### Install onlineFDR from GitHub

Source: https://dsrobertson.github.io/onlineFDR/index.html

Installs the latest development snapshot of the onlineFDR package directly from its GitHub repository. Requires the devtools package.

```r
# install.packages("devtools") # If devtools not installed

devtools::install_github("dsrobertson/onlineFDR")
```

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

### Initialize LOND with Sample Data

Source: https://dsrobertson.github.io/onlineFDR/articles/onlineFDR.html

Demonstrates the initial setup for the LOND procedure with a small sample dataset. Ensure the 'id', 'date', and 'pval' columns are correctly formatted.

```R
sample.df <- data.frame(
  id = c('A15432', 'B90969', 'C18705'),
  date = as.Date(c(rep("2014-12-01",3))),
  pval = c(2.90e-14, 0.06743, 0.01514))

set.seed(1)
LOND_results <- LOND(sample.df)
```

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

### Alpha Investing with Randomization

Source: https://dsrobertson.github.io/onlineFDR/reference/Alpha_investing.html

This example demonstrates using the Alpha_investing function with randomization enabled (default behavior). A fixed seed is set for reproducibility.

```R
set.seed(1); Alpha_investing(sample.df)
#>          pval      alphai R
#> 1  2.9000e-08 0.010818925 1
#> 2  6.7430e-02 0.021406257 0
#> 3  1.5140e-02 0.007164201 0
#> 4  8.1740e-02 0.003757589 0
#> 5  1.7100e-03 0.002374706 1
#> 6  2.7201e-01 0.023680499 0
#> 7  3.6000e-05 0.008803369 1
#> 8  7.9149e-01 0.029838354 0
#> 9  7.5900e-08 0.012084065 1
#> 10 2.8295e-01 0.032981505 0
#> 11 6.9274e-01 0.014137539 0
#> 12 7.2342e-01 0.008529625 0
#> 13 3.0443e-01 0.005905508 0
#> 14 5.4757e-01 0.004412045 0
#> 15 1.3600e-03 0.003461425 1
```

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

### Example Dataframe Creation

Source: https://dsrobertson.github.io/onlineFDR/reference/online_fallback.html

Creates a sample dataframe with p-values, identifiers, and dates for testing the online_fallback function.

```R
sample.df <- data.frame(
  id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
      'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
      'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
  date = as.Date(c(rep('2014-12-01',3),
               rep('2015-09-21',5),
                rep('2016-05-19',2),
                '2016-11-12',
               rep('2017-03-27',4))),
  pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
        3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
        0.69274, 0.30443, 0.00136, 0.72342, 0.54757))
)
```

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

### Run LOND with Expanded Sample Data

Source: https://dsrobertson.github.io/onlineFDR/articles/onlineFDR.html

Shows how to run the LOND procedure with a larger, more comprehensive sample dataset. This example includes more data points and varied dates.

```R
sample.df <- data.frame(
  id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
         'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
         'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
  date = as.Date(c(rep("2014-12-01",3),
                   rep("2015-09-21",5),
                   rep("2016-05-19",2),
                   "2016-11-12",
                   rep("2017-03-27",4))),
  pval = c(2.90e-14, 0.06743, 0.01514, 0.08174, 0.00171,
           3.61e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
           0.69274, 0.30443, 0.000487, 0.72342, 0.54757))

set.seed(1)
LOND_results <- LOND(sample.df)
```

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

### Install onlineFDR from Bioconductor (release)

Source: https://dsrobertson.github.io/onlineFDR/index.html

Installs the stable release version of the onlineFDR package from Bioconductor. Ensure BiocManager is installed first.

```r
if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

BiocManager::install("onlineFDR")
```

