Group Project in Preclinical and Clinical Data Analysis in DDD
Adam Nyström
2025-01-19
Part A
Task 1
n_arms <- unique(data_1$STUDY_ARM)
dose <- unique(data_1$DOSE) #which doses?
#Individuals within each dose
individuals_dose_0 <- data_1%>%
filter(DOSE==0)
n_0 <- length(unique(individuals_dose_0$ID))
individuals_dose_5 <- data_1%>%
filter(DOSE==5)
n_5 <- length(unique(individuals_dose_5$ID))
individuals_dose_10 <- data_1%>%
filter(DOSE==10)
n_10 <- length(unique(individuals_dose_10$ID))
individuals_dose_20 <- data_1%>%
filter(DOSE==20)
n_20 <- length(unique(individuals_dose_20$ID))
individuals_dose_150 <- data_1%>%
filter(DOSE==150)
n_150 <- length(unique(individuals_dose_150$ID))
individuals_dose_200 <- data_1%>%
filter(DOSE==200)
n_200 <- length(unique(individuals_dose_200$ID))Study arms: 1, 2, 3, 4, 5, 6, doses: 0, 5, 10, 20, 150, 200, participants per arm: 1=16 2=18 3=22 4=23 5=20 6=24.
#Efficacy for all patients
data_1 <- data_1%>%
mutate(DV=as.numeric(DV))%>%
mutate(Group = ceiling(row_number() / 4)) %>%
group_by(Group) %>%
mutate(Efficacy = DV[4] - DV[1]) %>%
ungroup() %>%
select(-Group)#Graphical visualization of efficacy by scatterplot
ggplot(data_1, aes(ID, Efficacy))+
geom_point()+
facet_wrap(~STUDY_ARM)+
labs(title = "Efficacy per participant stratified on study arm (i.e dose)")
#Graphical visualization of mean efficacy by dose with barplot
data_1_mean <- data_1%>%
group_by(DOSE)%>%
summarise(Mean_efficacy_dose=mean(Efficacy))
ggplot(data_1_mean, aes(DOSE, Mean_efficacy_dose))+
geom_bar(stat = "identity")+
labs(title = "Mean efficacy per dose",
x= "Dose (mg)",
y= "Efficacy")
Task 2
# Test 1 - whether any of the arms show effect
#STUDY ARM 2
dataset240_ARM2 <- data_1[ data_1$TIME == 240 & data_1$STUDY_ARM == 2, c("ID", "DV", "STUDY_ARM")]
dataset0_ARM2 <- data_1[ data_1$TIME == 0 & data_1$STUDY_ARM == 2, c("ID", "DV", "STUDY_ARM")]
merged_data_1_2 <- merge(dataset240_ARM2, dataset0_ARM2, by = "ID", suffixes = c("_240", "_0"))
wilcox.test(merged_data_1_2$DV_240, merged_data_1_2$DV_0, paired = TRUE)##
## Wilcoxon signed rank exact test
##
## data: merged_data_1_2$DV_240 and merged_data_1_2$DV_0
## V = 65, p-value = 0.3927
## alternative hypothesis: true location shift is not equal to 0#STUDY ARM 3
dataset240_ARM3 <- data_1[ data_1$TIME == 240 & data_1$STUDY_ARM == 3, c("ID", "DV", "STUDY_ARM")]
dataset0_ARM3 <- data_1[ data_1$TIME == 0 & data_1$STUDY_ARM == 3, c("ID", "DV", "STUDY_ARM")]
merged_data_1_3 <- merge(dataset240_ARM3, dataset0_ARM3, by = "ID", suffixes = c("_240", "_0"))
wilcox.test(merged_data_1_3$DV_240, merged_data_1_3$DV_0, paired = TRUE)##
## Wilcoxon signed rank exact test
##
## data: merged_data_1_3$DV_240 and merged_data_1_3$DV_0
## V = 102, p-value = 0.4434
## alternative hypothesis: true location shift is not equal to 0#STUDY ARM 4
dataset240_ARM4 <- data_1[ data_1$TIME == 240 & data_1$STUDY_ARM == 4, c("ID", "DV", "STUDY_ARM")]
dataset0_ARM4 <- data_1[ data_1$TIME == 0 & data_1$STUDY_ARM == 4, c("ID", "DV", "STUDY_ARM")]
merged_data_1_4 <- merge(dataset240_ARM4, dataset0_ARM4, by = "ID", suffixes = c("_240", "_0"))
wilcox.test(merged_data_1_4$DV_240, merged_data_1_4$DV_0, paired = TRUE)##
## Wilcoxon signed rank exact test
##
## data: merged_data_1_4$DV_240 and merged_data_1_4$DV_0
## V = 148, p-value = 0.7768
## alternative hypothesis: true location shift is not equal to 0#STUDY ARM 5
dataset240_ARM5 <- data_1[ data_1$TIME == 240 & data_1$STUDY_ARM == 5, c("ID", "DV", "STUDY_ARM")]
dataset0_ARM5 <- data_1[ data_1$TIME == 0 & data_1$STUDY_ARM == 5, c("ID", "DV", "STUDY_ARM")]
merged_data_1_5 <- merge(dataset240_ARM5, dataset0_ARM5, by = "ID", suffixes = c("_240", "_0"))
wilcox.test(merged_data_1_5$DV_240, merged_data_1_5$DV_0, paired = TRUE)##
## Wilcoxon signed rank exact test
##
## data: merged_data_1_5$DV_240 and merged_data_1_5$DV_0
## V = 195, p-value = 0.0002613
## alternative hypothesis: true location shift is not equal to 0#STUDY ARM 6
dataset240_ARM6 <- data_1[ data_1$TIME == 240 & data_1$STUDY_ARM == 6, c("ID", "DV", "STUDY_ARM")]
dataset0_ARM6 <- data_1[ data_1$TIME == 0 & data_1$STUDY_ARM == 6, c("ID", "DV", "STUDY_ARM")]
merged_data_1_6 <- merge(dataset240_ARM6, dataset0_ARM6, by = "ID", suffixes = c("_240", "_0"))
