Re-analysis of an Agreement Study"

In SimplyAgree: Flexible and Robust Agreement and Reliability Analyses

knitr::opts_chunk$set(
  collapse = TRUE,
  eval = TRUE,
  comment = "#>"
)

library(SimplyAgree)
#library(tidyverse)
library(dplyr)
library(tidyr)
library(ggplot2)
library(magrittr)
data("temps")
df_temps = temps

Re-analysis of a Previous Study of Agreement

In the study by @ravanelli2020change, they attempted to estimate the effect of varying the time of day (AM or PM) on the measurement of thermoregulatory variables (e.g., rectal and esophageal temperature). In total, participants completed 6 separate trials wherein these variables were measured. While this is a robust study of these variables the analyses focused on ANOVAs and t-tests to determine whether or not the time-of-day (AM or PM). This poses a problem because 1) they were trying to test for equivalence and 2) this is a study of agreement not differences (See @Lin1989). Due to the latter point, the use of t-test or ANOVAs (F-tests) is rather inappropriate since they provide an answer to different, albeit related, question.

Instead, the authors could test their hypotheses by using tools that estimate the absolute agreement between the AM and PM sessions within each condition. This is rather complicated because we have multiple measurement within each participant. However, between the tools included in SimplyAgree^[ @cccrm is another package to check out] I believe we can get closer to the right answer.

In order to understand the underlying processes of these functions and procedures I highly recommend reading the statistical literature that documents methods within these functions. For the cccrm package please see the work by @carrasco2003, @carrasco2009, and @carrasco2013. The loa_lme function was inspired by the work of @Parker2016 which documented how to implement multi-level models and bootstrapping to estimate the limits of agreement.

Concordance

An easy approach to measuring agreement between 2 conditions or measurement tools is through the concordance correlation coefficient (CCC). The CCC essentially provides a single coefficient (values between 0 and 1) that provides an estimate to how closely one measurement is to another. It is a type of intraclass correlation coefficient that takes into account the mean difference between two measurements. In other words, if we were to draw a line of identity on a graph and plot two measurements (X & Y), the closer those points are to the line of identity the higher the CCC (and vice versa).

qplot(1,1) + geom_abline(intercept = 0, slope = 1)

In the following sections, let us see how well esophageal and rectal temperature are in agreement after exercising in the heat for 1 hour at differing conditions.

Rectal Temperature

We can visualize the concordance between the two different types of measurements and the respective time-of-day and conditions. From the plot we can see there is clear bias in the raw post exercise values (higher in the PM), but even when "correcting for baseline differences" by calculating the differences scores we can see a higher degree of disagreement between the two conditions.

df_rec.delta = df_temps %>%
  mutate(id_spec = paste0(id,"_",trial_condition)) %>%
  select(id,id_spec,trec_delta,tod,trial_condition) %>%
  pivot_wider(id_cols = c(id,id_spec,trial_condition),
              names_from = tod,
              values_from = trec_delta) %>%
  mutate(diff = PM - AM,
         Average = (AM + PM)/2)

df_rec.post = df_temps %>%
  mutate(id_spec = paste0(id,"_",trial_condition)) %>%
  select(id,id_spec,trec_post,tod,trial_condition) %>%
  pivot_wider(id_cols = c(id,id_spec,trial_condition),
              names_from = tod,
              values_from = trec_post) %>%
  mutate(diff = PM - AM,
         Average = (AM + PM)/2)

p_rec.delta <- ggplot(df_rec.delta, aes(x=AM, y=PM)) +
  stat_smooth(aes(color=trial_condition), 
              method = "lm",
              formula = 'y ~ x',
              fullrange = TRUE,
              geom='line', alpha=0.5, se=FALSE)+
  scale_x_continuous("AM - Trec (delta)",
                     limits = c(.15,1.1))+
  scale_y_continuous("PM - Trec (delta)",
                     limits = c(.15,1.1))+
  geom_abline(intercept = 0, slope = 1, size = .85,
              alpha = .75) +
  geom_point(aes(color=trial_condition),
             alpha = .75) +
  theme_classic() +
  theme(legend.position = "bottom") +
  scale_color_viridis_d()

p_rec.post <- ggplot(df_rec.post, aes(x=AM, y=PM)) +
  stat_smooth(aes(color=trial_condition), 
              method = "lm",
              formula = 'y ~ x',
              fullrange = TRUE,
              geom='line', alpha=0.75, se=FALSE)+
  scale_x_continuous("AM - Trec (post)",
                     limits = c(36.4,38.5))+
  scale_y_continuous("PM - Trec (post)",
                     limits = c(36.4,38.5))+
  geom_abline(intercept = 0, slope = 1, size = .85,
              alpha = .75) +
  geom_point(aes(color=trial_condition),
             alpha = .75) +
  theme_classic() +
  theme(legend.position = "bottom") +
  scale_color_viridis_d()
p_rec.post
p_rec.delta

