SimplyAgree: Flexible and Robust Agreement and Reliability Analyses

Description

Reliability and agreement analyses often have limited software support. Therefore, this package was created to make agreement and reliability analyses easier for the average researcher. The functions within this package include simple tests of agreement, agreement analysis for nested and replicate data, and provide robust analyses of reliability. In addition, this package contains a set of functions to help when planning studies looking to assess measurement agreement.

Author(s)

Maintainer: Aaron Caldwell arcaldwell49@gmail.com

See Also

Useful links:

• https://aaroncaldwell.us/SimplyAgree/

• Report bugs at https://github.com/arcaldwell49/SimplyAgree/issues

Assurance Probability for Limits of Agreement

Description

Usage

agree_assurance(
  conf.level = 0.95,
  assurance = 0.9,
  omega = NULL,
  pstar = 0.95,
  sigma = 1,
  n = NULL
)

Arguments

Details

Calculate the sample size necessary for a confidence interval of the Bland-Altman range of agreement when the underlying data distribution is normal. This function uses the assurance probability criterion to determine the optimum sample size, based on the exact confidence interval method of Jan and Shieh (2018), which has been shown to be superior to approximate methods.

Overview

This function implements the exact method for determining sample size based on assurance probability for Bland-Altman limits of agreement, as described in Jan and Shieh (2018). The assurance probability criterion determines an N that guarantees with specified probability (1 - gamma) that the confidence interval half-width will be no more than a boundary value omega.

Technical Details

Suppose a study involves paired differences (X - Y) whose distribution is approximately N(mu, sigma^2). The range of agreement is defined as a confidence interval of the central portion of these differences, specifically the area between the 100(1-p)th and 100p-th percentiles, where p* = 2p - 1.

The exact two-sided, 100(1 - alpha)% confidence interval for the range of agreement is defined as:

Pr(theta_(1-p) < theta_hat_(1-p) and theta_hat_p < theta_p) = 1 - alpha

The equal-tailed tolerance interval recommended by Jan and Shieh (2018) is:

(X_bar - d, X_bar + d)

where d = g * S, g is the Odeh-Owen tolerance factor (tabulated as g” in Odeh and Owen (1980)), and S is the sample standard deviation.

Sample Size Determination

The sample size N is selected to satisfy: Pr(H <= omega) >= 1 - gamma

This leads to the expression:

psi(eta) >= 1 - gamma

where psi() is the CDF of a chi-square distribution with N-1 degrees of freedom and eta = (N-1) \* (omega/(g\*sigma))^2.

The method uses equal-tailed tolerance intervals based on the noncentral t-distribution to construct exact confidence intervals for the range of agreement. The tolerance factor g is calculated such that the interval maintains the specified confidence level under normality.

Jan and Shieh (2018) demonstrated through extensive simulations that this exact method should be adopted rather than the classical Bland-Altman approximate method.

Interpreting Results

Each subject produces two measurements (one for each method being compared). The sample size n returned is the number of subject pairs needed. The actual assurance probability may differ slightly from the target due to the discrete nature of sample size.

For dropout considerations, inflate the sample size using: N' = N / (1 - dropout_rate), always rounding up.

Value

An object of class "power.htest" containing the following components:

• n: The required sample size (number of subject pairs)

• conf.level: The confidence level (1 - alpha)

• assurance: The target assurance probability (1 - gamma)

• actual.assurance: The actual assurance probability achieved (may differ slightly from target due to discrete nature of n)

• omega: The upper bound of assurance half-width

• pstar: The central proportion covered (P*)

• sigma: The population standard deviation

• g.factor: The Odeh-Owen factor (g”) used to construct the tolerance interval, tabulated in Odeh and Owen (1980)

• method: Description of the method used

• note: Additional notes about the analysis

Assumptions

• The paired differences are normally distributed

• The variance is constant across the range of measurement

• Pairs are independent

References

Jan, S.L. and Shieh, G. (2018). The Bland-Altman range of agreement: Exact interval procedure and sample size determination. Computers in Biology and Medicine, 100, 247-252. doi:10.1016/j.compbiomed.2018.06.020

Odeh, R.E. and Owen, D.B. (1980). Tables for Normal Tolerance Limits, Sampling Plans, and Screening. Marcel Dekker, Inc., New York.

See Also

agree_expected_half() for sample size determination using expected half-width criterion, power_agreement_exact() for power analysis of agreement tests.

Examples

# Example: Planning a method comparison study
# Researchers want 95% confidence, 90% assurance that half-width
# will be within 2.5 SD units, covering central 95% of differences
agree_assurance(
  conf.level = 0.95,
  assurance = 0.90,
  omega = 2.5,
  pstar = 0.95,
  sigma = 1
)

Agreement Coefficents

Description

agree_coef produces inter-rater reliability or "agreement coefficients" as described by Gwet.

Usage

agree_coef(
  wide = TRUE,
  col.names = NULL,
  measure,
  item,
  id,
  data,
  weighted = FALSE,
  conf.level = 0.95
)

Arguments

Value

Returns single data frame of inter-rater reliability coefficients.

References

Gwet, K.L. (2014, ISBN:978-0970806284). "Handbook of Inter-Rater Reliability", 4th Edition. Advanced Analytics, LLC. Gwet, K. L. (2008). "Computing inter-rater reliability and its variance in the presence of high agreement," British Journal of Mathematical and Statistical Psychology, 61, 29-48.

Examples

data('reps')
agree_coef(data = reps, wide = TRUE, col.names = c("x","y"), weighted = TRUE)

Sample Size for Limits of Agreement Using Expected Half-Width

Description

Usage

agree_expected_half(
  conf.level = 0.95,
  delta = NULL,
  pstar = 0.95,
  sigma = 1,
  n = NULL
)

Arguments

Details

Calculate the sample size necessary for a confidence interval of the Bland-Altman range of agreement when the underlying data distribution is normal. This function uses the expected half-width criterion to determine the optimum sample size, based on the exact confidence interval method of Jan and Shieh (2018), which has been shown to be superior to approximate methods.

Overview

This function implements the exact method for determining sample size based on expected half-width for Bland-Altman limits of agreement, as described in Jan and Shieh (2018). The expected half-width criterion determines an N that guarantees that the expected half-width of the confidence interval is less than a boundary value delta.

Technical Details

Suppose a study involves paired differences (X - Y) whose distribution is approximately N(mu, sigma^2). The range of agreement is defined as a confidence interval of the central portion of these differences, specifically the area between the 100(1-p)th and 100p-th percentiles, where p* = 2p - 1.

