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Calculate Kroll's Linearity Test

Source: R/dilstats.R
calculate_adl_kroll_test.Rd

Calculate a statistical test for linearity from Kroll et. al. (2000) doi:10.5858/2000-124-1331-EOTEON using average deviation from linearity.

Usage

calculate_adl_kroll_test(curve_data, conc_var, signal_var)

Arguments

curve_data

A data frame or tibble containing curve data.

conc_var

Column name in curve_data to indicate concentration.

signal_var

Column name in curve_data to indicate signal.

Value

A data frame of statistical results from Kroll et. al. (2000) doi:10.5858/2000-124-1331-EOTEON

  • adl_kroll: Average deviation from linearity as defined in Kroll et. al. (2000) doi:10.5858/2000-124-1331-EOTEON

  • precision_on_percent_scale: Estimate of precision on percent scale. It is the ratio of the estimated regression standard error from the best-fit polynomial and the estimated solution mean.

  • uncorrected_critical_value: Critical value (Uncorrected) as defined in Kroll et. al. (2000) doi:10.5858/2000-124-1331-EOTEON

  • corrected_critical_value: Critical value (Corrected) as defined in Hsieh et. al. (2008) doi:10.1080/10543400802071378

  • uncorrected_kroll_results: Indicate if adl_kroll is less than uncorrected_critical_value If FALSE, there is sufficient evidence to reject the hypothesis that the points are linear.

  • corrected_kroll_results: Indicate if adl_kroll is less than corrected_critical_value If FALSE, there is sufficient evidence to reject the hypothesis that the points are linear.

  • best_model Gives values linear, quadratic or cubic to indicate the model that "best fit" the points. The function compare_performance is used to determine the best fit.

Details

The function will return NA if the number of curve points is less than or equal to three.

References

Kroll, M. H., Praestgaard, J., Michaliszyn, E., & Styer, P. E. (2000). Evaluation of the extent of nonlinearity in reportable range studies. Archives of pathology & laboratory medicine, 124(9), 1331–1338. doi:10.5858/2000-124-1331-EOTEON

Hsieh E., & Liu J. P. (2008). On Statistical Evaluation of the Linearity in Assay Validation Journal of Biopharmaceutical Statistics, 18(4), 677–690. doi:10.1080/10543400802071378

Examples


# Data from Kroll's 2000 paper
solution_number <- c(
  1, 1, 2, 2, 3, 3, 4, 4,
  5, 5, 6, 6, 7, 7
)

result <- c(
  352, 348, 1009, 991, 1603, 1584, 3100, 3200,
  4482, 4390, 5101, 5046, 5669, 5516
)

curve_data <- data.frame(
  Solution_Number = solution_number,
  Result = result
)

adl_result <- calculate_adl_kroll_test(
  curve_data,
  "Solution_Number",
  "Result"
)

adl_result
#> # A tibble: 1 × 7
#>   adl_kroll precision_on_percent_scale uncorre…¹ corre…² uncor…³ corre…⁴ best_…⁵
#>       <dbl>                      <dbl>     <dbl>   <dbl> <chr>   <chr>   <chr>  
#> 1      8.63                       5.54      7.61    2.86 FALSE   FALSE   cubic  
#> # … with abbreviated variable names ¹​uncorrected_critical_value,
#> #   ²​corrected_critical_value, ³​uncorrected_kroll_results,
#> #   ⁴​corrected_kroll_results, ⁵​best_model