### Install and Configure pmsampsize

Source: https://context7.com/cran/pmsampsize/llms.txt

Installation instructions and the general function signature for pmsampsize.

```r
# Install from CRAN
install.packages("pmsampsize")
library(pmsampsize)

# Basic usage structure
pmsampsize(
  type,           # "c" (continuous), "b" (binary), or "s" (survival)
  parameters,     # Number of candidate predictor parameters
  rsquared,       # For continuous: expected R-squared
  csrsquared,     # For binary/survival: Cox-Snell R-squared
  nagrsquared,    # For binary/survival: Nagelkerke's R-squared (alternative)
  cstatistic,     # For binary: C-statistic to approximate R-squared
  shrinkage = 0.9,# Target shrinkage (default 0.9 = 10% shrinkage)
  prevalence,     # For binary: outcome prevalence
  rate,           # For survival: overall event rate
  timepoint,      # For survival: prediction timepoint of interest
  meanfup,        # For survival: mean follow-up time
  intercept,      # For continuous: average outcome value
  sd,             # For continuous: standard deviation of outcome
  mmoe = 1.1      # For continuous: multiplicative margin of error (default 10%)
)
```

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

### Complete Clinical Prediction Model Workflow

Source: https://context7.com/cran/pmsampsize/llms.txt

A comprehensive example demonstrating the end-to-end process of planning a study, calculating sample size based on C-statistic, and reviewing planning metrics.

```r
library(pmsampsize)

# Scenario: Planning a study to develop a prediction model for
# 30-day mortality after cardiac surgery

# Step 1: Gather information from literature review
# - Existing model has C-statistic of 0.78
# - Expected mortality rate (prevalence) is 3%
# - Planning to evaluate 15 candidate predictors
# - Some predictors are categorical, estimating 30 total parameters

# Step 2: Calculate required sample size
mortality_model <- pmsampsize(
  type = "b",
  cstatistic = 0.78,
  parameters = 30,
  prevalence = 0.03,
  shrinkage = 0.9
)

# Step 3: Review results
print(mortality_model)

# Step 4: Extract key metrics for study planning
cat("\n=== Study Planning Summary ===\n")
cat("Minimum sample size:", mortality_model$sample_size, "patients\n")
cat("Minimum events needed:", ceiling(mortality_model$events), "deaths\n")
cat("Events per parameter:", mortality_model$EPP, "\n")
cat("Expected shrinkage:", mortality_model$final_shrinkage, "\n")

# Step 5: Check if sample size is feasible
# With 3% mortality rate, need ~3333 patients for 100 events
# If only 2000 patients available, consider:
# - Reducing number of predictors
# - Using penalized regression methods
# - Extending recruitment period
```

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

### Use Nagelkerke's R-squared

Source: https://context7.com/cran/pmsampsize/llms.txt

Placeholder for using Nagelkerke's R-squared in binary and survival models.

```r
library(pmsampsize)

# Using Nagelkerke's R-squared instead of Cox-Snell R-squared
```

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

### pmsampsize Main Function

Source: https://context7.com/cran/pmsampsize/llms.txt

The core function to calculate minimum sample size requirements for prediction model development. It evaluates multiple criteria and returns the largest sample size needed.

```APIDOC
## Main Function: pmsampsize

### Description
The core function that calculates minimum sample size requirements for prediction model development. It evaluates multiple criteria simultaneously and returns the largest sample size needed to satisfy all requirements, along with detailed output showing the breakdown by criterion.

### Method
`pmsampsize()`

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Parameters (Function Arguments)
- **type** (character) - Required - Type of outcome: "c" (continuous), "b" (binary), or "s" (survival).
- **parameters** (numeric) - Required - Number of candidate predictor parameters.
- **rsquared** (numeric) - Required for continuous type - Expected R-squared.
- **csrsquared** (numeric) - Required for binary/survival type - Cox-Snell R-squared.
- **nagrsquared** (numeric) - Optional for binary/survival type - Nagelkerke's R-squared (alternative to csrsquared).
- **cstatistic** (numeric) - Required for binary type when csrsquared is not available - C-statistic to approximate R-squared.
- **shrinkage** (numeric) - Optional - Target shrinkage (default 0.9 = 10% shrinkage).
- **prevalence** (numeric) - Required for binary type - Outcome prevalence.
- **rate** (numeric) - Required for survival type - Overall event rate.
- **timepoint** (numeric) - Required for survival type - Prediction timepoint of interest.
- **meanfup** (numeric) - Required for survival type - Mean follow-up time.
- **intercept** (numeric) - Optional for continuous type - Average outcome value.
- **sd** (numeric) - Optional for continuous type - Standard deviation of outcome.
- **mmoe** (numeric) - Optional for continuous type - Multiplicative margin of error (default 1.1 = 10%).

### Request Example
```r
# Install from CRAN
install.packages("pmsampsize")
library(pmsampsize)