wilcox.test(merged_data_1_6$DV_240, merged_data_1_6$DV_0, paired = TRUE)##
## Wilcoxon signed rank exact test
##
## data: merged_data_1_6$DV_240 and merged_data_1_6$DV_0
## V = 298, p-value = 3.576e-07
## alternative hypothesis: true location shift is not equal to 0#Test 2 - Wilcoxon on all the study arms whether they have levels above mu (194)
data_1_1 <- data_1%>%
filter(STUDY_ARM==1)
data_1_2 <- data_1%>%
filter(STUDY_ARM==2)
wilcox.test(data_1_2$Efficacy, mu=194, alternative= "greater", paired = FALSE)##
## Wilcoxon signed rank test with continuity correction
##
## data: data_1_2$Efficacy
## V = 0, p-value = 1
## alternative hypothesis: true location is greater than 194wilcox.test(data_1_2$Efficacy, mu=194, alternative= "greater", paired = FALSE)##
## Wilcoxon signed rank test with continuity correction
##
## data: data_1_2$Efficacy
## V = 0, p-value = 1
## alternative hypothesis: true location is greater than 194data_1_3 <- data_1%>%
filter(STUDY_ARM==3)
wilcox.test(data_1_3$Efficacy, mu=194, alternative= "greater", paired = FALSE)##
## Wilcoxon signed rank test with continuity correction
##
## data: data_1_3$Efficacy
## V = 0, p-value = 1
## alternative hypothesis: true location is greater than 194data_1_4 <- data_1%>%
filter(STUDY_ARM==4)
wilcox.test(data_1_4$Efficacy, mu=194, alternative= "greater", paired = FALSE)##
## Wilcoxon signed rank test with continuity correction
##
## data: data_1_4$Efficacy
## V = 0, p-value = 1
## alternative hypothesis: true location is greater than 194data_1_5 <- data_1%>%
filter(STUDY_ARM==5)
wilcox.test(data_1_5$Efficacy, mu=194, alternative= "greater", paired = FALSE)##
## Wilcoxon signed rank test with continuity correction
##
## data: data_1_5$Efficacy
## V = 1062, p-value = 0.9963
## alternative hypothesis: true location is greater than 194data_1_6<- data_1%>%
filter(STUDY_ARM==6)
wilcox.test(data_1_6$Efficacy, mu=194, alternative= "greater", paired = FALSE)##
## Wilcoxon signed rank test with continuity correction
##
## data: data_1_6$Efficacy
## V = 2882, p-value = 0.02153
## alternative hypothesis: true location is greater than 194First we evaluate which of the study arms show statistically significant effect and the conclusion was that only arms 5 and 6 do that. Next we evaluated which of the two arms is most likely to achieve MED whith the threshold of 194 (200 points above the placebo effect which was indicated in the assignment). Setting up null hypothesis that the arms do not have efficacy levels that are statisically significant above 194 (with 95 % confidence level), i.e the true mean is 194 . Alternative hypothesis is then that there are statistically significant levels above 194 We see that arm 6 show statistically significant scores above 194, i.e it has a p-value below 0.05. For arm 6 the p-value is 0.02153 and for arm 5 it was 0.9963. The conclusion is that there is statistically significant evidence to reject the null hypothesis on a 95 % confidence level for arm 6 but not for arm 5, i.e it can be stated that arm 6 shows significant efficacy above 194 and can therefore be regarded as MED.
Task 3
#linear models
ggplot(data_1, aes(DOSE, Efficacy))+
geom_point()+
geom_smooth(method = "lm")+
labs(title = "Efficacy-dose dependence")
fit_1 <- lm(Efficacy~DOSE,data_1)
summary(fit_1)##
## Call:
## lm(formula = Efficacy ~ DOSE, data = data_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -277.99 -48.03 -8.75 43.64 429.98
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -14.10878 6.06840 -2.325 0.0205 *
## DOSE 1.19559 0.05644 21.183 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 102.5 on 490 degrees of freedom
## Multiple R-squared: 0.478, Adjusted R-squared: 0.4769
## F-statistic: 448.7 on 1 and 490 DF, p-value: < 2.2e-16ggplot(data=data_1, aes(x=CMAX,y=Efficacy)) +
geom_point() +
geom_smooth(method="lm")+
labs(title = "Efficacy-Cmax dependency")
fit_2 <- lm(Efficacy~CMAX,data_1)
summary(fit_2)##
## Call:
## lm(formula = Efficacy ~ CMAX, data = data_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -65.58 0.00 0.00 0.00 81.22
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.036 2.349 -2.569 0.010563 *
