1 Abstract:

Objective: Describe hospital discharge functional outcome in pediatric traumatic brain injury (TBI) patients via discharge Functional Status Scale (FSS). Determine and report any associations between FSS and age, injury mechanism, neurological exam, imaging, and other predictors of outcome.

Design: Prospective observational cohort study.

Setting: Multiple American College of Surgeons level 1 Pediatric Trauma Centers.

Patients: Children under 18 years of age who were admitted to an intensive car unit (ICU) with acute TBI and underwent either a surgical or critical care intervention within initial twenty-four hours, or in-hospital mortality.

Interventions: None.

Measurements and Main Results: Hospital discharge FSS is the primary outcome. A majority, 288/388 (74.23%), had severe TBI (admission GCS 3-8). Overall in-hospital mortality was 65/388 (16.75%); 63/288 (21.88%) among those with severe TBI. Hospital discharge FSS had an inverse relationship with GCS: for each one unit increase in admission GCS the expected FSS total score decreases by 9.91 (95% CI: 9.33, 10.49) units.

2 Introduction

Approximately 2,200 pediatric-deaths and 35,000 pediatric-hospitalizations per annum are attributed to acute trauma brain injury (TBI). (2) Pediatric non-fatal TBI are commonly associated with new morbidities such as motor, communication, behavioral, or social impairments. (3)

Trials of acute interventions for children with TBI are hampered by a lack of relevant, easily administered functional outcome measures that can be used at the time of intensive care unit (ICU) or hospital discharge. Easily administered instruments such as the Pediatric Cerebral Performance Category (PCPC) and the Pediatric Overall Performance Category (POPC) lack the sensitivity and precision required for studies of interventions.(4–7) Other instruments such as the Glasgow Outcome Scale - Extended, Pediatric version (GOS-E Peds)(8) and the King’s Outcome Scale for Childhood Head Injury (KOSCHI)(9) are focused on patient function after return to home and community.

Improvements in the care of critically ill children have decreased ICU mortality to less than 5%, but survivors often have significant functional impairment.(10–14) In response to the need for a reliable, rapid measure of functional outcome appropriate for in-hospital use, the NIH-funded Collaborative Pediatric Critical Care Research Network (CPCCRN)(15) developed and validated the Functional Status Scale (FSS).(16, 17)

The FSS has 6 domains: Mental, Sensory, Communication, Motor, Feeding, and Respiratory. The scale in each domain is from 1 (no dysfunction) to 5 (very severe dysfunction), with a total score from 6 (normal) to 30 (very severe dysfunction in all domains). Appendix Table 1 shows the 6 domains and the 5 levels within each domain. The FSS is designed to be collected from hospital providers (e.g., a patient’s primary nurse), supplemented by medical records when necessary.(18) The FSS correlates with a gold-standard adaptive behavior instrument, the Adaptive Behavior Assessment System (ABAS II), with a Pearson’s correlation coefficient of 0.60. It also discriminates moderate and severe decrements in adaptive behavior well (areas under the curve 0.82 and 0.86, respectively).(16) Interrater reliability is excellent: the intraclass correlation coefficient is 0.95 for the six domain scores.(16) Importantly, Pollack et al. have validated that a FSS score at hospital discharge ≥ 3 points above a child’s pre-hospitalization baseline represents newly impaired functional status or “new morbidity” in survivors of critical illness or injury.(13)

However, the studies of the FSS to date have analyzed heterogeneous cohorts of critically ill children, and no study of children with TBI to date has reported FSS scores. The distributions of hospital discharge FSS and change in FSS from baseline to hospital discharge in critically injured children with TBI are unknown. We conducted this multi-center prospective observational study to accomplish the following aims: 1) to describe FSS and change in FSS from baseline in children admitted to an ICU after TBI and 2) to determine any associations between discharge FSS and age, injury mechanism, neurological exam findings, brain computed tomography (CT) findings, and other predictors of outcome in children with TBI.(19–22)

3 Methods

Study Sites and Subject Enrollment

This prospective cohort study was conducted at multiple American College of Surgeons (ACS) freestanding level I Pediatric Trauma Centers. Each site has between 2000 and 3000 Pediatric ICU admissions per year. We reviewed the ICU census at each site daily, checked ICU admission logbooks, and reviewed ICU screening logs to ensure that all eligible children were observed. Because the study was granted a waiver of consent at all sites (see Regulatory Approvals below), all eligible patients were enrolled.

