CBLS {BivRegBLS} | R Documentation |

## Correlated Bivariate Least Square regression (CBLS)

### Description

Estimate the Correlated Bivariate Least Square regression with replicated data (in a (M,D) plot) where M=(X+Y)/2 and D=Y-X.

### Usage

```
CBLS(data = NULL, xcol = 1, ycol = 2, var.x = NULL, var.y = NULL,
df.var.x = Inf, df.var.y = Inf, ratio.var = NULL, conf.level = 0.95,
pred.level = 0.95, npoints = 1000, qx = 1, qy = 1, xpred = NULL)
```

### Arguments

`data` |
a data set (data frame or matrix). |

`xcol` |
a numeric vector to specify the X column(s) or a character vector with the column names. |

`ycol` |
a numeric vector to specify the Y column(s) or a character vector with the column names. |

`var.x` |
a numeric variable for the variance of the measurement error of device X if known. |

`var.y` |
a numeric variable for the variance of the measurement error of device Y if known. |

`df.var.x` |
a numeric variable for the degrees of freedom of the variance of the measurement error of device X if known. |

`df.var.y` |
a numeric variable for the degrees of freedom of the variance of the measurement error of device Y if known. |

`ratio.var` |
a numeric value for λ, the ratio of the measurement error variances (Y over X) if known. |

`conf.level` |
a numeric value for the confidence level (expressed between 0 and 1). |

`pred.level` |
a numeric value for the predictive level (expressed between 0 and 1). |

`npoints` |
an integer (at least 10) for the number of points to smooth the hyperbolic curves. |

`qx` |
an integer to predict the mean of qy Y future values from the mean of qx X values (generalized interval). |

`qy` |
an integer to predict the mean of qy Y future values from the mean of qx X values (generalized interval). |

`xpred` |
a numeric vector for customized predictions at given M values. |

### Details

The data argument is mandatory. If the data are unreplicated, then the measurement error variances must be given or their ratio (λ) in order to calculate the correlation, ρ_{MD}, between the measurement errors of the differences (on the Y-axis) and the measurement errors of the means (on the X-axis). The confidence level is used for the confidence intervals of the parameters (ρ_{MD}, β (slope), α (intercept)), the hyperbolic confidence intervals (the prediction of the expectation of Y for a given X) and the hyperbolic confidence bands. The predictive level is used for the hyperbolic predictive intervals (the prediction of a future Y for a given X) and the hyperbolic generalized intervals (the prediction of the mean of q future Y values for a given X).

### Value

A CBLS class object, a list including the following elements:

`Xij` |
a table with the (replicated) X measurements (replicates are in columns). |

`Yik` |
a table with the (replicated) Y measurements (replicates are in columns). |

`Xi` |
a vector with the means of the X measurements. |

`Yi` |
a vector with the means of the Y measurements. |

`Mi` |
a vector with the means ((X+Y)/2) measurements. |

`Di` |
a vector with the differences (Y-X) measurements. |

`nxi` |
a vector with the number of X replicates per sample (patient). |

`nyi` |
a vector with the number of Y replicates per sample (patient). |

`variances_x` |
a vector with the variances calculated on the X replicates per sample (patient). |

`variances_y` |
a vector with the variances calculated on the Y replicates per sample (patient). |

`Rho.MD` |
a table with the value of ρMD (the correlation between the measurement errors of the means and the differences) and its confidence interval. |

`Ellipse.CBLS` |
a two columns matrix with the coordinates of the joint confidence interval (confidence region, ellipse) for the parameters (β, α). |

`Estimate.CBLS` |
a table (data frame) with the estimates of the intercept and the slope, standard error, confidence interval and pvalue (null hypothesis: slope = 0, intercept = 0). |

`Pred.CBLS` |
a data frame with npoints rows (from the minimum to the maximum of the observed X values) and the following columns: the X values where the predictions are calculated (X0), the Y predicted values (Ypred), the lower and upper bounds of the confidence interval, predictive interval, generalized interval and confidence bands. |

`xpred.CBLS` |
a data frame with the customized predictions and the same columns than |

### Author(s)

Bernard G FRANCQ

### References

Francq BG, Govaerts BB. How to regress and predict in a Bland-Altman plot? Review and contribution based on tolerance intervals and correlated-errors-in-variables models. Statistics in Medicine, 2016; 35:2328-2358.

### See Also

### Examples

```
library(BivRegBLS)
data(SBP)
# CBLS regression on replicated data
res.CBLS1=CBLS(data=SBP,xcol=c("J1","J2","J3"),ycol=8:10,qx=3,qy=3,xpred=c(100,120,140,160))
# CBLS regression on unreplicated data with measurement error variances previously estimated
res.CBLS2=CBLS(data=SBP,xcol=c("J1"),ycol="S1",var.x=80,var.y=50,df.var.x=100,df.var.y=100)
```

*BivRegBLS*version 1.1.1 Index]