## CMAX0.0409280643709855 -85.865 9.685 -8.865 < 2e-16 ***
## CMAX0.048766131536913 17.775 9.685 1.835 0.067249 .
## CMAX0.0551094523469211 3.579 9.685 0.369 0.711976
## CMAX0.06294583116746 65.717 9.685 6.785 4.41e-11 ***
## CMAX0.0649925709584611 35.949 9.685 3.712 0.000236 ***
## CMAX0.0687925361425764 -45.763 9.685 -4.725 3.24e-06 ***
## CMAX0.0736383950647283 -19.251 9.685 -1.988 0.047563 *
## CMAX0.0740444571312328 -50.382 9.685 -5.202 3.22e-07 ***
## CMAX0.081591334617505 134.346 9.685 13.871 < 2e-16 ***
## CMAX0.0859957531003795 -70.470 9.685 -7.276 1.95e-12 ***
## CMAX0.0892579225044205 -32.021 9.685 -3.306 0.001035 **
## CMAX0.0918497854744058 102.272 9.685 10.559 < 2e-16 ***
## CMAX0.0955116182115186 -5.605 9.685 -0.579 0.563155
## CMAX0.0970711808757759 -1.037 9.685 -0.107 0.914784
## CMAX0.0989288453941647 -2.719 9.685 -0.281 0.779055
## CMAX0.100116122241526 11.136 9.685 1.150 0.250975
## CMAX0.100524360882218 -30.536 9.685 -3.153 0.001744 **
## CMAX0.109375287860067 -26.678 9.685 -2.754 0.006159 **
## CMAX0.110013001906529 -29.761 9.685 -3.073 0.002272 **
## CMAX0.114840846842872 -12.534 9.685 -1.294 0.196412
## CMAX0.120196906529358 -50.266 9.685 -5.190 3.42e-07 ***
## CMAX0.120683581519563 -60.511 9.685 -6.248 1.11e-09 ***
## CMAX0.134804013760219 -18.211 9.685 -1.880 0.060830 .
## CMAX0.138505765346674 -4.863 9.685 -0.502 0.615885
## CMAX0.139244762099898 49.237 9.685 5.084 5.80e-07 ***
## CMAX0.140157439663805 -4.642 9.685 -0.479 0.632011
## CMAX0.140389966790967 -31.204 9.685 -3.222 0.001383 **
## CMAX0.14167620808267 17.367 9.685 1.793 0.073737 .
## CMAX0.152429742524064 47.528 9.685 4.907 1.37e-06 ***
## CMAX0.161721214354668 8.999 9.685 0.929 0.353405
## CMAX0.167650094410379 35.216 9.685 3.636 0.000315 ***
## CMAX0.192685369846392 -19.258 9.685 -1.988 0.047481 *
## CMAX0.206595008103513 -61.300 9.685 -6.329 6.88e-10 ***
## CMAX0.216409314958811 -10.475 9.685 -1.081 0.280155
## CMAX0.22502124766866 -67.200 9.685 -6.938 1.70e-11 ***
## CMAX0.229033191191921 -34.442 9.685 -3.556 0.000423 ***
## CMAX0.234127209319057 61.804 9.685 6.381 5.07e-10 ***
## CMAX0.236884009621847 -23.035 9.685 -2.378 0.017879 *
## CMAX0.237028222978225 42.940 9.685 4.433 1.21e-05 ***
## CMAX0.244218585539524 30.762 9.685 3.176 0.001613 **
## CMAX0.247040885863986 77.993 9.685 8.053 1.03e-14 ***
## CMAX0.248164140009402 -37.361 9.685 -3.857 0.000134 ***
## CMAX0.265830796072217 -19.119 9.685 -1.974 0.049094 *
## CMAX0.267139968396263 4.303 9.685 0.444 0.657073
## CMAX0.268175200823551 -5.191 9.685 -0.536 0.592280
## CMAX0.269920877121256 114.792 9.685 11.852 < 2e-16 ***
## CMAX0.279045949463964 -38.645 9.685 -3.990 7.92e-05 ***
## CMAX0.297492001928354 -68.766 9.685 -7.100 6.08e-12 ***
## CMAX0.300734220741858 -20.619 9.685 -2.129 0.033901 *
## CMAX0.318828560463668 42.768 9.685 4.416 1.31e-05 ***
## CMAX0.31887002386934 5.447 9.685 0.562 0.574200
## CMAX0.326205272223197 24.452 9.685 2.525 0.011985 *
## CMAX0.341347516764726 81.959 9.685 8.462 5.59e-16 ***
## CMAX0.344428076475648 16.634 9.685 1.717 0.086713 .
## CMAX0.36035262037735 136.977 9.685 14.143 < 2e-16 ***
## CMAX0.361319167226589 -8.307 9.685 -0.858 0.391630
## CMAX0.36609264764387 9.247 9.685 0.955 0.340299
## CMAX0.367817777134613 7.668 9.685 0.792 0.429041
## CMAX0.47454814377214 150.784 9.685 15.568 < 2e-16 ***
## CMAX0.4823142032289 -80.927 9.685 -8.356 1.20e-15 ***
## CMAX0.52971604152518 58.661 9.685 6.057 3.32e-09 ***
## CMAX0.603918157914429 4.648 9.685 0.480 0.631573
## CMAX0.606617728777948 2.623 9.685 0.271 0.786677
## CMAX1.14178384437321 136.553 9.685 14.099 < 2e-16 ***
## CMAX1.37461276525523 -5.527 9.685 -0.571 0.568555
## CMAX1.54436494600216 -11.108 9.685 -1.147 0.252148
## CMAX1.62296945903605 -44.651 9.685 -4.610 5.49e-06 ***
## CMAX1.86003448115233 152.665 9.685 15.762 < 2e-16 ***
## CMAX1.88096237185573 41.845 9.685 4.320 1.99e-05 ***
## CMAX1.95429723884831 129.119 9.685 13.331 < 2e-16 ***
## CMAX2.09155436716288 49.082 9.685 5.068 6.28e-07 ***
## CMAX2.15873197849731 72.393 9.685 7.474 5.30e-13 ***
## CMAX2.21063217462729 54.857 9.685 5.664 2.91e-08 ***
## CMAX2.35560272390329 79.909 9.685 8.250 2.55e-15 ***
## CMAX2.35869279745125 208.585 9.685 21.536 < 2e-16 ***
## CMAX2.42506839735924 -46.942 9.685 -4.847 1.83e-06 ***
## CMAX2.5233282097352 179.810 9.685 18.565 < 2e-16 ***
## CMAX2.82196812796291 241.226 9.685 24.906 < 2e-16 ***
## CMAX2.82484124821596 56.325 9.685 5.815 1.27e-08 ***
## CMAX2.83622020247648 601.250 9.685 62.077 < 2e-16 ***
## CMAX2.85448834560022 95.540 9.685 9.864 < 2e-16 ***
## CMAX2.86251513601486 202.489 9.685 20.906 < 2e-16 ***
## CMAX2.86438723871794 157.418 9.685 16.253 < 2e-16 ***
## CMAX2.97425594270275 263.955 9.685 27.253 < 2e-16 ***
## CMAX3.06163915077943 314.897 9.685 32.512 < 2e-16 ***
## CMAX3.12667713686447 -18.854 9.685 -1.947 0.052312 .