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

### Running supLORD with Simulated Data

Source: https://dsrobertson.github.io/onlineFDR/reference/supLORD.html

This example demonstrates how to use the supLORD function with simulated p-values. It shows the typical workflow from generating data to applying the function and inspecting the results.

```R
set.seed(1)
N <- 1000
B <- rbinom(N, 1, 0.5)
Z <- rnorm(N, mean = 3*B)
pval <- pnorm(-Z)

out <- supLORD(pval, eps=0.15, r=30, eta=0.05, rho=30, random=FALSE)
head(out)
#>              d       alphai R
#> 1 4.691912e-01 0.0019301522 0
#> 2 6.167166e-01 0.0004197471 0
#> 3 3.462711e-02 0.0003575072 0
#> 4 1.300690e-03 0.0002973164 0
#> 5 1.606961e-01 0.0002520627 0
#> 6 2.174486e-06 0.0002180533 1
sum(out$R)
#> [1] 390
```

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

### BatchBH Example Usage

Source: https://dsrobertson.github.io/onlineFDR/reference/BatchBH.html

Demonstrates how to use the BatchBH function with a sample dataframe containing identifiers, p-values, and batch numbers. It shows the output with discoveries indicated.

```R
sample.df <- data.frame(
    id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
        'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
        'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
    pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
            3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
            0.69274, 0.30443, 0.00136, 0.72342, 0.54757),
    batch = c(rep(1,5), rep(2,6), rep(3,4)))

BatchBH(sample.df)
```

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

### View onlineFDR Vignette

Source: https://dsrobertson.github.io/onlineFDR/index.html

Opens the vignette for the installed version of the onlineFDR package in R. Vignettes provide detailed examples and explanations.

```r
browseVignettes("onlineFDR")
```

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

### StoreyBH Example Usage

Source: https://dsrobertson.github.io/onlineFDR/reference/StoreyBH.html

Demonstrates how to use the StoreyBH function with a sample vector of p-values to control FDR.

```R
pvals <- c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
        3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
        0.69274, 0.30443, 0.00136, 0.72342, 0.54757)

StoreyBH(pvals)
#>          pval R
#> 1  2.9000e-08 1
#> 2  6.7430e-02 0
#> 3  1.5140e-02 1
#> 4  8.1740e-02 0
#> 5  1.7100e-03 1
#> 6  3.6000e-05 1
#> 7  7.9149e-01 0
#> 8  2.7201e-01 0
#> 9  2.8295e-01 0
#> 10 7.5900e-08 1
#> 11 6.9274e-01 0
#> 12 3.0443e-01 0
#> 13 1.3600e-03 1
#> 14 7.2342e-01 0
#> 15 5.4757e-01 0
```

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

### Install onlineFDR from Bioconductor (devel)

Source: https://dsrobertson.github.io/onlineFDR/index.html

Installs the development version of the onlineFDR package from Bioconductor. This may include newer features but could be less stable.

```r
if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

BiocManager::install(version = "devel")
BiocManager::install("onlineFDR")
```

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

### R: Alpha Spending with Custom Alpha Level

Source: https://dsrobertson.github.io/onlineFDR/reference/Alpha_spending.html

This example demonstrates how to specify a custom overall alpha level (e.g., 0.1) for the Alpha_spending function. This affects the calculation of adjusted p-values and the significance threshold.

```r
set.seed(1); Alpha_spending(sample.df, alpha=0.1)
#>        id       date       pval       alphai R
#> 1  A15432 2014-12-01 2.9000e-17 0.0053516771 1
#> 2  B90969 2014-12-01 6.7430e-02 0.0011638206 0
#> 3  C18705 2014-12-01 1.5140e-02 0.0009912499 0
#> 4  B49731 2015-09-21 8.1740e-02 0.0008243606 0
#> 5  E99902 2015-09-21 1.7100e-03 0.0006988870 0
#> 6  D46627 2015-09-21 2.7201e-01 0.0006045900 0
#> 7  C38292 2015-09-21 3.6000e-05 0.0005319444 1
#> 8  A30619 2015-09-21 7.9149e-01 0.0004745225 0
#> 9  A41418 2016-05-19 7.5900e-08 0.0004280949 1
#> 10 E29198 2016-05-19 2.8295e-01 0.0003898252 0
#> 11 D51456 2016-11-12 6.9274e-01 0.0003577593 0
#> 12 A63155 2017-03-27 7.2342e-01 0.0003305137 0
#> 13 C88669 2017-03-27 3.0443e-01 0.0003070841 0
#> 14 B66033 2017-03-27 5.4757e-01 0.0002867254 0
#> 15 E03673 2017-03-27 1.3600e-03 0.0002688736 0
```

