### Example: Concordance Probability Estimate for Cox Model

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Demonstrates how to use the `coxphCPE` function with the `pbc` dataset. It fits a Cox model and then calculates the CPE. This example is not run by default.

```R
library(survival)
  data(pbc)
  pbcfit <- coxph(Surv(time, status==2) ~ trt + log(copper), pbc,
    subset=(trt>0 & copper>0))
  coxphCPE(pbcfit)
```

--------------------------------

### Example: Explained Relative Risk for Cox Model (Subset of Covariates)

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Demonstrates calculating the explained relative risk (ERR) for a subset of covariates (age and ECOG performance status) using `coxphERR`. The indices of the covariates are provided.

```R
library(survival)
 ovarianfit <- coxph(Surv(futime, fustat) ~ age + resid.ds + rx + 
                                           ecog.ps, data=ovarian,x=T) 
 # Compute the contribution of age and ECOG performance status to
 # the explained relative risk. Age and ECOG performance status are 
 # the first and fourth covariates in the model.
 coxphERR(ovarianfit, c(1,4))
```

--------------------------------

### Example: Explained Relative Risk for Cox Model (Full Model)

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Demonstrates calculating the full explained relative risk (ERR) and its standard error using `coxphERR` with the `ovarian` dataset. The model is fitted with `x=T`.

```R
library(survival)
 ovarianfit <- coxph(Surv(futime, fustat) ~ age + resid.ds + rx + 
                                           ecog.ps, data=ovarian,x=T) 
 # Compute the explained relative risk (ERR) and
 # its standard error (se.ERR) for the full model.
 coxphERR(ovarianfit)
```

--------------------------------

### Jonckheere-Terpstra Test Examples

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Demonstrates the jonckheere.test function for ordered alternatives, including handling tied data and specifying permutations. Requires no specific imports.

```R
set.seed(1234)
g <- rep(1:5, rep(10,5))
x <- rnorm(50)
jonckheere.test(x+0.3*g, g)
x[1:2] <- mean(x[1:2]) # tied data
jonckheere.test(x+0.3*g, g)
jonckheere.test(x+0.3*g, g, nperm=5000)
```

--------------------------------

### Normal Data Group Sequential Design Example

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Example of using gsdesign.normal for normal data. The first call uses a two-sided alternative and specifies a futility boundary, while the second uses a one-sided alternative with a lower significance level.

```R
gsdesign.normal(1:4/4, 0.25, sig.level=0.05, alt="t", delta.fb=0.5)
  gsdesign.normal(1:4/4, 0.25, sig.level=0.025, alt="o", delta.fb=0.5)
```

--------------------------------

### Get Boundary for Sequential Designs

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Determines the boundary for sequential clinical trial designs. This function is used internally and not typically called directly by the user.

```R
getBoundary(pLo, pHi, n, cP0=0.1, cP1=0.9, ngrid=6, niter=10, delta=0,
    priorityNull=TRUE)
```

--------------------------------

### Initialize clinfun Package

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Loads the clinfun library. Ensure this is run before using any functions from the package.

```r
library(clinfun)
```

--------------------------------

### Plotting and Cox Proportional Hazards Model with clinfun

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Demonstrates plotting survival data and fitting a Cox proportional hazards model using the survival package, followed by using coxphQuantile from clinfun for quantile estimation.

```R
library(survival)
data(pbc)
pbcfit <- coxph(Surv(time, status==2) ~ trt + log(copper), pbc,
                      subset=(trt>0 & copper>0)) 
plot(log(pbc$copper[pbc$trt>0 & pbc$copper>0]), pbc$time[pbc$trt>0 &
  pbc$copper>0], pch=c("o","x")[1+pbc$status[pbc$trt>0 & pbc$copper>0]], 
  xlab="log Copper", ylab="Survival time")
coxphQuantile(pbcfit, c(2.5,6), whichx=2, otherx=1)
coxphQuantile(pbcfit, c(2.5,6), p=0.75, whichx=2, otherx=2, col=2)
```

--------------------------------

### Calculate Selection Probabilities with pselect

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Demonstrates various uses of the pselect function for calculating selection probabilities under different scenarios, including type I error, differing probabilities, and unequal sample sizes.

```r
  # selection when no diffrence i.e. type I error
  pselect(18, c(0.2, 0.2, 0.2))
  # selection probability
  pselect(18, c(0.2, 0.2, 0.4))
  pselect(26, c(0.2, 0.2, 0.4), min.diff=2, min.resp=3)
  # unequal sample size case
  pselect(c(27,54), c(0.5, 0.65), min.diff=0.05)
  # unequal sample size case
  pselect(c(27,54), c(0.5, 0.65), min.diff=0.05, min.resp=c(14,27))
```