# Basic usage structure
pmsampsize(
  type,           # "c" (continuous), "b" (binary), or "s" (survival)
  parameters,     # Number of candidate predictor parameters
  rsquared,       # For continuous: expected R-squared
  csrsquared,     # For binary/survival: Cox-Snell R-squared
  nagrsquared,    # For binary/survival: Nagelkerke's R-squared (alternative)
  cstatistic,     # For binary: C-statistic to approximate R-squared
  shrinkage = 0.9,# Target shrinkage (default 0.9 = 10% shrinkage)
  prevalence,     # For binary: outcome prevalence
  rate,           # For survival: overall event rate
  timepoint,      # For survival: prediction timepoint of interest
  meanfup,        # For survival: mean follow-up time
  intercept,      # For continuous: average outcome value
  sd,             # For continuous: standard deviation of outcome
  mmoe = 1.1      # For continuous: multiplicative margin of error (default 10%)
)
```

### Response
#### Success Response (200)
Returns a data frame with sample size calculations based on different criteria, including the final minimum sample size required, shrinkage factor, number of parameters, R-squared values, and Events Per Predictor Parameter (EPP).

#### Response Example
```
# Output:
# NB: Assuming 0.05 acceptable difference in apparent & adjusted R-squared
# NB: Assuming 0.05 margin of error in estimation of intercept
# NB: Events per Predictor Parameter (EPP) assumes prevalence = 0.174
#
#            Samp_size Shrinkage Parameter CS_Rsq Max_Rsq Nag_Rsq  EPP
# Criteria 1       339       0.9        24  0.288   0.377   0.764 2.46
# Criteria 2       417     0.912        24  0.288   0.377   0.764 3.02
# Criteria 3       531     0.912        24  0.288   0.377   0.764 3.85
# Final            531     0.912        24  0.288   0.377   0.764 3.85
#
# Minimum sample size required = 531, with 93 events and EPP = 3.85
```
```

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

### Access C-statistic Conversion

Source: https://context7.com/cran/pmsampsize/llms.txt

Demonstrates internal conversion of C-statistic to Cox-Snell R-squared.

```r
# The function internally converts C-statistic to Cox-Snell R-squared
result_cstat$rsquared  # 0.3418 (approximated from C-statistic)
```

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

### Adjust Shrinkage Target

Source: https://context7.com/cran/pmsampsize/llms.txt

Compares sample size requirements based on different shrinkage targets to control overfitting.

```r
library(pmsampsize)

# Compare sample sizes with different shrinkage targets
# Higher shrinkage = less overfitting = larger sample size needed

# Default shrinkage of 0.9 (10% shrinkage acceptable)
result_90 <- pmsampsize(
  type = "b",
  csrsquared = 0.288,
  parameters = 24,
  prevalence = 0.174,
  shrinkage = 0.9
)

# Stricter shrinkage of 0.95 (only 5% shrinkage acceptable)
result_95 <- pmsampsize(
  type = "b",
  csrsquared = 0.288,
  parameters = 24,
  prevalence = 0.174,
  shrinkage = 0.95
)

# Compare results
cat("Shrinkage 0.90: N =", result_90$sample_size, "\n")
cat("Shrinkage 0.95: N =", result_95$sample_size, "\n")
# Shrinkage 0.90: N = 531
# Shrinkage 0.95: N = 719
```

