta - Beta (o < beta < 1) (default=0.2); power = 1 - beta;
theta1 - Lower Level (default=0.8);
theta2 - Upper level (default=1.25);
n - subject n;
design - trial design;
- :parallel
- :d2x2 (default)
- :d2x2x4
- :d2x4x4
- :d2x3x3
- :d2x4x2
- :d3x3
- :d3x6x3
mso
Calculate MS only
- false(default)
- true
cvms
Calculate CV and MS
- false(default)
- true
Get pooled CV from multiple sources.
pooledcv(data::DataFrame; cv=:cv, df=:df, alpha=0.05, returncv=true)::ConfInt
data::DataFrame - Dataframe with CV data
cv::Symbol - CV column in dataframe
df::Symbol - DF column in dataframe
alpha - Alpha for var/cv confidence interval.
returncv - Return CV or var:
- true - return cv
- false - return var
-
Confidence interval calculation - Doc
- oneProp
- oneMeans
- twoProp
- twoMeans
- cmh
-
Pharmacokinetics calculation - Doc
- nca
-
Simulations - Doc
- bepower
- bepowerSIM
- ctPropPower
- ctPropSampleN
- ctMeansPower
- ctMeansPowerFS
Confidence intervals
struct ConfInt
lower::Float64
upper::Float64
estimate::Float64
end
Pharmacokinetics noncompartment analysis output
struct NCA
result::DataFrame
elimination::DataFrame
settings::DataFrame
textout::String
errorlog::String
errors::Array
end
#Sample size for one proportion equality
ctsamplen(param=:prop, type=:ea, group=:one, a=0.3, b=0.5)
#Equivalence for two means
ctsamplen(param=:mean, type=:ei, group=:two, diff=0.3, sd=1, a=0.3, b=0.5)
#Odd ratio non-inferiority
ctsamplen(param=:or, type=:ns, diff=-0.1, a=0.3, b=0.5, k=2)
#Odd ratio equality
ctsamplen(param=:or, type=:ea, a=0.3, b=0.5, k=2)
#Power
ctpower(param=:mean, type=:ea, group=:one, a=1.5, b=2, sd=1,n=32, alpha=0.05)
#Bioequivalence sample size
besamplen(alpha=0.05, theta1=0.8, theta2=1.25, theta0=0.95, cv=0.15, method=:owenq)
besamplen(cv=0.20, method=:nct)
besamplen(cv=0.347, design=:parallel)
besamplen(cv=0.40)
besamplen(cv=0.347, design=:d2x2x4, method=:nct)
#Bioequivalence power for 2x2 design, default method - OwensQ
bepower(alpha=0.05, logscale=true, theta1=0.8, theta2=1.25, theta0=0.95, cv=0.2, n=20, design=:d2x2, method=:owenq)
#Same
bepower(alpha=0.05, cv=0.2, n=20, design=:d2x2)
#Bioequivalence power for cv 14%, 21 subjects, default OwensQ method, logscale false
bepower(alpha=0.1, logscale=false, theta1=-0.1, theta2=0.1, theta0=0, cv=0.14, n=21)
#Bioequivalence power for cv 14%, 21 subjects, shifted method, logscale false
bepower(alpha=0.1, logscale=false, theta1=-0.1, theta2=0.1, theta0=0, cv=0.14, n=21, method=:shifted)
#Simple notations
bepower(cv=0.4, n=35, design=:d2x4x4)
bepower(cv=0.14, n=21)
#CV from CI
cvfromci(;alpha = 0.05, theta1 = 0.9, theta2 = 1.25, n=30, design=:d2x2x4)
#Polled CV
data = DataFrame(cv = Float64[], df = Int[])
push!(data, (0.12, 12))
push!(data, (0.2, 20))
push!(data, (0.25, 30))
pooledcv(data; cv=:cv, df=:df, alpha=0.05, returncv=true)
- Owen's T function:
owensT(h::Float64,a::Float64)::Float64
- Owen's Q function (a,b always should be >= 0):
owensQ(nu, t::Float64, delta::Float64, a::Float64, b::Float64)::Float64
- Distributions
- StatsBase
- Statistics
- QuadGK
- SpecialFunctions
- Random
- Roots
- DataFrames
Clinical Trial Utilities
Author: Vladimir Arnautov aka PharmCat
Copyright © 2019 Vladimir Arnautov aka PharmCat ([email protected])
OwensQ/PowerTOST functions rewritten from https://github.com/Detlew/PowerTOST by Detlew Labes, Helmut Schuetz, Benjamin Lang
Calculation based on Chow S, Shao J, Wang H. 2008. Sample Size Calculations in Clinical Research. 2nd Ed. Chapman & Hall/CRC Biostatistics Series.
Connor R. J. 1987. Sample size for testing differences in proportions for the paired-sample design. Biometrics 43(1):207-211. page 209.
Phillips KF.Power of the Two One-Sided Tests Procedure in BioequivalenceJ Pharmacokin Biopharm. 1990;18(2):137–44. doi: 10.1007/BF01063556
Diletti D, Hauschke D, Steinijans VW.Sample Size Determination for Bioequivalence Assessment by Means of Confidence IntervalsInt J Clin Pharmacol Ther Toxicol. 1991;29(1):1–8.
Owen, D B (1965) "A Special Case of a Bivariate Non-central t-Distribution" Biometrika Vol. 52, pp.437-446.
FORTRAN code by J. Burkhardt, license GNU LGPL
D.B. Owen "Tables for computing bivariate normal Probabilities" The Annals of Mathematical Statistics, Vol. 27 (4) Dec. 1956, pp. 1075-1090
matlab code by J. Burkhardt license GNU LGPL
If you want to check and get R code - you can find some here: http://powerandsamplesize.com/Calculators/
Some ideas was taken from R project packages:
PropCIs by Ralph Scherer https://cran.r-project.org/web/packages/PropCIs/index.html
pairwiseCI by Frank Schaarschmidt, Daniel Gerhard https://CRAN.R-project.org/package=pairwiseCI
binGroup by Boan Zhang, Christopher Bilder, Brad Biggerstaff, Frank Schaarschmidt Brianna Hitt https://CRAN.R-project.org/package=binGroup
proportion by M.Subbiah, V.Rajeswaran https://CRAN.R-project.org/package=proportion
binom by Sundar Dorai-Raj https://CRAN.R-project.org/package=binom
ORCI by Libo Sun https://CRAN.R-project.org/package=ORCI
metafor by Wolfgang Viechtbauer https://cran.r-project.org/package=metafor
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