--------------------------------

### Calculate Two-Stage Simon Design Parameters

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Defines parameters for a two-stage Simon design, specifying null and alternative probabilities, and type I/II error rates. Use this to set up the trial's operating characteristics.

```r
# Specify the parameters and constraints
trial = ph2simon(0.05, 0.2, 0.1, 0.1)

# Print
trial
```

--------------------------------

### print.futilbdry

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Prints the results of a futility boundary calculation.

```APIDOC
## print.futilbdry

### Description
Prints the results of a futility boundary calculation.

### Usage
```R
print(x, ...)
```

### Arguments
- `x`: Object returned by the function `futilbdry`.
- `...`: Additional arguments to print.
```

--------------------------------

### Simulate Two-Stage Phase II Designs

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Simulates two-stage Phase II clinical trial designs. Use to explore different scenarios for trial parameters.

```R
ph2simon(0.2, 0.4, 0.1, 0.1)
  ph2simon(0.2, 0.35, 0.05, 0.05)
  ph2simon(0.2, 0.35, 0.05, 0.05, nmax=150)
```

--------------------------------

### Admissible Two-Stage Design Options

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Lists admissible two-stage design options based on the output of ph2simon. Use to find designs that balance efficacy and toxicity considerations.

```R
  oo = ph2simon(0.5, 0.7, 0.05, 0.1)
  twostage.admissible(oo)
```

--------------------------------

### futilbdry

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Computes a stopping rule and its operating characteristics for futility monitoring.

```APIDOC
## futilbdry

### Description
Computes a stopping rule and its operating characteristics for futility monitoring.

### Usage
```R
futilbdry(rLo, rHi, n, size=0.1, power=0.9, ngrid=3, niter=10, delta=0.5)
```

### Arguments
- `rLo` (numeric): Baseline (null) response rate.
- `rHi` (numeric): Desirable response rate. Stop when it is too unlikely.
- `n` (numeric vector): Vector of times (sample size) when response is monitored.
- `size` (numeric, optional): Probability of calling drug effective if response rate is `rLo`. Defaults to 0.1.
- `power` (numeric, optional): Probability of calling drug effective if response rate is `rHi`. Defaults to 0.9.
- `ngrid` (integer, optional): The number of response rates from `rLo` to `rHi` for which the operating characteristics are computed. Defaults to 3.
- `niter` (integer, optional): The number of iterations run to obtain the boundary. Defaults to 10.
- `delta` (numeric, optional): Power determining the shape of the boundary. Should be between 0 and 0.5. Defaults to 0.5.

### Details
For futility monitoring, instead two sets of probabilities - `pstop` and `peffective` - are given corresponding to the probability of stopping early for futility and probability of finishing the trial and declaring it a success. Note that `peffective` is the complement of `pcross` in toxicity monitoring. The futility boundary can have a -1 in earlier looks which means that even zero responses is not sufficient for stopping at that look. Default values of `delta` for futility stopping is 0.5.
```

--------------------------------

### Sample Size Calculation using Casagrande, Pike, Smith (CPS.ssize)

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates sample size using the CPS approximation, which is suitable for small differences between proportions (large sample sizes) and provides instantaneous results.

```R
CPS.ssize(p1, p2, alpha=0.05, power=0.8, r=1)
```

--------------------------------

### Calculate Single-Stage Trial Parameters

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Defines and prints the parameters for a single-stage clinical trial. This function is used for simpler trial designs.

```r
# Specify the parameters and constraints & print
ph2single(0.4, 0.6, 0.1, 0.1)
```

--------------------------------

### ktau

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates Kendall's tau-b estimate, providing a faster algorithm than the default cor() method.

```APIDOC
## Kendall's tau-b estimate

### Description
Calculates the Kendall's tau-b.

### Usage
```R
ktau(x, y)
```

### Arguments
`x` |  first variable  
---|---
`y` |  second variable  

### Details
`ktau` computes the same quantity as `cor(x, y, method="kendall")`. It uses a faster algorithm than pairwise comparisons used by `cor`.

### Value
`ktau` returns Kendall's tau-b.

### Examples
```R
set.seed(1234)
x <- rnorm(10000); y <- x+rnorm(10000)
cor(x, y, method="k")
clinfun:::ktau(x,y)
```
```

--------------------------------

### print.toxbdry

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Prints the results of a toxicity boundary calculation.

```APIDOC
## print.toxbdry

### Description
Prints the results of a toxicity boundary calculation.

### Usage
```R
print(x, ...)
```

### Arguments
- `x`: Object returned by the function `toxbdry`.
- `...`: Additional arguments to print.
```

--------------------------------

### Kendall's Tau-b Estimate

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates Kendall's tau-b, an alternative to cor(x, y, method="kendall"). Uses a faster algorithm than pairwise comparisons. Requires no specific imports.

```R
set.seed(1234)
x <- rnorm(10000); y <- x+rnorm(10000)
cor(x, y, method="k")
clinfun:::ktau(x,y)
```

