How to Use This App

This app fits hill equation models to your data using Bayesian inference (NUTS sampler). The hill equation is commonly used in pharmacology to model dose-response relationships.

What it does: Given x-y data pairs, the app estimates the four parameters (y0, y1, K, n) that best fit the hill equation, along with uncertainty estimates (σ) from MCMC sampling.

Data Format

Supported File Types
  • CSV (.csv) - Comma-separated values
  • Excel (.xlsx) - Microsoft Excel files
Single Dataset

For a single curve, use exactly 2 columns: the first column is x (e.g., dose), the second is y (e.g., response).

Multiple Datasets

To fit multiple curves in one file, use consecutive x-y pairs:

  • Columns 1-2: x₁, y₁ (first curve)
  • Columns 3-4: x₂, y₂ (second curve)
  • And so on...
Important: Each x-y pair must have exactly 2 columns. The app will ignore any incomplete pairs at the end of the file.

Example Data

Here's an example of a valid CSV file with decreasing response:

dose response
0.010.06
0.110.10
1.08.07
2.05.07
4.02.18
6.01.15
10.00.40
15.00.13
Download Example Files
single_decreasing.csv single_increasing.csv multi_dataset.csv

Fitted Parameters

The app fits the following parameters to your data:

Parameter Description
y₀Baseline response (y value when x = 0)
y₁Range of response (y₁ = ymax - ymin)
KHalf-maximal concentration (EC₅₀ or IC₅₀)
nHill coefficient (slope of the curve)
σError estimate (standard deviation)

Results

After fitting, you'll receive:

  • Fitted curve plot - Visual comparison of your data vs. the fitted model
  • MCMC chain plot - Diagnostic plots showing the sampling quality
  • Parameter estimates - Best-fit values for y₀, y₁, K, n, σ
  • Trend detection - Automatically detected as increasing or decreasing
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