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

### R: Alpha Spending with Randomization Disabled

Source: https://dsrobertson.github.io/onlineFDR/reference/Alpha_spending.html

This example shows how to use Alpha_spending without randomization by setting the 'random' argument to FALSE. This ensures deterministic results for the same input data.

```r
Alpha_spending(sample.df, random=FALSE)
#>        id       date       pval       alphai R
#> 1  A15432 2014-12-01 2.9000e-17 0.0026758385 1
#> 2  B90969 2014-12-01 6.7430e-02 0.0005819103 0
#> 3  C18705 2014-12-01 1.5140e-02 0.0004956249 0
#> 4  B49731 2015-09-21 8.1740e-02 0.0004121803 0
#> 5  E99902 2015-09-21 1.7100e-03 0.0003494435 0
#> 6  C38292 2015-09-21 3.6000e-05 0.0003022950 1
#> 7  A30619 2015-09-21 7.9149e-01 0.0002659722 0
#> 8  D46627 2015-09-21 2.7201e-01 0.0002372613 0
#> 9  E29198 2016-05-19 2.8295e-01 0.0002140474 0
#> 10 A41418 2016-05-19 7.5900e-08 0.0001949126 1
#> 11 D51456 2016-11-12 6.9274e-01 0.0001788796 0
#> 12 C88669 2017-03-27 3.0443e-01 0.0001652568 0
#> 13 E03673 2017-03-27 1.3600e-03 0.0001535420 0
#> 14 A63155 2017-03-27 7.2342e-01 0.0001433627 0
#> 15 B66033 2017-03-27 5.4757e-01 0.0001344368 0
```

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

### Example Usage of BatchPRDS

Source: https://dsrobertson.github.io/onlineFDR/reference/BatchPRDS.html

Demonstrates how to use the BatchPRDS function with a sample dataframe containing identifiers, p-values, and batch numbers. The output includes the original data and an indicator of discoveries.

```r
sample.df <- data.frame(
    id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
        'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
        'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
    pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
            3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
            0.69274, 0.30443, 0.00136, 0.72342, 0.54757),
    batch = c(rep(1,5), rep(2,6), rep(3,4)))

BatchPRDS(sample.df)
```

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

### BatchStBH Example Usage

Source: https://dsrobertson.github.io/onlineFDR/reference/BatchStBH.html

Demonstrates how to use the BatchStBH function with a sample dataframe containing identifiers, p-values, and batch numbers. The output includes the original data with an added 'R' column indicating discoveries and adjusted significance thresholds.

```R
sample.df <- data.frame(
    id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
        'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
        'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
    pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
            3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
            0.69274, 0.30443, 0.00136, 0.72342, 0.54757),
    batch = c(rep(1,5), rep(2,6), rep(3,4)))

BatchStBH(sample.df)
```

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

### Create Sample Dataframe

Source: https://dsrobertson.github.io/onlineFDR/articles/onlineFDR.html

Initializes a toy dataset with identifier, date, and p-value columns. Ensure the date is in 'YYYY-MM-DD' format.

```r
sample.df <- data.frame(
  id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
         'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
         'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
  date = as.Date(c(rep("2014-12-01",3),
                   rep("2015-09-21",5),
                   rep("2016-05-19",2),
                   "2016-11-12",
                   rep("2017-03-27",4))),
  pval = c(2.90e-14, 0.00143, 0.06514, 0.00174, 0.00171,
           3.61e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
           0.69274, 0.30443, 0.000487, 0.72342, 0.54757))
)
```