The exact two-sided, 100(1 - alpha)% confidence interval for the range of agreement is defined as:

Pr(theta_(1-p) < theta_hat_(1-p) and theta_hat_p < theta_p) = 1 - alpha

The equal-tailed tolerance interval recommended by Jan and Shieh (2018) is:

(X_bar - d, X_bar + d)

where d = g * S, g is the Odeh-Owen tolerance factor (tabulated as g” in Odeh and Owen (1980) and Hahn and Meeker (1991)), and S is the sample standard deviation.

Sample Size Determination

The sample size N is selected to satisfy: E(H) <= delta

where H is the half-width of the confidence interval. This leads to the expression:

g(P*, 1-alpha, N-1) / c <= delta / sigma

where c is a bias correction factor:

c = (Gamma((N-1)/2) * sqrt((N-1)/2)) / Gamma(N/2)

The expected half-width is E(H) = (g/c) * sigma. This accounts for the fact that the sample standard deviation S is a biased estimator of sigma, requiring correction when computing expected values.

The method uses equal-tailed tolerance intervals based on the noncentral t-distribution to construct exact confidence intervals for the range of agreement. The tolerance factor g is calculated such that the interval maintains the specified confidence level under normality.

Comparison with Assurance Probability Method

This function uses the expected half-width criterion, which ensures that E(H) <= delta. An alternative approach is the assurance probability criterion (see agree_assurance()), which ensures that Pr(H <= omega) >= 1 - gamma.

The expected half-width criterion:

• Controls the average half-width across repeated sampling

• Generally requires smaller sample sizes than assurance probability

• Is appropriate when the average performance is of primary interest

The assurance probability criterion:

• Provides a probability guarantee about the half-width

• Generally requires larger sample sizes

• Is appropriate when a stronger guarantee is needed for planning purposes

Interpreting Results

Each subject produces two measurements (one for each method being compared). The sample size n returned is the number of subject pairs needed. The actual expected half-width may differ slightly from the target due to the discrete nature of sample size.

For dropout considerations, inflate the sample size using: N' = N / (1 - dropout_rate), always rounding up.

Value

An object of class "power.htest" containing the following components:

• n: The required sample size (number of subject pairs)

• conf.level: The confidence level (1 - alpha)

• delta.target: The target upper bound of expected half-width

• delta.actual: The actual upper bound of expected half-width achieved (may differ slightly from target due to discrete nature of n)

• pstar: The central proportion covered (P*)

• sigma: The population standard deviation

• g.factor: The Odeh-Owen factor (g”) used to construct the tolerance interval, tabulated in Odeh and Owen (1980)

• c.factor: The bias correction factor used in the expected half-width calculation

• method: Description of the method used

• note: Additional notes about the analysis

Assumptions

• The paired differences are normally distributed

• The variance is constant across the range of measurement

• Pairs are independent

References

Jan, S.L. and Shieh, G. (2018). The Bland-Altman range of agreement: Exact interval procedure and sample size determination. Computers in Biology and Medicine, 100, 247-252. doi:10.1016/j.compbiomed.2018.06.020

Bland, J.M. and Altman, D.G. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. The Lancet, 327(8476), 307-310.

Hahn, G.J. and Meeker, W.Q. (1991). Statistical Intervals: A Guide for Practitioners. John Wiley & Sons, New York.

Odeh, R.E. and Owen, D.B. (1980). Tables for Normal Tolerance Limits, Sampling Plans, and Screening. Marcel Dekker, Inc., New York.

See Also

agree_assurance() for sample size determination using assurance probability criterion, power_agreement_exact() for power analysis of agreement tests.

Examples

# Example 1: Reproduce Jan and Shieh (2018), page 251
# Expected half-width criterion with P* = 0.95
agree_expected_half(
  conf.level = 0.95,
  delta = 2.25 * 19.61,
  pstar = 0.95,
  sigma = 19.61
)
# Expected result: n = 155

# Example 2: Planning a method comparison study
# Researchers want 95% confidence with expected half-width
# no more than 2.4 SD units, covering central 90% of differences
agree_expected_half(
  conf.level = 0.95,
  delta = 2.4,
  pstar = 0.90,
  sigma = 1
)

Tests for Absolute Agreement with Nested Data

Description

Development on agree_nest() is complete, and for new code we recommend switching to agreement_limit(), which is easier to use, has more features, and still under active development.

agree_nest produces an absolute agreement analysis for data where there is multiple observations per subject but the mean varies within subjects as described by Zou (2013). Output mirrors that of agree_test but CCC is calculated via U-statistics.

Usage

agree_nest(
  x,
  y,
  id,
  data,
  delta,
  agree.level = 0.95,
  conf.level = 0.95,
  TOST = TRUE,
  prop_bias = FALSE,
  ccc = TRUE
)

Arguments

Value

Returns single simple_agree class object with the results of the agreement analysis.

• loa: A data frame of the limits of agreement including the average difference between the two sets of measurements, the standard deviation of the difference between the two sets of measurements and the lower and upper confidence limits of the difference between the two sets of measurements.

• h0_test: Decision from hypothesis test.

• ccc.xy: Lin's concordance correlation coefficient and confidence intervals using U-statistics. Warning: if underlying value varies this estimate will be inaccurate.

• call: the matched call.

• var_comp: Table of Variance Components.

• class: The type of simple_agree analysis.

References

Zou, G. Y. (2013). Confidence interval estimation for the Bland–Altman limits of agreement with multiple observations per individual. Statistical methods in medical research, 22(6), 630-642.

King, TS and Chinchilli, VM. (2001). A generalized concordance correlation coefficient for continuous and categorical data. Statistics in Medicine, 20, 2131:2147.

King, TS; Chinchilli, VM; Carrasco, JL. (2007). A repeated measures concordance correlation coefficient. Statistics in Medicine, 26, 3095:3113.

Carrasco, JL; Phillips, BR; Puig-Martinez, J; King, TS; Chinchilli, VM. (2013). Estimation of the concordance correlation coefficient for repeated measures using SAS and R. Computer Methods and Programs in Biomedicine, 109, 293-304.

Examples

data('reps')
agree_nest(x = "x", y = "y", id = "id", data = reps, delta = 2)

Nonparametric Test for Limits of Agreement

Description

agree_np A non-parametric approach to limits of agreement. The hypothesis test is based on binomial proportions within the maximal allowable differences, and the limits are calculated with quantile regression.

Usage

agree_np(
  x,
  y,
  id = NULL,
  data,
  delta = NULL,
  prop_bias = FALSE,
  TOST = TRUE,
  agree.level = 0.95,
  conf.level = 0.95
)

Arguments

Value

Returns simple_agree object with the results of the agreement analysis.

