# Rating of Perceived Exertion # A large cross-sectional study defining intensity levels for individual physical activity recommendations # Grummt M, Hafermann L, Claussen L, Herrmann C, Wolfarth B # 29.01.2024 sessionInfo() # see R_Session_Info.txt pacman::p_load(readxl, tidyverse, ggplot2, janitor, tableone, naniar,plyr, ggpubr,stringr, reshape2, scales,MASS) ## Data Cleaning ---------------------------------------------------------------------------------------- # read data sets # results for lactat values are stored in a different data set # and therefore data sets need to be matched Data_RPE <- read_excel("Borg_Export_Grummt_Anonymisiert.xlsx",col_types = c("text", rep("numeric", 59))) Data_RPE <- as_tibble(Data_RPE) # data for missing lactat values full_lactat <- read_excel("imed_Datenexport_anonymisiert.xlsx", col_types = c("skip", "text", "skip", "text", rep("numeric", 45), "skip")) # recoding full_lactat <- full_lactat %>% mutate(Ergometrieart = case_when( Ergometrieart == "F" ~1, Ergometrieart == "L" ~2, Ergometrieart == "H" ~3))%>% mutate(Ergometrieart = as.numeric(Ergometrieart)) colnames(full_lactat) <- c( "ID", "Ergometrieart", "Laktat_Ruhe", "Laktat_1", "Laktat_2", "Laktat_3", "Laktat_4", "Laktat_5", "Laktat_6", "Laktat_7", "Laktat_8", "Laktat_9", "Laktat_10", "Laktat_11", "Laktat_12", "Laktat_13", "Laktat_14", "Laktat_15", "Laktat_16", "Laktat_17", "Laktat_18", "Laktat_19", "Laktat_20", "Laktat_21", "Laktat_max", "RPE_Ruhe","RPE_1", "RPE_2", "RPE_3", "RPE_4","RPE_5", "RPE_6", "RPE_7", "RPE_8", "RPE_9", "RPE_10", "RPE_11","RPE_12", "RPE_13", "RPE_14", "RPE_15", "RPE_16", "RPE_17","RPE_18", "RPE_19","RPE_20", "RPE_max") full_lactat <- full_lactat %>% dplyr::select(-RPE_Ruhe) Data_RPE <- clean_names(Data_RPE) colnames(Data_RPE) <- c("ID", "Ergometrieart", "Alter", "Geschlecht", "Koerpergewicht", "Koerpergroesse", "BMI", "Laktat_Ruhe", "Laktat_1", "Laktat_2", "Laktat_3", "Laktat_4", "Laktat_5", "Laktat_6", "Laktat_7", "Laktat_8", "Laktat_9", "Laktat_10", "Laktat_11", "Laktat_12", "Laktat_13", "Laktat_14", "Laktat_15", "Laktat_16", "Laktat_17", "Laktat_18", "Laktat_19", "Laktat_20", "Laktat_21", "Laktat_min", "Laktat_max", "RPE_Ruhe","RPE_1", "RPE_2", "RPE_3", "RPE_4", "RPE_5", "RPE_6", "RPE_7", "RPE_8", "RPE_9", "RPE_10", "RPE_11","RPE_12", "RPE_13", "RPE_14", "RPE_15", "RPE_16", "RPE_17","RPE_18", "RPE_19", "RPE_max", "Lactat_an_LT", "Lactatkonzentration_IAS", "Perzentil_IAS_Laufen allgemein", "Perzentil_IAS_Laufen_Mitte", "Perzentil_IAS_Laufen_Ausdauersport", "Perzentil_IAS_Radfahren_allgemein", "Perzentil_IAS_Radfahren_Mitte", "Perzentil_IAS_Radfahren_Ausdauersport" ) # Left join of Data_RPE and full lactat LJ <- left_join(Data_RPE, full_lactat, by = c("ID", "Ergometrieart","Laktat_Ruhe", "Laktat_1","Laktat_2")) LJ <- LJ%>% mutate( Laktat_3 = coalesce(Laktat_3.x, Laktat_3.y), Laktat_4 = coalesce(Laktat_4.x, Laktat_4.y), Laktat_5 = coalesce(Laktat_5.x, Laktat_5.y), Laktat_6 = coalesce(Laktat_6.x, Laktat_6.y), Laktat_7 = coalesce(Laktat_7.x, Laktat_7.y), Laktat_8 = coalesce(Laktat_8.x, Laktat_8.y), Laktat_9 = coalesce(Laktat_9.x, Laktat_9.y), Laktat_10 = coalesce(Laktat_10.x, Laktat_10.y), Laktat_11 = coalesce(Laktat_11.x, Laktat_11.y), Laktat_12 = coalesce(Laktat_12.x, Laktat_12.y), Laktat_13 = coalesce(Laktat_13.x, Laktat_13.y), Laktat_14 = coalesce(Laktat_14.x, Laktat_14.y), Laktat_15 = coalesce(Laktat_15.x, Laktat_15.y), Laktat_16 = coalesce(Laktat_16.x, Laktat_16.y), Laktat_17 = coalesce(Laktat_17.x, Laktat_17.y), Laktat_18 = coalesce(Laktat_18.x, Laktat_18.y), Laktat_19 = coalesce(Laktat_19.x, Laktat_19.y), Laktat_20 = coalesce(Laktat_20.x, Laktat_20.y), Laktat_21 = coalesce(Laktat_21.x, Laktat_21.y), Laktat_max = coalesce(Laktat_max.x, Laktat_max.y), RPE_1 = coalesce(RPE_1.x, RPE_1.y), RPE_2 = coalesce(RPE_2.x, RPE_2.y), RPE_3 = coalesce(RPE_3.x, RPE_3.y), RPE_4 = coalesce(RPE_4.x, RPE_4.y), RPE_5 = coalesce(RPE_5.x, RPE_5.y), RPE_6 = coalesce(RPE_6.x, RPE_6.y), RPE_7 = coalesce(RPE_7.x, RPE_7.y), RPE_8 = coalesce(RPE_8.x, RPE_8.y), RPE_9 = coalesce(RPE_9.x, RPE_9.y), RPE_10 = coalesce(RPE_10.x, RPE_10.y), RPE_11 = coalesce(RPE_11.x, RPE_11.y), RPE_12 = coalesce(RPE_12.x, RPE_12.y), RPE_13 = coalesce(RPE_13.x, RPE_13.y), RPE_14 = coalesce(RPE_14.x, RPE_14.y), RPE_15 = coalesce(RPE_15.x, RPE_15.y), RPE_16 = coalesce(RPE_16.x, RPE_16.y), RPE_17 = coalesce(RPE_17.x, RPE_17.y), RPE_18 = coalesce(RPE_18.x, RPE_18.y), RPE_19 = coalesce(RPE_19.x, RPE_19.y), RPE_max= coalesce(RPE_max.x, RPE_max.y) ) %>% dplyr::select( -Laktat_3.x, -Laktat_3.y, -Laktat_4.x, -Laktat_4.y, -Laktat_5.x, -Laktat_5.y,-Laktat_6.x, -Laktat_6.y, -Laktat_7.x, -Laktat_7.y,-Laktat_7.x, -Laktat_7.y,-Laktat_8.x, -Laktat_8.y, -Laktat_9.x, -Laktat_9.y,-Laktat_10.x, -Laktat_10.y,-Laktat_11.x, -Laktat_11.y, -Laktat_12.x, -Laktat_12.y,-Laktat_13.x, -Laktat_13.y,-Laktat_14.x, -Laktat_14.y, - Laktat_15.x, -Laktat_15.y,-Laktat_16.x, -Laktat_16.y,-Laktat_17.x, -Laktat_17.y, -Laktat_18.x, -Laktat_18.y,-Laktat_19.x, -Laktat_19.y,-Laktat_20.x, -Laktat_20.y, -Laktat_21.x, -Laktat_21.y, -Laktat_max.x, -Laktat_max.y, -RPE_1.x, -RPE_1.y,-RPE_2.x, -RPE_2.y,-RPE_3.x, -RPE_3.y, -RPE_4.x, -RPE_4.y, -RPE_5.x, -RPE_5.y,-RPE_6.x, -RPE_6.y, -RPE_7.x, -RPE_7.y,-RPE_7.x, -RPE_7.y, -RPE_8.x, -RPE_8.y, -RPE_9.x, -RPE_9.y,-RPE_10.x, -RPE_10.y,-RPE_11.x, -RPE_11.y, -RPE_12.x, -RPE_12.y,-RPE_13.x, -RPE_13.y,-RPE_14.x, -RPE_14.y, -RPE_15.x, -RPE_15.y,-RPE_16.x, -RPE_16.y,-RPE_17.x, -RPE_17.y, -RPE_18.x, -RPE_18.y,-RPE_19.x, -RPE_19.y, -RPE_max.x, -RPE_max.y ) # rearranging of the data set Data_RPE <- LJ[,c(dput(colnames(Data_RPE))[1:51],"RPE_20",dput(colnames(Data_RPE))[52:60])] # correction of mistakes in the data set # lactat = 0.5 false value Data_RPE[Data_RPE$ID == "42557456","Lactat_Ruhe"] <- 0.05 # delete exactly identical rows Data_RPE <- Data_RPE %>% distinct() # one person has done a bike and treadmill ergometry at exactly the same time -> treadmill data deleted Data_RPE<- Data_RPE[!(Data_RPE$ID =="42345006" & Data_RPE$Ergometrieart == 2),] Data_RPE<- Data_RPE[!(Data_RPE$ID =="42449098" & is.na(Data_RPE$RPE_10)),] # some people came more than once, therefore only the first visit is used ID_numb <- tabyl(Data_RPE$ID) %>% arrange(desc(n)) %>% filter(n >1) ID_numb <- ID_numb[,1] double_IDs <- Data_RPE %>% filter(ID %in% ID_numb) %>% arrange(ID) list_doubleIDs <-split(double_IDs, double_IDs$ID) # gives a list where every list entry belongs to one ID list_maxAlter <- lapply(list_doubleIDs, function(x) max(x$Alter)) # age is used as proxy for earlier visits IDs_list <- names(list_maxAlter) # re-entries (older entry) are excluded for(i in 1:length(IDs_list)){ Data_RPE<- Data_RPE[!(Data_RPE$ID ==IDs_list[i] & Data_RPE$Alter == list_maxAlter[[i]]),] } # Patient with implausible lactat at IAs Data_RPE<- Data_RPE[!(Data_RPE$ID =="41348763"),] #without hand bikes(Ergometrieart 3) Data_RPE <- Data_RPE %>%filter(Ergometrieart != 3) # VO2max values --------------------------------------------------------------------- # calculations of VO2max are stored in a different table, which needs to merged data_power <- read_excel("Borg_Export_Grummt_VO2max_Berechnung.xlsx") data_vo2max <- tibble(ID = data_power$PIZ, Vo2max = data_power$VO2max, Alter = data_power$`Alter (Jahre)`, Laktat_1 = data_power$`Laktat(1) (mmol/l)`) Join <- left_join(Data_RPE, data_vo2max, by = c("ID", "Alter", "Laktat_1")) Freq <- as.data.frame(tabyl(Join$ID)) Freq[Freq$n > 1,] Join <- Join[!duplicated(Join),] Join %>% filter(ID == "42345006") Join <- Join[-which(Join$ID== "42345006")[1],] Join[which(Join$ID== "42345006"),"Ergometrieart"] <-2 Data_RPE$VO2max_full <- Join$Vo2max ## Table 1 ----------------------------------------------------------------------------------------------- Data_RPE <- Data_RPE %>% mutate(BMI_cat = case_when( BMI < 18.5 ~ "BMI_untergewicht", BMI >= 18.5 & BMI < 25 ~ "BMI_normal", BMI >= 25 & BMI < 30 ~ "BMI_übergewicht", BMI >= 30 & BMI < 35 ~ "BMI_adipositas_g1", BMI >= 35 & BMI < 40 ~ "BMI_adipositas_g2", BMI >= 40 ~ "BMI_adipositas_g3")) get_t1 <- function(data,strata){ tab1_data <- data %>% dplyr::select(c(Ergometrieart, Alter,Geschlecht,BMI_cat, Koerpergewicht, Koerpergroesse, Lactat_an_LT, Lactatkonzentration_IAS, VO2max_full )) %>% mutate(Ergometrieart = as_factor(Ergometrieart), Geschlecht = as_factor(Geschlecht), BMI_cat = as_factor(BMI_cat)) T_one <- CreateTableOne(data = tab1_data, strata = strata) missings <- colSums(is.na(tab1_data)) return(list(T_one, missings)) } T_one_total <- get_t1(Data_RPE) T_one_sex <- get_t1(Data_RPE, strata = "Geschlecht") T_one_ergometry <- get_t1(Data_RPE, strata = "Ergometrieart") ## 1st Step: Calculation of the RPE values at LT2---------------------------------------------------- # extraction of the lactat and rpe values plus generation of data indicating which value is given Lactat <- Data_RPE[,c(9:28)] Lactat <- apply(Lactat,c(1,2), function(x) {ifelse(is.na(x), 0,1)} ) Lactat_count <- Lactat %>% count() %>% arrange(desc(freq)) Lactat_count <- as.data.frame(Lactat_count) rownames(Lactat_count)<- make.names(as.character(Lactat_count$freq), unique = TRUE) rpe <- Data_RPE[,c(33:52)] rpe <- apply(rpe,c(1,2), function(x) {ifelse(is.na(x), 0,1)} ) rpe_count <- rpe %>% count() %>% arrange(desc(freq)) rpe_count <- as.data.frame(rpe_count) rownames(rpe_count)<- make.names(as.character(rpe_count$freq), unique = TRUE) # number of pairs of lactat values and rpe values L_sum <- apply(Lactat, 1, sum) B_sum <- apply(rpe, 1, sum) length(which(L_sum != B_sum)) dop_value <- NA for(i in 1: nrow(Lactat)){ add <- Lactat[i,] + rpe[i, ] dop_value[i] <- length(which(add ==2)) } tabyl(dop_value) dop_value_t <-tibble(dop_value <- dop_value) # Calculation of the number of steps in the ergometry ---------------------------------------------- max_stage <- rep(0, length(Lactat[,1])) for(j in 1:length(Lactat[,1])){ for(i in 20:1){ if(Lactat[j,i] == 1){ max_stage[j] <- i break} } } Data_RPE$max_stage <- max_stage # Spline Interpolation------------------------------------------------------------------- # RPE values at LT2, 2mmol/l, 3mmmol/l and 4mmol/l rpe_LT2 <- rep(NA,nrow(Data_RPE)) rpe_lactat2 <- rep(NA,nrow(Data_RPE)) rpe_lactat3 <- rep(NA,nrow(Data_RPE)) rpe_lactat4 <- rep(NA,nrow(Data_RPE)) ind <- NA for(i in 1:nrow(Data_RPE)){ # at least 3 pairs of values (excludes 5 patients) if(dop_value[i] >= 3){ rpe <- Data_RPE[i,33:52] lactat <- Data_RPE[i, 9:28] LT2 <- as.numeric(Data_RPE[i,"Lactatkonzentration_IAS"]) Lak2 <- 2 Lak3 <- 3 Lak4 <- 4 if(is.na(lactat[2]) || (lactat[2] >= lactat[1])){ ind[i] <-1 } else { ind[i] <-0 rpe <- rpe[-1] lactat <- lactat[-1] } data_rpe_lactat <- tibble(rpe = t(rpe), lactat = t(lactat)) sp_rpe <- splinefun(x =data_rpe_lactat$lactat, y = data_rpe_lactat$rpe, method = "monoH.FC") #monoH.FC rpe_LT2[i] <- sp_rpe(LT2) rpe_lactat2[i] <- sp_rpe(Lak2) rpe_lactat3[i] <- sp_rpe(Lak3) rpe_lactat4[i] <- sp_rpe(Lak4) }} ## manual change of wrong splinefun interpolation # 1730 -> rpe -2781 (measurement error) # 6224 -> rpe 49 (no correct function) # 4285 -> rpe 24 (IAS higher than 20) -> set to 20 # 2985 -> rpe 21 -> set to 20 # 970 -> rpe 5 -> change to 11 # implausibler curves: implausibel <- which(round(rpe_LT2) == -2781) # lactat: 