Inclusion/Exclusion Criteria

We prospectively identified all patients under 18 years of age admitted to an ICU with a diagnosis of acute TBI and either a Glasgow Coma Scale (GCS) score at most 12 or a neurosurgical procedure (intracranial pressure [ICP] monitor, external ventricular drain (EVD), craniotomy, or craniectomy) within the first twenty-four hours of admission. We excluded surviving patients discharged from the ICU within twenty-four hours of ICU admission without an intervention (invasive or noninvasive ventilation, ICP monitoring, any operative procedure, an arterial or central venous catheter, or osmolar therapy). We categorized TBI severity using the ED GCS: 3-8 = severe, 9-12 = moderate, 13-15 = mild. For the 20 patients who did not have a GCS measured in the ED (direct admissions to the ICU), we used the GCS measured on ICU admission. Children with mild TBI who did not receive a neurosurgical procedure in the first 24 hours were excluded.

Prospective Data Collection

For variables such as GCS that might be documented by multiple providers or in multiple locations in the medical record, we defined a hierarchy of data sources. In the Emergency Department (ED), we used the following data sources in order of priority: Trauma Surgery attending physician note, then Neurosurgery attending physician note, then ED attending physician note. Similarly, in the ICU we used the ICU attending physician note, then ICU advanced practice provider note, then ICU resident note, then ICU nursing flowsheet. At the time of each GCS assessment, the study team recorded whether the patient was intubated, sedated, chemically paralyzed, or had obstruction to eye assessment.(23)

We captured the time and text report of the first brain CT study formally read by a PCH or CHCO pediatric radiologist. The presence or absence of CT features (e.g. subdural hematoma [SDH]) were extracted from the CT report by the study team.

Functional Status Scale Collection

We categorized FSS scores using the rubric developed by Pollack et al.(13) That 5-category rubric is designed to follow the categories of the PCPC/POPC system, but has greater granularity within each category.(5, 17)

Statistical Methods

Means are shown ± standard deviation (SD). Medians are shown with interquartile range (IQR). We tested two-sample differences in FSS using Student’s t-test assuming unequal variances. To estimate variation of FSS scores within categories of admission GCS, we used the approach of Pollack et al. and calculated the width (“dispersion”) of the 10^th to 90^th percentile range.(13) To test the FSS-age, FSS-mechanism, and FSS-GCS relationships, we fit three separate linear regression models. Age (in years) and GCS were fit as continuous variables and injury mechanism as a categorical variable. Scatterplots are shown as “bubble charts.” The area of each point is directly proportional to the number of patients with that particular combination of X and Y values.(24) We grouped IVH and SAH to be consistent with the Rotterdam CT scoring system(19, 21)

Data analysis was conducted in R version 4.1.2. (25)

Regulatory Approvals

This study was granted a waiver of consent by the institutional review boards at both institutions.

4 Results

some_dysfunction <-
  lapply(grep("^fss(?!total)", names(pedalfast), perl = TRUE, value = TRUE),
         function(x) {
           rtn <-
             data.frame(variable = x,
                        p        = mean(na.omit(pedalfast[[x]]) > 1))
           rtn$plb <- paste0(frmt(rtn$p * 100), "% (", sub("^fss(\\w)", "\\U\\1", x, perl = TRUE), ")")
           rtn
         })

some_dysfunction <- do.call(rbind, some_dysfunction)
some_dysfunction
##     variable         p              plb
## 1  fssmental 0.3867069  38.67% (Mental)
## 2 fsssensory 0.2379518 23.80% (Sensory)
## 3  fsscommun 0.4652568  46.53% (Commun)
## 4   fssmotor 0.4518072   45.18% (Motor)
## 5 fssfeeding 0.4066265 40.66% (Feeding)
## 6    fssresp 0.1054217    10.54% (Resp)

