10  Quality Control

10.1 Analysis Objectives

Quality control (QC) determines whether a measurement system is in control by periodically measuring quality-control materials and monitoring whether the results deviate from target values. ivdtools provides Levey–Jennings charts with Westgard multi-rule evaluation (qc_chart()), grouped monitoring in lot-change/group-change scenarios, and the Youden plot for two-level QC (youden_plot()).

This document demonstrates: obtaining and understanding the Westgard rules, whether daily QC results exceed the limits, how to evaluate grouping correctly when a reagent lot changes, and the Youden plot for two-level QC. The example data are deterministic teaching data; the Westgard rule combination and allowable limits should be pre-determined according to the laboratory’s risk-management strategy and protocol.

library(ivdtools)
library(readr)

10.2 Overview of Functions

Function	Main purpose	Key input or output
list_westgard()	View Westgard rule names and meanings	brief=TRUE returns only the rule vector
qc_chart()	Levey–Jennings chart + rule judgment	rules, mean/sd, group, run
youden_plot()	Youden plot for two-level QC	two sample columns, target means/SDs

10.3 Example 1: Obtaining Rules and Daily QC

10.3.1 Viewing the Westgard Rules

list_westgard()

Westgard QC Rules
  -------------------------------------------------- 
  1-2s    1 point exceeds +/-2s (warning)
  1-3s    1 point exceeds +/-3s (out of control)
  2-2s    2 consecutive points exceed +/-2s (same side)
  R-4s    2 consecutive points differ by at least 4s
  4-1s    4 consecutive points exceed +/-1s (same side)
  8x      8 consecutive points on same side of mean
  10x     10 consecutive points on same side of mean
  -------------------------------------------------- 

10.3.2 Reading Daily QC Data

qc_daily <- read_csv("./data/qc-daily.csv", show_col_types = FALSE)
qc_daily <- as.data.frame(qc_daily)
head(qc_daily)

The data are daily QC results with target mean = 100, SD = 3, for a total of 30 run points.

10.3.3 Running Quality Judgments

qc <- qc_chart(
  qc_daily,
  value = "value",
  rules = "1-2s,1-3s,2-2s,R-4s,4-1s,10x",
  mean = 100,
  sd = 3,
  run = "run"
)
print(qc)

QC Control Chart
  Value column:    value
  Mean (target):   100.0000
  SD (target):     3.0000
  N (total):       30  |  Complete: 30  |  Missing: 0
  Rules applied:   1-2s, 1-3s, 2-2s, R-4s, 4-1s, 10x

  Violations:
  -------------------------------------------------- 
    1-2s  : points 15, 23
    1-3s  : points 15
  -> 2 violation(s): 1 warning(s), 1 out of control

plot(qc)

qc_chart() records the points violating each rule in $violations:

qc$violations

$`1-2s`
[1] 15 23

$`1-3s`
[1] 15

$`2-2s`
integer(0)

$`R-4s`
integer(0)

$`4-1s`
integer(0)

$`10x`
integer(0)

In this example, point 15 exceeds +3s (triggering 1-3s and 1-2s, judged out of control), and point 23 falls below −2s (triggering 1-2s, judged a warning). n_warn and n_oc give the warning and out-of-control point counts, respectively.

Parameter notes: The rules of qc_chart() is a comma-separated rule string; mean/sd are the target values (when not given, they are estimated from the data, but monitored QC should use target values from the instructions). run specifies the run-order column, and group specifies the grouping column (see Example 2).

10.4 Example 2: Grouped Evaluation on Reagent Lot Change

10.4.1 Reading Data

In the data, the first 10 points are lot L1, the middle 10 are lot L2 (with an overall shift), and the last 10 are lot L3:

qc_lot <- read_csv("./data/qc-lot-change.csv", show_col_types = FALSE)
qc_lot <- as.data.frame(qc_lot)
table(qc_lot$lot)

L1 L2 L3 
10 10 10 

10.4.2 Grouping the Whole Sequence

Use group = "lot" for plotting; the Westgard rules are still judged on the entire sequence:

qc_lot_all <- qc_chart(
  qc_lot,
  value = "value",
  mean = 100,
  sd = 3,
  run = "run",
  group = "lot"
)
qc_lot_all$n_oc

[1] 0

plot(qc_lot_all)

Although the plot is faceted by lot, the rules are computed on the entire sequence, so observe the systematic shift caused by the lot change.

10.5 Example 3: Youden Plot for Two-Level QC

10.5.1 Reading Data

The Youden plot uses the results of two quality-control materials at different concentrations (levels) in the same run (wide-table format, one column per level):

youden_dat <- read_csv("./data/qc-youden.csv", show_col_types = FALSE)
youden_dat <- as.data.frame(youden_dat)
head(youden_dat)

10.5.2 Drawing the Youden Plot

yd <- youden_plot(
  youden_dat,
  sample1 = "low",
  sample2 = "high",
  mean1 = 80,
  mean2 = 200,
  sd1 = 2,
  sd2 = 5
)
print(yd)

Youden Plot
  Sample 1 (low):
    Mean:   80.0000
    SD:     2.0000
  Sample 2 (high):
    Mean:   200.0000
    SD:     5.0000
  Correlation: 0.5428
  N (total):   30  |  Complete: 30  |  Missing: 0
  Points outside +/-2SD: 3  (rows: 3, 17, 19)

plot(yd)

yd$outside_rows

[1]  3 17 19

youden_plot() uses a ±2s rectangle to mark points outside the range. In this example, 3 run points fall outside the rectangle (including an artificially set out-of-control point), suggesting that these runs may be affected by a systematic error at the same time. A shared shift at both levels (points moving outward along the diagonal) suggests a systematic error, while a large shift in a single direction is more likely to come from random error or a single-level problem.

Parameter notes: The sample1/sample2 of youden_plot() are the numeric columns of the two levels; mean1/mean2/sd1/sd2 are the target values (when not given, they are estimated from the data). $n_outside and $outside_rows give the points outside the rectangle.

10.6 Key Points for Interpreting Results

1. Target-value source: The target mean and SD of the QC chart should come from the instructions or validation data, not be estimated on the fly from the data.
2. Rule combination: The Westgard rule combination and the disposition process for judging out of control should be pre-specified in the protocol and re-evaluated with the risk.
3. Two-level complementarity: The Youden plot looks at the joint performance of both levels simultaneously, identifying signs of systematic and random error.
4. Out-of-control disposition: After detecting an out-of-control point, stop reporting, investigate the cause, re-validate and recall if necessary, and record the complete disposition chain.
5. Statistics ≠ release: QC judgment is one basis for the release decision; the final decision should comply with the laboratory’s quality-system requirements.