--------------------------------

### Obtain Admissible Two-Stage Simon Design

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Calculates and returns an admissible design for a two-stage Simon trial based on predefined parameters. This is used to find optimal trial configurations.

```r
# Obtain admissible design
twostage.admissible(trial)
```

--------------------------------

### Futility Boundary Calculation

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Computes a stopping rule for futility monitoring. Requires baseline and desirable response rates, and sample sizes for monitoring. The 'delta' parameter influences the boundary shape.

```R
futilbdry(rLo, rHi, n, size=0.1, power=0.9, ngrid=3, niter=10, delta=0.5)
```

--------------------------------

### ph2simon

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates Optimal and Minimax 2-stage Phase II clinical trial designs based on Simon's methodology.

```APIDOC
## Simon's 2-stage Phase II design

### Description
Calculates Optimal and Minimax 2-stage Phase II designs given by Richard Simon 

### Usage
```R
ph2simon(pu, pa, ep1, ep2, nmax=100)
## S3 method for class 'ph2simon'
print(x, ...)
## S3 method for class 'ph2simon'
plot(x, ...)
```

### Arguments
`pu` |  unacceptable response rate; baseline response rate that needs to be exceeded for treatment to be deemed promising  
---|---
`pa` |  response rate that is desirable; should be larger than pu  
`ep1` |  threshold for the probability of declaring drug desirable under pu (target type 1 error rate); between 0 and 1  
`ep2` |  threshold for the probability of rejecting the drug under pa (target type 2 error rate); between 0 and 1  
`nmax` |  maximum total sample size (default 100; can be at most 1000)  
`x` |  object returned by ph2simon  
`...` |  arguments to be passed onto plot and print commands called within  

### Value
`ph2simon` returns a list with pu, pa, alpha, beta and nmax as above and:
`out` |  matrix of best 2 stage designs for each value of total sample size n. The 6 columns in the matrix are:  |  r1 |  number of responses needed to exceeded in first stage   
---|---
n1 |  number of subjects treated in first stage   
r |  number of responses needed to exceeded at the end of trial   
n |  total number of subjects to be treated in the trial   
EN(pu) |  expected number pf patients in the trial under pu   
PET(pu) |  probability of stopping after the first stage under pu   
Trial is stopped early if <= r1 responses are seen in the first stage and treatment is considered desirable only when >r responses seen. 

### Methods (by generic)
  * `print(ph2simon)`: formats and returns the minimax, optimal and any admissible designs. 
  * `plot(ph2simon)`: plots the expected sample size against the maximum sample size as in Jung et al., 2001 
```

--------------------------------

### Simon's 2-stage Phase II Design

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates Optimal and Minimax 2-stage Phase II designs. Requires unacceptable and desirable response rates, and thresholds for type I and II error rates. An optional maximum sample size can be specified.

```R
ph2simon(pu, pa, ep1, ep2, nmax=100)
```

--------------------------------

### Sample Size Calculation for Fisher's Exact Test (fe.ssize)

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates sample size for comparing two binomial proportions using Fisher's exact test. It returns a matrix with sample sizes for both CPS and Fisher's exact methods.

```R
fe.ssize(p1, p2, alpha=0.05, power=0.8, r=1, npm=5, mmax=1000)
```

--------------------------------

### Inference for Two-Stage Binary Response Design

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates p-value, UMVUE, and confidence intervals for data from a two-stage design. Use for hypothesis testing and estimation after a study.

```R
twostage.inference(x, r1, n1, n, pu, alpha=0.05)
```

--------------------------------

### Plot Two-Stage Simon Design

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Generates a plot visualizing the operating characteristics of a two-stage Simon design. This helps in understanding the trial's performance.

```r
# Plot
plot(trial)
```

--------------------------------

### Group Sequential Design - Constant Boundary

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates parameters for a group sequential design with a constant efficacy boundary. It requires the fraction of information and the desired error probabilities.

```R
gsd.bdryconstant(ifrac, eprob = 0.05, delta = 0.5,
    alternative = c("two.sided", "one.sided"), tol = 0.00001, ...)
```

--------------------------------

### Group Sequential Designs

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Functions to calculate sample size for group sequential designs.

```APIDOC
## Group Sequential Designs

### Description
Functions to calculate sample size for group sequential designs 

```

--------------------------------

### Group Sequential Design - Drift Both Efficacy and Futility

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates parameters for a group sequential design considering drift in both efficacy and futility. This is useful for complex trial designs.

```R
gsd.drift.both(ifrac, delta.eb, delta.fb, sig.level = 0.05, pow=0.8,
    alternative = c("two.sided", "one.sided"), tol = 0.00001, ...)
```