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

### LONDstar with Async Version

Source: https://dsrobertson.github.io/onlineFDR/reference/LONDstar.html

Demonstrates creating a sample data frame and applying the LONDstar function with the 'async' version. This is useful for standard FDR control.

```R
sample.df <- data.frame(
id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
    'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
    'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
        3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
        0.69274, 0.30443, 0.00136, 0.72342, 0.54757),
decision.times = seq_len(15) + 1)

LONDstar(sample.df, version='async')
```

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

### Alpha Investing with Default Parameters

Source: https://dsrobertson.github.io/onlineFDR/reference/Alpha_investing.html

This snippet shows how to use the Alpha_investing function with a sample dataframe and default parameters (random=FALSE). It displays the calculated p-values, alpha values, and R indicators.

```R
sample.df <- data.frame(
id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
    'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
    'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
date = as.Date(c(rep('2014-12-01',3),
               rep('2015-09-21',5),
                rep('2016-05-19',2),
                '2016-11-12',
               rep('2017-03-27',4))),
pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
        3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
        0.69274, 0.30443, 0.00136, 0.72342, 0.54757))

Alpha_investing(sample.df, random=FALSE)
#>          pval      alphai R
#> 1  2.9000e-08 0.010818925 1
#> 2  6.7430e-02 0.021406257 0
#> 3  1.5140e-02 0.007164201 0
#> 4  8.1740e-02 0.003757589 0
#> 5  1.7100e-03 0.002374706 1
#> 6  3.6000e-05 0.023680499 1
#> 7  7.9149e-01 0.044095287 0
#> 8  2.7201e-01 0.015842430 0
#> 9  2.8295e-01 0.008711190 0
#> 10 7.5900e-08 0.005700295 1
#> 11 6.9274e-01 0.026865786 0
#> 12 3.0443e-01 0.011205456 0
#> 13 1.3600e-03 0.006863124 1
#> 14 7.2342e-01 0.027979664 0
#> 15 5.4757e-01 0.011945806 0
```

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

### Alpha Investing with Custom Alpha and W0

Source: https://dsrobertson.github.io/onlineFDR/reference/Alpha_investing.html

This snippet demonstrates how to use the Alpha_investing function with custom values for the 'alpha' and 'w0' parameters. A fixed seed is used for reproducible results.

```R
set.seed(1); Alpha_investing(sample.df, alpha=0.1, w0=0.025)
#>          pval      alphai R
#> 1  2.9000e-08 0.010818925 1
#> 2  6.7430e-02 0.041915265 0
#> 3  1.5140e-02 0.014226480 0
#> 4  8.1740e-02 0.007487045 0
#> 5  1.7100e-03 0.004738159 1
#> 6  2.7201e-01 0.046265410 0
#> 7  3.6000e-05 0.017453092 1
#> 8  7.9149e-01 0.057947646 0
#> 9  7.5900e-08 0.023879569 1
#> 10 2.8295e-01 0.063856912 0
#> 11 6.9274e-01 0.027880910 0
#> 12 7.2342e-01 0.016914972 0
#> 13 3.0443e-01 0.011741675 0
#> 14 5.4757e-01 0.008785330 0
#> 15 1.3600e-03 0.006898971 1
```