## CMAX3.13100468457449 314.138 9.685 32.434 < 2e-16 ***
## CMAX3.3129380315837 78.197 9.685 8.074 8.88e-15 ***
## CMAX3.3296177751755 62.808 9.685 6.485 2.74e-10 ***
## CMAX3.37788812878032 401.483 9.685 41.452 < 2e-16 ***
## CMAX3.52319882744812 594.045 9.685 61.334 < 2e-16 ***
## CMAX3.58165324653708 272.705 9.685 28.156 < 2e-16 ***
## CMAX3.66593221089162 420.903 9.685 43.457 < 2e-16 ***
## CMAX3.79275907197478 469.000 9.685 48.423 < 2e-16 ***
## CMAX4.01413693563741 30.177 9.685 3.116 0.001973 **
## CMAX4.04276653753908 160.145 9.685 16.535 < 2e-16 ***
## CMAX4.51352819265435 380.564 9.685 39.292 < 2e-16 ***
## CMAX5.4492325187986 414.759 9.685 42.823 < 2e-16 ***
## CMAX5.87070001876108 323.798 9.685 33.431 < 2e-16 ***
## CMAX5.99671862712973 359.861 9.685 37.155 < 2e-16 ***
## CMAX6.3309976261207 362.290 9.685 37.405 < 2e-16 ***
## CMAX6.5728491418564 194.718 9.685 20.104 < 2e-16 ***
## CMAX6.63267411144924 234.595 9.685 24.221 < 2e-16 ***
## CMAX6.88522091998727 300.128 9.685 30.987 < 2e-16 ***
## CMAX6.89409056209306 183.011 9.685 18.895 < 2e-16 ***
## CMAX8.22583005667615 187.277 9.685 19.336 < 2e-16 ***
## CMAX8.89991986328509 271.209 9.685 28.002 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.79 on 384 degrees of freedom
## Multiple R-squared: 0.9863, Adjusted R-squared: 0.9824
## F-statistic: 257.5 on 107 and 384 DF, p-value: < 2.2e-16ggplot(data=data_1, aes(x=AUC,y=Efficacy)) +
geom_point() +
geom_smooth(method="lm")+
labs(title = "Efficacy-AUC dependency")
fit_3 <- lm(Efficacy~DOSE,data_1)
summary(fit_3)##
## Call:
## lm(formula = Efficacy ~ DOSE, data = data_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -277.99 -48.03 -8.75 43.64 429.98
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -14.10878 6.06840 -2.325 0.0205 *
## DOSE 1.19559 0.05644 21.183 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 102.5 on 490 degrees of freedom
## Multiple R-squared: 0.478, Adjusted R-squared: 0.4769
## F-statistic: 448.7 on 1 and 490 DF, p-value: < 2.2e-16ggplot(data=data_1, aes(x=CMAX,y=DOSE)) +
geom_point() +
geom_smooth(method="lm")+
labs(title = "Efficacy-Cmax dependency")
#multilinear models
lin_model <- lm(Efficacy~DOSE*WT, data = data_1)
summary(lin_model)##
## Call:
## lm(formula = Efficacy ~ DOSE * WT, data = data_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.810e-12 0.000e+00 0.000e+00 0.000e+00 2.889e-12
##
## Coefficients: (123 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.941e+01 2.065e-13 -2.393e+14 <2e-16 ***
## DOSE 1.258e+00 1.460e-14 8.616e+13 <2e-16 ***
## WT39.0926556253334 9.651e+01 2.529e-13 3.816e+14 <2e-16 ***
## WT43.385370870966 1.394e+02 2.632e-13 5.294e+14 <2e-16 ***
## WT44.1645866416275 4.066e+01 2.632e-13 1.545e+14 <2e-16 ***
## WT44.4408249073636 -4.809e+01 2.786e-12 -1.726e+13 <2e-16 ***
## WT45.1517422320562 1.826e+01 2.529e-13 7.219e+13 <2e-16 ***
## WT45.6670705971498 -2.221e+01 2.920e-13 -7.606e+13 <2e-16 ***
## WT46.299742376232 7.373e+01 2.529e-13 2.915e+14 <2e-16 ***
## WT46.3345640624208 -9.625e+01 2.060e-12 -4.673e+13 <2e-16 ***
## WT46.6495409795975 2.286e+01 2.920e-13 7.828e+13 <2e-16 ***
## WT46.8822393257666 7.057e+00 2.920e-13 2.417e+13 <2e-16 ***
## WT46.8973190114622 -1.900e+02 2.060e-12 -9.223e+13 <2e-16 ***
## WT47.4826867538601 4.816e+01 2.529e-13 1.904e+14 <2e-16 ***
## WT47.6143432438632 -2.122e+01 2.920e-13 -7.268e+13 <2e-16 ***
## WT47.6851482283133 -1.283e+02 2.786e-12 -4.606e+13 <2e-16 ***
## WT48.3117070076055 4.683e+01 2.920e-13 1.604e+14 <2e-16 ***
## WT48.3446507313387 5.967e+01 2.920e-13 2.043e+14 <2e-16 ***
## WT48.4771999017763 2.593e+01 2.529e-13 1.025e+14 <2e-16 ***
## WT48.5966048753623 -1.047e+00 2.920e-13 -3.586e+12 <2e-16 ***
## WT49.1572187675018 1.088e+02 2.529e-13 4.301e+14 <2e-16 ***
## WT49.2969564594932 -3.339e+01 2.632e-13 -1.268e+14 <2e-16 ***
## WT49.8617705593529 3.244e+01 2.632e-13 1.232e+14 <2e-16 ***
## WT49.868488821644 -1.519e+02 2.786e-12 -5.453e+13 <2e-16 ***
## WT50.158878263407 1.688e+02 2.060e-12 8.195e+13 <2e-16 ***
## WT50.2077352982534 2.032e+01 2.529e-13 8.033e+13 <2e-16 ***
## WT50.2368325095966 -2.522e+01 2.786e-12 -9.053e+12 <2e-16 ***
## WT50.2636476710892 1.042e+02 2.920e-13 3.567e+14 <2e-16 ***
## WT50.3494396610472 2.636e+01 2.786e-12 9.463e+12 <2e-16 ***
## WT50.3915854131725 7.321e+00 2.632e-13 2.781e+13 <2e-16 ***
## WT50.8289463391973 1.167e+01 2.529e-13 4.615e+13 <2e-16 ***
## WT51.0472336107365 9.590e+01 2.060e-12 4.656e+13 <2e-16 ***
## WT51.0793328880538 1.246e+02 2.920e-13 4.266e+14 <2e-16 ***
## WT51.5370663687331 -9.047e+01 2.060e-12 -4.392e+13 <2e-16 ***
## WT51.8079344024178 4.266e+01 2.920e-13 1.461e+14 <2e-16 ***
## WT52.4503890630421 5.716e+01 2.060e-12 2.775e+13 <2e-16 ***
## WT52.9895701498835 5.699e+01 2.920e-13 1.951e+14 <2e-16 ***
## WT53.0690868837438 1.690e+02 2.920e-13 5.787e+14 <2e-16 ***
## WT53.6689904718367 4.608e+01 2.632e-13 1.751e+14 <2e-16 ***
## WT53.8304347347303 2.251e+01 2.920e-13 7.710e+13 <2e-16 ***
## WT54.726983025146 2.756e+02 2.060e-12 1.338e+14 <2e-16 ***
## WT54.8548620414376 1.651e+02 2.529e-13 6.530e+14 <2e-16 ***
## WT55.0662615987696 5.060e+00 2.632e-13 1.922e+13 <2e-16 ***
## WT55.0820017068382 2.083e+01 2.920e-13 7.134e+13 <2e-16 ***
## WT55.189354362534 1.156e+02 2.786e-12 4.148e+13 <2e-16 ***
## WT55.4661838306457 1.040e+01 2.632e-13 3.952e+13 <2e-16 ***
## WT56.0331804198636 -1.351e+01 2.786e-12 -4.851e+12 <2e-16 ***
## WT56.5706246440395 -2.552e+02 2.786e-12 -9.160e+13 <2e-16 ***
## WT56.6217213823502 -2.972e+01 2.529e-13 -1.175e+14 <2e-16 ***
## WT56.7464609528505 -1.035e+02 2.060e-12 -5.024e+13 <2e-16 ***
## WT56.8341586420691 -8.778e+00 2.060e-12 -4.261e+12 <2e-16 ***
## WT56.9941031587336 1.516e+02 2.786e-12 5.443e+13 <2e-16 ***
## WT57.0349868781429 -2.992e+00 2.920e-13 -1.024e+13 <2e-16 ***
## WT57.2529607952786 -1.509e+02 2.060e-12 -7.324e+13 <2e-16 ***
## WT57.3828325288484 -1.959e+01 2.529e-13 -7.746e+13 <2e-16 ***
## WT57.4427679113438 6.298e+01 2.786e-12 2.261e+13 <2e-16 ***
## WT57.4706335255625 1.128e+02 2.529e-13 4.458e+14 <2e-16 ***
## WT58.0810428414755 2.807e+01 2.529e-13 1.110e+14 <2e-16 ***
## WT58.3877459984707 1.696e+02 2.060e-12 8.232e+13 <2e-16 ***
## WT58.3884120934077 1.186e+02 2.060e-12 5.759e+13 <2e-16 ***
## WT58.6413350670283 -1.621e+01 2.060e-12 -7.871e+12 <2e-16 ***
## WT59.0600656548766 3.323e+01 2.920e-13 1.138e+14 <2e-16 ***
## WT59.2419303221282 4.822e+01 2.632e-13 1.832e+14 <2e-16 ***
## WT59.4634759747235 3.858e+02 2.786e-12 1.385e+14 <2e-16 ***
## WT59.629109470457 -1.915e+01 2.920e-13 -6.557e+13 <2e-16 ***
## WT59.7483475846391 -1.564e+02 2.060e-12 -7.595e+13 <2e-16 ***
## WT59.8793148533197 5.486e+01 2.632e-13 2.084e+14 <2e-16 ***
## WT60.1947327086809 1.302e+01 2.920e-13 4.458e+13 <2e-16 ***
## WT60.6392531904703 3.448e+01 2.060e-12 1.674e+13 <2e-16 ***
## WT60.9773525638669 2.975e+01 2.529e-13 1.176e+14 <2e-16 ***
## WT61.0098811892406 7.303e+01 2.632e-13 2.774e+14 <2e-16 ***
## WT61.2055129626385 7.334e+00 2.060e-12 3.560e+12 <2e-16 ***
## WT61.2587832531637 5.343e+01 2.920e-13 1.830e+14 <2e-16 ***
## WT61.323014282204 2.746e+01 2.920e-13 9.403e+13 <2e-16 ***
## WT61.5125060704702 -1.454e+02 2.786e-12 -5.220e+13 <2e-16 ***
## WT62.0082176608355 -1.358e+02 2.786e-12 -4.876e+13 <2e-16 ***
## WT62.5588732638254 3.148e+01 2.632e-13 1.196e+14 <2e-16 ***
## WT62.687184307522 9.190e+01 2.786e-12 3.299e+13 <2e-16 ***
## WT62.8383015359403 -8.681e+00 2.632e-13 -3.298e+13 <2e-16 ***
## WT62.8533647595014 9.254e+01 2.920e-13 3.169e+14 <2e-16 ***
## WT62.8954159361529 8.369e+01 2.920e-13 2.866e+14 <2e-16 ***
## WT63.1802789246418 1.933e+02 2.786e-12 6.937e+13 <2e-16 ***
## WT63.2085175325467 7.687e+01 2.920e-13 2.632e+14 <2e-16 ***
## WT63.74748163791 -1.947e+01 2.529e-13 -7.700e+13 <2e-16 ***
## WT64.0513937799648 2.588e+01 2.920e-13 8.862e+13 <2e-16 ***
## WT64.0845147080079 9.889e+01 2.632e-13 3.757e+14 <2e-16 ***
## WT64.1953608112469 -2.408e+00 2.920e-13 -8.245e+12 <2e-16 ***
## WT64.4887367273998 4.195e+01 2.060e-12 2.036e+13 <2e-16 ***
## WT64.867603592169 1.723e+02 2.786e-12 6.186e+13 <2e-16 ***
## WT66.1087736227983 -1.127e+02 2.786e-12 -4.045e+13 <2e-16 ***
## WT66.716577146186 2.608e+02 2.786e-12 9.361e+13 <2e-16 ***
## WT67.3753486626367 2.065e+02 2.786e-12 7.414e+13 <2e-16 ***
## WT67.5217446512654 -1.642e+02 2.060e-12 -7.971e+13 <2e-16 ***
## WT67.6664905819041 1.541e+02 2.786e-12 5.530e+13 <2e-16 ***
## WT67.869609391395 1.783e+01 2.632e-13 6.774e+13 <2e-16 ***
## WT68.2619190177503 1.330e+02 2.920e-13 4.554e+14 <2e-16 ***
## WT68.310006443405 -3.051e+01 2.529e-13 -1.206e+14 <2e-16 ***
## WT68.3772567248618 -5.081e+01 2.786e-12 -1.824e+13 <2e-16 ***
## WT69.3704816970312 4.897e+01 2.920e-13 1.677e+14 <2e-16 ***
## WT69.4238088940889 -3.797e+01 2.529e-13 -1.502e+14 <2e-16 ***
## WT69.8916700927637 8.632e+01 2.632e-13 3.279e+14 <2e-16 ***
## WT70.9081532523187 6.545e+00 2.632e-13 2.486e+13 <2e-16 ***
## WT70.93283102851 1.552e+02 2.920e-13 5.314e+14 <2e-16 ***
## WT71.5216041562313 -3.651e+00 2.529e-13 -1.444e+13 <2e-16 ***
## WT71.552469405632 6.447e+01 2.786e-12 2.314e+13 <2e-16 ***
## WT72.100784315348 -6.272e+01 2.920e-13 -2.148e+14 <2e-16 ***
## WT72.1192682593673 6.098e+01 2.920e-13 2.088e+14 <2e-16 ***
## WT72.5130093985331 7.832e+01 2.529e-13 3.097e+14 <2e-16 ***
## WT73.8272223400376 -4.878e+01 2.632e-13 -1.853e+14 <2e-16 ***
## WT73.8946071426946 2.569e+01 2.920e-13 8.798e+13 <2e-16 ***
## WT74.576520395053 4.582e+00 2.920e-13 1.569e+13 <2e-16 ***
## WT76.5191166392504 -1.152e+02 2.060e-12 -5.591e+13 <2e-16 ***
## WT76.861100749222 -1.300e+02 2.786e-12 -4.668e+13 <2e-16 ***
## WT76.8798565991695 3.624e+01 2.529e-13 1.433e+14 <2e-16 ***
## WT76.9483478573463 1.014e+02 2.920e-13 3.471e+14 <2e-16 ***
## WT76.9891003678536 -2.043e+01 2.920e-13 -6.997e+13 <2e-16 ***
## WT78.9413223689479 -4.824e+00 2.920e-13 -1.652e+13 <2e-16 ***
## WT79.3702320383895 -4.125e-01 2.529e-13 -1.631e+12 <2e-16 ***
## WT80.7885681864807 3.536e-01 2.786e-12 1.269e+11 <2e-16 ***
## WT80.9634414352473 4.559e+02 2.060e-12 2.213e+14 <2e-16 ***
## WT81.9346836005642 3.484e+01 2.920e-13 1.193e+14 <2e-16 ***
## WT86.0480197659978 -3.641e+01 2.529e-13 -1.440e+14 <2e-16 ***
## WT87.9787879168647 NA NA NA NA
## WT88.3822765460914 9.905e+00 2.920e-13 3.392e+13 <2e-16 ***
## DOSE:WT39.0926556253334 NA NA NA NA
## DOSE:WT43.385370870966 NA NA NA NA
## DOSE:WT44.1645866416275 NA NA NA NA
## DOSE:WT44.4408249073636 NA NA NA NA
## DOSE:WT45.1517422320562 NA NA NA NA
## DOSE:WT45.6670705971498 NA NA NA NA
## DOSE:WT46.299742376232 NA NA NA NA
## DOSE:WT46.3345640624208 NA NA NA NA
## DOSE:WT46.6495409795975 NA NA NA NA
## DOSE:WT46.8822393257666 NA NA NA NA
## DOSE:WT46.8973190114622 NA NA NA NA
## DOSE:WT47.4826867538601 NA NA NA NA
## DOSE:WT47.6143432438632 NA NA NA NA
## DOSE:WT47.6851482283133 NA NA NA NA
## DOSE:WT48.3117070076055 NA NA NA NA
## DOSE:WT48.3446507313387 NA NA NA NA
## DOSE:WT48.4771999017763 NA NA NA NA
## DOSE:WT48.5966048753623 NA NA NA NA
## DOSE:WT49.1572187675018 NA NA NA NA
## DOSE:WT49.2969564594932 NA NA NA NA
## DOSE:WT49.8617705593529 NA NA NA NA
## DOSE:WT49.868488821644 NA NA NA NA
## DOSE:WT50.158878263407 NA NA NA NA
## DOSE:WT50.2077352982534 NA NA NA NA
## DOSE:WT50.2368325095966 NA NA NA NA
## DOSE:WT50.2636476710892 NA NA NA NA
## DOSE:WT50.3494396610472 NA NA NA NA
## DOSE:WT50.3915854131725 NA NA NA NA
## DOSE:WT50.8289463391973 NA NA NA NA
## DOSE:WT51.0472336107365 NA NA NA NA
## DOSE:WT51.0793328880538 NA NA NA NA
## DOSE:WT51.5370663687331 NA NA NA NA
## DOSE:WT51.8079344024178 NA NA NA NA
## DOSE:WT52.4503890630421 NA NA NA NA
## DOSE:WT52.9895701498835 NA NA NA NA
## DOSE:WT53.0690868837438 NA NA NA NA
## DOSE:WT53.6689904718367 NA NA NA NA
## DOSE:WT53.8304347347303 NA NA NA NA
## DOSE:WT54.726983025146 NA NA NA NA
## DOSE:WT54.8548620414376 NA NA NA NA
## DOSE:WT55.0662615987696 NA NA NA NA
## DOSE:WT55.0820017068382 NA NA NA NA
## DOSE:WT55.189354362534 NA NA NA NA
## DOSE:WT55.4661838306457 NA NA NA NA
## DOSE:WT56.0331804198636 NA NA NA NA
## DOSE:WT56.5706246440395 NA NA NA NA
## DOSE:WT56.6217213823502 NA NA NA NA
## DOSE:WT56.7464609528505 NA NA NA NA
## DOSE:WT56.8341586420691 NA NA NA NA
## DOSE:WT56.9941031587336 