Effect of Endurance Training and Growth on Hbmass and VO2max in Adolescence

sTfR

Delete values with a distance > 3 sd from the mean

cutoff <- data$sTfR %>% mean() + 3 * data$sTfR %>% sd()
data$sTfR[data$sTfR > cutoff] <- NA

EPO

Delete values > 20

data$epo[data$epo > 20] <- NA

VO2max

model <- get_lmer("VO2max_LBM")

## [1] "baseline to lmem_age: 3.95690095457991e-05"
## [1] "baseline to lmem_tr: 5.90362390665932e-07"
## [1] "baseline to lmem_age_tr_i: 3.13790752784746e-09"
## [1] "lmem_age to lmem_age_tr: 4.18237467831728e-07"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.958873195031813"

cls_data <- get_boot_cls(model, "VO2max_LBM")
p <- plot_lmer(model, "VO2max_LBM", cls_data)

# To finish we adjust some labels and scales and save the plot
p + 
  labs(y = expression(paste(dot(italic(V)),O[2],"max (",mL%.%kg^-1," LBM)"))) +
  scale_y_continuous(breaks = seq(55, 85, 5)) +
  coord_cartesian(ylim = c(50,85), xlim = c(14.3,20), expand = FALSE)

ggsave(filename = "plots/plot_vo2max.svg", width = 8, height = 8, units = "cm")

HbMass

model <- get_lmer("HbM_LBM")

## [1] "baseline to lmem_age: 4.40893341816593e-05"
## [1] "baseline to lmem_tr: 0.796690717779254"
## [1] "baseline to lmem_age_tr_i: 0.000792829111660387"
## [1] "lmem_age to lmem_age_tr: 0.803351532692963"
## [1] "lmem_age to lmem_age_tr_i: 0.965361650660179"

cls_data <- get_boot_cls(model, "HbM_LBM")
p <- plot_lmer(model, "HbM_LBM", cls_data, no_AK = TRUE)

# To finish we adjust some labels and scales and save the plot
p + 
  labs(y = expression(paste("Hbmass (",g%.%kg^-1," LBM)"))) +
  scale_y_continuous(breaks = seq(11, 17, 1)) +
  coord_cartesian(ylim = c(10,17), xlim = c(14.3,20), expand = FALSE)

ggsave(filename = "plots/plot_hbm.svg", width = 8, height = 8, units = "cm")

BV

model <- get_lmer("BV_LBM")

## [1] "baseline to lmem_age: 8.21284254715656e-06"
## [1] "baseline to lmem_tr: 0.0255462801053532"
## [1] "baseline to lmem_age_tr_i: 3.84612230795517e-06"
## [1] "lmem_age to lmem_age_tr: 0.0239636299700087"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.0887688223002285"

cls_data <- get_boot_cls(model, "BV_LBM")
p <- plot_lmer(model, "BV_LBM", cls_data)

# To finish we adjust some labels and scales and save the plot
p + 
  labs(y = expression(paste("BV (",mL%.%kg^-1," LBM)"))) +
  scale_y_continuous(breaks = seq(85, 125, 5)) +
  coord_cartesian(ylim = c(80,125), xlim = c(14.3,20), expand = FALSE)

ggsave(filename = "plots/plot_bv.svg", width = 8, height = 8, units = "cm")

PV

model <- get_lmer("PV_LBM")

## [1] "baseline to lmem_age: 0.851395615526362"
## [1] "baseline to lmem_tr: 0.00826051719414878"
## [1] "baseline to lmem_age_tr_i: 0.0122235746075533"
## [1] "lmem_tr to lmem_age_tr: 0.777149918852902"
## [1] "lmem_tr to lmem_age_tr_i: 0.139894989312945"

cls_data <- get_boot_cls(model, "PV_LBM")
p <- plot_lmer(model, "PV_LBM", cls_data)

# To finish we adjust some labels and scales and save the plot
p + 
  labs(y = expression(paste("PV (",mL%.%kg^-1," LBM)"))) +
  scale_y_continuous(breaks = seq(50, 75, 5)) +
  coord_cartesian(ylim = c(45,75), xlim = c(14.3,20), expand = FALSE)

ggsave(filename = "plots/plot_pv.svg", width = 8, height = 8, units = "cm")