6.78, 6.82, 6.79, 6.79, rpe: 7, 10,13,18 implausibel2 <- which(round(rpe_LT2) == 49) # lactat: 1.33, 1.11, 1.38, 1.53, 3.6 # but only rpe values for the fist 4 stages 11,13,15,19 available # -> Lactat at LT2 = 2.36 rpe_LT2[implausibel] <- NA rpe_LT2[implausibel2] <- NA rpe_lactat2[implausibel] <- NA rpe_lactat2[implausibel2] <- NA rpe_lactat3[implausibel] <- NA rpe_lactat3[implausibel2] <- NA rpe_lactat4[implausibel] <- NA rpe_lactat4[implausibel2] <- NA rpe_LT2[which(round(rpe_LT2) == 24)] <- 20 rpe_LT2[which(round(rpe_LT2) == 21)] <- 20 rpe_LT2[which(round(rpe_LT2) == 5)] <- 11 rpe_lactat2[which(round(rpe_lactat2) <6)] <- 6 rpe_lactat2[which(round(rpe_lactat2) > 20)] <- 20 rpe_lactat3[which(round(rpe_lactat3) <6)] <- 6 rpe_lactat3[which(round(rpe_lactat3) > 20)] <- 20 rpe_lactat4[which(round(rpe_lactat4) <6)] <- 6 rpe_lactat4[which(round(rpe_lactat4) > 20)] <- 20 Data_RPE$rpe_LT2 <- round(rpe_LT2) Data_RPE$rpe_lactat2 <- round(rpe_lactat2) Data_RPE$rpe_lactat3 <- round(rpe_lactat3) Data_RPE$rpe_lactat4 <- round(rpe_lactat4) # Figure 1, Example for the spline interpolation ####################################### # Example Patient expl_patient <- tibble(rpe = t(unname(Data_RPE[Data_RPE$ID == "1394189",33:38])), lactat = t(unname(Data_RPE[Data_RPE$ID == "1394189", 9:14]))) lak_LT2 <-as.numeric(Data_RPE[Data_RPE$ID == "1394189", "Lactatkonzentration_IAS"]) plot(sp_rpe) fun = splinefun(x =expl_patient$lactat, y = expl_patient$rpe, method = "monoH.FC") fun_data <- tibble( x= seq(1.38,7.36,0.001), y = fun(x)) ggplot(data = expl_patient, aes(x = lactat, y = rpe)) + geom_point(shape =19)+ geom_line(aes(x = x, y=y), data = fun_data)+ geom_vline(xintercept = c(2,3,4,lak_LT2), col = c("dodgerblue3","dodgerblue3","dodgerblue3","firebrick1"), linetype = c(2,2,2,1)) + geom_segment(aes(x = 0, y = fun(lak_LT2), xend = lak_LT2, yend = fun(lak_LT2)), color = "firebrick1") + theme_classic()+ scale_x_continuous(breaks = c(0:8, lak_LT2), labels = c( "0", "1", "2", "3", "4", "5", "6","7", "8", "LT2"), expand = c(0.001, 0.05), limits = c(0,8), name = "Blood lactate (bLa)")+ theme(axis.text.x = element_text(face=c("plain","plain","bold","bold","bold", rep("plain",4),"bold"), size = 14), axis.text.y = element_text(size = 14), axis.title.x = element_text(size = 14), axis.title.y = element_text(size = 14), panel.grid.major = element_line(size = 0.5, linetype = 'solid', colour = "grey90")) + scale_y_continuous(name = "RPE", breaks = 6:20, limits = c(6,20)) #ggsave("Fig1.tiff",width = 20, height = 15, units = "cm", dpi= 300) ######################################################################################## # Barplots (Figure 2)################################################################## g1 <- ggplot(data = Data_RPE, aes(x =rpe_LT2 )) + geom_bar(stat = "count") + scale_y_continuous(limits = c(0, 1510))+ xlab("RPE")+ ylab("Count")+ ggtitle("LT2")+ theme_bw()+ theme(axis.text = element_text(size = 12), axis.title = element_text(size = 12)) g2 <- ggplot(data = Data_RPE, aes(x =rpe_lactat2 )) + geom_bar(stat = "count") + scale_y_continuous(limits = c(0, 1510))+ xlab("RPE")+ ylab("Count")+ ggtitle("2 mmol/l")+ theme_bw()+ theme(axis.text = element_text(size = 12), axis.title = element_text(size = 12)) g3 <- ggplot(data = Data_RPE, aes(x =rpe_lactat3 )) + geom_bar(stat = "count") + scale_y_continuous(limits = c(0, 1510))+ xlab("RPE")+ ylab("Count")+ ggtitle("3 mmol/l")+ theme_bw()+ theme(axis.text = element_text(size = 12), axis.title = element_text(size = 12)) g4 <- ggplot(data = Data_RPE, aes(x =rpe_lactat4 )) + geom_bar(stat = "count") + scale_y_continuous(limits = c(0, 1510))+ xlab("RPE")+ ylab("Count")+ ggtitle("4 mmol/l")+ theme_bw()+ theme(axis.text = element_text(size = 12), axis.title = element_text(size = 12)) ggarrange(g1,g2,g3,g4, nrow =2, ncol = 2) #ggsave("Fig2.tiff",width = 20, height = 15, units = "cm", dpi= 300) ######################################################################################################## ## 2nd Step: Ordinal Regression--------------------------------------------------------------------- ## LT2--------------------------------------------------------------------------------------- # with polr (MASS) fit_ord_LT2 <- polr(as.factor(rpe_LT2) ~ Alter + as.factor(Geschlecht) + as.factor(Ergometrieart)+VO2max_full + max_stage , data = Data_RPE, Hess = T) pred <- predict(fit_ord_LT2, type = "probs") summary(fit_ord_LT2) ctable <- coef(summary(fit_ord_LT2)) p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2 ctable <- cbind(ctable, "p value" = p) ci <- confint(fit_ord_LT2, type = "profile") #calculate confidence interavals exp(coef(fit_ord_LT2)) exp(cbind(OR = coef(fit_ord_LT2), ci)) # Prediction plots # VO2max newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter),400), VO2max_full = rep(seq(from = 4.8, to = 87, length.out = 100), 4), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_LT2, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-Alter, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "VO2max_full"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("15", "15","16","14","15","16","15","14"), Ergometrieart.labs = c("Bicycle", "Treadmill","Bicycle","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = rep(8,8), y = c(0.26, 0.255,0.225,0.22,0.26,0.23,0.255,0.215) ) ggplot(lnewdat, aes(x = VO2max_full, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw() + xlab("VO2max") + scale_colour_discrete(name = "RPE") + theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_S_LT2_VO2max.tiff",width = 20, height = 15, units = "cm", dpi= 300) # Age newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(seq(from = 10, to = 85, length.out = 100), 4), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_LT2, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "Alter"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("15", "16","15","14","15","16","15","14"), Ergometrieart.labs = c("Bicycle","Bicycle","Treadmill","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = rep(12,8), y = c(0.26, 0.21,0.245,0.225,0.26,0.215,0.245,0.225) ) ggplot(lnewdat, aes(x = Alter, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ xlab("Age")+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_LT2_Age.tiff",width = 20, height = 15, units = "cm", dpi= 300) # Number of stages newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter, 400)), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(seq(from = 2, to = 10, length.out = 100), 4)) newdat <- cbind(newdat, predict(fit_ord_LT2, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -Alter) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "max_stage"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("15", "14","16","14","15","16","15","14","16","14","15","16"), Ergometrieart.labs = c("Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill", "Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female","Female","Female", "Male", "Male", "Male", "Male", "Male", "Male"), x = c(rep(c(2.25,2.25, 9.7),2), rep(2.25,3), 2.25,2.25,9.7), y = c(0.24, 0.21,0.225,0.24,0.2,0.21,0.24,0.21,0.155,0.24,0.205,0.21) ) ggplot(lnewdat, aes(x = max_stage, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ scale_x_continuous(breaks = 2:10)+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) + xlab("Number of stages") ggsave("Fig_LT2_Nstages.tiff",width = 20, height = 15, units = "cm", dpi= 300) ## RPE at 2mmol/l lactat-------------------------------------------------------- fit_ord_lact2 <- polr(as.factor(rpe_lactat2) ~ Alter + as.factor(Geschlecht) + as.factor(Ergometrieart)+VO2max_full + max_stage , data = Data_RPE, Hess = T) tabyl(predict(fit_ord_lact2)) pred <- predict(fit_ord_lact2, type = "probs") summary(fit_ord_lact2) ctable <- coef(summary(fit_ord_lact2)) p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2 ctable <- cbind(ctable, "p value" = p) ci <- confint(fit_ord_lact2, type = "profile") exp(coef(fit_ord_lact2)) exp(cbind(OR = coef(fit_ord_lact2), ci)) # Prediction plots # VO2max newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter),400), VO2max_full = rep(seq(from = 4.8, to = 87, length.out = 100), 4), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_lact2, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-Alter, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "VO2max_full"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("15","14","13","14","13","14","14","13"), Ergometrieart.labs = c("Bicycle","Bicycle","Treadmill","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = c(82,14,8,65,8,70,82, 20), y = c(0.249, 0.192,0.174,0.225,0.168,0.225,0.225,0.168) ) g_2mmol_VO2max <- ggplot(lnewdat, aes(x = VO2max_full, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw() + xlab("VO2max") + scale_colour_discrete(name = "RPE") + theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_S_2mmol_VO2max.tiff",width = 20, height = 15, units = "cm", dpi= 300) # Age newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(seq(from = 10, to = 85, length.out = 100), 4), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_lact2, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "Alter"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("15", "14","14","15","14","13","14","13"), Ergometrieart.labs = c("Bicycle","Bicycle","Treadmill","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = c(80,12,rep(82,2),80,13,82,13), y = c(0.235, 0.202,0.225,0.194,0.225,0.18,0.22,0.17) ) g_2mmol_age <-ggplot(lnewdat, aes(x = Alter, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ xlab("Age")+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_S_2mmol_Age.tiff",width = 20, height = 15, units = "cm", dpi= 300) ## Figure 3, 2mmol/l, VO2max and age ############################################## ggarrange(g_2mmol_age,g_2mmol_VO2max, ncol = 2,labels="AUTO") ggsave("Fig3.tiff",width = 35, height = 15, units = "cm", dpi= 300) ################################################################################ # Number of stages newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter, 400)), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(seq(from = 2, to = 10, length.out = 100), 4)) newdat <- cbind(newdat, predict(fit_ord_lact2, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -Alter) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "max_stage"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("15", "14","13","15","14","13","14","15","13","14","15","13"), Ergometrieart.labs = c("Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill", "Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female","Female","Female", "Male", "Male", "Male","Male","Male","Male"), x = c(rep(9.7,2),3,9.7,9.7,9, rep(9.7,6)), y = c(0.24, 0.21,0.165,0.225,0.2,0.16,0.225,0.21,0.16, 0.22,0.19,0.17) ) ggplot(lnewdat, aes(x = max_stage, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ scale_x_continuous(breaks = 2:10)+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) + xlab("Number of stages") ggsave("Fig_S_2mmol_Nstages.tiff",width = 20, height = 15, units = "cm", dpi= 300) ## RPE at 3mmol/l lactat-------------------------------------------------------------------------------------------------- fit_ord_lact3 <- polr(as.factor(rpe_lactat3) ~ Alter + as.factor(Geschlecht) + as.factor(Ergometrieart)+VO2max_full + max_stage , data = Data_RPE, Hess = T) tabyl(predict(fit_ord_lact3)) pred <- predict(fit_ord_lact3, type = "probs") apply(pred,2, mean) apply(pred,2, sd) summary(fit_ord_lact3) ctable <- coef(summary(fit_ord_lact3)) p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2 ctable <- cbind(ctable, "p value" = p) ci <- confint(fit_ord_lact3, type = "profile") exp(coef(fit_ord_lact3)) exp(cbind(OR = coef(fit_ord_lact3), ci)) # Prediction plots # VO2max newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter),400), VO2max_full = rep(seq(from = 4.8, to = 87, length.out = 100), 4), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_lact3, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-Alter, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "VO2max_full"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("16","15","16","15","15","16","15","16"), Ergometrieart.labs = c("Bicycle","Bicycle","Treadmill","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = rep(82,8), y = c(0.245, 0.20,0.235,0.21,0.235,0.205,0.235,0.195) ) ggplot(lnewdat, aes(x = VO2max_full, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw() + xlab("VO2max") + scale_colour_discrete(name = "RPE") + theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_S_3mmol_VO2max.tiff",width = 20, height = 15, units = "cm", dpi= 300) # Age newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(seq(from = 10, to = 85, length.out = 100), 4), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_lact3, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "Alter"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("15", "16","15","16","15","14","15","14"), Ergometrieart.labs = c("Bicycle","Bicycle","Treadmill","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = c(rep(82,5),12,82,12), y = c(0.23, 0.21,0.235,0.215,0.235,0.205,0.237,0.192) ) ggplot(lnewdat, aes(x = Alter, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ xlab("Age")+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_S_3mmol_Age.tiff",width = 20, height = 15, units = "cm", dpi= 300) # Number of stages newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter, 400)), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(seq(from = 2, to = 10, length.out = 100), 4)) newdat <- cbind(newdat, predict(fit_ord_lact3, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -Alter) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "max_stage"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("16", "15","14","16","15","14","16","15","14","15","16","14"), Ergometrieart.labs = c("Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill", "Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female","Female","Female", "Male", "Male", "Male", "Male", "Male", "Male"), x = rep(c(9.5,9.5,2.5),4), y = c(0.245, 0.215,0.215,0.24,0.22,0.21,0.235,0.205,0.205,0.235,0.205,0.2) ) ggplot(lnewdat, aes(x = max_stage, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ scale_x_continuous(breaks = 2:10)+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) + xlab("Number of stages") #ggsave("Fig_S_3mmol_Nstages.tiff",width = 20, height = 15, units = "cm", dpi= 300) ## RPE at 4mmol/l lactat------------------------------------------------------------------------------------------------- fit_ord_lact4 <- polr(as.factor(rpe_lactat4) ~ Alter + as.factor(Geschlecht) + as.factor(Ergometrieart)+VO2max_full + max_stage , data = Data_RPE, Hess = T) tabyl(predict(fit_ord_lact4)) pred <- predict(fit_ord_lact4, type = "probs") summary(fit_ord_lact4) ctable <- coef(summary(fit_ord_lact4)) p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2 ctable <- cbind(ctable, "p