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

### Binary Models Using C-statistic

Source: https://context7.com/cran/pmsampsize/llms.txt

Calculate sample size for binary outcome models using the C-statistic (AUC) when Cox-Snell R-squared is unavailable.

```APIDOC
## Binary Models Using C-statistic

### Description
When Cox-Snell R-squared is not available from existing studies, use the C-statistic (AUC) instead. The function approximates R-squared using the method from Riley et al. (2020).

### Method
`pmsampsize(type = "b", cstatistic, parameters, prevalence, ...)`

### Endpoint
N/A (R function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Parameters (Function Arguments)
- **type** (character) - Must be set to "b" for binary outcomes.
- **cstatistic** (numeric) - Required - C-statistic (AUC) from an existing model.
- **parameters** (numeric) - Required - Number of candidate predictor parameters.
- **prevalence** (numeric) - Required - Expected outcome prevalence.
- **seed** (numeric) - Optional - Seed for reproducibility of R-squared approximation.
- **shrinkage** (numeric) - Optional - Target shrinkage (default 0.9).

### Request Example
```r
library(pmsampsize)

# Example: Using C-statistic when R-squared is not reported
# - 24 candidate predictor parameters
# - Prevalence of 17.4%
# - C-statistic of 0.89 from existing model

result_cstat <- pmsampsize(
  type = "b",
  cstatistic = 0.89,
  parameters = 24,
  prevalence = 0.174,
  seed = 123456  # For reproducibility of R-squared approximation
)

print(result_cstat)
```

### Response
#### Success Response (200)
Returns a data frame with sample size calculations for binary outcomes using C-statistic, including minimum sample size, shrinkage, parameters, R-squared values, and EPP.

#### Response Example
```
# Given input C-statistic = 0.89 & prevalence = 0.174
# Cox-Snell R-sq = 0.3418
#
#            Samp_size Shrinkage Parameter CS_Rsq Max_Rsq Nag_Rsq  EPP
# Criteria 1       262       0.9        24 0.3418   0.377   0.907 1.90
# Criteria 2       283     0.914        24 0.3418   0.377   0.907 2.05
# Criteria 3       531     0.914        24 0.3418   0.377   0.907 3.85
# Final            531     0.914        24 0.3418   0.377   0.907 3.85
#
# Minimum sample size required = 531, with 93 events and EPP = 3.85
```
```

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

### Calculate Sample Size using Nagelkerke's R-squared

Source: https://context7.com/cran/pmsampsize/llms.txt

Uses Nagelkerke's R-squared as an input parameter for sample size calculation. The function internally converts this to Cox-Snell R-squared.

```r
result_nagelkerke <- pmsampsize(
  type = "b",
  nagrsquared = 0.35,  # Nagelkerke's R-squared from existing model
  parameters = 20,
  prevalence = 0.25
)

print(result_nagelkerke)

# The function converts Nagelkerke to Cox-Snell internally
# Output includes both metrics for reference
result_nagelkerke$rsquared  # Cox-Snell R-squared (converted)
result_nagelkerke$nag_r2    # Nagelkerke R-squared (back-calculated)
```

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

### Calculate Sample Size Using C-statistic

Source: https://context7.com/cran/pmsampsize/llms.txt

Use the C-statistic to approximate R-squared when Cox-Snell R-squared is unavailable.

```r
library(pmsampsize)

# Example: Using C-statistic when R-squared is not reported
# - 24 candidate predictor parameters
# - Prevalence of 17.4%
# - C-statistic of 0.89 from existing model

result_cstat <- pmsampsize(
  type = "b",
  cstatistic = 0.89,
  parameters = 24,
  prevalence = 0.174,
  seed = 123456  # For reproducibility of R-squared approximation
)

print(result_cstat)
# Output:
# Given input C-statistic = 0.89 & prevalence = 0.174
# Cox-Snell R-sq = 0.3418
#
#            Samp_size Shrinkage Parameter CS_Rsq Max_Rsq Nag_Rsq  EPP
# Criteria 1       262       0.9        24 0.3418   0.377   0.907 1.90
# Criteria 2       283     0.914        24 0.3418   0.377   0.907 2.05
# Criteria 3       531     0.914        24 0.3418   0.377   0.907 3.85
# Final            531     0.914        24 0.3418   0.377   0.907 3.85
```