Main Tables

Now we calculate the tables summarising the raw data by group and testnumber and export a CSV.

important_vars <- c("LBM_kg", "fat_kg", "fat_perc", 
                    "weight_kg", "height_cm", "biolage_y","vmax_kmh",
                    "PV_LBM", "BV_LBM","EV_LBM",
                    "HbM_LBM", "HbM_g", "HbM_gkg",
                    "VO2max_LBM", "VO2max_abs", "VO2max_rel",
                    "VO2_per_BV", "VO2_per_Hb", "VO2_per_PV",
                    "hb", "hkt", "reti_proz", "epo", "sTfR", "ferritin")

# function to return a nicely formatted mean ± SD summary
mean_sd <- function(x){
  if (mean(x, na.rm = TRUE) < 120) 
    sprintf("%.1f ± %.1f", mean(x, na.rm = TRUE), sd(x, na.rm = TRUE))
  else 
    sprintf("%.0f ± %.0f", mean(x, na.rm = TRUE), sd(x, na.rm = TRUE))
}

# take data, select variables, group by A/C and testnumber and calculate summary
overview_table <- data %>% 
  select(A_K, testnumber, age_y, important_vars, train_h_ausd) %>% 
  group_by(A_K, testnumber) %>% 
  summarise_all(mean_sd) %>% 
  arrange(A_K, testnumber)

write_csv(overview_table, "overview_table.csv")

Values by group

Summaries of variables by group.

data %>% group_by(A_K) %>% summarise_at(
  vars(VO2_per_Hb, vmax_kmh, hb, reti_proz, epo, sTfR, ferritin), mean_sd)

## # A tibble: 2 x 8
##   A_K   VO2_per_Hb vmax_kmh   hb         reti_proz epo     sTfR   ferritin
##   <fct> <chr>      <chr>      <chr>      <chr>     <chr>   <chr>  <chr>   
## 1 A     5.4 ± 0.4  15.6 ± 0.5 14.4 ± 1.1 0.8 ± 0.3 10.9 ±~ 7.6 ±~ 60.0 ± ~
## 2 K     4.9 ± 0.4  13.0 ± 0.8 15.1 ± 0.7 0.8 ± 0.3 10.6 ±~ 7.4 ±~ 47.1 ± ~

Data Preparation

Log-transformation for fat, percent fat and ferritin.

data$fat_kg <- log(data$fat_kg)
data$fat_perc <- log(data$fat_perc)
data$ferritin  <- log(data$ferritin)

Detailed Model Outputs

The following loop will for each variable: Plot the individual lines, fit the appropriate mixed model, print the model summary and the residual plot.

# change the order of factor levels (intercept = controls)
data$A_K <- data$A_K %>% fct_relevel("K", "A")

# define function
print_lmer <- function(variable){
  print("--------------------------------------------------------------")
  print(variable)
  print("--------------------------------------------------------------")
  
  plot_develop_indiv(variable) %>% print()
  model <- get_lmer(variable)
  model %>% summary() %>% print()
  model %>% plot() %>% print()
}

# applies function to every important variable
walk(important_vars, print_lmer)

## [1] "--------------------------------------------------------------"
## [1] "LBM_kg"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 2.34944726424691e-09"
## [1] "baseline to lmem_tr: 0.877808818743114"
## [1] "baseline to lmem_age_tr_i: 3.41186287966931e-08"
## [1] "lmem_age to lmem_age_tr: 0.88556380362213"
## [1] "lmem_age to lmem_age_tr_i: 0.37646121700274"
## Linear mixed model fit by REML ['lmerMod']
## Formula: LBM_kg ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 576.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.00078 -0.64913 -0.05592  0.65768  1.97456 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 30.0138  5.4785        
##           age_16       0.8638  0.9294   -0.12
##  Residual              0.8498  0.9218        
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  58.5152     1.1758  49.767
## age_16        1.9522     0.2117   9.222
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.140

