Akritas-Theil-Sen line for censored data

Source: R/ATS.R

Computes Kendall's tau and the Akritas-Theil-Sen (ATS) line for censored data, along with the test that the slope (and Kendall's tau) equal zero. For one x variable regression.

ATS(
  y.var,
  y.cen,
  x.var,
  x.cen = rep(0, times = length(x.var)),
  LOG = TRUE,
  retrans = FALSE,
  xlabel = NULL,
  ylabel = NULL,
  printstat = TRUE
)

Arguments

y.var

The column of y (response variable) values plus detection limits
y.cen

The y-variable indicators, where 1 (or TRUE) indicates a detection limit in the y.var column, and 0 (or FALSE) indicates a detected value in y.var.
x.var

The column of x (explanatory variable) values plus detection limits
x.cen

The x-variable indicators, where 1 (or TRUE) indicates a detection limit in the x.var column, and 0 (or FALSE) indicates a detected value in x.var.
LOG

Indicator of whether to compute the ATS line in the original y units, or for their logarithms. The default is to use the logarithms (LOG = TRUE). To compute in original units, specify the option LOG = FALSE (or LOG = 0).
retrans

Indicator of whether to retransform the plot and line back to original Y-variable units. Not needed when LOG = FALSE. When retrans = FALSE & LOG = TRUE the plot is drawn with logY units (default). When retrans = TRUE & LOG = TRUE the plot is drawn with original Y units.
xlabel

Custom label for the x axis of plots. Default is x variable column name.
ylabel

Custom label for the y axis of plots. Default is y variable column name.
printstat

Logical TRUE/FALSE option of whether to print the resulting statistics in the console window, or not. Default is TRUE.

Value

Coefficients (intercept and slope) for the ATS line are printed, along with Kendall's tau correlation coefficient, test statistic S, and the (single) p-value for the test that tau and slope both equal zero. A scatterplot with the fitted trend-line superimposed is also drawn.

References

Akritas, M.G., Murphy, S.A., LaValley, M.P., 1995. The Theil-Sen Estimator With Doubly Censored Data and Applications to Astronomy. Journal of the American Statistical Association 90, 170–177. https://doi.org/10.2307/2291140

Helsel, D.R., 2011. Statistics for Censored Environmental Data using Minitab and R, 2nd ed. John Wiley & Sons, USA, N.J.

Examples

# Both y and x are censored
data(PbHeron)
with(PbHeron, ATS(Blood, BloodCen, Kidney, KidneyCen))

#> Akritas-Theil-Sen line for censored data 
#>  
#> ln(Blood) = -4.1556 + 0.2926 * Kidney 
#> Kendall's tau = 0.4217   p-value = 0.00043 
#>  

# x is not censored
data(Brumbaugh)
with(Brumbaugh,ATS(Hg, HgCen, PctWetland))

#> Akritas-Theil-Sen line for censored data 
#>  
#> ln(Hg) = -1.7779 + 0.0214 * PctWetland 
#> Kendall's tau = 0.192   p-value = 0.00063 
#>