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

### SAFFRONstar with 'async' version

Source: https://dsrobertson.github.io/onlineFDR/reference/SAFFRONstar.html

This snippet demonstrates how to use SAFFRONstar with the 'async' version. It requires a data frame with 'id', 'pval', and 'decision.times' columns.

```R
sample.df <- data.frame(
id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
    'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
    'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
        3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
        0.69274, 0.30443, 0.00136, 0.72342, 0.54757),
decision.times = seq_len(15) + 1)

SAFFRONstar(sample.df, version='async')
#>          pval      alphai R
#> 1  2.9000e-08 0.005468627 1
#> 2  6.7430e-02 0.001803974 0
#> 3  1.5140e-02 0.007272601 0
#> 4  8.1740e-02 0.003607948 0
#> 5  1.7100e-03 0.003607948 1
#> 6  3.6000e-05 0.003607948 1
#> 7  7.9149e-01 0.014545202 0
#> 8  2.7201e-01 0.018153151 0
#> 9  2.8295e-01 0.007379710 0
#> 10 7.5900e-08 0.007379710 1
#> 11 6.9274e-01 0.007379710 0
#> 12 3.0443e-01 0.018316965 0
#> 13 1.3600e-03 0.007874188 1
#> 14 7.2342e-01 0.007874188 0
#> 15 5.4757e-01 0.018811442 0
```

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

### SAFFRON with Custom Alpha and W0

Source: https://dsrobertson.github.io/onlineFDR/reference/SAFFRON.html

This snippet demonstrates using the SAFFRON function with custom alpha and w0 parameters. 'set.seed(1)' is used for reproducibility.

```R
set.seed(1); SAFFRON(sample.df, alpha=0.1, w0=0.025)
#>          pval      alphai R     id
#> 1  2.9000e-08 0.005468627 1 A15432
#> 2  6.7430e-02 0.021874508 0 B90969
#> 3  1.5140e-02 0.021874508 1 C18705
#> 4  8.1740e-02 0.043749017 0 B49731
#> 5  1.7100e-03 0.043749017 1 E99902
#> 6  2.7201e-01 0.065623525 0 D46627
#> 7  3.6000e-05 0.065623525 1 C38292
#> 8  7.9149e-01 0.087498033 0 A30619
#> 9  7.5900e-08 0.028863587 1 A41418
#> 10 2.8295e-01 0.050738095 0 E29198
#> 11 6.9274e-01 0.050738095 0 D51456
#> 12 7.2342e-01 0.022302945 0 A63155
#> 13 3.0443e-01 0.013293195 0 C88669
#> 14 5.4757e-01 0.013293195 0 B66033
#> 15 1.3600e-03 0.009042997 1 E03673
```

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

### Run LOND Algorithm and View Results

Source: https://dsrobertson.github.io/onlineFDR/articles/onlineFDR.html

Applies the LOND algorithm to the sample data and displays the results, including p-values, adjusted significance thresholds (alphai), and an indicator of discovery (R). Setting a seed ensures reproducibility.

```r
library(onlineFDR)

set.seed(1)
LOND_results <- LOND(sample.df)
LOND_results
```

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

### Set FDR Bound for LOND

Source: https://dsrobertson.github.io/onlineFDR/articles/onlineFDR.html

Illustrates how to set a priori bounds for the LOND procedure using the setBound function. This is useful when the number of expected hypotheses is known. Ensure alpha matches the algorithm's alpha.

```R
sample.df <- data.frame(
  id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
         'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
         'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
  date = as.Date(c(rep("2014-12-01",3),
                   rep("2015-09-21",5),
                   rep("2016-05-19",2),
                   "2016-11-12",
                   rep("2017-03-27",4))),
  pval = c(2.90e-14, 0.06743, 0.01514, 0.08174, 0.00171,
           3.61e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
           0.69274, 0.30443, 0.000487, 0.72342, 0.54757))

# Assuming a bound of 20 hypotheses
bound <- setBound("LOND", alpha = 0.04, 20)

set.seed(1)
LOND_results <- LOND(sample.df, alpha = 0.04, betai = bound)
```

