---
title: "Setting Quality Goals with Biological Variation"
author: "Marcello Grassi"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Setting Quality Goals with Biological Variation}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
 collapse = TRUE,
 comment = "#>",
  fig.width = 6,
  fig.height = 4,
  fig.align = "center"
)
```

## Introduction
A fundamental question in laboratory medicine is: "How good does my analytical method need to be?" The answer depends on the intended clinical use. A method that is acceptable for population screening may be inadequate for monitoring individual patients.
This vignette introduces the biological variation model for setting analytical performance specifications, implemented in the `valytics` package through three functions:
- `ate_from_bv()`: Calculate specifications from biological variation data
- `sigma_metric()`: Quantify performance using the Six Sigma metric
- `ate_assessment()`: Evaluate observed performance against specifications

```{r load-package}
library(valytics)
```

## The Biological Variation Model

### Concept
Every measurand (analyte) exhibits natural variation even in healthy individuals. This variation has two components:
- **Within-subject variation (CV~I~)**: Day-to-day fluctuation within an individual
- **Between-subject variation (CV~G~)**: Differences between individuals in a population
The biological variation model, developed by Fraser, Petersen, and colleagues, uses these inherent variations to derive meaningful analytical performance goals. The logic is straightforward: analytical error should be small enough that it does not significantly increase the total variation observed in test results.

### The Formulas

At the **desirable** performance level, the formulas are:  

**Allowable Imprecision:**
$$CV_A \leq 0.50 \times CV_I$$  
**Allowable Bias:**  
$$Bias \leq 0.25 \times \sqrt{CV_I^2 + CV_G^2}$$  
**Total Allowable Error:**  
$$TEa \leq k \times CV_A + Bias$$
Where *k* is a coverage factor (typically 1.65 for ~95% of results).

### Performance Hierarchy

Three performance tiers are defined, each with different multipliers:

| Level | Imprecision | Bias | Stringency |
|-------|-------------|------|------------|
| Optimal | 0.25 × CV~I~ | 0.125 × √(CV~I~² + CV~G~²) | Most stringent |
| Desirable | 0.50 × CV~I~ | 0.25 × √(CV~I~² + CV~G~²) | Standard target |
| Minimum | 0.75 × CV~I~ | 0.375 × √(CV~I~² + CV~G~²) | Least stringent |

## Calculating Specifications with ate_from_bv()

### Basic Usage

The `ate_from_bv()` function calculates all three specifications from biological variation data:

```{r ate-basic}
# Example: Glucose
# CV_I = 5.6%, CV_G = 7.5% (illustrative values)
ate_glucose <- ate_from_bv(cvi = 5.6, cvg = 7.5)
ate_glucose
```

### Comparing Performance Levels

The `summary()` method shows all three performance tiers:

```{r ate-summary}
summary(ate_glucose)
```

### Different Performance Levels

You can calculate specifications for any tier:

```{r ate-levels}
# Optimal (most stringent)
ate_optimal <- ate_from_bv(cvi = 5.6, cvg = 7.5, level = "optimal")
ate_optimal$specifications$tea

# Minimum (least stringent)
ate_minimum <- ate_from_bv(cvi = 5.6, cvg = 7.5, level = "minimum")
ate_minimum$specifications$tea
```

### When CV~G~ is Unknown

If only within-subject variation is available, imprecision goals can still be calculated:

```{r ate-cvi-only}
ate_cv_only <- ate_from_bv(cvi = 5.6)
ate_cv_only
```

## The Six Sigma Metric

### Concept

The sigma metric provides a standardized way to express method quality. It answers: "How many standard deviations of analytical error fit between my observed performance and the allowable limit?"
$$\sigma = \frac{TEa - |Bias|}{CV}$$

Higher sigma values indicate better performance:  

| Sigma | Category | Defects per Million |
|-------|----------|---------------------|
| ≥ 6 | World Class | ~3.4 |
| ≥ 5 | Excellent | ~230 |
| ≥ 4 | Good | ~6,200 |
| ≥ 3 | Marginal | ~66,800 |
| ≥ 2 | Poor | ~308,500 |
| < 2 | Unacceptable | > 690,000 |

### Calculating Sigma
```{r sigma-basic}
# Assume observed: bias = 1.5%, CV = 2.5%
# Using TEa from biological variation
sm <- sigma_metric(
 bias = 1.5,
  cv = 2.5,
  tea = ate_glucose$specifications$tea
)
sm
```

### Detailed Sigma Summary

```{r sigma-summary}
summary(sm)
```

### Interpreting Sigma in Clinical Context

In clinical laboratories:  

- **Sigma ≥ 6**: Minimal QC needed; method is highly reliable
- **Sigma 4-6**: Standard QC procedures adequate
- **Sigma 3-4**: Enhanced QC recommended; monitor closely
- **Sigma < 3**: High risk of errors; consider method improvement

## Comprehensive Assessment with ate_assessment()

### Basic Assessment

The `ate_assessment()` function evaluates observed performance against specifications:

```{r assess-basic}
assess <- ate_assessment(
  bias = 1.5,
  cv = 2.5,
  tea = ate_glucose$specifications$tea
)
assess
```

### Full Component Assessment

When you have specifications for all components:

```{r assess-full}
assess_full <- ate_assessment(
  bias = 1.5,
  cv = 2.5,
  tea = ate_glucose$specifications$tea,
  allowable_bias = ate_glucose$specifications$allowable_bias,
  allowable_cv = ate_glucose$specifications$allowable_cv
)
summary(assess_full)
```

### Handling a Failing Method

```{r assess-fail}
# A method with poor performance
assess_poor <- ate_assessment(
  bias = 4.0,
  cv = 5.0,
  tea = ate_glucose$specifications$tea,
  allowable_bias = ate_glucose$specifications$allowable_bias,
  allowable_cv = ate_glucose$specifications$allowable_cv
)
summary(assess_poor)
```

## Complete Workflow Example

Here is a typical workflow for evaluating a new glucose method:

```{r workflow}
# Step 1: Define quality goals from biological variation
specs <- ate_from_bv(cvi = 5.6, cvg = 7.5, level = "desirable")
cat("Quality Specifications:\n")
cat(sprintf("  Allowable CV: %.2f%%\n", specs$specifications$allowable_cv))
cat(sprintf("  Allowable Bias: %.2f%%\n", specs$specifications$allowable_bias))
cat(sprintf("  TEa: %.2f%%\n\n", specs$specifications$tea))

# Step 2: Assume we measured method performance
# (In practice, from validation studies)
observed_bias <- 1.8
observed_cv <- 2.2

# Step 3: Calculate sigma metric
sm <- sigma_metric(observed_bias, observed_cv, specs$specifications$tea)
cat(sprintf("Sigma Metric: %.2f (%s)\n\n", sm$sigma, sm$interpretation$category))

# Step 4: Full assessment
assessment <- ate_assessment(
  bias = observed_bias,
  cv = observed_cv,
  tea = specs$specifications$tea,
  allowable_bias = specs$specifications$allowable_bias,
  allowable_cv = specs$specifications$allowable_cv
)

# Step 5: Decision
if (assessment$assessment$overall) {
  cat("DECISION: Method acceptable for clinical use\n")
} else {
  cat("DECISION: Method requires improvement\n")
}
```

## Obtaining Biological Variation Data

The quality of your specifications depends on reliable biological variation estimates.

### Recommended Source

The **EFLM Biological Variation Database** is the current authoritative source:  

- Website: https://biologicalvariation.eu/  
- Provides rigorously reviewed BV estimates  
- Includes quality grades for each estimate  
- Updated regularly with new studies  

### Using the Database

1. Navigate to https://biologicalvariation.eu/  
2. Search for your analyte  
3. Review the CV~I~ and CV~G~ values  
4. Note the quality grade (A, B, C, D) and number of studies  
5. Use values appropriate for your population and context  

### Important Considerations

- BV data may vary by population, age, sex, and health status  
- Ensure the BV data match your intended use population  
- Higher quality grades (A, B) indicate more reliable estimates  
- When multiple estimates exist, consider the range  

## Beyond Biological Variation

While the biological variation model is widely used, it is not the only approach to setting quality specifications. Other models include:  

1. **Clinical outcome-based**: Specifications derived from clinical decision limits  
2. **State-of-the-art**: Based on achievable performance (e.g., proficiency testing data)  
3. **Regulatory requirements**: Fixed limits from agencies (e.g., CLIA)  

The `ate_assessment()` and `sigma_metric()` functions work with TEa values from any source—simply provide your specification directly rather than calculating from biological variation.

```{r other-sources}
# Using a CLIA-based TEa for glucose (example: ±6 mg/dL or ±10%)
# For a sample at 100 mg/dL, 10% = 10 mg/dL
sm_clia <- sigma_metric(bias = 2, cv = 3, tea = 10)
sm_clia
```

## Summary
The biological variation model provides a scientifically grounded approach to setting analytical quality specifications:  

1. **`ate_from_bv()`** translates biological variation into actionable specifications  
2. **`sigma_metric()`** provides a universal quality scale for comparing methods  
3. **`ate_assessment()`** gives a clear pass/fail evaluation  

These tools help laboratories make informed decisions about method acceptability while recognizing that the final decision depends on clinical context and regulatory requirements.

## References

Fraser CG, Petersen PH (1993). Desirable standards for laboratory tests if they are to fulfill medical needs. Clinical Chemistry, 39(7):1447-1453.  

Ricos C, Alvarez V, Cava F, et al. (1999). Current databases on biological variation: pros, cons and progress. Scandinavian Journal of Clinical and Laboratory Investigation, 59(7):491-500.  

Aarsand AK, Fernandez-Calle P, Webster C, et al. (2020). The EFLM Biological Variation Database. https://biologicalvariation.eu/  

Westgard JO, Westgard SA (2006). The quality of laboratory testing today: an assessment of sigma metrics for analytic quality using performance data from proficiency testing surveys and the CLIA criteria for acceptable performance. American Journal of Clinical Pathology, 125(3):343-354.