# when at least one of the fss scales reported a value of 2, and 2 is the max
# value across all six sclaes, the most common scale with a value of 2 is:
fss_matrix <- pedalfast[, grep("^fss(?!total)", names(pedalfast), perl = TRUE, value = TRUE)]

fss_matrix <- suppressWarnings(cbind(fss_matrix, max = apply(fss_matrix, 1, max, na.rm = TRUE)))
fss_matrix <- fss_matrix[fss_matrix$max > -Inf, ]

score_mode <-
  lapply(2:5, function(i) apply(fss_matrix[fss_matrix$max == i, ], 2, function(x) sum(x == i, na.rm = TRUE)))
score_mode <- do.call(rbind, score_mode)
score_mode
##      fssmental fsssensory fsscommun fssmotor fssfeeding fssresp max
## [1,]        21         14        32       21          6       1  65
## [2,]        15          4         8       62         62       4  91
## [3,]         2          2         2       15         17       3  34
## [4,]        12         12        17       19         16      13  27
colSums(score_mode)
##  fssmental fsssensory  fsscommun   fssmotor fssfeeding    fssresp        max 
##         50         32         59        117        101         21        217

apply(score_mode[, -7], 1, which.max)
## [1] 3 4 5 4

fit <- lm(fsstotal ~ injurymech + 0 + I(age / 365.25), data = pedalfast)
summary(fit)
## 
## Call:
## lm(formula = fsstotal ~ injurymech + 0 + I(age/365.25), data = pedalfast)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -6.521 -2.716 -1.758  1.310 22.039 
## 
## Coefficients:
##                                     Estimate Std. Error t value Pr(>|t|)    
## injurymechFall                      8.025623   0.777351  10.324  < 2e-16 ***
## injurymechKnown or suspected abuse 12.068286   0.631627  19.107  < 2e-16 ***
## injurymechOther                     8.197217   0.862843   9.500  < 2e-16 ***
## injurymechSelf-harm                14.590302   2.670070   5.464 9.28e-08 ***
## injurymechTraffic                  10.809890   0.755778  14.303  < 2e-16 ***
## I(age/365.25)                      -0.007137   0.062265  -0.115    0.909    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.102 on 324 degrees of freedom
##   (58 observations deleted due to missingness)
## Multiple R-squared:  0.7982, Adjusted R-squared:  0.7944 
## F-statistic: 213.6 on 6 and 324 DF,  p-value: < 2.2e-16
car::Anova(fit, type = 2)
## Anova Table (Type II tests)
## 
## Response: fsstotal
##                Sum Sq  Df  F value Pr(>F)    
## injurymech    14116.5   5 108.4440 <2e-16 ***
## I(age/365.25)     0.3   1   0.0131 0.9088    
## Residuals      8435.2 324                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
fsstotal_lm_cis <- qwraps2::frmtci(cbind(coef(fit), confint(fit)), show_level = TRUE)
fsstotal_lm_cis
##                     injurymechFall injurymechKnown or suspected abuse 
##        "8.03 (95% CI: 6.50, 9.55)"     "12.07 (95% CI: 10.83, 13.31)" 
##                    injurymechOther                injurymechSelf-harm 
##        "8.20 (95% CI: 6.50, 9.89)"      "14.59 (95% CI: 9.34, 19.84)" 
##                  injurymechTraffic                      I(age/365.25) 
##      "10.81 (95% CI: 9.32, 12.30)"      "-0.01 (95% CI: -0.13, 0.12)"

fit <- lm(fsstotal ~ gcs_using, data = pedalfast)
fss_by_gcs_ci <- qwraps2::frmtci(cbind(coef(fit), confint(fit)), show_level = TRUE)

mean_fss_by_gcs <-
  aggregate(fsstotal ~ gcs_using, data = pedalfast, FUN = mean_sd, show_n = "never", na_rm = TRUE)

mean_fss_by_gcsm <-
  aggregate(fsstotal ~ gcsmotor_using, data = pedalfast, FUN = mean_sd, show_n = "never", na_rm = TRUE)