• loa: A data frame of the limits of agreement.

• agree: A data frame of the binomial proportion of results in agreement.

• h0_test: Decision from hypothesis test.

• qr_mod: The quantile regression model.

• call: The matched call

References

Bland, J. M., & Altman, D. G. (1999). Measuring agreement in method comparison studies. In Statistical Methods in Medical Research (Vol. 8, Issue 2, pp. 135–160). SAGE Publications. doi:10.1177/096228029900800204

Examples

data('reps')
agree_np(x = "x", y = "y", id = "id", data = reps, delta = 2)

Tests for Absolute Agreement with Replicates

Description

Development on agree_reps() is complete, and for new code we recommend switching to agreement_limit(), which is easier to use, has more features, and still under active development.

agree_nest produces an absolute agreement analysis for data where there is multiple observations per subject but the mean does not vary within subjects as described by Zou (2013). Output mirrors that of agree_test but CCC is calculated via U-statistics.

Usage

agree_reps(
  x,
  y,
  id,
  data,
  delta,
  agree.level = 0.95,
  conf.level = 0.95,
  prop_bias = FALSE,
  TOST = TRUE,
  ccc = TRUE
)

Arguments

Value

Returns single list with the results of the agreement analysis.

• loa: a data frame of the limits of agreement including the average difference between the two sets of measurements, the standard deviation of the difference between the two sets of measurements and the lower and upper confidence limits of the difference between the two sets of measurements.

• h0_test: Decision from hypothesis test.

• ccc.xy: Lin's concordance correlation coefficient and confidence intervals using U-statistics.

• call: The matched call.

• var_comp: Table of Variance Components.

• class: The type of simple_agree analysis.

References

Zou, G. Y. (2013). Confidence interval estimation for the Bland–Altman limits of agreement with multiple observations per individual. Statistical methods in medical research, 22(6), 630-642.

King, TS and Chinchilli, VM. (2001). A generalized concordance correlation coefficient for continuous and categorical data. Statistics in Medicine, 20, 2131:2147.

King, TS; Chinchilli, VM; Carrasco, JL. (2007). A repeated measures concordance correlation coefficient. Statistics in Medicine, 26, 3095:3113.

Carrasco, JL; Phillips, BR; Puig-Martinez, J; King, TS; Chinchilli, VM. (2013). Estimation of the concordance correlation coefficient for repeated measures using SAS and R. Computer Methods and Programs in Biomedicine, 109, 293-304.

Examples

data('reps')
agree_reps(x = "x", y = "y", id = "id", data = reps, delta = 2)

Tests for Absolute Agreement

Description

Development on agree_test() is complete, and for new code we recommend switching to agreement_limit(), which is easier to use, has more features, and still under active development.

The agree_test function calculates a variety of agreement statistics. The hypothesis test of agreement is calculated by the method described by Shieh (2019). Bland-Altman limits of agreement, and confidence intervals, are also provided (Bland & Altman 1999; Bland & Altman 1986). In addition, the concordance correlation coefficient (CCC; Lin 1989) is additional part of the output.

Usage

agree_test(
  x,
  y,
  delta,
  conf.level = 0.95,
  agree.level = 0.95,
  TOST = TRUE,
  prop_bias = FALSE
)

Arguments

Value

Returns single list with the results of the agreement analysis.

• shieh_test: The TOST hypothesis test as described by Shieh.

• ccc.xy: Lin's concordance correlation coefficient and confidence intervals.

• s.shift: Scale shift from x to y.

• l.shift: Location shift from x to y.

• bias: a bias correction factor that measures how far the best-fit line deviates from a line at 45 degrees. No deviation from the 45 degree line occurs when bias = 1. See Lin 1989, page 258.

• loa: Data frame containing the limits of agreement calculations

• h0_test: Decision from hypothesis test.

• call: the matched call

References

Shieh (2019). Assessing Agreement Between Two Methods of Quantitative Measurements: Exact Test Procedure and Sample Size Calculation, Statistics in Biopharmaceutical Research, doi:10.1080/19466315.2019.1677495

Bland, J. M., & Altman, D. G. (1999). Measuring agreement in method comparison studies. Statistical methods in medical research, 8(2), 135-160.

Bland, J. M., & Altman, D. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. The lancet, 327(8476), 307-310.

Lawrence, I., & Lin, K. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics, 255-268.

Examples

data('reps')
agree_test(x=reps$x, y=reps$y, delta = 2)

Limits of Agreement

Description

A function for calculating for Bland-Altman limits of agreement based on the difference between two measurements (difference = x-y). Please note that the package developer recommends reporting/using tolerance limits (see "tolerance_limit" function).

Usage

agreement_limit(
  x,
  y,
  id = NULL,
  data,
  data_type = c("simple", "nest", "reps"),
  loa_calc = c("mover", "blandaltman"),
  agree.level = 0.95,
  alpha = 0.05,
  prop_bias = FALSE,
  log_tf = FALSE,
  log_tf_display = c("ratio", "sympercent"),
  lmer_df = c("satterthwaite", "asymptotic"),
  lmer_limit = 3000
)

Arguments

Details

The limits of agreement (LoA) are calculated in this function are based on the method originally detailed by Bland & Atlman (1986 & 1999). The loa_calc allow users to specify the calculative method for the LoA which can be based on Bland-Altman (1999) (loa_calc = "blandaltman"), or by the more accurate MOVER method of Zou (2013) and Donner & Zou (2012) (loa_calc = "mover").

Value

Returns single loa class object with the results of the agreement analysis.

• loa: A data frame containing the Limits of Agreement.

• call:The matched call.

References

MOVER methods:

Zou, G. Y. (2013). Confidence interval estimation for the Bland–Altman limits of agreement with multiple observations per individual. Statistical methods in medical research, 22(6), 630-642.

Donner, A., & Zou, G. Y. (2012). Closed-form confidence intervals for functions of the normal mean and standard deviation. Statistical Methods in Medical Research, 21(4), 347-359.

Bland & Altman methods:

Bland, J. M., & Altman, D. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. The Lancet, 327(8476), 307-310.

Bland, J. M., & Altman, D. (1999). Measuring agreement in method comparison studies. Statistical methods in medical research, 8(2), 135-160.

Bland, J. M., & Altman, D. G. (1996). Statistics notes: measurement error proportional to the mean. BMJ, 313(7049), 106.

Examples

data('reps')

# Simple
agreement_limit(x = "x", y ="y", data = reps)

# Replicates
agreement_limit(x = "x", y ="y", data = reps, id = "id", data_type = "rep")

# Nested
agreement_limit(x = "x", y ="y", data = reps, id = "id", data_type = "nest")

Power Curve for Bland-Altman Limits of Agreement

Description

This function calculates the power for the Bland-Altman method under varying parameter settings and for a range of sample sizes.