Esophageal Temperature

df_eso.delta = df_temps %>%
  mutate(id_spec = paste0(id,"_",trial_condition)) %>%
  select(id,id_spec,teso_delta,tod,trial_condition) %>%
  pivot_wider(id_cols = c(id,id_spec,trial_condition),
              names_from = tod,
              values_from = teso_delta) %>%
  mutate(diff = PM - AM,
         Average = (AM + PM)/2)

df_eso.post = df_temps %>%
  mutate(id_spec = paste0(id,"_",trial_condition)) %>%
  select(id,id_spec,teso_post,tod,trial_condition) %>%
  pivot_wider(id_cols = c(id,id_spec,trial_condition),
              names_from = tod,
              values_from = teso_post) %>%
  mutate(diff = PM - AM,
         Average = (AM + PM)/2)

p_eso.delta <- ggplot(df_eso.delta, aes(x=AM, y=PM)) +
  stat_smooth(aes(color=trial_condition), 
              method = "lm",
              formula = 'y ~ x',
              fullrange = TRUE,
              geom='line', alpha=0.5, se=FALSE)+
  scale_x_continuous("AM - Teso (delta)",
                     limits = c(.15,1.1))+
  scale_y_continuous("PM - Teso (delta)",
                     limits = c(.15,1.1))+
  geom_abline(intercept = 0, slope = 1, size = .85,
              alpha = .75) +
  geom_point(aes(color=trial_condition),
             alpha = .75) +
  theme_classic() +
  theme(legend.position = "bottom") +
  scale_color_viridis_d()

p_eso.post <- ggplot(df_eso.post, aes(x=AM, y=PM)) +
  stat_smooth(aes(color=trial_condition), 
              method = "lm",
              formula = 'y ~ x',
              fullrange = TRUE,
              geom='line', alpha=0.75, se=FALSE)+
  scale_x_continuous("AM - Teso (post)",
                     limits = c(36.4,38.5))+
  scale_y_continuous("PM - Teso (post)",
                     limits = c(36.4,38.5))+
  geom_abline(intercept = 0, slope = 1, size = .85,
              alpha = .75) +
  geom_point(aes(color=trial_condition),
             alpha = .75) +
  theme_classic() +
  theme(legend.position = "bottom") +
  scale_color_viridis_d()

p_eso.post

p_eso.delta

Limits of Agreement

The loa_lme function can be used to calculate the "limits of agreement". Typically the 95% Limits of Agreement are calculated which provide the difference between two measuring systems for 95% of future measurements pairs. In order to do that we will need the data in a "wide" format where each measurement (in this case AM and PM) are their own column and then we can calculate a column that is the difference score. Once we have the data in this "wide" format, we can then use the loa_lme function to calculate the average difference (mean bias) and the variance (which determines the limits of agreement).

rec.post_loa = readr::read_rds("rec_post_loa.rds")
rec.delta_loa = readr::read_rds("rec_delta_loa.rds")

eso.post_loa = readr::read_rds("eso_post_loa.rds")
eso.delta_loa = readr::read_rds("eso_delta_loa.rds")

Rectal Temperature

So we will calculate the limits of agreement using the loa_lme function. We will need to identify the columns with the right information using the diff, avg, condition, and id arguments. We then select the right data set using the data argument. Lastly, we specify the specifics of the conditions for how the limits are calculated. For this specific analysis I decided to calculate 95% limits of agreement with 95% confidence intervals, and I will use percentile bootstrap confidence intervals.

rec.post_loa = SimplyAgree::loa_lme(diff = "diff",
                                    condition = "trial_condition",
                                    id = "id",
                                    avg = "Average",
                                    data = df_rec.post,
                                    conf.level = .95,
                                    agree.level = .95,
                                    replicates = 199,
                                    type = "perc")

When we create a table of the limits of agreement (LoA), at least for Trec post exercise, are providing the same conclusion (poor agreement).

knitr::kable(rec.post_loa$loa,
             caption = "LoA: Trec Post Exercise")

Furthermore, we can visualize the results with a typical Bland-Altman plot of the LoA.

plot(rec.post_loa)

Now, when we look at the Delta values for Trec we find that there is much closer agreement (maybe even acceptable agreement) when we look at LoA. However, we cannot say that the average difference would be less than 0.25 which may not be acceptable for some researchers.

knitr::kable(rec.delta_loa$loa,
             caption = "LoA: Delta Trec")

plot(rec.delta_loa)

Esophageal Temperature

We can repeat the process for esophageal temperature. Overall, the results are fairly similar, and while there is better agreement on the delta (change scores), it is still fairly difficult to determine that there is "good" agreement between the AM and PM measurements.

eso.post_loa = SimplyAgree::loa_mixed(diff = "diff",
                                     condition = "trial_condition",
                                     id = "id",
                                     data = df_eso.post,
                                     conf.level = .95,
                                     agree.level = .95,
                                     replicates = 199,
                                     type = "bca")

knitr::kable(eso.post_loa$loa,
             caption = "LoA: Teso Post Exercise")

plot(eso.post_loa)

knitr::kable(eso.delta_loa$loa,
             caption = "LoA: Delta Teso")

plot(eso.delta_loa)

References

SimplyAgree documentation built on Dec. 28, 2022, 2:06 a.m.