--------------------------------

### Create Smoothed MRC Object

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Constructs a smoothed MRC object, likely for use in non-parametric modeling. Requires coefficients, design matrix, sample sizes, and a bandwidth parameter.

```R
smmrcobj(coefs, xmat, n, nn, bw)
```

--------------------------------

### permlogrank

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Performs a small sample survival difference test using permutation reference distributions, serving as the permutation version of survdiff.

```APIDOC
## Permutation version of survdiff

### Description
Small sample survdiff using permutation reference distributions.

### Usage
```R
permlogrank(formula, data, subset, na.action, rho=0, nperm=5000)
```

### Arguments
`nperm` |  number of permutations for the reference distribution  
---|---
`formula`, `data`, `subset`, `na.action`, `rho` |  see survdiff for details  

### Details
`permlogrank` is the permutation version of k-sample survdiff. see survdiff in survival package for details.

### References
Heller G, Venkatraman ES. (1996). Resampling procedures to compare two survival distributions in the presence of right censored data. _Biometrics_ 52:1204-1213.
```

--------------------------------

### Trial Designs Based On Fisher's Exact Test

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Functions to calculate sample size, effect size, and power based on Fisher's exact test and other related methods.

```APIDOC
## Trial Designs Based On Fisher's Exact Test

### Description
Calculates sample size, effect size and power based on Fisher's exact test

### Usage
```
fe.ssize(p1, p2, alpha=0.05, power=0.8, r=1, npm=5, mmax=1000)
CPS.ssize(p1, p2, alpha=0.05, power=0.8, r=1)
fe.mdor(ncase, ncontrol, pcontrol, alpha=0.05, power=0.8)
mdrr(n, cprob, presp, alpha=0.05, power=0.8, niter=15)
fe.power(d, n1, n2, p1, alpha = 0.05)
or2pcase(pcontrol, OR)

```

### Arguments
`p1` |  response rate of standard treatment  
---|---
`p2` |  response rate of experimental treatment  
`d` |  difference = p2-p1  
`pcontrol` |  control group probability  
`n1` |  sample size for the standard treatment group  
`n2` |  sample size for the standard treatment group  
`ncontrol` |  control group sample size  
`ncase` |  case group sample size  
`alpha` |  size of the test (default 5%)  
`power` |  power of the test (default 80%)  
`r` |  treatments are randomized in 1:r ratio (default r=1)  
`npm` |  the sample size program searches for sample sizes in a range (+/- npm) to get the exact power  
`mmax` |  the maximum group size for which exact power is calculated  
`n` |  total number of subjects  
`cprob` |  proportion of patients who are marger positive  
`presp` |  probability of response in all subjects  
`niter` |  number of iterations in binary search  
`OR` |  odds-ratio  

### Details
CPS.ssize returns Casagrande, Pike, Smith sample size which is a very close to the exact. Use this for small differences p2-p1 (hence large sample sizes) to get the result instantaneously. 
Since Fisher's exact test orders the tables by their probability the test is naturally two-sided. 
fe.ssize return a 2x3 matrix with CPS and Fisher's exact sample sizes with power. 
fe.mdor return a 3x2 matrix with Schlesselman, CPS and Fisher's exact minimum detectable odds ratios and the corresponding power. 
fe.power returns a Kx2 matrix with probabilities (p2) and exact power. 
mdrr computes the minimum detectable P(resp|marker+) and P(resp|marker-) configurations when total sample size (n), P(response) (presp) and proportion of subjects who are marker positive (cprob) are specified. 
or2pcase give the probability of disease among the cases for a given probability of disease in controls (pcontrol) and odds-ratio (OR). 

### References
Casagrande, JT., Pike, MC. and Smith PG. (1978). An improved approximate formula for calculating sample sizes for comparing two binomial distributions. _Biometrics_ 34, 483-486. 
Fleiss, J. (1981) Statistical Methods for Rates and Proportions. 
Schlesselman, J. (1987) Re: Smallest Detectable Relative Risk With Multiple Controls Per Case. _Am. J. Epi._

```

--------------------------------

### Create MRC Object

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Constructs an MRC (Marginal Regression Coefficients) object from coefficients, design matrix, and sample sizes. This is an internal function.

```R
mrcobj(coefs, xmat, n, nn)
```

--------------------------------

### Exact Null Distribution

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the exact null distribution for a given group size and keyword.

```R
exactNull(gsize, kw)
```

--------------------------------

### Calculate Probability of Selection Under Pick the Winner Rule

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the probability of selecting the treatment with the higher response rate using the pick the winner rule. Can handle single or unequal sample sizes per arm.

```R
pselect(n, p, min.diff=NULL, min.resp=NULL)
```

