Website: https://yiqunchen.github.io/pppower/

pppower

pppower is an R package for power analysis and sample-size calculation under the Prediction-Powered Inference (PPI/PPI++) framework.

Prevalence Estimation with PPI

For binary outcomes (prevalence), you can estimate required labeled sample size while leveraging model predictions on a large unlabeled set. This is exactly what PPI is for:

• Inputs: target effect size $\Delta$, unlabeled size $N$, and model quality (e.g., sensitivity/specificity)
• Output: required labeled $n$ for your target power
• Benefit: better predictions can reduce labeled annotation burden

Use power_ppi_mean(..., n = NULL) for one-sample prevalence and power_ppi_ttest_binary() for two-group prevalence differences.

Interactive Calculator

Open Interactive PPI Sample Size Calculator

Direct link to the live calculator page.

What is Prediction-Powered Inference?

Many modern studies have access to:

• Labeled data $(X_i, Y_i)$ for $i = 1, \ldots, n$ — expensive to obtain (human annotations, lab assays, expert reviews)
• Unlabeled data $\tilde{X}_j$ for $j = 1, \ldots, N$ — cheap and abundant, with ML predictions $f(\tilde{X}_j)$ available

PPI combines both sources for valid, efficient inference. The PPI++ estimator for the population mean $\theta^* = E[Y]$ is:

$$\hat{\theta}_\lambda = \bar{Y}_L + \lambda(\bar{f}_U - \bar{f}_L)$$

where $\lambda$ controls the blend between labeled data and predictions. The key insight: good predictions reduce the amount of labeled data needed for a given level of statistical power.

Key Formulas

The PPI++ variance under the oracle $\lambda^*$ is:

$$\text{Var}(\hat{\theta}_{\lambda^*}) = \frac{\sigma_Y^2}{n} - \frac{\text{Cov}(Y,f)^2}{\sigma_f^2} \cdot \frac{N}{n(n+N)}$$

Solving for the required labeled sample size (quadratic in $n$):

$$n \geq \frac{\sigma_Y^2 - S^2 N + \sqrt{(\sigma_Y^2 - S^2 N)^2 + 4 S^2 N \sigma_Y^2 (1 - \rho_{Yf}^2)}}{2S^2}$$

where $S^2 = (\Delta / (z_{1-\alpha/2} + z_{1-\beta}))^2$.

Rule of thumb: The sample size ratio satisfies $n_{\texttt{PPI++}} / n_{\text{classical}} \approx 1 - R^2$, where $R^2$ is the squared correlation between $Y$ and $f(X)$. A predictor explaining 80% of the variance cuts labeled data needs by ~80%.

Supported Designs

Design	Power / Sample Size	Simulation
One-sample mean (continuous)	power_ppi_mean()	simulate_ppi_mean()
One-sample mean (binary)	power_ppi_mean()	simulate_ppi_vanilla_mean()
Two-sample $t$-test	power_ppi_ttest()	simulate_ppi_ttest_binary()
Paired $t$-test	power_ppi_paired()	—
2x2 contingency table	power_ppi_2x2()	—
Regression contrast	power_ppi_regression()	—

Installation

You can install the development version of pppower from GitHub with:

# install.packages("devtools")
devtools::install_github("yiqunchen/pppower")

Quick Example

A three-step workflow: compute power → solve for required $n$ → verify with Monte Carlo.

library(pppower)

# Step 1: Compute power for a given sample size
power_ppi_mean(
  delta    = 0.2,
  N        = 5000,
  n        = 200,
  var_f    = 0.6,
  var_res  = 0.4,
  cov_y_f  = 0.6,
  alpha    = 0.05
)

# Step 2: Solve for required labeled n to achieve 80% power
power_ppi_mean(
  delta       = 0.2,
  N           = 5000,
  n           = NULL,
  power       = 0.80,
  sigma_y2    = 1.0,
  sigma_f2    = 0.49,
  cov_y_f     = 0.63,
  lambda_mode = "oracle"
)

# Step 3: Verify with Monte Carlo simulation
simulate_ppi_mean(
  R     = 2000,
  n     = 100,
  N     = 5000,
  delta = 0.2,
  var_f   = 0.49,
  var_res = 0.51,
  alpha = 0.05
)

Input Modes

pppower supports three ways to specify variance components:

1. Direct moments — supply $\sigma_Y^2$, $\sigma_f^2$, and $\text{Cov}(Y, f)$ directly:

power_ppi_mean(delta = 0.2, N = 5000, n = 200,
                  sigma_y2 = 1.0, sigma_f2 = 0.49, cov_y_f = 0.63)

2. Prediction variance / residual variance — decompose outcome variance via var_f and var_res:

power_ppi_mean(delta = 0.2, N = 5000, n = 200,
                  var_f = 0.49, var_res = 0.51, cov_y_f = 0.49)

3. Metrics interface — supply sensitivity/specificity (binary) or MSE/$R^2$ (continuous):

power_ppi_mean(delta = 0.05, N = 5000, n = 200,
                  metrics = list(sensitivity = 0.85, specificity = 0.90,
                                 p_y = 0.3, m_obs = 200),
                  metric_type = "classification")

Vignettes

• Quickstart: Prediction-Powered Power & Sample Size — end-to-end walkthrough of power curves and Type I error checks (vignette("intro-ppi"))
• Detailed Dive: Sample Size & Metrics Interface — how power_ppi_mean(..., n = NULL) works across input modes, including regression contrasts (vignette("ppi-sample-size"))
• Detailed Dive: Variance Formulas and lambda-star — mathematical derivations behind the PPI++ variance and oracle $\lambda^*$ (vignette("deep-dive-math"))
• 2x2 Contingency Table Calculator — odds-ratio and relative-risk planning with binary surrogates (vignette("calculator-2x2"))

Citation

If you use pppower in your research, please cite:

@software{pppower,
  title = {pppower: Prediction-Powered Inference Power Calculations},
  author = {Guo, Moran and Chen, Yiqun},
  url = {https://github.com/yiqunchen/pppower},
  year = {2025}
}