Usage

blandPowerCurve(
  samplesizes = seq(10, 100, 1),
  mu = 0,
  SD,
  delta,
  conf.level = 0.95,
  agree.level = 0.95
)

Arguments

Value

A dataframe is returned containing the power analysis results. The results can then be plotted with the plot.powerCurve function.

References

Lu, M. J., et al. (2016). Sample Size for Assessing Agreement between Two Methods of Measurement by Bland-Altman Method. The international journal of biostatistics, 12(2), doi:10.1515/ijb-2015-0039

Examples

powerCurve <- blandPowerCurve(samplesizes = seq(10, 200, 1),
mu = 0,
SD = 3.3,
delta = 8,
conf.level = .95,
agree.level = .95)
# Plot the power curve
plot(powerCurve, type = 1)
# Find at what N power of .8 is achieved
find_n(powerCurve, power = .8)

# If the desired power is not found then
## Sample size range must be expanded

Deming Regression

Description

A function for fitting a straight line to two-dimensional data (i.e., X and Y) that are measured with error.

Usage

dem_reg(
  formula = NULL,
  data,
  id = NULL,
  x = NULL,
  y = NULL,
  conf.level = 0.95,
  weighted = FALSE,
  weights = NULL,
  error.ratio = 1,
  model = TRUE,
  keep_data = FALSE,
  ...
)

Arguments

Details

This function provides a Deming regression analysis wherein the sum of distances in both x and y direction is minimized. Deming regression, also known as error-in-variable regression, is useful in situations where both X & Y are measured with error. The use of Deming regression is beneficial when comparing to methods for measuring the same continuous variable.

Currently, the dem_reg function covers simple Deming regression and weighted Deming regression. Weighted Deming regression can be used by setting the weighted argument to TRUE. The weights can be provided by the user or can be calculated within function.

If the data are measured in replicates, then the measurement error can be directly derived from the data. This can be accomplished by indicating the subject identifier with the id argument. When the replicates are not available in the data, then the ratio of error variances (y/x) can be provided with the error.ratio argument.

Value

The function returns a simple_eiv (eiv meaning "error in variables") object with the following components:

• coefficients: Named vector of coefficients (intercept and slope).

• residuals: Optimized residuals from the fitted model.

• fitted.values: Estimated true Y values (Y-hat).

• model_table: Data frame presenting the full results from the Deming regression analysis.

• vcov: Variance-covariance matrix for slope and intercept.

• df.residual: Residual degrees of freedom.

• call: The matched call.

• terms: The terms object used.

• xlevels: (Only for models with factors) levels of factors.

• model: The model frame.

• x_vals: Original x values used in fitting.

• y_vals: Original y values used in fitting.

• x_hat: Estimated true X values.

• y_hat: Estimated true Y values.

• error.ratio: Error ratio used in fitting.

• weighted: Whether weighted regression was used.

• weights: Weights used in fitting.

• conf.level: Confidence level used.

• resamples: List containing resamples from jacknife procedure (if keep_data = TRUE).

Interface Change

The x and y arguments are deprecated. Please use the formula interface instead:

• Old: dem_reg(x = "x_var", y = "y_var", data = df)

• New: dem_reg(y_var ~ x_var, data = df)

References

Linnet, K. (1990) Estimation of the linear relationship between the measurements of two methods with proportional errors. Statistics in Medicine, 9, 1463-1473.

Linnet, K. (1993). Evaluation of regression procedures for methods comparison studies. Clinical chemistry, 39, 424-432.

Sadler, W.A. (2010). Joint parameter confidence regions improve the power of parametric regression in method-comparison studies. Accreditation and Quality Assurance, 15, 547-554.

Examples

## Not run: 
# New formula interface (recommended)
model <- dem_reg(y ~ x, data = mydata)

# Old interface (still works with deprecation warning)
model <- dem_reg(x = "x", y = "y", data = mydata)

## End(Not run)

Simulate Deming Regression Power

Description

Functions for conducting power analysis and sample size determination for Deming regression in method comparison studies. These functions help determine the sample size needed to detect specified biases (proportional and/or constant) between two measurement methods.

Estimates statistical power to detect deviations from the line of identity using simulated data with known properties.

Usage

deming_power_sim(
  n_sims = 1000,
  sample_size = 50,
  x_range = c(10, 100),
  x_dist = "uniform",
  actual_slope = 1.05,
  actual_intercept = 0,
  ideal_slope = 1,
  ideal_intercept = 0,
  y_var_params = list(beta1 = 1, beta2 = 0, J = 1, type = "constant"),
  x_var_params = list(beta1 = 1, beta2 = 0, J = 1, type = "constant"),
  weighted = FALSE,
  conf.level = 0.95
)

Arguments

Details

Power Analysis for Deming Regression

This function generates simulated datasets with specified error characteristics and tests whether confidence intervals and joint confidence regions detect deviations from hypothesized values. The joint confidence region typically provides higher statistical power, especially when the X-range is narrow (high slope-intercept correlation).

The variance functions allow flexible modeling of heteroscedastic errors:

• constant: sigma^2 = beta1

• proportional: sigma^2 = beta1 * U^2 (constant CV%)

• power: sigma^2 = (beta1 + beta2*U)^J

Value

A list of class "deming_power" containing:

References

Sadler, W.A. (2010). Joint parameter confidence regions improve the power of parametric regression in method-comparison studies. Accreditation and Quality Assurance, 15, 547-554.

Examples

## Not run: 
# Simple example: detect 5% proportional bias with constant variance
power_result <- deming_power_sim(
  n_sims = 500,
  sample_size = 50,
  x_range = c(10, 100),
  actual_slope = 1.05,
  ideal_slope = 1.0,
  y_var_params = list(beta1 = 25, beta2 = 0, J = 1, type = "constant"),
  x_var_params = list(beta1 = 20, beta2 = 0, J = 1, type = "constant")
)
print(power_result)

# More complex: heteroscedastic errors
power_result2 <- deming_power_sim(
  n_sims = 500,
  sample_size = 75,
  x_range = c(1, 100),
  actual_slope = 1.03,
  y_var_params = list(beta1 = 0.5, beta2 = 0.05, J = 2, type = "power"),
  x_var_params = list(beta1 = 0.4, beta2 = 0.04, J = 2, type = "power"),
  weighted = TRUE
)

## End(Not run)

Determine Required Sample Size for Deming Regression

Description

#'

Automatically determines the minimum sample size needed to achieve target statistical power for detecting specified bias in method comparison studies using Deming regression.

