Tolerance Limits from an Agreement Study

A function for calculating tolerance limits for the difference between two measurements (difference = x-y). This is a procedure that should produce results similar to the Bland-Altman limits of agreement. See vignettes for more details.

tolerance_limit(
  data,
  x,
  y,
  id = NULL,
  condition = NULL,
  time = NULL,
  pred_level = 0.95,
  tol_level = 0.95,
  tol_method = c("approx", "perc"),
  prop_bias = FALSE,
  log_tf = FALSE,
  log_tf_display = c("ratio", "sympercent"),
  cor_type = c("sym", "car1", "ar1", "none"),
  correlation = NULL,
  weights = NULL,
  keep_model = TRUE,
  replicates = 999
)

Arguments

data

A data frame containing the variables.

x

Name of the column for the first measurement.

y

Name of the column for the second measurement.

id

Name of the column for the subject ID.

condition

Name of the column indicating different conditions subjects were tested under. This can be left missing if there are no differing conditions to be tested.

time

Name of the column indicating the time points. Only necessary if the data is from time series or repeated measures collection.

pred_level

Prediction level for the prediction interval. Default is 95%.

tol_level

Tolerance level for the tolerance limit (i.e., the CI of the prediction limit). Default is 95%.

tol_method

Method for calculating the tolerance interval. Options are "approx" for a chi-square based approximation and "perc" for a parametric percentile bootstrap method.

prop_bias

Whether to include a proportional bias term in the model. Determines whether proportional bias should be considered for the prediction/tolerance limits calculations.

log_tf

Calculate limits of agreement using log-transformed data.

log_tf_display

The type of presentation for log-transformed results. The differences between methods can be displayed as a "ratio" or "sympercent".

cor_type

The type of correlation structure. "sym" is for Compound Symmetry, "car1" is for continuous autocorrelation structure of order 1, or "ar1" for autocorrelation structure of order 1.

correlation

an optional corStruct object describing the within-group correlation structure that overrides the default setting. See the documentation of corClasses for a description of the available corStruct classes. If a grouping variable is to be used, it must be specified in the form argument to the corStruct constructor. Defaults to NULL.

weights

an optional varFunc object or one-sided formula describing the within-group heteroskedasticity structure that overrides the default setting. If given as a formula, it is used as the argument to varFixed, corresponding to fixed variance weights. See the documentation on varClasses for a description of the available varFunc classes.

keep_model

Logical indicator to retain the GLS model. Useful when working with large data and the model is very large.

replicates

The number of bootstrap replicates. Passed on to the boot function. Default is 999.

Value

Returns single tolerance_delta class object with the results of the agreement analysis with a prediction interval and tolerance limits.

• limits: A data frame containing the prediction/tolerance limits.

• model: The GLS model; NULL if keep_model set to FALSE.

• call: The matched call.

Details

The tolerance limits calculated in this function are based on the papers by Francq & Govaerts (2016), Francq, et al. (2019), and Francq, et al. (2020). When tol_method is set to "approx", the tolerance limits are calculated using the approximation detailed in Francq et al. (2020). However, these are only an approximation and conservative. Therefore, as suggested by Francq, et al. (2019), a parametric bootstrap approach can be utilized to calculate percentile tolerance limits (tol_method = "perc").

References

Francq, B. G., & Govaerts, B. (2016). 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 mMdicine, 35(14), 2328-2358.

Francq, B. G., Lin, D., & Hoyer, W. (2019). Confidence, prediction, and tolerance in linear mixed models. Statistics in Medicine, 38(30), 5603-5622.

Francq, B. G., Berger, M., & Boachie, C. (2020). To tolerate or to agree: A tutorial on tolerance intervals in method comparison studies with BivRegBLS R Package. Statistics in Medicine, 39(28), 4334-4349.

Examples

data('reps')

# Simple
tolerance_limit(x = "x", y ="y", data = reps)
#> Agreement between Measures (Difference: x-y)
#> 95% Prediction Interval with 95% Tolerance Limits
#> 
#>    Bias           Bias CI Prediction Interval Tolerance Limits
#>  0.4383 [-0.1669, 1.0436]   [-2.1998, 3.0764] [-2.993, 3.8697]
#> 
#> 

# Nested
tolerance_limit(x = "x", y ="y", data = reps, id = "id")
#> Agreement between Measures (Difference: x-y)
#> 95% Prediction Interval with 95% Tolerance Limits
#> 
#>    Bias           Bias CI Prediction Interval   Tolerance Limits
#>  0.7046 [-1.5571, 2.9663]   [-4.4686, 5.8778] [-8.6101, 10.0192]
#> 
#>