## [1] "--------------------------------------------------------------"
## [1] "fat_kg"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 1.93048282469141e-05"
## [1] "baseline to lmem_tr: 0.0196999078663384"
## [1] "baseline to lmem_age_tr_i: 2.22526351168085e-05"
## [1] "lmem_age to lmem_age_tr: 0.0193847702018757"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.471988563139435"
## Linear mixed model fit by REML ['lmerMod']
## Formula: fat_kg ~ age_16 + A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: -57
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2660 -0.5881 -0.0789  0.6027  2.4161 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 0.203018 0.45058       
##           age_16      0.006596 0.08121  -0.57
##  Residual             0.018019 0.13424       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  1.46024    0.12283  11.889
## age_16       0.10664    0.02042   5.223
## A_KA        -0.39157    0.16301  -2.402
## 
## Correlation of Fixed Effects:
##        (Intr) age_16
## age_16 -0.448       
## A_KA   -0.602  0.000

## [1] "--------------------------------------------------------------"
## [1] "fat_perc"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.000436534762697919"
## [1] "baseline to lmem_tr: 0.00400583770097151"
## [1] "baseline to lmem_age_tr_i: 0.000101167777608284"
## [1] "lmem_age to lmem_age_tr: 0.00389217919377166"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.537147822051965"
## Linear mixed model fit by REML ['lmerMod']
## Formula: fat_perc ~ age_16 + A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: -102.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.20113 -0.54550 -0.08097  0.61028  2.37438 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 0.124754 0.35321       
##           age_16      0.004797 0.06926  -0.62
##  Residual             0.013951 0.11811       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  1.92870    0.09553  20.189
## age_16       0.07019    0.01757   3.995
## A_KA        -0.37912    0.12389  -3.060
## 
## Correlation of Fixed Effects:
##        (Intr) age_16
## age_16 -0.487       
## A_KA   -0.588  0.000

## [1] "--------------------------------------------------------------"
## [1] "weight_kg"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 1.81518186660196e-08"
## [1] "baseline to lmem_tr: 0.570706662747848"
## [1] "baseline to lmem_age_tr_i: 3.68525120101223e-07"
## [1] "lmem_age to lmem_age_tr: 0.565034634210204"
## [1] "lmem_age to lmem_age_tr_i: 0.594614819368363"
## Linear mixed model fit by REML ['lmerMod']
## Formula: weight_kg ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 695.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0507 -0.5863 -0.0621  0.5325  2.8154 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 56.790   7.536         
##           age_16       1.585   1.259    -0.20
##  Residual              1.982   1.408         
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  62.6177     1.6198  38.658
## age_16        2.3971     0.2915   8.224
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.219

## [1] "--------------------------------------------------------------"
## [1] "height_cm"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 1.38894428913354e-08"
## [1] "baseline to lmem_tr: 0.94280698828231"
## [1] "baseline to lmem_age_tr_i: 4.73140135469937e-07"
## [1] "lmem_age to lmem_age_tr: 0.946649973985829"
## [1] "lmem_age to lmem_age_tr_i: 0.997471404694807"
## Linear mixed model fit by REML ['lmerMod']
## Formula: height_cm ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 490.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.89615 -0.45978 -0.00515  0.51653  2.29413 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 45.0247  6.7100       
##           age_16       0.4015  0.6336   0.18
##  Residual              0.4183  0.6468       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept) 176.6888     1.4337 123.239
## age_16        1.2099     0.1448   8.353
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 0.144

## [1] "--------------------------------------------------------------"
## [1] "biolage_y"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 3.97065180591532e-21"
## [1] "baseline to lmem_tr: 0.625869499041139"
## [1] "baseline to lmem_age_tr_i: 2.29743140671939e-19"
## [1] "lmem_age to lmem_age_tr: 0.656249912278727"
## [1] "lmem_age to lmem_age_tr_i: 0.632880389143895"
## Linear mixed model fit by REML ['lmerMod']
## Formula: biolage_y ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: -118
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.6564 -0.4343  0.0273  0.5093  3.9639 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 0.152608 0.39065       
##           age_16      0.002802 0.05293  -0.50
##  Residual             0.012186 0.11039       
## Number of obs: 153, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept) 16.35416    0.08482  192.81
## age_16       0.49601    0.01442   34.39
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.480