Usage

deming_sample_size(
  target_power = 0.9,
  initial_n = 20,
  max_n = 500,
  n_sims = 500,
  use_joint = TRUE,
  step_size = 5,
  ...
)

Arguments

Details

This function performs a grid search over sample sizes to find the minimum N needed to achieve the target power. It tests both confidence interval and joint confidence region approaches, allowing comparison of required sample sizes.

Using joint confidence regions typically requires 20-50% fewer samples than confidence intervals when the measurement range is narrow (max:min ratio < 10:1).

Value

A list of class "deming_sample_size" containing:

Examples

## Not run: 
# Determine N needed for 90% power to detect 5% bias
sample_size_result <- deming_sample_size(
  target_power = 0.90,
  initial_n = 30,
  max_n = 200,
  n_sims = 500,
  x_range = c(20, 200),
  actual_slope = 1.05,
  ideal_slope = 1.0,
  y_var_params = list(beta1 = 1, beta2 = 0.05, J = 2, type = "power"),
  x_var_params = list(beta1 = 0.8, beta2 = 0.04, J = 2, type = "power")
)

print(sample_size_result)
plot(sample_size_result)

## End(Not run)

Simple Agreement Analysis

Description

Simple Agreement Analysis

Usage

jmvagree(
  data,
  method1,
  method2,
  ciWidth = 95,
  agreeWidth = 95,
  testValue = 2,
  CCC = TRUE,
  plotbland = TRUE,
  plotcon = FALSE,
  plotcheck = FALSE,
  prop_bias = FALSE,
  xlabel = "Average of Both Methods",
  ylabel = "Difference between Methods"
)

Arguments

Value

A results object containing:

Tables can be converted to data frames with asDF or as.data.frame. For example:

results$blandtab$asDF

as.data.frame(results$blandtab)

Nested/Replicate Data Agreement Analysis

Description

Nested/Replicate Data Agreement Analysis

Usage

jmvagreemulti(
  data,
  method1,
  method2,
  id,
  ciWidth = 95,
  agreeWidth = 95,
  testValue = 2,
  CCC = TRUE,
  valEq = FALSE,
  plotbland = FALSE,
  plotcon = FALSE,
  prop_bias = FALSE,
  xlabel = "Average of Both Methods",
  ylabel = "Difference between Methods"
)

Arguments

Value

A results object containing:

Tables can be converted to data frames with asDF or as.data.frame. For example:

results$blandtab$asDF

as.data.frame(results$blandtab)

Deming Regression

Description

Deming Regression

Usage

jmvdeming(
  data,
  method1,
  method2,
  ciWidth = 95,
  testValue = 1,
  plotcon = FALSE,
  plotcheck = FALSE,
  weighted = FALSE,
  xlabel = "Method: 1",
  ylabel = "Method: 2"
)

Arguments

Value

A results object containing:

Tables can be converted to data frames with asDF or as.data.frame. For example:

results$demtab$asDF

as.data.frame(results$demtab)

Reliability Analysis

Description

Reliability Analysis

Usage

jmvreli(data, vars, ciWidth = 95, desc = FALSE, plots = FALSE)

Arguments

Value

A results object containing:

Tables can be converted to data frames with asDF or as.data.frame. For example:

results$icctab$asDF

as.data.frame(results$icctab)

Joint Confidence Region Test for Method Agreement

Description

Tests whether the estimated intercept and slope jointly fall within a confidence region around specified ideal values (typically intercept=0 and slope=1 for method comparison studies).

Usage

joint_test(object, ...)

## S3 method for class 'simple_eiv'
joint_test(
  object,
  ideal_intercept = 0,
  ideal_slope = 1,
  conf.level = 0.95,
  ...
)

Arguments

Details

The test computes the Mahalanobis distance between the estimated coefficients and the hypothesized values using the variance-covariance matrix of the estimates. Under the null hypothesis, this distance follows a chi-squared distribution with 2 degrees of freedom.

For Deming regression, the variance-covariance matrix is computed via jackknife. For Passing-Bablok regression, bootstrap resampling must have been performed (i.e., boot_ci = TRUE in the original call).

Value

An object of class htest containing:

statistic

The Mahalanobis distance (chi-squared distributed with df=2).

parameter

Degrees of freedom (always 2).

p.value

The p-value for the test.

conf.int

The confidence level used.

estimate

Named vector of estimated intercept and slope.

null.value

Named vector of hypothesized intercept and slope.

alternative

Description of the alternative hypothesis.

method

Description of the test.

data.name

Name of the input object.

Methods for loa objects

Description

Methods defined for objects returned from the agreement_limit function.

Usage

## S3 method for class 'loa'
print(x, digits = 4, ...)

## S3 method for class 'loa'
plot(
  x,
  geom = c("geom_point", "geom_bin2d", "geom_density_2d", "geom_density_2d_filled",
    "stat_density_2d"),
  delta = NULL,
  ...
)

## S3 method for class 'loa'
check(x, ...)

Arguments

Value

print

Prints short summary of the Limits of Agreement.

plot

Returns a plot of the limits of agreement.

check

Returns plots testing the assumptions of a Bland-Altman analysis. P-values for the normality and heteroskedascity tests are provided as captions to the plot.

Limits of Agreement with Linear Mixed Effects

Description

This function allows for the calculation of (parametric) bootstrapped limits of agreement when there are multiple observations per subject. The package author recommends using tolerance_limit as an alternative to this function.

Usage

loa_lme(
  diff,
  avg,
  condition = NULL,
  id,
  data,
  type = c("perc", "norm", "basic"),
  conf.level = 0.95,
  agree.level = 0.95,
  replicates = 999,
  prop_bias = FALSE,
  het_var = FALSE
)

Arguments

Value

Returns single list with the results of the agreement analysis.

• var_comp: Table of variance components

• loa: A data frame of the limits of agreement including the average difference between the two sets of measurements, the standard deviation of the difference between the two sets of measurements and the lower and upper confidence limits of the difference between the two sets of measurements.

• call: The matched call.

References

Parker, R. A., Weir, C. J., Rubio, N., Rabinovich, R., Pinnock, H., Hanley, J., McLoughan, L., Drost, E.M., Mantoani, L.C., MacNee, W., & McKinstry, B. (2016). "Application of mixed effects limits of agreement in the presence of multiple sources of variability: exemplar from the comparison of several devices to measure respiratory rate in COPD patients". PLOS One, 11(12), e0168321. doi:10.1371/journal.pone.0168321

Methods for loa_mermod objects

Description

Methods defined for objects returned from the loa_lme.

