The Reportable Range plan validates the test under many different conditions. 3 RNA input levels (low, medium, high) and the target at 12 different concentrations, ranging from 0.0488% to 100%. By testing 36 different conditions (12*3), we’ll get:

- Summary statistics for each fusion concentration and RNA input level
- Amplification efficiencies at the different % fusion concentrations
- Relationships between:
- Texas Red Ct and RNA Input Level
*(should be positively correlated)* - FAM and Texas Red Ct Values
*(should be positively correlated)* - ∆Ct and Texas Red Ct Values
*(should not be correlated)* - FAM Ct and % Fusion Concentration
*(should be negatively correlated)* - TxRd Ct and % Fusion Concentration
*(should not be correlated)* - ∆Ct Value and % Fusion Concentration
*(should be negatively correlated)*

- Texas Red Ct and RNA Input Level
- Multiple Linear Regression

Many relationships between *x* and *y* being tested; this is to make sure the assay is behaving as expected.

**1. Summary statistics for each fusion concentration and RNA input level**

For the summary statistics, we’ll just use the `summary_function`

as described in a previous post. The `summary_function`

prints out the common metrics like average, median, std dev, percentiles, etc.

**2. Amplification efficiencies at the different % fusion concentrations **

The amplification efficiency for the reaction is calculated using the formula:

Amplification Efficiency = (10 ^ (-1 / slope)) -1, (^ denotes “to the power of”).

This is our R function (because we are going to pass in different linear models based on RNA input or fusion concentration:

`calc_amplification_efficiency <- function (lm) {`

` slope <- lm$coefficients[2]`

` amplification_efficiency <- (10 ^ (-1 / slope)) -1`

` return (amplification_efficiency)`

`}`

`all.lm <- lm (FAM.Cq ~ log10(Fusion_Concentration), data=channels)`

`print (calc_amplification_efficiency (all.lm))`

Ideally your amplification efficiency is close to 1.

**3. Relationships Between Two Variables**

In this section, we fit a lot of linear regressions to check that the data behaves as expected. We generate a lot of plots, but it's really the slope of the linear regression that tells us whether the data behaves as expected.

Since we're looking at so many variables, a for-loop was necessary. This is a for-loop that looks at each concentration across the different measures (FAM, ΔCt, etc).

`params_to_plot = c("deltaCq", "FAM.Cq", "Target_PTPRK_Ct")`

`conc <- c(100, 50, 25, 12.5, 6.25, 3.125, 1.563, .7810, .3906 , .1953, .0977, 0.0488 )`

`for (param in params) {`

`for (fus_conc in conc) {`

`subset_df = channels[channels$Fusion_Concentration == fus_conc,]`

`subset_df.lm <- lm ( eval (parse( text=param)) ~ TexasRed.Cq, data=subset_df)`

`confidence_interval <- predict (subset_df.lm, interval='confidence', level=0.95)`

`print (c("% fusion", fus_conc) )`

`print (coef (subset_df.lm))`

`print (confint(subset_df.lm, 'TexasRed.Cq', level=0.95))`

`}`

`}`

Here are the linear regressions between FAM and Texas Red at various concentrations:

% Concentration | Intercept | Slope | 95% Confidence Interval around Slope |
---|---|---|---|

100 | 1.49 | 0.94 | (0.91, 0.98) |

50 | 1.53 | 0.99 | (0.95, 1.01) |

25 | 2.22 | 1 | (0.93, 1.06) |

12.5 | 3.59 | 0.99 | (0.92, 1.04) |

6.25 | 5.33 | 0.95 | (0.89, 1.01) |

3.125 | 4.04 | 1.06 | (0.97, 1.14) |

1.5625 | 6.93 | 0.99 | (0.85, 1.12) |

0.78125 | 3.96 | 1.17 | (0.96, 1.39) |

0.3906 | 9.46 | 1.02 | (0.75, 1.30) |

0.1953 | 18.67 | 0.72 | (0.16, 1.27) |

0.0977 | 10.66 | 1.15 | (-0.52, 2.83) |

0.0488 | 51.82 | -0.48 | (-25.19, 24.23) |

The corresponding figure is below:

FAM Ct and Texas Red Ct Values

At higher concentrations, the slope is close to 1 so there is a strong correlation, but the slope deviates from 1 at lower concentrations.

Another for-loop in the code generates a whole lot of graphs...

Texas Red Ct and RNA Input Level

∆Ct and % Fusion Concentration

FAM Ct and % Fusion Concentration

Texas Red Ct and % Fusion Concentration

**4. Multiple Linear Regression**

This multiple linear regression has Texas Red and the fusion concentration as dependent variables.

`mult.lin.regression <- lm (formula = deltaCq ~ TexasRed.Cq + log2(Fusion_Concentration) , data=channels)`

`summary (mult.lin.regression)`

`confint(mult.lin.regression, level=0.95)`

∆Ct should not depend on the RNA input level (Texas Red Cq), so the coefficient should be close to or approximately 0, indicating that there was little relationship between ∆Ct and RNA input level. If the coefficient for log2 (% fusion) is large coefficient, this means % fusion concentration can predict ΔCt.