## [1] "--------------------------------------------------------------"
## [1] "vmax_kmh"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.682562268243043"
## [1] "baseline to lmem_tr: 2.81556367613805e-11"
## [1] "baseline to lmem_age_tr_i: 1.18478030487875e-09"
## [1] "lmem_tr to lmem_age_tr: 0.669179910229647"
## [1] "lmem_tr to lmem_age_tr_i: 0.907729720545447"
## Linear mixed model fit by REML ['lmerMod']
## Formula: vmax_kmh ~ A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 195.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.82273 -0.57320  0.09308  0.58563  2.56108 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 0.39777  0.6307        
##           age_16      0.06697  0.2588   -0.56
##  Residual             0.10612  0.3258        
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  13.0068     0.1550   83.94
## A_KA          2.6245     0.2305   11.39
## 
## Correlation of Fixed Effects:
##      (Intr)
## A_KA -0.672

## [1] "--------------------------------------------------------------"
## [1] "PV_LBM"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.851395615526362"
## [1] "baseline to lmem_tr: 0.00826051719414931"
## [1] "baseline to lmem_age_tr_i: 0.0122235746075533"
## [1] "lmem_tr to lmem_age_tr: 0.777149918852594"
## [1] "lmem_tr to lmem_age_tr_i: 0.139894989312937"
## Linear mixed model fit by REML ['lmerMod']
## Formula: PV_LBM ~ A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 828.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.68121 -0.72851  0.01516  0.65179  2.15842 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 9.8806   3.1433        
##           age_16      0.1431   0.3782   -0.16
##  Residual             9.6513   3.1067        
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  57.6255     0.9582  60.142
## A_KA          4.3290     1.4223   3.044
## 
## Correlation of Fixed Effects:
##      (Intr)
## A_KA -0.674

## [1] "--------------------------------------------------------------"
## [1] "BV_LBM"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 8.21284254715656e-06"
## [1] "baseline to lmem_tr: 0.0255462801053515"
## [1] "baseline to lmem_age_tr_i: 3.84612230795517e-06"
## [1] "lmem_age to lmem_age_tr: 0.0239636299700118"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.0887688223002162"
## Linear mixed model fit by REML ['lmerMod']
## Formula: BV_LBM ~ age_16 + A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 863.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6601 -0.7416 -0.1305  0.7467  2.1637 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 16.0640  4.0080       
##           age_16       0.9421  0.9706   0.13
##  Residual             10.8707  3.2971       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  96.5276     1.3027  74.097
## age_16        1.8681     0.3358   5.564
## A_KA          4.6247     1.9042   2.429
## 
## Correlation of Fixed Effects:
##        (Intr) age_16
## age_16 -0.180       
## A_KA   -0.662  0.000

## [1] "--------------------------------------------------------------"
## [1] "EV_LBM"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 3.54742183717463e-09"
## [1] "baseline to lmem_tr: 0.457466908407772"
## [1] "baseline to lmem_age_tr_i: 8.31398894420757e-08"
## [1] "lmem_age to lmem_age_tr: 0.475902031632312"
## [1] "lmem_age to lmem_age_tr_i: 0.628871260584055"
## Linear mixed model fit by REML ['lmerMod']
## Formula: EV_LBM ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 675.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7949 -0.6328 -0.1044  0.5826  2.5630 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 7.9135   2.8131       
##           age_16      0.5658   0.7522   0.30
##  Residual             2.6547   1.6293       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  39.1197     0.6441  60.738
## age_16        1.8662     0.2072   9.008
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 0.028

## [1] "--------------------------------------------------------------"
## [1] "HbM_LBM"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 4.40893341816593e-05"
## [1] "baseline to lmem_tr: 0.796690717779169"
## [1] "baseline to lmem_age_tr_i: 0.000792829111660354"
## [1] "lmem_age to lmem_age_tr: 0.803351532693272"
## [1] "lmem_age to lmem_age_tr_i: 0.965361650660138"
## Linear mixed model fit by REML ['lmerMod']
## Formula: HbM_LBM ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 241
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.11311 -0.57254  0.00248  0.54531  3.02417 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 0.78795  0.8877       
##           age_16      0.03756  0.1938   0.11
##  Residual             0.13712  0.3703       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept) 13.24398    0.19672  67.324
## age_16       0.24820    0.05097   4.869
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.041