--------------------------------

### bdrycross.prob

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the probability of boundary crossing for futility monitoring.

```APIDOC
## bdrycross.prob

### Description
Computes the probability of boundary crossing for futility monitoring.

### Usage
```R
bdrycross.prob(n, r, ptox)
```

### Arguments
- `n` (numeric vector): Vector of times (sample size) when toxicity/response is monitored.
- `r` (numeric vector): Vector of maximum acceptable toxicities (non-responders for futility) corresponding to `n`.
- `ptox` (numeric vector): The toxicity rates for which the operating characteristics are calculated. For futility this is the non-response rate.
```

--------------------------------

### Toxicity Boundary Calculation

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Computes a stopping rule for toxicity monitoring based on repeated significance testing. Requires acceptable and unacceptable toxicity rates, and sample sizes for monitoring.

```R
toxbdry(pLo, pHi, n, cP0=0.1, cP1=0.9, ngrid=6, niter=10, delta=0,
          priority=c("null","alt"))
```

--------------------------------

### Group Sequential Design Functions for Clinfun

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

These functions are used to design group sequential clinical trials. They allow specification of information fractions, treatment effects, and desired statistical properties like significance level and power. Use these for planning trials where interim analyses are planned.

```R
gsdesign.binomial(ifrac, pC, pE, r = 1, sig.level = 0.05, power = 0.8,
  delta.eb=0.5, delta.fb = NULL, alternative = c("two.sided",
  "one.sided"), pooled.variance = FALSE, CPS = TRUE, tol=0.00001, ...)
gsdesign.normal(ifrac, delta, sd = 1, r = 1, sig.level = 0.05,
  power = 0.8, delta.eb = 0.5, delta.fb = NULL, alternative = 
  c("two.sided", "one.sided"), tol=0.00001, ...)
gsdesign.survival(ifrac, haz.ratio, r = 1, sig.level = 0.05, 
  power = 0.8, delta.eb = 0.5, delta.fb = NULL, alternative = 
  c("two.sided", "one.sided"), tol=0.00001, ...)
```

--------------------------------

### Recalculate Admissible Two-Stage Simon Design

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Redefines parameters for a two-stage Simon design and then obtains an admissible design. This is useful for exploring different parameter settings.

```r
# Specify the parameters and constraints
trial = ph2simon(0.25, 0.45, 0.05, 0.1)

# Obtain admissible design
twostage.admissible(trial)
```

--------------------------------

### Permutation Version of survdiff

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Performs a small sample survival difference test using permutation reference distributions. It is the permutation version of k-sample survdiff from the survival package. Requires formula and data inputs, with optional arguments for subset, na.action, rho, and nperm.

```R
permlogrank(formula, data, subset, na.action, rho=0, nperm=5000)
```

--------------------------------

### Two-stage Boundary Operating Characteristics

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the operating characteristics of a two-stage boundary. Requires parameters for unacceptable and desirable response rates, thresholds, and sample sizes.

```R
oc.twostage.bdry(pu, pa, r1, n1, r, n)
```

--------------------------------

### Convert Odds Ratio to Probability of Case Disease (or2pcase)

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Converts an odds ratio to the probability of disease among cases, given the probability of disease in controls.

```R
or2pcase(pcontrol, OR)
```

--------------------------------

### Calculate Proportion Power Test Sample Size

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Performs a power and sample size calculation for a two-sample proportion test. Specify the proportions under the null and alternative hypotheses, and the desired power.

```r
power.prop.test(p1 = 0.2, p2 = 0.3, power = 0.8)
```

--------------------------------

### toxbdry

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Computes a stopping rule and its operating characteristics for toxicity monitoring based on repeated significance testing.

```APIDOC
## toxbdry

### Description
Computes a stopping rule and its operating characteristics for toxicity monitoring based repeated significance testing.

### Usage
```R
toxbdry(pLo, pHi, n, cP0=0.1, cP1=0.9, ngrid=6, niter=10, delta=0,
          priority=c("null","alt"))
```

### Arguments
- `pLo` (numeric): The toxicity rate that is acceptable.
- `pHi` (numeric): The toxicity rate that is too high and hence unacceptable.
- `n` (numeric vector): Vector of times (sample size) when toxicity is monitored.
- `cP0` (numeric, optional): Boundary crossing probability under `pLo` (type I error). Defaults to 0.1.
- `cP1` (numeric, optional): Boundary crossing probability under `pHi` (power). Defaults to 0.9.
- `ngrid` (integer, optional): The number of toxicity rates from `pLo` to `pHi` for which the operating characteristics are computed. Defaults to 6.
- `niter` (integer, optional): The number of iterations run to obtain the boundary. Defaults to 10.
- `delta` (numeric, optional): Power determining the shape of the boundary. Should be between 0 (default) and 0.5. Defaults to 0.
- `priority` (character vector, optional): The error threshold to prioritize when the max sample size is too small to have both error thresholds satisfied. Default is the null i.e. error under `pLo`. Defaults to c("null","alt").

### Details
The shape parameter `delta` is used to determine the stopping boundary with 0 corresponding to the Pocock boundary where the same significance level is used for all looks and 0.5 corresponding to the O'Brien-Fleming boundary which has smaller probability of stopping at early looks. Default value of `delta` for toxicity monitoring is 0; value between 0.1 and 0.2 is a reasonable choice to make it less likely to stop early. For toxicity monitoring two sets of probabilities - `pstop` and `pcross` - are given which correspond to probability of stopping early and probability of declaring the treatment too toxic with the full complement of study subjects accrued and treated.
```

