nlmixr2autoinit (version 1.0.0)

metrics.: Calculate metrics for model predictive performance evaluation

Description

Computes common error metrics that quantify the predictive performance of pharmacometric models by comparing predicted (pred.x) and observed (obs.y) concentration values.

Usage

metrics.(pred.x, obs.y)

Value

A numeric vector with named elements:

• APE: absolute prediction error

• MAE: mean absolute error

• MAPE: mean absolute percentage error

• RMSE: root mean squared error

• rRMSE1: relative RMSE (type 1)

• rRMSE2: relative RMSE (type 2)

Arguments

pred.x

Numeric vector of model-predicted values.

obs.y

Numeric vector of corresponding observed values.

Details

The function stops with an error if pred.x and obs.y have unequal lengths. The following metrics are calculated:

$$APE = \sum |pred.x - obs.y|$$ Absolute prediction error (APE) is the sum of absolute differences.

$$MAE = \frac{1}{n} \sum |pred.x - obs.y|$$ Mean absolute error (MAE) expresses the average absolute deviation.

$$MAPE = \frac{100}{n} \sum \left| \frac{pred.x - obs.y}{obs.y} \right|$$ Mean absolute percentage error (MAPE) normalizes the error by observed values.

$$RMSE = \sqrt{\frac{1}{n} \sum (pred.x - obs.y)^2}$$ Root mean squared error (RMSE) penalizes larger deviations.

$$rRMSE1 = \frac{RMSE}{\bar{obs.y}} \times 100$$ Relative RMSE type 1 is the RMSE normalized by the mean observed value.

$$rRMSE2 = 100 \times \sqrt{\frac{1}{n} \sum \left( \frac{pred.x - obs.y}{(pred.x + obs.y)/2} \right)^2}$$ Relative RMSE type 2 is symmetric and normalizes by the mean of each predicted–observed pair.

Examples

obs.y  <- rnorm(100, mean = 100, sd = 10)
pred.x <- obs.y + rnorm(100, mean = 0, sd = 5)
metrics.(pred.x = pred.x, obs.y = obs.y)