## [1] "--------------------------------------------------------------"
## [1] "HbM_g"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 6.50293558122721e-08"
## [1] "baseline to lmem_tr: 0.958155735043722"
## [1] "baseline to lmem_age_tr_i: 1.55150475223909e-06"
## [1] "lmem_age to lmem_age_tr: 0.967104144547207"
## [1] "lmem_age to lmem_age_tr_i: 0.759279628379613"
## Linear mixed model fit by REML ['lmerMod']
## Formula: HbM_g ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 1548
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1029 -0.6230 -0.0170  0.5861  4.0476 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 8738.3   93.48        
##           age_16       587.7   24.24    0.14
##  Residual              565.9   23.79        
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  775.396     20.230  38.328
## age_16        42.041      5.514   7.624
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 0.083

## [1] "--------------------------------------------------------------"
## [1] "HbM_gkg"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.00146278409049112"
## [1] "baseline to lmem_tr: 0.205418296998794"
## [1] "baseline to lmem_age_tr_i: 0.0084677643210548"
## [1] "lmem_age to lmem_age_tr: 0.210228376837079"
## [1] "lmem_age to lmem_age_tr_i: 0.453976685115016"
## Linear mixed model fit by REML ['lmerMod']
## Formula: HbM_gkg ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 258.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.18833 -0.61944  0.02217  0.59601  2.02979 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 0.85014  0.9220       
##           age_16      0.02941  0.1715   0.01
##  Residual             0.16117  0.4015       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept) 12.40620    0.20499  60.521
## age_16       0.17014    0.04882   3.485
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.143

## [1] "--------------------------------------------------------------"
## [1] "VO2max_LBM"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 3.95690095457991e-05"
## [1] "baseline to lmem_tr: 5.90362390665445e-07"
## [1] "baseline to lmem_age_tr_i: 3.13790752784746e-09"
## [1] "lmem_age to lmem_age_tr: 4.18237467831802e-07"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.958873195029178"
## Linear mixed model fit by REML ['lmerMod']
## Formula: VO2max_LBM ~ age_16 + A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 767.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.37877 -0.42027 -0.03865  0.52653  2.50250 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 7.2417   2.6910        
##           age_16      0.6519   0.8074   -0.51
##  Residual             6.1507   2.4801        
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  63.9088     0.8310  76.908
## age_16        1.3250     0.2622   5.053
## A_KA          7.0930     1.0747   6.600
## 
## Correlation of Fixed Effects:
##        (Intr) age_16
## age_16 -0.495       
## A_KA   -0.582 -0.003

## [1] "--------------------------------------------------------------"
## [1] "VO2max_abs"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 1.82067644253205e-08"
## [1] "baseline to lmem_tr: 0.00659471027681868"
## [1] "baseline to lmem_age_tr_i: 9.39548202782665e-09"
## [1] "lmem_age to lmem_age_tr: 0.00651551672281263"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.277586775151503"
## Linear mixed model fit by REML ['lmerMod']
## Formula: VO2max_abs ~ age_16 + A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 2068
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.01996 -0.58979  0.02481  0.46945  2.44125 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 121603   348.7         
##           age_16       11915   109.2    -0.10
##  Residual              23796   154.3         
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  3724.62     104.13  35.767
## age_16        216.88      26.39   8.220
## A_KA          445.14     153.12   2.907
## 
## Correlation of Fixed Effects:
##        (Intr) age_16
## age_16 -0.142       
## A_KA   -0.666 -0.001

## [1] "--------------------------------------------------------------"
## [1] "VO2max_rel"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.00190749371299934"
## [1] "baseline to lmem_tr: 3.28242766635589e-07"
## [1] "baseline to lmem_age_tr_i: 7.57121461487558e-08"
## [1] "lmem_age to lmem_age_tr: 2.89758843980826e-07"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.876574181383188"
## Linear mixed model fit by REML ['lmerMod']
## Formula: VO2max_rel ~ age_16 + A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 771.7
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.39881 -0.49169  0.01296  0.45157  2.43083 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 10.8752  3.2977        
##           age_16       0.7189  0.8479   -0.52
##  Residual              5.9590  2.4411        
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  59.0571     0.9772  60.438
## age_16        0.9137     0.2662   3.432
## A_KA          8.6963     1.2845   6.770
## 
## Correlation of Fixed Effects:
##        (Intr) age_16
## age_16 -0.468       
## A_KA   -0.593 -0.002