--------------------------------

### Group Sequential Design - General Drift

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

A general function for group sequential designs that accounts for drift. It can handle various scenarios including efficacy and futility drift.

```R
gsd.drift(ifrac, sig.level = 0.05, pow = 0.8, delta.eb = 0.5, delta.fb = NULL,
    alternative = c("two.sided", "one.sided"), tol = 0.00001, ...)
```

--------------------------------

### Calculate Exact Single Stage Phase II Design

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the exact one-stage Phase II clinical trial design. Specify unacceptable and desirable response rates along with probability thresholds.

```R
ph2single(pu,pa,ep1,ep2,nsoln=5)
```

--------------------------------

### oc.twostage.bdry

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the operating characteristics of a two-stage boundary for clinical trials.

```APIDOC
## Two-stage boundary operating characteristics

### Description
Calculates the operating characteristics of a two-stage boundary.

### Usage
```R
oc.twostage.bdry(pu, pa, r1, n1, r, n)
```

### Arguments
`pu` |  unacceptable response rate  
---|---
`pa` |  response rate that is desirable  
`r1` |  first stage threshold to declare treatment undesirable  
`n1` |  first stage sample size  
`r` |  overall threshold to declare treatment undesirable  
`n` |  total sample size  

### Value
`oc.twostage.bdry` returns the type I and II error rates as well as the probability of early temination and expected sample size under `pu` for a specific boundary.
```

--------------------------------

### jonckheere.test

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Performs the exact Jonckheere-Terpstra test for ordered alternatives. Handles ties and provides permutation p-values when exact calculation is not possible.

```APIDOC
## jonckheere.test

### Description
Performs the exact Jonckheere-Terpstra test.

### Details
`jonckheere.test` is the exact (permutation) version of the Jonckheere-Terpstra test. It uses the statistic \(\\sum_{k<l} \sum_{ij} I(X_{ik} < X_{jl}) + 0.5 I(X_{ik} = X_{jl})\), where \(i, j\) are observations in groups \(k\) and \(l\) respectively. The asymptotic version is equivalent to `cor.test(x, g, method="k")`. The exact calculation requires that there be no ties and that the sample size is less than 100. When data are tied and sample size is at most 100, a permutation p-value is returned.

### References
Jonckheere, A. R. (1954). A distribution-free k-sample test again ordered alternatives. _Biometrika_ 41:133-145.
Terpstra, T. J. (1952). The asymptotic normality and consistency of Kendall's test against trend, when ties are present in one ranking. _Indagationes Mathematicae_ 14:327-333.

### Examples
```R
set.seed(1234)
g <- rep(1:5, rep(10,5))
x <- rnorm(50)
jonckheere.test(x+0.3*g, g)
x[1:2] <- mean(x[1:2]) # tied data
jonckheere.test(x+0.3*g, g)
jonckheere.test(x+0.3*g, g, nperm=5000)
```
```

--------------------------------

### Calculate Power of k-Sample Rank Test

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the power of rank tests for animal studies under the Lehmann alternative. Supports Kruskal-Wallis and Jonckheere-Terpstra statistics.

```R
power.ladesign(c(9,7), 4, statistic="K")
  power.ladesign(c(9,7,9), c(2,4), statistic="J")
  power.ladesign(c(9,7,9), c(2,4), statistic="J", alt="o")
```