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

### Run Online Fallback with Dataframe (random=FALSE)

Source: https://dsrobertson.github.io/onlineFDR/reference/online_fallback.html

Applies the online_fallback procedure to a sample dataframe with p-values, ensuring a fixed order by setting random=FALSE.

```R
online_fallback(sample.df, random=FALSE)
#>          pval       alphai R
#> 1  2.9000e-08 0.0026758385 1
#> 2  6.7430e-02 0.0032577488 0
#> 3  1.5140e-02 0.0004956249 0
#> 4  8.1740e-02 0.0004121803 0
#> 5  1.7100e-03 0.0003494435 0
#> 6  3.6000e-05 0.0003022950 1
#> 7  7.9149e-01 0.0005682672 0
#> 8  2.7201e-01 0.0002372613 0
#> 9  2.8295e-01 0.0002140474 0
#> 10 7.5900e-08 0.0001949126 1
#> 11 6.9274e-01 0.0003737922 0
#> 12 3.0443e-01 0.0001652568 0
#> 13 1.3600e-03 0.0001535420 0
#> 14 7.2342e-01 0.0001433627 0
#> 15 5.4757e-01 0.0001344368 0
```

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

### ADDIS-spending with Locally Dependent P-values

Source: https://dsrobertson.github.io/onlineFDR/reference/ADDIS_spending.html

Demonstrates the usage of ADDIS_spending with a sample dataframe for locally dependent p-values by setting `dep = TRUE`. The output structure is similar to the independent case, showing p-values, adjusted testing levels, and discoveries.

```R
ADDIS_spending(sample.df, dep = TRUE) #Locally dependent
#>          pval       alphai R
#> 1  2.9000e-08 0.0054686271 1
#> 2  6.7430e-02 0.0018039742 0
#> 3  1.5140e-02 0.0018039742 0
#> 4  8.1740e-02 0.0018039742 0
#> 5  1.7100e-03 0.0018039742 1
#> 6  3.6000e-05 0.0018039742 1
#> 7  7.9149e-01 0.0018039742 0
#> 8  2.7201e-01 0.0018039742 0
#> 9  2.8295e-01 0.0009429405 0
#> 10 7.5900e-08 0.0005950895 1
#> 11 6.9274e-01 0.0005950895 0
#> 12 3.0443e-01 0.0005950895 0
#> 13 1.3600e-03 0.0004164149 0
#> 14 7.2342e-01 0.0004164149 0
#> 15 5.4757e-01 0.0004164149 0
```

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

### ADDIS-spending with Independent P-values

Source: https://dsrobertson.github.io/onlineFDR/reference/ADDIS_spending.html

Demonstrates the usage of ADDIS_spending with a sample dataframe for independent p-values. The output includes p-values, adjusted testing levels (alphai), and an indicator of discoveries (R).

```R
sample.df <- data.frame(
    id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
        'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
        'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
    pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
            3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
            0.69274, 0.30443, 0.00136, 0.72342, 0.54757),
    lags = rep(1,15))

ADDIS_spending(sample.df) #independent
#>          pval       alphai R
#> 1  2.9000e-08 0.0054686271 1
#> 2  6.7430e-02 0.0054686271 0
#> 3  1.5140e-02 0.0054686271 0
#> 4  8.1740e-02 0.0054686271 0
#> 5  1.7100e-03 0.0054686271 1
#> 6  3.6000e-05 0.0054686271 1
#> 7  7.9149e-01 0.0054686271 0
#> 8  2.7201e-01 0.0054686271 0
#> 9  2.8295e-01 0.0018039742 0
#> 10 7.5900e-08 0.0009429405 1
#> 11 6.9274e-01 0.0009429405 0
#> 12 3.0443e-01 0.0009429405 0
#> 13 1.3600e-03 0.0005950895 0
#> 14 7.2342e-01 0.0005950895 0
#> 15 5.4757e-01 0.0005950895 0
```