Usage

## S3 method for class 'loa_mermod'
print(x, ...)

## S3 method for class 'loa_mermod'
plot(
  x,
  x_label = "Average of Both Methods",
  y_label = "Difference Between Methods",
  geom = "geom_point",
  smooth_method = NULL,
  smooth_se = TRUE,
  ...
)

## S3 method for class 'loa_mermod'
check(x, ...)

Arguments

Value

print

Prints short summary of the Limits of Agreement

plot

Returns a plot of the limits of agreement

Mixed Effects Limits of Agreement

Description

loa_mixed() is outdated, and for new code we recommend switching to loa_lme() or tolerance_limit, which are easier to use, have more features, and are still under active development.

This function allows for the calculation of bootstrapped limits of agreement when there are multiple observations per subject.

Usage

loa_mixed(
  diff,
  condition,
  id,
  data,
  plot.xaxis = NULL,
  delta,
  conf.level = 0.95,
  agree.level = 0.95,
  replicates = 1999,
  type = "bca"
)

Arguments

Value

Returns single list with the results of the agreement analysis.

• var_comp: Table of variance components

• loa: a data frame of the limits of agreement including the average difference between the two sets of measurements, the standard deviation of the difference between the two sets of measurements and the lower and upper confidence limits of the difference between the two sets of measurements.

• h0_test: Decision from hypothesis test.

• bland_alt.plot: Simple Bland-Altman plot. Red line are the upper and lower bounds for shieh test; grey box is the acceptable limits (delta). If the red lines are within the grey box then the shieh test should indicate 'reject h0', or to reject the null hypothesis that this not acceptable agreement between x & y.

• conf.level: Returned as input.

• agree.level: Returned as input.

References

Parker, R. A., Weir, C. J., Rubio, N., Rabinovich, R., Pinnock, H., Hanley, J., McLoughan, L., Drost, E.M., Mantoani, L.C., MacNee, W., & McKinstry, B. (2016). "Application of mixed effects limits of agreement in the presence of multiple sources of variability: exemplar from the comparison of several devices to measure respiratory rate in COPD patients". Plos One, 11(12), e0168321. doi:10.1371/journal.pone.0168321

Methods for loa_mixed_bs objects

Description

Methods defined for objects returned from the loa_mixed functions.

Usage

## S3 method for class 'loa_mixed_bs'
print(x, ...)

## S3 method for class 'loa_mixed_bs'
plot(x, ...)

Arguments

Value

print

Prints short summary of the Limits of Agreement

plot

Returns a plot of the limits of agreement

Passing-Bablok Regression for Method Comparison

Description

A robust, nonparametric method for fitting a straight line to two-dimensional data where both variables (X and Y) are measured with error. Particularly useful for method comparison studies.

Usage

pb_reg(
  formula,
  data,
  id = NULL,
  method = c("scissors", "symmetric", "invariant"),
  conf.level = 0.95,
  weights = NULL,
  error.ratio = 1,
  replicates = 0,
  model = TRUE,
  keep_data = TRUE,
  ...
)

Arguments

Details

Passing-Bablok regression is a robust nonparametric method that estimates the slope as the shifted median of all possible slopes between pairs of points. The intercept is then calculated as the median of y - slope*x. This method is particularly useful when:

• Both X and Y are measured with error

• You want a robust method not sensitive to outliers

• The relationship is assumed to be linear

• X and Y are highly positively correlated

Methods

Three Passing-Bablok methods are available:

"scissors" (default): The scissors estimator (1988), most robust and scale-invariant. Uses the median of absolute values of angles.

"symmetric": The original method (1983), symmetric about the y = x line. Uses the line y = -x as the reference for partitioning points.

"invariant": Scale-invariant method (1984). First finds the median angle of slopes below the horizontal, then uses this as the reference line.

Measurement Error Handling

If the data are measured in replicates, then the measurement error ratio can be directly derived from the data. This can be accomplished by indicating the subject identifier with the id argument. When replicates are not available in the data, then the ratio of error variances (var(x)/var(y)) can be provided with the error.ratio argument (default = 1, indicating equal measurement errors).

The error ratio affects how pairwise slopes are weighted in the robust median calculation. When error.ratio = 1, all pairs receive equal weight. When error.ratio != 1, pairs are weighted to account for heterogeneous measurement precision.

Weighting

Case weights can be provided via the weights argument. These are distinct from measurement error weighting (controlled by error.ratio). Case weights allow you to down-weight or up-weight specific observations in the analysis.

Bootstrap

Wild bootstrap resampling is used when replicates > 0. This is particularly useful for:

• Weighted regression (case weights or error.ratio != 1)

• Methods 'invariant' and 'scissors' (where analytical CI validity is uncertain)

• Small sample sizes

The method automatically:

• Tests for high positive correlation using Kendall's tau

• Tests for linearity using a CUSUM test

• Computes confidence intervals (analytical or bootstrap)

Value

The function returns a simple_eiv object with the following components:

• coefficients: Named vector of coefficients (intercept and slope).

• residuals: Residuals from the fitted model.

• fitted.values: Predicted Y values.

• model_table: Data frame presenting the full results from the Passing-Bablok regression.

• vcov: Variance-covariance matrix for slope and intercept (if bootstrap used).

• df.residual: Residual degrees of freedom.

• call: The matched call.

• terms: The terms object used.

• model: The model frame.

• x_vals: Original x values used in fitting.

• y_vals: Original y values used in fitting.

• weights: Case weights (if provided).

• error.ratio: Error ratio used in fitting.

• conf.level: Confidence level used.

• method: Character string describing the method.

• method_num: Numeric method identifier (1, 2, or 3).

• kendall_test: Results of Kendall's tau correlation test.

• cusum_test: Results of CUSUM linearity test.

• n_slopes: Number of slopes used in estimation.

• boot: Bootstrap results (if replicates > 0).

References

Passing, H. and Bablok, W. (1983). A new biometrical procedure for testing the equality of measurements from two different analytical methods. Journal of Clinical Chemistry and Clinical Biochemistry, 21, 709-720.

Passing, H. and Bablok, W. (1984). Comparison of several regression procedures for method comparison studies and determination of sample sizes. Journal of Clinical Chemistry and Clinical Biochemistry, 22, 431-445.

Bablok, W., Passing, H., Bender, R. and Schneider, B. (1988). A general regression procedure for method transformation. Journal of Clinical Chemistry and Clinical Biochemistry, 26, 783-790.