summary(pedalfast[, grep("^ct", names(pedalfast))])
##   ctskullfrac          ctce       ctmidlineshift     ctcompress    
##  Min.   :0.0000   Min.   :0.000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :1.0000   Median :0.000   Median :0.0000   Median :0.0000  
##  Mean   :0.5065   Mean   :0.426   Mean   :0.2416   Mean   :0.2494  
##  3rd Qu.:1.0000   3rd Qu.:1.000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.000   Max.   :1.0000   Max.   :1.0000  
##  NA's   :5        NA's   :3       NA's   :3        NA's   :3       
##  ctintraparhem     ctsubarchhem    ctintraventhem   ctsubhematoma
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :1.0  
##  Mean   :0.3325   Mean   :0.3273   Mean   :0.1273   Mean   :0.6  
##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.0  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0  
##  NA's   :3        NA's   :3        NA's   :3        NA's   :3    
##  ctepihematoma   
##  Min.   :0.0000  
##  1st Qu.:0.0000  
##  Median :0.0000  
##  Mean   :0.1403  
##  3rd Qu.:0.0000  
##  Max.   :1.0000  
##  NA's   :3
pedalfast$anyblood <- with(pedalfast, as.integer(ctintraparhem + ctsubarchhem + ctintraventhem + ctsubhematoma + ctepihematoma > 0))

5 References

6 Figures

Figure 1: FSS Domain Scores at Hospital Discharge. Histograms of Functional Status Scores (FSS) domain scores at hospital discharge. A score of 1 represents no dysfunction, 2 is mild, 3 is moderate, 4 is severe, and 5 is very severe dysfunction.

# data.table::melt or tidyr::pivot_longer would make this data step much easier
figure1_data <-
  lapply(grep("^fss(?!total)", names(pedalfast), perl = TRUE, value = TRUE),
         function(x) data.frame(variable = x, value = pedalfast[, x]))
figure1_data <- do.call(rbind, figure1_data)

ggplot(figure1_data) +
  aes(x = value, y = (..count..)/sum(..count..)) +
  geom_bar() +
  facet_wrap( ~ variable) +
  theme_classic(base_size = 18) +
  ylab("") +
  scale_y_continuous(labels = scales::percent)

Figure 2: Discharge FSS by Admission GCS. FSS = Functional Status Scale; GCS = Glasgow Coma Scale. A FSS score of six represents no dysfunction.

ggplot(pedalfast) +
  aes(x = gcs_using, y = fsstotal) +
  stat_sum(aes(size = ..n..), alpha = 0.2) +
  scale_size_area(breaks = c(5, 10, 15), "Count", max_size = 7) +
  stat_smooth(method = "lm", formula = y ~ x, size = 0.5, alpha = 0.4, level = 0.95, color = "black", linetype = 2) +
  scale_x_continuous(breaks = seq(3, 15, 1)) +
  scale_y_continuous(breaks = c(6, 10, 15, 20, 25), limits = c(5, 25)) +
  xlab("Glasgow Coma Scale") +
  ylab("Discharge FSS") +
  theme_classic(base_size = 16) +
  theme(legend.position = c(0.9, 0.9))

Figure 3: Discharge FSS by Intracranial Hemorrhage Type. A FSS score of 6 represents no dysfunction.

figure3_data <-
  lapply(grep("^ct.+(hem|toma)$", names(pedalfast), perl = TRUE, value = TRUE),
         function(x) data.frame(studyid = pedalfast[["studyid"]],
                                fsstotal = pedalfast[["fsstotal"]],
                                variable = x,
                                value = pedalfast[, x]))
figure3_data <- do.call(rbind, figure3_data)

figure3_data$variable <-
  factor(figure3_data$variable,
         levels = c("ctintraparhem", "ctsubarchhem", "ctintraventhem", "ctsubhematoma", "ctepihematoma"),
         labels = c("Intraparenchymal\nHemorrhage", "Subarachnoid\nHemorrhage", "Intraventricular\nHemorrhage", "Subdural Hematoma", "Epidural Hematoma"))

ggplot(data = figure3_data) +
  aes(x = fsstotal, fill = as.factor(value)) +
  geom_bar() +
  facet_wrap( ~ variable) +
  scale_fill_manual(name = "Hemorrhage", labels = c("No", "Yes"), values = c("grey", "black")) +
  xlim(5.5,30.5) +
  xlab("Discharge FSS") +
  ylab("Count") +
  theme_classic(base_size=16) +
  theme(legend.position = "bottom")

Figure 4: Discharge FSS by New Gastrostomy Status. Legend: FSS = Functional Status Scale; G-Tube = gastrostomy tube; TBI = traumatic brain injury. A FSS score of 6 represents no dysfunction.