## [1] "--------------------------------------------------------------"
## [1] "VO2_per_BV"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.830525931271103"
## [1] "baseline to lmem_tr: 0.069144475761104"
## [1] "baseline to lmem_age_tr_i: 0.179430662559077"
## Linear mixed model fit by REML ['lmerMod']
## Formula: VO2_per_BV ~ 1 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: -559.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.35907 -0.57903  0.04661  0.66833  1.98519 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  ID       (Intercept) 0.0020410 0.04518       
##           age_16      0.0001129 0.01063  -0.65
##  Residual             0.0009720 0.03118       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept) 0.683370   0.008065   84.73

## [1] "--------------------------------------------------------------"
## [1] "VO2_per_Hb"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.678122318821988"
## [1] "baseline to lmem_tr: 0.00183102418265141"
## [1] "baseline to lmem_age_tr_i: 0.0188635860043452"
## [1] "lmem_tr to lmem_age_tr: 0.614793764811338"
## [1] "lmem_tr to lmem_age_tr_i: 0.880901625284346"
## Linear mixed model fit by REML ['lmerMod']
## Formula: VO2_per_Hb ~ A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 45.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6010 -0.5138 -0.1029  0.6358  2.4302 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 0.127367 0.35689       
##           age_16      0.001084 0.03292  -0.23
##  Residual             0.049797 0.22315       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)   4.8697     0.1036  47.002
## A_KA          0.5131     0.1537   3.337
## 
## Correlation of Fixed Effects:
##      (Intr)
## A_KA -0.674

## [1] "--------------------------------------------------------------"
## [1] "VO2_per_PV"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.00468287008461115"
## [1] "baseline to lmem_tr: 0.273903455047344"
## [1] "baseline to lmem_age_tr_i: 0.00975486650505664"
## [1] "lmem_age to lmem_age_tr: 0.271441897599715"
## [1] "lmem_age to lmem_age_tr_i: 0.182633767496736"
## Linear mixed model fit by REML ['lmerMod']
## Formula: VO2_per_PV ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: -299.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.29782 -0.67068  0.01658  0.72803  1.83007 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr 
##  ID       (Intercept) 0.0063081 0.07942       
##           age_16      0.0003672 0.01916  -0.37
##  Residual             0.0054236 0.07364       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  1.13255    0.01996  56.739
## age_16       0.02180    0.00716   3.045
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.536

## [1] "--------------------------------------------------------------"
## [1] "hb"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.927399218206841"
## [1] "baseline to lmem_tr: 0.0204580244537933"
## [1] "baseline to lmem_age_tr_i: 0.0568271784500187"
## [1] "lmem_tr to lmem_age_tr: 0.997133211908229"
## [1] "lmem_tr to lmem_age_tr_i: 0.340231875805212"
## Linear mixed model fit by REML ['lmerMod']
## Formula: hb ~ A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 303.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.76366 -0.59333  0.07593  0.54393  3.06648 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 0.68308  0.8265        
##           age_16      0.01604  0.1267   -0.56
##  Residual             0.27357  0.5230        
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  15.1266     0.2164  69.887
## A_KA         -0.8140     0.3213  -2.534
## 
## Correlation of Fixed Effects:
##      (Intr)
## A_KA -0.674

## [1] "--------------------------------------------------------------"
## [1] "hkt"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 3.20532403570735e-07"
## [1] "baseline to lmem_tr: 0.331476259693046"
## [1] "baseline to lmem_age_tr_i: 4.78738440486987e-06"
## [1] "lmem_age to lmem_age_tr: 0.345779491666498"
## [1] "lmem_age to lmem_age_tr_i: 0.520360557012096"
## Linear mixed model fit by REML ['lmerMod']
## Formula: hkt ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 696.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2819 -0.6716 -0.1114  0.7167  2.1271 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 5.6252   2.3718       
##           age_16      0.1457   0.3817   0.07
##  Residual             3.6359   1.9068       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  43.5830     0.5745  75.859
## age_16        1.2049     0.1732   6.958
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.313

## [1] "--------------------------------------------------------------"
## [1] "reti_proz"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.00161412234817861"
## [1] "baseline to lmem_tr: 0.953891304115965"
## [1] "baseline to lmem_age_tr_i: 0.0188104315879513"
## [1] "lmem_age to lmem_age_tr: 0.975605908506663"
## [1] "lmem_age to lmem_age_tr_i: 0.98615915445703"
## Linear mixed model fit by REML ['lmerMod']
## Formula: reti_proz ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 6.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0953 -0.6857 -0.0596  0.4550  3.1965 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 0.014292 0.1195       
##           age_16      0.001246 0.0353   1.00
##  Residual             0.044794 0.2116       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  0.91505    0.03906  23.429
## age_16      -0.06126    0.01839  -3.332
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.297