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

### Binary Outcome Models (Logistic Regression)

Source: https://context7.com/cran/pmsampsize/llms.txt

Calculate sample size for prediction models with binary outcomes using Cox-Snell R-squared.

```APIDOC
## Binary Outcome Models (Logistic Regression)

### Description
Calculate sample size for prediction models with binary outcomes (e.g., disease presence/absence, treatment response). Requires outcome prevalence and an R-squared estimate from existing models.

### Method
`pmsampsize(type = "b", csrsquared, parameters, prevalence, ...)`

### Endpoint
N/A (R function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Parameters (Function Arguments)
- **type** (character) - Must be set to "b" for binary outcomes.
- **csrsquared** (numeric) - Required - Cox-Snell R-squared from an existing model.
- **parameters** (numeric) - Required - Number of candidate predictor parameters.
- **prevalence** (numeric) - Required - Expected outcome prevalence.
- **shrinkage** (numeric) - Optional - Target shrinkage (default 0.9).
- **seed** (numeric) - Optional - Seed for reproducibility if using C-statistic approximation.

### Request Example
```r
library(pmsampsize)

# Example: Developing a logistic prediction model for a binary outcome
# - 24 candidate predictor parameters
# - Prevalence of 17.4%
# - Cox-Snell R-squared of 0.288 from an existing model

result_binary <- pmsampsize(
  type = "b",
  csrsquared = 0.288,
  parameters = 24,
  prevalence = 0.174
)

print(result_binary)
```

### Response
#### Success Response (200)
Returns a data frame with sample size calculations for binary outcomes, including minimum sample size, shrinkage, parameters, R-squared values, and EPP.

#### Response Example
```
# Output:
# NB: Assuming 0.05 acceptable difference in apparent & adjusted R-squared
# NB: Assuming 0.05 margin of error in estimation of intercept
# NB: Events per Predictor Parameter (EPP) assumes prevalence = 0.174
#
#            Samp_size Shrinkage Parameter CS_Rsq Max_Rsq Nag_Rsq  EPP
# Criteria 1       339       0.9        24  0.288   0.377   0.764 2.46
# Criteria 2       417     0.912        24  0.288   0.377   0.764 3.02
# Criteria 3       531     0.912        24  0.288   0.377   0.764 3.85
# Final            531     0.912        24  0.288   0.377   0.764 3.85
#
# Minimum sample size required = 531, with 93 events and EPP = 3.85

# Access individual results
result_binary$sample_size    # 531
result_binary$events         # 92.394 (rounded to 93)
result_binary$EPP            # 3.85
result_binary$nag_r2         # Nagelkerke R-squared
```
```

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

### Calculate Continuous Outcome Sample Size

Source: https://context7.com/cran/pmsampsize/llms.txt

Estimates sample size for linear regression prediction models.

```r
library(pmsampsize)

# Example: Developing a linear prediction model for FEV1 (lung function)
# - 25 candidate predictor parameters
# - R-squared of 0.2 from existing model
# - Mean FEV1 of 1.9 L
# - Standard deviation of 0.6 L

result_continuous <- pmsampsize(
  type = "c",
  rsquared = 0.2,
  parameters = 25,
  intercept = 1.9,
  sd = 0.6
)

print(result_continuous)
# Output:
# NB: Assuming 0.05 acceptable difference in apparent & adjusted R-squared
# NB: Assuming MMOE <= 1.1 in estimation of intercept & residual standard deviation
# SPP - Subjects per Predictor Parameter
#
#             Samp_size Shrinkage Parameter Rsq   SPP
# Criteria 1        918     0.900        25 0.2 36.72
# Criteria 2        401     0.976        25 0.2 16.04
# Criteria 3        259     0.985        25 0.2 10.36
# Criteria 4*       918     0.900        25 0.2 36.72
# Final             918     0.900        25 0.2 36.72
#
# Minimum sample size required = 918
#
# * 95% CI for intercept = (1.77, 2.03), for sample size n = 918

# Access individual components
result_continuous$sample_size  # 918
result_continuous$SPP          # 36.72 (Subjects per Predictor Parameter)
result_continuous$int_lci      # 1.77 (lower 95% CI for intercept)
result_continuous$int_uci      # 2.03 (upper 95% CI for intercept)
```