NA NA NA NA
## DOSE:WT57.0349868781429 NA NA NA NA
## DOSE:WT57.2529607952786 NA NA NA NA
## DOSE:WT57.3828325288484 NA NA NA NA
## DOSE:WT57.4427679113438 NA NA NA NA
## DOSE:WT57.4706335255625 NA NA NA NA
## DOSE:WT58.0810428414755 NA NA NA NA
## DOSE:WT58.3877459984707 NA NA NA NA
## DOSE:WT58.3884120934077 NA NA NA NA
## DOSE:WT58.6413350670283 NA NA NA NA
## DOSE:WT59.0600656548766 NA NA NA NA
## DOSE:WT59.2419303221282 NA NA NA NA
## DOSE:WT59.4634759747235 NA NA NA NA
## DOSE:WT59.629109470457 NA NA NA NA
## DOSE:WT59.7483475846391 NA NA NA NA
## DOSE:WT59.8793148533197 NA NA NA NA
## DOSE:WT60.1947327086809 NA NA NA NA
## DOSE:WT60.6392531904703 NA NA NA NA
## DOSE:WT60.9773525638669 NA NA NA NA
## DOSE:WT61.0098811892406 NA NA NA NA
## DOSE:WT61.2055129626385 NA NA NA NA
## DOSE:WT61.2587832531637 NA NA NA NA
## DOSE:WT61.323014282204 NA NA NA NA
## DOSE:WT61.5125060704702 NA NA NA NA
## DOSE:WT62.0082176608355 NA NA NA NA
## DOSE:WT62.5588732638254 NA NA NA NA
## DOSE:WT62.687184307522 NA NA NA NA
## DOSE:WT62.8383015359403 NA NA NA NA
## DOSE:WT62.8533647595014 NA NA NA NA
## DOSE:WT62.8954159361529 NA NA NA NA
## DOSE:WT63.1802789246418 NA NA NA NA
## DOSE:WT63.2085175325467 NA NA NA NA
## DOSE:WT63.74748163791 NA NA NA NA
## DOSE:WT64.0513937799648 NA NA NA NA
## DOSE:WT64.0845147080079 NA NA NA NA
## DOSE:WT64.1953608112469 NA NA NA NA
## DOSE:WT64.4887367273998 NA NA NA NA
## DOSE:WT64.867603592169 NA NA NA NA
## DOSE:WT66.1087736227983 NA NA NA NA
## DOSE:WT66.716577146186 NA NA NA NA
## DOSE:WT67.3753486626367 NA NA NA NA
## DOSE:WT67.5217446512654 NA NA NA NA
## DOSE:WT67.6664905819041 NA NA NA NA
## DOSE:WT67.869609391395 NA NA NA NA
## DOSE:WT68.2619190177503 NA NA NA NA
## DOSE:WT68.310006443405 NA NA NA NA
## DOSE:WT68.3772567248618 NA NA NA NA
## DOSE:WT69.3704816970312 NA NA NA NA
## DOSE:WT69.4238088940889 NA NA NA NA
## DOSE:WT69.8916700927637 NA NA NA NA
## DOSE:WT70.9081532523187 NA NA NA NA
## DOSE:WT70.93283102851 NA NA NA NA
## DOSE:WT71.5216041562313 NA NA NA NA
## DOSE:WT71.552469405632 NA NA NA NA
## DOSE:WT72.100784315348 NA NA NA NA
## DOSE:WT72.1192682593673 NA NA NA NA
## DOSE:WT72.5130093985331 NA NA NA NA
## DOSE:WT73.8272223400376 NA NA NA NA
## DOSE:WT73.8946071426946 NA NA NA NA
## DOSE:WT74.576520395053 NA NA NA NA
## DOSE:WT76.5191166392504 NA NA NA NA
## DOSE:WT76.861100749222 NA NA NA NA
## DOSE:WT76.8798565991695 NA NA NA NA
## DOSE:WT76.9483478573463 NA NA NA NA
## DOSE:WT76.9891003678536 NA NA NA NA
## DOSE:WT78.9413223689479 NA NA NA NA
## DOSE:WT79.3702320383895 NA NA NA NA
## DOSE:WT80.7885681864807 NA NA NA NA
## DOSE:WT80.9634414352473 NA NA NA NA
## DOSE:WT81.9346836005642 NA NA NA NA
## DOSE:WT86.0480197659978 NA NA NA NA
## DOSE:WT87.9787879168647 NA NA NA NA
## DOSE:WT88.3822765460914 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.13e-13 on 369 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 4.741e+29 on 122 and 369 DF, p-value: < 2.2e-16mult_model <- lm(Efficacy~DOSE+AUC+WT+DOSE*WT,
data = data_1)
summary(mult_model)##
## Call:
## lm(formula = Efficacy ~ DOSE + AUC + WT + DOSE * WT, data = data_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.013e-12 0.000e+00 0.000e+00 0.000e+00 4.740e-12
##
## Coefficients: (230 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.941e+01 2.417e-13 -2.044e+14 <2e-16 ***
## DOSE 1.836e+00 1.709e-15 1.074e+15 <2e-16 ***
## AUC0.58137001605587 -5.167e+01 3.376e-13 -1.531e+14 <2e-16 ***
## AUC0.713399571742059 9.073e+01 3.336e-13 2.720e+14 <2e-16 ***
## AUC0.739752421579671 5.197e+01 3.376e-13 1.539e+14 <2e-16 ***
## AUC0.798897789768316 1.494e+01 3.376e-13 4.426e+13 <2e-16 ***
## AUC0.820112640944766 1.594e+02 3.336e-13 4.777e+14 <2e-16 ***
## AUC0.852877230705246 3.777e+01 3.376e-13 1.119e+14 <2e-16 ***
## AUC0.966857748289669 -1.157e+01 3.376e-13 -3.427e+13 <2e-16 ***
## AUC1.04121735777482 -3.628e+01 3.376e-13 -1.075e+14 <2e-16 ***
## AUC1.08247932879118 1.248e+01 3.336e-13 3.741e+13 <2e-16 ***
## AUC1.09649998823614 7.014e+01 3.376e-13 2.078e+14 <2e-16 ***
## AUC1.1048889200803 -2.537e+01 3.336e-13 -7.606e+13 <2e-16 ***
## AUC1.14211088525991 2.171e+00 3.376e-13 6.432e+12 <2e-16 ***
## AUC1.25169831855773 2.229e+01 3.336e-13 6.683e+13 <2e-16 ***
## AUC1.392955401302 