figure4_data <-
  rbind(cbind(cp = "All TBI", pedalfast[, c("fsstotal", "newgastyn")]),
        cbind(cp = "Non-Severe TBI", subset(pedalfast, severetbi == 0, c("fsstotal", "newgastyn"))),
        cbind(cp = "Severe TBI",     subset(pedalfast, severetbi == 1, c("fsstotal", "newgastyn"))))
figure4_data$cp <- factor(figure4_data$cp, levels = c("All TBI", "Non-Severe TBI", "Severe TBI"))

ggplot(data = figure4_data) +
  aes(x = fsstotal, fill = newgastyn) +
  geom_histogram(binwidth = 1, bins = seq(5.5, 30.5, by = 1)) +
  scale_fill_manual(name = "New G-Tube", values = c("gray", "black")) +
  xlim(5.5,30.5) +
  xlab("Discharge FSS") +
  ylab("Count") +
  theme_classic(base_size=20) +
  theme(legend.position = "bottom") +
  facet_wrap( ~ cp)

Figure 5: Discharge FSS by CT imaging. The violin plots show the distribution of FSS scores, the wider the plot the more common the FSS value is. The point shown on each plot is the mean discharge FSS score.

ggplot(data = subset(figure3_data, !is.na(value))) +
  aes(y = fsstotal, x = factor(value, c(0, 1), c("No", "Yes"))) +
  geom_violin() +
  stat_summary(fun = mean, geom = "point") +
  xlab("") +
  ylab("Discharge FSS") +
  facet_wrap( ~ variable) +
  theme_classic(base_size=16) +
  theme(legend.position = "bottom")

7 Tables

Table 1 Patient and Injury Characteristics. Summary statistics are either mean ± standard deviation, or n (%).

qs <- list(
             "Patient Characteristics" =
               list("Age (in years)" = ~ mean_sd(age / 365.25),
                    "Female"         = ~ n_perc0(female == 1))
           , "Injury Mechanism" = qsummary(subset(pedalfast, select = "injurymech"))[[1]]
           , "TBI Severity" =
               list("GCS = 3"             = ~ n_perc0(gcs_using == 3),
                    "Severe (GCS 3-8)"    = ~ n_perc0(gcs_using %in% seq(3, 8)),
                    "Moderate (GCS 9-12)" = ~ n_perc0(gcs_using %in% seq(9, 12)),
                    "Mild (GCS 13-15)"    = ~ n_perc0(gcs_using %in% seq(13, 15))
                   )
           , "GCS Eye"    = qsummary(subset(pedalfast, select = "gcseye_using_cat"))[[1]]
           , "GCS Verbal" = qsummary(subset(pedalfast, select = "gcsverbal_using_cat"))[[1]]
           , "GCS Motor"  = qsummary(subset(pedalfast, select = "gcsmotor_using_cat"))[[1]]
           , "Pupil Reactivity on ICU admission" = qsummary(subset(pedalfast, select = "puplrcticu"))[[1]]
           , "Initial ICU LOS" = list("median (IQR) (days)" = ~ median_iqr(admittoicudc1, na_rm = TRUE, digits = 0))
           , "Hospital LOS" = list("median (IQR) (days)" = ~ median_iqr(hosplos, na_rm = TRUE, digits = 0))
           , "Hospital Disposition" = qsummary(subset(pedalfast, select = "hospdisposition"))[[1]]
           )

# NOTE: the levels of Pupil Reactivity in the ICU include "Unknown" which is
# qwraps2::qsummary default label for NA values.  A patch is provided here, a
# bug report and feature request for qwraps2 has been posted on github.
names(qs[["Pupil Reactivity on ICU admission"]])[ length( names(qs[["Pupil Reactivity on ICU admission"]]) )] <- "Missing"