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

### Calculate Survival Outcome Sample Size

Source: https://context7.com/cran/pmsampsize/llms.txt

Estimates sample size for time-to-event models using Cox regression parameters.

```r
library(pmsampsize)

# Example: Developing a Cox prediction model for survival outcome
# - 30 candidate predictor parameters
# - Cox-Snell R-squared of 0.051 from existing model
# - Event rate of 0.065 per year
# - Prediction at 2-year timepoint
# - Mean follow-up of 2.07 years

result_survival <- pmsampsize(
  type = "s",
  csrsquared = 0.051,
  parameters = 30,
  rate = 0.065,
  timepoint = 2,
  meanfup = 2.07
)

print(result_survival)
# Output:
# NB: Assuming 0.05 acceptable difference in apparent & adjusted R-squared
# NB: Assuming 0.05 margin of error in estimation of overall risk at time point = 2
# NB: Events per Predictor Parameter (EPP) assumes overall event rate = 0.065
#
#              Samp_size Shrinkage Parameter CS_Rsq Max_Rsq Nag_Rsq  EPP
# Criteria 1        1073       0.9        30  0.051   0.499   0.102 4.81
# Criteria 2        3014     0.965        30  0.051   0.499   0.102 13.51
# Criteria 3 *      3014     0.965        30  0.051   0.499   0.102 13.51
# Final SS          3014     0.965        30  0.051   0.499   0.102 13.51
#
# Minimum sample size required = 3014,
# corresponding to 6238.98 person-time of follow-up, with 406 outcome events
# assuming overall event rate = 0.065 and EPP = 13.51
#
# * 95% CI for overall risk = (0.109, 0.148), for true value of 0.122

# Access detailed results
result_survival$sample_size       # 3014
result_survival$events            # 405.6846
result_survival$EPP               # 13.51
result_survival$tot_per_yrs_final # 6238.98 person-time
result_survival$int_cuminc        # 0.122 (true cumulative incidence at timepoint)
result_survival$int_lci           # 0.109 (lower 95% CI)
result_survival$int_uci           # 0.148 (upper 95% CI)
```

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

### Calculate Sample Size for Binary Outcomes

Source: https://context7.com/cran/pmsampsize/llms.txt

Calculate required sample size for logistic regression models using prevalence and Cox-Snell R-squared.

```r
library(pmsampsize)

# Example: Developing a logistic prediction model for a binary outcome
# - 24 candidate predictor parameters
# - Prevalence of 17.4% expected
# - Cox-Snell R-squared of 0.288 from an existing model

result_binary <- pmsampsize(
  type = "b",
  csrsquared = 0.288,
  parameters = 24,
  prevalence = 0.174
)

print(result_binary)
# Output:
# NB: Assuming 0.05 acceptable difference in apparent & adjusted R-squared
# NB: Assuming 0.05 margin of error in estimation of intercept
# NB: Events per Predictor Parameter (EPP) assumes prevalence = 0.174
#
#            Samp_size Shrinkage Parameter CS_Rsq Max_Rsq Nag_Rsq  EPP
# Criteria 1       339       0.9        24  0.288   0.377   0.764 2.46
# Criteria 2       417     0.912        24  0.288   0.377   0.764 3.02
# Criteria 3       531     0.912        24  0.288   0.377   0.764 3.85
# Final            531     0.912        24  0.288   0.377   0.764 3.85
#
# Minimum sample size required = 531, with 93 events and EPP = 3.85

# Access individual results
result_binary$sample_size    # 531
result_binary$events         # 92.394 (rounded to 93)
result_binary$EPP            # 3.85
result_binary$nag_r2         # Nagelkerke R-squared
```

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