value" = p) ci <- confint(fit_ord_lact4, type = "profile") exp(coef(fit_ord_lact4)) exp(cbind(OR = coef(fit_ord_lact4), ci)) # Prediction plots # VO2max newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter),400), VO2max_full = rep(seq(from = 4.8, to = 87, length.out = 100), 4), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_lact4, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-Alter, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "VO2max_full"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("16","15","16","15","16","15","16","15"), Ergometrieart.labs = c("Bicycle","Bicycle","Treadmill","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = rep(5,8), y = c(0.23, 0.18,0.235,0.185,0.235,0.185,0.235,0.185) ) ggplot(lnewdat, aes(x = VO2max_full, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw() + xlab("VO2max") + scale_colour_discrete(name = "RPE") + theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_S_4mmol_VO2max.tiff",width = 20, height = 15, units = "cm", dpi= 300) # Age newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(seq(from = 10, to = 85, length.out = 100), 4), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(mean(Data_RPE$max_stage),400)) newdat <- cbind(newdat, predict(fit_ord_lact4, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -max_stage) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "Alter"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("16", "15","16","15","16","15","16","15"), Ergometrieart.labs = c("Bicycle","Bicycle","Treadmill","Treadmill", "Bicycle","Bicycle","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female", "Male", "Male", "Male", "Male"), x = c(rep(82,8)), y = c(0.235, 0.21,0.235,0.21,0.235,0.21,0.235,0.21) ) ggplot(lnewdat, aes(x = Alter, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ xlab("Age")+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) #ggsave("Fig_S_4mmol_Age.tiff",width = 20, height = 15, units = "cm", dpi= 300) # Number of stages newdat <- data.frame( Ergometrieart = rep(1:2, 200), Geschlecht = rep(0:1, each = 200), Alter = rep(mean(Data_RPE$Alter, 400)), VO2max_full = rep(mean(Data_RPE$VO2max_full),400), max_stage = rep(seq(from = 2, to = 10, length.out = 100), 4)) newdat <- cbind(newdat, predict(fit_ord_lact4, newdat, type = "probs")) newdat <- newdat %>% dplyr::select(-VO2max_full, -Alter) lnewdat <- melt(newdat, id.vars = c("Ergometrieart", "Geschlecht", "max_stage"), variable.name = "Level", value.name="Probability") lnewdat$Ergometrieart.labs = c("Bicycle","Treadmill") lnewdat$Geschlecht.labs = rep(c("Female","Male"),each = 200) rpe_text <- data.frame( label = c("17", "15","16", "17","15","16","17","15","16","17","15","16"), Ergometrieart.labs = c("Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill", "Bicycle","Bicycle","Bicycle","Treadmill","Treadmill","Treadmill"), Geschlecht.labs = c("Female","Female","Female","Female","Female","Female", "Male", "Male", "Male", "Male", "Male", "Male"), x = rep(c(9.7,2.2,7.5),8), y = c(0.24, 0.235,0.235,0.24,0.235,0.235,0.24,0.235,0.235,0.24,0.235,0.235) ) ggplot(lnewdat, aes(x = max_stage, y = Probability, colour = Level)) + geom_line() + facet_grid(Geschlecht.labs ~ Ergometrieart.labs, labeller=label_value)+ geom_text(data = rpe_text, mapping = aes(label = label,x=x, y=y), inherit.aes = FALSE, size = 4)+ theme_bw()+ scale_x_continuous(breaks = 2:10)+ scale_colour_discrete(name = "RPE")+ theme(axis.text = element_text(size = 15), axis.title = element_text(size = 15), strip.text = element_text(size =15), legend.text = element_text(size = 15), legend.title = element_text(size = 15)) + xlab("Number of stages") #ggsave("Fig_S_4mmol_Nstages.tiff",width = 20, height = 15, units = "cm", dpi= 300)