--------------------------------

### power.ladesign

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the power of rank tests for k-sample comparisons, specifically for animal studies, under the Lehmann alternative hypothesis. It allows specifying sample sizes, odds ratios, significance level, and the type of test statistic.

```APIDOC
## power.ladesign

### Description
Functions to calculate the power of rank tests for animal studies.

### Usage
```
power.ladesign(gsize, odds.ratio, sig.level = 0.05, statistic = c("Kruskal-Wallis", "Jonckheere-Terpstra"), alternative = c("two.sided", "one.sided"), nrep = 1e+06)
## S3 method for class 'ladesign'
print(x, ...)
```

### Arguments
`gsize` | sample size of the k (= length of vector) groups.
`odds.ratio` | odds ratio parameters for the k-1 groups. The first group is considered the control.
`sig.level` | the significance level of the test (default = 0.05)
`statistic` | the test statistic for the k-group comparison. Is one of Kruskal-Wallis (default) or Jonckeere-Terpstra.
`alternative` | one- or two-sided test. Valid only for the Jonckheere-Terpstra test.
`nrep` | number of reps (default 1 million) for Monte Carlo.
`x` | object of class ladesign returned by power.ladesign
`...` | arguments to be passed on left for S3 method consistency.

### Details
Although the power for Jonckheere-Terpstra test is calculated for any set of odds ratio, the test is meant for monotone alternative. Thus it is preferable to specify odds ratios that are monotonically increasing with all values larger than 1 or decreasing with all values smaller than 1.

### Value
returns a list with objects group.size, odds.ratio, statistic, sig.level and power. The "print" method formats the output.

### References
Heller G. (2006). Power calculations for preclinical studies using a K-sample rank test and the Lehmann alternative hypothesis. _Statistics in Medicine_ 25, 2543-2553.
```

--------------------------------

### gsdesign.binomial, gsdesign.normal, gsdesign.survival

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Functions to design group sequential clinical trials for binomial, normal, and survival data, respectively. They allow for the calculation of sample sizes and critical values at different interim analyses, considering efficacy and futility boundaries.

```APIDOC
## gsdesign.binomial, gsdesign.normal, gsdesign.survival

### Description
Functions to design group sequential clinical trials for binomial, normal, and survival data, respectively. They allow for the calculation of sample sizes and critical values at different interim analyses, considering efficacy and futility boundaries.

### Usage
```R
gsdesign.binomial(ifrac, pC, pE, r = 1, sig.level = 0.05, power = 0.8,
  delta.eb=0.5, delta.fb = NULL, alternative = c("two.sided",
  "one.sided"), pooled.variance = FALSE, CPS = TRUE, tol=0.00001, ...)
gsdesign.normal(ifrac, delta, sd = 1, r = 1, sig.level = 0.05,
  power = 0.8, delta.eb = 0.5, delta.fb = NULL, alternative = 
  c("two.sided", "one.sided"), tol=0.00001, ...)
gsdesign.survival(ifrac, haz.ratio, r = 1, sig.level = 0.05, 
  power = 0.8, delta.eb = 0.5, delta.fb = NULL, alternative = 
  c("two.sided", "one.sided"), tol=0.00001, ...)
```

### Arguments
`ifrac` |  information fraction or the ratio of current sample size or number of events to the total sample size or number of events. This should be an increasing vector of numbers from 0 to 1 with the last one being 1. If just 1 is given a fixed sample design is derived.
`pC` |  prob of success of the standard therapy (for binomial data)
`pE` |  prob of success of the experimental therapy (for binomial data)
`delta` |  true difference in means (for normal data)
`sd` |  standard deviation (for normal data)
`haz.ratio` |  hazard ratio (for survival comparison)
`r` |  treatment allocation of r (default=1) experimental per 1 control.
`sig.level` |  significance level (type I error probability)
`power` |  power of test (1 minus type II error probability)
`delta.eb` |  power for efficacy boundary in the Pocock (=0) to O'Brien-Fleming (=0.5) family (default is 0.5)
`delta.fb` |  power for futility boundary in the Pocock (=0) to O'Brien-Fleming (=0.5) family (default is NULL i.e. no futility boundary is requested.)
`alternative` |  one- or two-sided test.
`pooled.variance` |  whether the test statistic is standardized by pooled (2*pbar*(1-pbar)) or unpooled variance (pC*(1-pC) + pE*(1-pE)). Default is unpooled variance.
`CPS` |  whether continuity correction is used for sample size calculation as in Casagrande, Pike & Smith. Default is to use it.
`tol` |  tolerance level for multivariate normal probability computation.
`...` |  additional options passed on the pmvnorm function.

### Details
The futility boundary is not returned when delta.fb is not specified i.e. stopping for futility is not requested. The futility boundary is non-binding. That is the significance level is not adjusted to account for early stopping for futility. This makes the test a bit conservative in that the true size is less than the nominal level.
If the alternative is two-sided by default the futility boundary will also be two-sided i.e. continuation region is wedge shaped. However, if the goal is to show the superiority of the experimental treatment then futility boundary should be one sided. This can be achieved by deriving the boundaries for one-sided alternative and significance level set at half of the value used for two sided alternative. See the examples section for a representative design for which the trial cannot be stopped at the first look for futility.
The Casagrande-Pike-Smith type continuity correction is obtained using the formula 
`n∗[1+1+4/(∣pC−pE∣∗n)]2n*[1 + \sqrt{1+4/(|pC-pE|*n)}]^2n∗[1+1+4/(∣pC−pE∣∗n)​]2`
where n is the uncorrected sample size.

### Value
a list with ifrac, sig.level, power, alternative, delta.eb, delta.fb and:
`efbdry` |  the critical value to use at the different looks. For two-sided alternative the absolute test statistic should exceed this.
`futbdry` |  the critical value to use at the different looks. For two-sided alternative the absolute test statistic should be below this.
`sample.size` |  the sample size per arm for binomial/normal data.
`num.events` |  the total number of failures which should be converted to number of subjects using censoring proportion.

### Examples
```R
  gsdesign.normal(1:4/4, 0.25, sig.level=0.05, alt="t", delta.fb=0.5)
  gsdesign.normal(1:4/4, 0.25, sig.level=0.025, alt="o", delta.fb=0.5)
```
```