## [1] "--------------------------------------------------------------"
## [1] "epo"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.000703111177174793"
## [1] "baseline to lmem_tr: 0.587766639093916"
## [1] "baseline to lmem_age_tr_i: 0.00630581478778203"
## [1] "lmem_age to lmem_age_tr: 0.705516579066661"
## [1] "lmem_age to lmem_age_tr_i: 0.650954579900834"
## Linear mixed model fit by REML ['lmerMod']
## Formula: epo ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 700.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.77286 -0.66087 -0.08092  0.69931  2.56440 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 2.4515   1.5657       
##           age_16      0.1955   0.4422   1.00
##  Residual             5.3154   2.3055       
## Number of obs: 146, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)   9.7665     0.4664  20.942
## age_16        0.7769     0.2121   3.664
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.175

## [1] "--------------------------------------------------------------"
## [1] "sTfR"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.00100403314739059"
## [1] "baseline to lmem_tr: 0.272303144006043"
## [1] "baseline to lmem_age_tr_i: 0.00580841414528383"
## [1] "lmem_age to lmem_age_tr: 0.268406458384257"
## [1] "lmem_age to lmem_age_tr_i: 0.42822823182741"
## Linear mixed model fit by REML ['lmerMod']
## Formula: sTfR ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 458.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.87754 -0.52489  0.02802  0.59450  2.24882 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 1.3818   1.1755        
##           age_16      0.1652   0.4064   -0.81
##  Residual             0.8092   0.8995        
## Number of obs: 152, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)   8.0609     0.2850  28.281
## age_16       -0.4212     0.1135  -3.709
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.798

## [1] "--------------------------------------------------------------"
## [1] "ferritin"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 4.78822316526038e-08"
## [1] "baseline to lmem_tr: 0.248620775037785"
## [1] "baseline to lmem_age_tr_i: 2.76496573271033e-07"
## [1] "lmem_age to lmem_age_tr: 0.173139360613315"
## [1] "lmem_age to lmem_age_tr_i: 0.17261492638739"
## Linear mixed model fit by REML ['lmerMod']
## Formula: ferritin ~ age_16 + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 174.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.5116 -0.5632 -0.0024  0.5015  3.4369 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  ID       (Intercept) 0.180082 0.42436       
##           age_16      0.006716 0.08195  -1.00
##  Residual             0.134725 0.36705       
## Number of obs: 154, groups:  ID, 22
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  3.46445    0.10477  33.068
## age_16       0.25124    0.03389   7.413
## 
## Correlation of Fixed Effects:
##        (Intr)
## age_16 -0.802

data$A_K <- data$A_K %>% fct_relevel("A", "K")

Table with fitted values at age 16

We can use the mixed models to predict individual values at age 16.

data_at16 <- data %>% 
  select(ID, A_K, testnumber) %>% 
  filter(testnumber == 1) %>% 
  mutate(age_16 = 0)

# define function that fits model, predicts values at 16 and returns mean ± sd
return_meansd_16_df <- function(variable){
  
  model <- get_lmer(variable)

  data_at16 %>% 
    add_predictions(model) %>% 
    group_by(A_K) %>% 
    summarise(mean = mean(pred) %>% round(4), 
              sd = sd(pred) %>% round(4)) %>% 
    unite(mean, sd, col = "mean_sd", sep=" ± ") %>% 
    spread(A_K, mean_sd) %>% 
    mutate(model = variable)
}

# apply function to all variables
meansd_16 <- map_df(important_vars, return_meansd_16_df)

meansd_16 %>% print(n = 100)

