An example of linearity verification

Level | P_{H} |
Measured value | σ value | Weight | Predicted value (P) | Deviation | 90% CI | ±ADL | Overlaps with ±ADL | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

#1 | #2 | #3 | Mean (M) | SD | Lower limit | Upper limit | ||||||||

1 | 1 | 3,250 | 3,393 | 3,301 | 3,314.7 | 72.473 | 70.658 | 1/(70.658)^{2} |
3,234.93 | 79.74 | -17.36 | 176.83 | ±161.75 | Acceptable |

2 | 0.75 | 2,502 | 2,401 | 2,378 | 2,427.0 | 65.962 | 51.736 | 1/(51.736)^{2} |
2,435.03 | -8.03 | -79.12 | 63.06 | ±121.75 | Acceptable |

3 | 0.5 | 1,619 | 1,650 | 1,639 | 1,636.0 | 15.716 | 34.874 | 1/(34.874)^{2} |
1,635.13 | 0.87 | -47.05 | 48.79 | ±81.76 | Acceptable |

4 | 0.25 | 788 | 790 | 799 | 792.3 | 5.859 | 16.890 | 1/(16.890)^{2} |
835.24 | -42.90 | -66.11 | -19.69 | ±41.76 | Acceptable |

5 | 0.1 | 331 | 340 | 342 | 337.7 | 5.859 | 7.198 | 1/(7.198)^{2} |
355.30 | -17.63 | -27.52 | -7.74 | ±17.76 | Acceptable |

6 | 0 | 35 | 36 | 35 | 35.3 | 0.577 | 1/(0.577)^{2} |
35.34 | 0.00 | -0.80 | 0.79 | ±1.77 | Acceptable | |

A(WLS) | 3,199.6 | B(WLS) | 35.336 |

Construct a function with no intercept: Y=S∙X (X-axis: M; Y-axis: SD)

When calculating the slope S using Microsoft Excel, use the command ‘LINEST((SD region), (M region),0)’ instead of the command ‘slope’ because it presupposes that there is a non-zero intercept.

Then, σ=S∙M

Construct a function of the least square linear regression: Y=A∙X+B (X-axis: P_{H}, Y-axis: M)

When calculating the slope A using Microsoft Excel, use the command ‘LINEST((M region), (P_{H} region)^2)’. And when calculating the intercept B using Microsoft Excel, use the command “SQRT(SUMSQ(Level 6 data)/3), where 3 is the number of replicates in this example.

Then, *P*=A∙P_{H}+B

Deviation=M–P; 90% CI=Deviation±

Abbreviations: P_{H}, the proportion of the high-level sample; SD, standard deviation; CI, confidence interval; ADL, allowable deviation from linearity; WLS, weighted linear square regression.

Lab Med Online 2024;14:163~175 https://doi.org/10.47429/lmo.2024.14.3.163

© Lab Med Online