--------------------------------

### Toxicity Boundary Calculation

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates toxicity boundaries for clinical trials. Use to define acceptable toxicity rates and stopping rules based on observed toxicities.

```R
toxbdry(0.2, 0.35, c(20,40,60,75))
  toxbdry(0.2, 0.3, c(20,40,60,75), cP0=0.15, cP1=0.8)
  # continuous monitoring
  toxbdry(0.1, 0.3, 2:30)
  # prioritize cP1 error threshold
  toxbdry(0.1, 0.3, 2:25, priority="alt")
```

--------------------------------

### Boundary Crossing Probability Calculation

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the probability of crossing a stopping boundary. Requires sample size, maximum acceptable toxicities, and toxicity rates for operating characteristics.

```R
bdrycross.prob(n, r, ptox)
```

--------------------------------

### ph2single

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the exact one-stage Phase II clinical trial design. It determines the sample size (n) and the number of responses (r) required to declare a drug desirable based on specified unacceptable and desirable response rates, along with thresholds for Type I and Type II errors.

```APIDOC
## ph2single

### Description
Calculates the exact one stage Phase II design

### Usage
```
ph2single(pu, pa, ep1, ep2, nsoln = 5)
```

### Arguments
`pu` | unacceptable response rate
`pa` | response rate that is desirable
`ep1` | threshold for the probability of declaring drug desirable under p0
`ep2` | threshold for the probability of rejecting the drug under p1
`nsoln` | number of designs with given alpha and beta

### Value
ph2single returns a data frame with variables: n, r, and the Type I and Type II errors. Treatment desirable if >r respenses seen.
```

--------------------------------

### Minimum Detectable Relative Risk (mdrr)

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Computes the minimum detectable probability of response for marker-positive and marker-negative subjects given total sample size, overall response probability, and proportion of marker-positive subjects.

```R
mdrr(n, cprob, presp, alpha=0.05, power=0.8, niter=15)
```

--------------------------------

### Calculate Fixed-Outcome Sample Size

Source: https://cran.r-project.org/web/packages/clinfun/vignettes/clinical-trial-functions.R

Computes the required sample size for a fixed-outcome trial based on two proportions, a desired power, and a significance level. This is a common calculation for planning study size.

```r
fe.ssize(p1 = 0.2, p2 = 0.3, power = 0.8)
```

--------------------------------

### Exact Power Calculation for Fisher's Exact Test (fe.power)

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Calculates the exact power of Fisher's exact test for a given difference in proportions, sample sizes, and significance level.

```R
fe.power(d, n1, n2, p1, alpha = 0.05)
```

--------------------------------

### twostage.inference

Source: https://cran.r-project.org/web/packages/clinfun/refman/clinfun.html

Performs statistical inference for a two-stage clinical trial design. It calculates p-values, Uniformly Minimum Variance Unbiased Estimators (UMVUE), and confidence intervals for the response rate.

```APIDOC
## Inference following a two-stage design for binary response

### Description
Calculates the p-value, UMVUE and CI for the data from a study using a two stage design for response. 

### Usage
twostage.inference(x, r1, n1, n, pu, alpha=0.05)

### Arguments
`x` |  number of responses observed at the end of the study  
`r1` |  first stage threshold to declare treatment undesirable  
`n1` |  first stage sample size  
`n` |  total sample size  
`pu` |  unacceptable response rate (null hypothesis)  
`alpha` |  the confidence level. For consistency with the design use the same value from the design. (default is 0.05)  

### Value
twostage.inference returns the UMVUE (Jung & Kim, 2004), p-value and CI (Koyama & Chen, 2008). The CI has confidence level 1-2*alpha and the one-sided (1-alpha) interval consistent with the design is obtained by changing the upper confidence limit (UCL) to 1. 

### References
Jung SH and Kim KM. (2004). On the estimation of the binomial probability in multistage clinical trials. _Statistics in Medicine_ 23, 881-896. 
Koyama T and Chen H. (2008). Proper inference from Simon's two-stage designs. _Statistics in Medicine_ 27, 3145-3154. 

```