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

### Compare Adjusted Significance Thresholds for Different LORD Versions

Source: https://dsrobertson.github.io/onlineFDR/articles/advanced-usage.html

This snippet demonstrates how to compare adjusted significance thresholds (alphai) across different versions of the LORD method ('++', 3, 'discard', 'dep'). It's useful for evaluating the impact of version choice on FDR control.

```r
set.seed(1); results.LORD.plus <- LORD(sample.df)
set.seed(1); results.LORD3 <- LORD(sample.df, version=3)
set.seed(1); results.LORD.discard <- LORD(sample.df, version='discard')
set.seed(1); results.LORD.dep <- LORD(sample.df, version='dep') 

# compare adjusted significance thresholds
cbind(LORD.plus = results.LORD.plus$alphai,
    LORD3 = results.LORD3$alphai,
    LORD.discard  = results.LORD.discard$alphai,
    LORD.dep = results.LORD.dep$alphai)
#>          LORD.plus        LORD3 LORD.discard     LORD.dep
#>  [1,] 0.0002675839 0.0002675839 0.0002675839 2.091542e-03
#>  [2,] 0.0024664457 0.0026615183 0.0011285264 1.002025e-02
#>  [3,] 0.0005732818 0.0005787961 0.0002823266 1.677763e-03
#>  [4,] 0.0004872805 0.0004929725 0.0002394680 6.262659e-04
#>  [5,] 0.0004059066 0.0004099744 0.0001998165 3.201787e-04
#>  [6,] 0.0003447286 0.0003475734 0.0001700069 1.933725e-04
#>  [7,] 0.0002986627 0.0003006772 0.0001475152 1.293954e-04
#>  [8,] 0.0029389397 0.0072216015 0.0014680343 1.548152e-04
#>  [9,] 0.0008168502 0.0015704700 0.0014680343 1.166482e-04
#> [10,] 0.0033835974 0.0091593329 0.0017451837 1.422614e-04
#> [11,] 0.0011873999 0.0019918653 0.0006438778 1.145119e-04
#> [12,] 0.0010225858 0.0016965126 0.0006438778 9.432408e-05
#> [13,] 0.0008785607 0.0014108836 0.0006438778 7.916885e-05
#> [14,] 0.0007679398 0.0011961369 0.0005497556 6.749313e-05
#> [15,] 0.0006820264 0.0010347488 0.0005497556 5.830055e-05
```

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

### LONDstar with Batch Version

Source: https://dsrobertson.github.io/onlineFDR/reference/LONDstar.html

Illustrates using the LONDstar function in 'batch' mode with specified batch sizes. This is suitable for processing data in chunks.

```R
sample.df3 <- data.frame(
id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
    'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
    'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
        3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
        0.69274, 0.30443, 0.00136, 0.72342, 0.54757))

LONDstar(sample.df3, version='batch', batch.sizes = c(4,6,5))
```

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

### SAFFRON with Default Randomization

Source: https://dsrobertson.github.io/onlineFDR/reference/SAFFRON.html

This snippet shows the SAFFRON function using its default randomization settings. Ensure 'set.seed(1)' is called for reproducible results.

```R
set.seed(1); SAFFRON(sample.df)
#>          pval      alphai R     id
#> 1  2.9000e-08 0.005468627 1 A15432
#> 2  6.7430e-02 0.010937254 0 B90969
#> 3  1.5140e-02 0.010937254 0 C18705
#> 4  8.1740e-02 0.010937254 0 B49731
#> 5  1.7100e-03 0.010937254 1 E99902
#> 6  2.7201e-01 0.021874508 0 D46627
#> 7  3.6000e-05 0.021874508 1 C38292
#> 8  7.9149e-01 0.032811762 0 A30619
#> 9  7.5900e-08 0.010823845 1 A41418
#> 10 2.8295e-01 0.021761099 0 E29198
#> 11 6.9274e-01 0.021761099 0 D51456
#> 12 7.2342e-01 0.009265591 0 A63155
#> 13 3.0443e-01 0.005456418 0 C88669
#> 14 5.4757e-01 0.005456418 0 B66033
#> 15 1.3600e-03 0.003688669 1 E03673
```