Examples

## Not run: 
# Basic Passing-Bablok regression (scissors method, default)
model <- pb_reg(method2 ~ method1, data = mydata)

# With known error ratio
model_er <- pb_reg(method2 ~ method1, data = mydata, error.ratio = 2)

# With replicate measurements
model_rep <- pb_reg(method2 ~ method1, data = mydata, id = "subject_id")

# With bootstrap confidence intervals
model_boot <- pb_reg(method2 ~ method1, data = mydata,
                     error.ratio = 1.5, replicates = 1000)

# Symmetric method
model_sym <- pb_reg(method2 ~ method1, data = mydata, method = "symmetric")

# Scale-invariant method
model_inv <- pb_reg(method2 ~ method1, data = mydata, method = "invariant")

# With case weights
model_wt <- pb_reg(method2 ~ method1, data = mydata,
                   weights = mydata$case_weights)

# View results
print(model)
summary(model)
plot(model)

## End(Not run)

Methods for powerCurve objects

Description

Methods defined for objects returned from the powerCurve function.

Usage

find_n(x, power = 0.8)

## S3 method for class 'powerCurve'
plot(x, ...)

Arguments

Value

plot

Returns a plot of the limits of agreement (type = 1) or concordance plot (type = 2)

find_n

Find sample size at which desired power is achieved

Power Calculation for Exact Agreement/Tolerance Test

Description

Computes sample size, power, or other parameters for the exact method of assessing agreement between two measurement methods, as described in Shieh (2019). This method tests whether the central portion of paired differences falls within specified bounds. This roughly equates to the power for tolerance limits.

Usage

power_agreement_exact(
  n = NULL,
  delta = NULL,
  mu = 0,
  sigma = NULL,
  p0_star = 0.95,
  power = NULL,
  alpha = 0.05,
  max_iter = 1000
)

Arguments

Details

This function implements the exact agreement test procedure of Shieh (2019) for method comparison studies. The test evaluates whether the central proportion of the distribution of paired differences lies within the interval [-delta, delta].

The null hypothesis is: H0: theta_(1-p) <= -delta or delta <= theta_p The alternative is: H1: -delta < theta_(1-p) and theta_p < delta

where p = (1 + p0_star)/2, and theta_p represents the 100p-th percentile of the paired differences.

Specify three of: n, delta, power, and sigma. The fourth will be calculated. If mu is not specified, it defaults to 0.

Tolerance Interval Interpretation:

The parameter p0_star represents the tolerance coverage proportion, i.e., the proportion of the population that must fall within the specified bounds [-delta, delta] under the null hypothesis. This is conceptually related to tolerance intervals, but formulated as a hypothesis test rather than an estimation problem.

Note: This differs from Bland-Altman's "95% limits of agreement," which are confidence intervals for the 2.5th and 97.5th percentiles, not tolerance intervals.

Value

An object of class "power.htest", a list with components:

References

Shieh, G. (2019). Assessing Agreement Between Two Methods of Quantitative Measurements: Exact Test Procedure and Sample Size Calculation. Statistics in Biopharmaceutical Research, 12(3), 352-359. https://doi.org/10.1080/19466315.2019.1677495

Examples

# Example 1: Find required sample size
power_agreement_exact(delta = 7, mu = 0.5, sigma = 2.5,
                      p0_star = 0.95, power = 0.80, alpha = 0.05)

# Example 2: Calculate power for given sample size
power_agreement_exact(n = 15, delta = 0.1, mu = 0.011,
                      sigma = 0.044, p0_star = 0.80, alpha = 0.05)

# Example 3: Find required delta for given power and sample size
power_agreement_exact(n = 50, mu = 0, sigma = 2.5,
                      p0_star = 0.95, power = 0.90, alpha = 0.05)

Reliability Statistics

Description

The reli_stats and reli_aov functions produce reliability statistics described by Weir (2005). This includes intraclass correlation coefficients, the coefficient of variation, and the standard MSE of measurement.

Usage

reli_stats(
  measure,
  item,
  id,
  data,
  wide = FALSE,
  col.names = NULL,
  se_type = c("MSE", "ICC1", "ICC2", "ICC3", "ICC1k", "ICC2k", "ICC3k"),
  cv_calc = c("MSE", "residuals", "SEM"),
  conf.level = 0.95,
  other_ci = FALSE,
  type = c("chisq", "perc", "norm", "basic"),
  replicates = 1999
)

reli_aov(
  measure,
  item,
  id,
  data,
  wide = FALSE,
  col.names = NULL,
  se_type = c("MSE", "ICC1", "ICC2", "ICC3", "ICC1k", "ICC2k", "ICC3k"),
  cv_calc = c("MSE", "residuals", "SEM"),
  conf.level = 0.95,
  other_ci = FALSE,
  type = c("chisq", "perc", "norm", "basic"),
  replicates = 1999
)

Arguments

Details

These functions return intraclass correlation coefficients and other measures of reliability (CV, SEM, SEE, and SEP). The estimates of variances for any of the measures are derived from linear mixed models. When other_ci is set to TRUE, then a parametric bootstrap approach to calculating confidence intervals is used for the CV, SEM, SEE, and SEP.

reli_stats uses a linear mixed model to estimate variance components. In some cases there are convergence issues. When this occurs it is prudent to use reli_aov which instead utilizes sums of squares approach. The results may differ slightly between the functions. If reli_aov is used then rows with missing observations (e.g., if a participant has a missing observation) will be dropped.

The CV calculation has 3 versions. The "MSE" uses the "mean squared error" from the linear mixed model used to calculate the ICCs. The "SEM" option instead uses the SEM calculation and expresses CV as a ratio of the SEM to the overall mean. The "residuals" option u uses the model residuals to calculate the root mean square error which is then divided by the grand mean.

The CV, SEM, SEE, and SEP values can have confidence intervals produced if the other_ci argument is set to TRUE. For the CV, the default method (type = "chisq") is Vangal's modification of the McKay approximation. For the other measures, a simple chi-squared approximation is utilized (Hann & Meeker, 1991). All other methods are bootstrapping based methods (see ?boot::boot). The reli_stats functions utilizes a parametric bootstrap while the reli_aov function utilizes an ordinary (non-parametric) bootstrap method.

Value

Returns single list with the results of the agreement analysis.

• icc: Table of ICC results

• lmer: Linear mixed model from lme4

• anova: Analysis of Variance table

• var_comp: Table of Variance Components

• n.id: Number of subjects/participants

• n.items: Number of items/time points

• cv: Coefficient of Variation

• SEM: List with Standard MSE of Measurement estimate (est)

• SEE: List with Standard MSE of the Estimate estimate (est)

• SEP: List with Standard MSE of Predictions (est)

• call: the matched call

References

Weir, J. P. (2005). Quantifying test-retest reliability using the intraclass correlation coefficient and the SEM. The Journal of Strength & Conditioning Research, 19(1), 231-240.