## # A tibble: 25 x 3
##    A                    K                    model     
##    <chr>                <chr>                <chr>     
##  1 58.5017 ± 5.064      58.5264 ± 5.9682     LBM_kg    
##  2 1.033 ± 0.3078       1.49 ± 0.5304        fat_kg    
##  3 1.524 ± 0.2291       1.95 ± 0.4198        fat_perc  
##  4 61.4123 ± 5.8373     63.6221 ± 8.7475     weight_kg 
##  5 176.7958 ± 4.997     176.5996 ± 8.0726    height_cm 
##  6 16.3482 ± 0.3654     16.3591 ± 0.4171     biolage_y 
##  7 15.5944 ± 0.4066     12.9844 ± 0.7264     vmax_kmh  
##  8 61.8791 ± 3.0698     57.6724 ± 2.7445     PV_LBM    
##  9 101.2739 ± 2.6105    96.4262 ± 4.4031     BV_LBM    
## 10 39.6297 ± 3.2449     38.6947 ± 2.1647     EV_LBM    
## 11 13.2905 ± 1.0737     13.2052 ± 0.6865     HbM_LBM   
## 12 778.33 ± 102.7272    772.9518 ± 87.0965   HbM_g     
## 13 12.6569 ± 1.0438     12.1973 ± 0.7294     HbM_gkg   
## 14 71.011 ± 2.0188      63.9011 ± 2.6306     VO2max_LBM
## 15 4162.4943 ± 364.1558 3730.6793 ± 310.3456 VO2max_abs
## 16 67.7116 ± 2.0273     59.092 ± 3.6617      VO2max_rel
## 17 0.7023 ± 0.025       0.6659 ± 0.0471      VO2_per_BV
## 18 5.3798 ± 0.3738      4.8666 ± 0.3177      VO2_per_Hb
## 19 1.1541 ± 0.0672      1.1146 ± 0.072       VO2_per_PV
## 20 14.3931 ± 1.0579     15.0567 ± 0.4556     hb        
## 21 43.1064 ± 3.1034     43.9801 ± 1.0948     hkt       
## 22 0.9139 ± 0.1111      0.916 ± 0.1113       reti_proz 
## 23 9.789 ± 1.0978       9.7477 ± 1.7238      epo       
## 24 8.1341 ± 0.9639      7.9998 ± 1.1483      sTfR      
## 25 3.6211 ± 0.3014      3.3339 ± 0.4139      ferritin

Mixed model for training time

For this variable, we exclude the first values, because they were reported from memory before training was actually tracked in a training log.

data <- data %>% filter(testnumber != 1)

data$A_K <- data$A_K %>% fct_relevel("K", "A")
print_lmer("train_h_ausd")

## [1] "--------------------------------------------------------------"
## [1] "train_h_ausd"
## [1] "--------------------------------------------------------------"

## [1] "baseline to lmem_age: 0.0705273294570296"
## [1] "baseline to lmem_tr: 6.55713431212708e-14"
## [1] "baseline to lmem_age_tr_i: 1.52537911633164e-14"
## [1] "lmem_tr to lmem_age_tr: 0.0247951906081345"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.0129100498801037"
## Linear mixed model fit by REML ['lmerMod']
## Formula: train_h_ausd ~ age_16 * A_K + (age_16 | ID)
##    Data: data
## 
## REML criterion at convergence: 480.7
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.04263 -0.14470 -0.02919  0.18315  2.73260 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 0.39583  0.6291       
##           age_16      0.01066  0.1032   1.00
##  Residual             1.84261  1.3574       
## Number of obs: 132, groups:  ID, 22
## 
## Fixed effects:
##              Estimate Std. Error t value
## (Intercept)  0.202901   0.398212   0.510
## age_16      -0.009516   0.187173  -0.051
## A_KA         6.651585   0.576570  11.536
## age_16:A_KA  0.674714   0.268996   2.508
## 
## Correlation of Fixed Effects:
##             (Intr) age_16 A_KA  
## age_16      -0.711              
## A_KA        -0.691  0.491       
## age_16:A_KA  0.495 -0.696 -0.695

This is obviously a bad model fit, but the differences are clear.

return_meansd_16_df("train_h_ausd")

## [1] "baseline to lmem_age: 0.0705273294570296"
## [1] "baseline to lmem_tr: 6.55713431212708e-14"
## [1] "baseline to lmem_age_tr_i: 1.52537911633164e-14"
## [1] "lmem_tr to lmem_age_tr: 0.0247951906081345"
## [1] "lmem_age_tr to lmem_age_tr_i: 0.0129100498801037"

## # A tibble: 1 x 3
##   A               K               model       
##   <chr>           <chr>           <chr>       
## 1 6.8545 ± 0.7647 0.2029 ± 0.0888 train_h_ausd