# print the summary table
st <-
  cbind(summary_table(pedalfast, summaries = qs),
        summary_table(pedalfast, summaries = qs, by = "severetbi"))

colnames(st) <-
  c("Whole Cohort", "Non-severe TBI (GCS > 8)", "Severe TBI (GCS <= 8)")

st

Table 2: Hospital Discharge FSS

qs <- list(
             "FSS Total" =
               list("median (IQR)" = ~ median_iqr(fsstotal, show_n = "never", na_rm = TRUE, digits = 0),
                    "mean (standard deviation)"    = ~ mean_sd(fsstotal, show_n = "never", na_rm = TRUE, digits = 0))
           , "FSS Total - Categorical: n (%)" = qsummary(subset(pedalfast, select = "fsstotal_cat2"))[[1]]
           , "FSS Mental"        = list("n; Median (IQR)" = ~ median_iqr(fssmental, na_rm = TRUE))
           , "FSS Motor"         = list("n; Median (IQR)" = ~ median_iqr(fssmotor, na_rm = TRUE))
           , "FSS Sensory"       = list("n; Median (IQR)" = ~ median_iqr(fsssensory, na_rm = TRUE))
           , "FSS Respiratory"   = list("n; Median (IQR)" = ~ median_iqr(fssresp, na_rm = TRUE))
           , "FSS Feeding"       = list("n; Median (IQR)" = ~ median_iqr(fssfeeding, na_rm = TRUE))
           , "FSS Communication" = list("n; Median (IQR)" = ~ median_iqr(fsscommun, na_rm = TRUE))
           )


st <-
  cbind(summary_table(pedalfast, summaries = qs),
        summary_table(pedalfast, summaries = qs, by = "severetbi"))

colnames(st) <-
  c("Whole Cohort", "Non-severe TBI (GCS > 8)", "Severe TBI (GCS <= 8)")

st

Appendix Table 1 Functional Status Scale Domains

The FSS has 6 domains: Mental, Sensory, Communication, Motor, Feeding, and Respiratory. The scale in each domain is from 1 (no dysfunction) to 5 (very severe dysfunction), with a total score from 6 (normal) to 30 (very severe dysfunction in all domains). Appendix Table 1 shows the 6 domains and the 5 levels within each domain.

appendix_table_1 <-
  subset(pedalfast_metadata,
         variable %in% grep("^fss(?!total)", pedalfast_metadata$variable, perl = TRUE, value = TRUE))

appendix_table_1 <-
  cbind(appendix_table_1, do.call(rbind, strsplit(gsub("\\d,\\ ", "", appendix_table_1$values), split = "\\ \\|\\ ")))

appendix_table_1 <- appendix_table_1[, c("description", as.character(1:5))]
colnames(appendix_table_1) <-
  c("",
    "Normal (Score = 1)",
    "Mild Dysfunction (Score = 2)",
    "Moderate Dysfunction (Score = 3)",
    "Severely Dysfunction (Score = 4)",
    "Severely Dysfunction (Score = 5)")

knitr::kable(appendix_table_1, row.names = FALSE)

8 R Session Info

sessionInfo()
## R version 4.1.2 (2021-11-01)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur 10.16
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] ggplot2_3.3.5        qwraps2_0.5.2        knitr_1.36          
## [4] pedalfast.data_1.0.0
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.1.1 xfun_0.28        bslib_0.3.1      purrr_0.3.4     
##  [5] splines_4.1.2    lattice_0.20-45  carData_3.0-4    colorspace_2.0-2
##  [9] vctrs_0.3.8      generics_0.1.1   htmltools_0.5.2  yaml_2.2.1      
## [13] mgcv_1.8-38      utf8_1.2.2       rlang_0.4.12     jquerylib_0.1.4 
## [17] pillar_1.6.4     glue_1.5.1       withr_2.4.3      DBI_1.1.1       
## [21] lifecycle_1.0.1  stringr_1.4.0    munsell_0.5.0    gtable_0.3.0    
## [25] evaluate_0.14    labeling_0.4.2   fastmap_1.1.0    fansi_0.5.0     
## [29] highr_0.9        Rcpp_1.0.7       scales_1.1.1     jsonlite_1.7.2  
## [33] abind_1.4-5      farver_2.1.0     digest_0.6.28    stringi_1.7.6   
## [37] dplyr_1.0.7      grid_4.1.2       tools_4.1.2      magrittr_2.0.1  
## [41] sass_0.4.0       tibble_3.1.6     crayon_1.4.2     car_3.0-12      
## [45] pkgconfig_2.0.3  Matrix_1.3-4     ellipsis_0.3.2   assertthat_0.2.1
## [49] rmarkdown_2.11   R6_2.5.1         nlme_3.1-153     compiler_4.1.2