Shrout, P.E. and Fleiss, J.L. (1976). Intraclass correlations: uses in assessing rater reliability. Psychological Bulletin, 86, 420-3428.

McGraw, K. O. and Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1, 30-46. See errata on page 390 of same volume.

Hahn, G. J., & Meeker, W. Q. (2011). Statistical intervals: a guide for practitioners (Vol. 92). John Wiley & Sons. pp. 55-56.

Vangel, M. G. (1996). Confidence intervals for a normal coefficient of variation. The American Statistician, 50(1), 21-26.

Examples

data('reps')
reli_stats(data = reps, wide = TRUE, col.names = c("x","y"))

reps

Description

A fake data set of a agreement study where both measures have replicates.

The data set published in the original Bland & Altman paper on agreement.

Usage

reps

ba1986

Format

A data frame with 20 rows with 3 variables

id

Subject identifier

x

X measurement

y

Y measurement

A data frame with 17 rows with 5 variables

id

Subject identifier

wright1

PERF measurement #1 using Wright device

wright2

PERF measurement #2 using Wright device

mini1

PERF measurement #1 using Mini device

mini2

PERF measurement #2 using Mini device

References

Bland, J. M., & Altman, D. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. The Lancet, 327(8476), 307-310.

Methods for simple_agree objects

Description

Methods defined for objects returned from the agree functions.

Usage

## S3 method for class 'simple_agree'
print(x, ...)

## S3 method for class 'simple_agree'
plot(
  x,
  type = 1,
  x_name = "x",
  y_name = "y",
  geom = c("geom_point", "geom_bin2d", "geom_density_2d", "geom_density_2d_filled",
    "stat_density_2d"),
  smooth_method = NULL,
  smooth_se = TRUE,
  ...
)

check(x, ...)

## S3 method for class 'simple_agree'
check(x, ...)

Arguments

Value

print

Prints short summary of the Limits of Agreement

plot

Returns a plot of the limits of agreement (type = 1) or concordance plot (type = 2)

check

Returns 2 plots, p_norm and p_het, testing the assumptions of a Bland-Altman analysis. P-values for the normality and heteroskedasticity tests are provided as captions to the plot.

Methods for simple_eiv objects

Description

Methods defined for objects returned from error-in-variables models (e.g., dem_reg, pb_reg).

Usage

## S3 method for class 'simple_eiv'
print(x, ...)

## S3 method for class 'simple_eiv'
formula(x, ...)

## S3 method for class 'simple_eiv'
model.frame(formula, data = NULL, na.action = na.pass, ...)

## S3 method for class 'simple_eiv'
summary(object, ...)

## S3 method for class 'simple_eiv'
confint(object, parm, level = NULL, ...)

## S3 method for class 'simple_eiv'
plot(
  x,
  x_name = NULL,
  y_name = NULL,
  interval = c("none", "confidence"),
  level = NULL,
  n_points = 100,
  data = NULL,
  ...
)

## S3 method for class 'simple_eiv'
check(x, data = NULL, ...)

plot_joint(x, ...)

## S3 method for class 'simple_eiv'
plot_joint(
  x,
  ideal_slope = 1,
  ideal_intercept = 0,
  show_intervals = TRUE,
  n_points = 100,
  ...
)

## S3 method for class 'simple_eiv'
vcov(object, ...)

## S3 method for class 'simple_eiv'
coef(object, ...)

## S3 method for class 'simple_eiv'
fitted(object, type = c("y", "x", "both"), data = NULL, ...)

## S3 method for class 'simple_eiv'
residuals(object, type = c("optimized", "x", "y", "raw_y"), data = NULL, ...)

## S3 method for class 'simple_eiv'
predict(
  object,
  newdata = NULL,
  interval = c("none", "confidence"),
  level = NULL,
  se.fit = FALSE,
  data = NULL,
  ...
)

Arguments

Value

print

Prints short summary of the EIV regression model.

summary

Prints detailed summary.

plot

Returns a plot of the regression line and data.

check

Returns plots of residuals.

plot_joint

Returns plot of joint confidence region (Deming only).

predict

Predicts Y values for new X values.

fitted

Extracts fitted values.

residuals

Extracts residuals.

coef

Extracts model coefficients.

vcov

Extracts variance-covariance matrix.

Methods for simple_reli objects

Description

Methods defined for objects returned from the agree functions.

Usage

## S3 method for class 'simple_reli'
print(x, ...)

## S3 method for class 'simple_reli'
plot(x, ...)

## S3 method for class 'simple_reli'
check(x, ...)

Arguments

Value

print

Prints short summary of the Limits of Agreement

plot

Returns a plot of the data points used in the reliability analysis

Data

Description

A dataset from a study on the reliability of human body temperature at different times of day before and after exercise.

Usage

temps

recpre_long

Format

A data frame with 60 rows and 10 variables:

id

Subject identifier

trial_num

order in which the experimental trial was completed

trial_condition

Environmental condition and metabolic heat production

tod

Time of Day

trec_pre

Rectal temperature before the beginning of the trial

trec_post

Rectal temperature at the end of the trial

trec_delta

Change in rectal temperature

teso_pre

Esophageal temperature before the beginning of the trial

teso_post

Esophageal temperature at the end of the trial

teso_delta

Change in esophageal temperature

An object of class tbl_df (inherits from tbl, data.frame) with 30 rows and 6 columns.

Source

Ravanelli N, Jay O. The Change in Core Temperature and Sweating Response during Exercise Are Unaffected by Time of Day within the Wake Period. Med Sci Sports Exerc. 2020 Dec 1. doi: 10.1249/MSS.0000000000002575. Epub ahead of print. PMID: 33273272.

Methods for tolerance_delta objects

Description

Methods defined for objects returned from the tolerance_delta function(s).

Usage

## S3 method for class 'tolerance_delta'
print(x, digits = 4, ...)

## S3 method for class 'tolerance_delta'
plot(
  x,
  geom = c("geom_point", "geom_bin2d", "geom_density_2d", "geom_density_2d_filled",
    "stat_density_2d"),
  delta = NULL,
  ...
)

## S3 method for class 'tolerance_delta'
check(x, ...)

Arguments

Value

print

Prints short summary of the tolerance limits.

plot

Returns a plot of the tolerance limits.

check

Returns plots testing the assumptions of the model. P-values for the normality and heteroskedasticity tests are provided as captions to the plot.

Tolerance Limits from an Agreement Study

Description

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.

Usage

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

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").

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.

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)

# Nested
tolerance_limit(x = "x", y ="y", data = reps, id = "id")