1.365e+02 3.376e-13 4.042e+14 <2e-16 ***
## AUC1.41626834270835 2.398e+01 3.336e-13 7.188e+13 <2e-16 ***
## AUC1.44894418903913 3.656e+00 3.376e-13 1.083e+13 <2e-16 ***
## AUC1.47963421655577 4.533e+01 3.376e-13 1.343e+14 <2e-16 ***
## AUC1.51411821354426 4.431e+00 3.376e-13 1.313e+13 <2e-16 ***
## AUC1.56497850582066 2.859e+01 3.376e-13 8.468e+13 <2e-16 ***
## AUC1.58114309357246 -1.156e+01 3.260e-13 -3.545e+13 <2e-16 ***
## AUC1.66815325160534 -2.525e+01 3.336e-13 -7.571e+13 <2e-16 ***
## AUC1.68362402319226 7.514e+00 3.376e-13 2.226e+13 <2e-16 ***
## AUC1.90250925238805 8.343e+01 3.376e-13 2.471e+14 <2e-16 ***
## AUC1.92683508488211 -3.550e+01 3.336e-13 -1.064e+14 <2e-16 ***
## AUC1.94506947759397 4.238e+01 3.336e-13 1.271e+14 <2e-16 ***
## AUC10.385160796293 1.130e+01 3.260e-13 3.467e+13 <2e-16 ***
## AUC102.382944918014 -8.920e+01 3.418e-13 -2.610e+14 <2e-16 ***
## AUC104.76071200832 -1.408e+02 3.418e-13 -4.119e+14 <2e-16 ***
## AUC110.735618188519 -1.291e+02 3.418e-13 -3.777e+14 <2e-16 ***
## AUC115.554331811852 3.849e+01 3.418e-13 1.126e+14 <2e-16 ***
## AUC116.48449057737 -2.367e+01 3.418e-13 -6.926e+13 <2e-16 ***
## AUC134.123620388118 -5.259e+01 3.418e-13 -1.539e+14 <2e-16 ***
## AUC151.024200950105 -4.473e+01 3.081e-13 -1.452e+14 <2e-16 ***
## AUC17.0614558420294 -2.767e+02 3.081e-13 -8.980e+14 <2e-16 ***
## AUC17.2623846602278 -9.545e+01 3.081e-13 -3.098e+14 <2e-16 ***
## AUC18.842060544626 -2.375e+02 3.081e-13 -7.710e+14 <2e-16 ***
## AUC2.06662704182518 4.187e+01 3.260e-13 1.284e+14 <2e-16 ***
## AUC2.23373370853778 2.015e+01 3.336e-13 6.041e+13 <2e-16 ***
## AUC2.2385343719125 7.254e+01 3.336e-13 2.175e+14 <2e-16 ***
## AUC2.34035904397742 -6.191e+00 3.336e-13 -1.856e+13 <2e-16 ***
## AUC2.44895684008362 2.955e+01 3.376e-13 8.753e+13 <2e-16 ***
## AUC2.52661936727981 -1.260e+01 3.260e-13 -3.866e+13 <2e-16 ***
## AUC2.8043453674809 4.319e+01 3.376e-13 1.279e+14 <2e-16 ***
## AUC21.1859097363873 -2.431e+02 3.081e-13 -7.891e+14 <2e-16 ***
## AUC26.2165056229887 -1.902e+02 3.081e-13 -6.172e+14 <2e-16 ***
## AUC26.7480077583995 -2.514e+02 3.418e-13 -7.356e+14 <2e-16 ***
## AUC26.8308704203974 -7.934e+01 3.081e-13 -2.575e+14 <2e-16 ***
## AUC27.2869200564132 -1.771e+02 3.081e-13 -5.750e+14 <2e-16 ***
## AUC3.02738597444341 -3.629e+01 3.336e-13 -1.088e+14 <2e-16 ***
## AUC3.28869257986581 1.096e+01 3.260e-13 3.361e+13 <2e-16 ***
## AUC3.34603596724053 -4.219e+01 3.336e-13 -1.265e+14 <2e-16 ***
## AUC3.45631507710408 1.454e+01 3.336e-13 4.358e+13 <2e-16 ***
## AUC3.60771990074467 3.742e+01 3.260e-13 1.148e+14 <2e-16 ***
## AUC3.64189318794162 -1.638e+01 3.260e-13 -5.024e+13 <2e-16 ***
## AUC3.67588641219015 -3.071e+01 3.260e-13 -9.418e+13 <2e-16 ***
## AUC3.68455430781716 6.795e+01 3.336e-13 2.037e+14 <2e-16 ***
## AUC3.72753458846846 -3.199e+01 3.260e-13 -9.812e+13 <2e-16 ***
## AUC3.89336030249041 9.600e+01 3.376e-13 2.844e+14 <2e-16 ***
## AUC3.94491759229558 1.214e+02 3.260e-13 3.725e+14 <2e-16 ***
## AUC3.96450114665744 5.893e+00 3.336e-13 1.767e+13 <2e-16 ***
## AUC30.0295198010622 -3.707e+02 3.418e-13 -1.085e+15 <2e-16 ***
## AUC30.65231401549 -1.829e+02 3.081e-13 -5.938e+14 <2e-16 ***
## AUC35.2821055837656 -1.029e+02 3.081e-13 -3.340e+14 <2e-16 ***
## AUC35.7650663124228 -2.439e+02 3.418e-13 -7.136e+14 <2e-16 ***
## AUC37.9059659316011 7.769e+01 3.418e-13 2.273e+14 <2e-16 ***
## AUC38.051256196333 -1.152e+02 3.418e-13 -3.371e+14 <2e-16 ***
## AUC39.4666748158898 -5.220e+01 3.081e-13 -1.694e+14 <2e-16 ***
## AUC39.9098951718768 -2.952e+01 3.081e-13 -9.581e+13 <2e-16 ***
## AUC4.0114638171294 1.463e+00 3.260e-13 4.488e+12 <2e-16 ***
## AUC4.04346228745987 -9.429e+00 3.336e-13 -2.827e+13 <2e-16 ***
## AUC4.12086128770654 -4.375e+01 3.336e-13 -1.312e+14 <2e-16 ***
## AUC4.1460455150858 1.432e+01 3.260e-13 4.393e+13 <2e-16 ***
## AUC4.2361832625076 1.030e+02 3.336e-13 3.088e+14 <2e-16 ***
## AUC4.42184383011266 3.046e+01 3.336e-13 9.132e+13 <2e-16 ***
## AUC4.43899770736685 4.942e+01 3.260e-13 1.516e+14 <2e-16 ***
## AUC4.67714240056946 1.590e+01 3.260e-13 4.877e+13 <2e-16 ***
## AUC41.536866917836 -5.109e+01 3.418e-13 -1.495e+14 <2e-16 ***
## AUC42.0707560534761 -2.675e+02 3.418e-13 -7.826e+14 <2e-16 ***
## AUC42.83521470782 -2.283e+02 3.418e-13 -6.678e+14 <2e-16 ***
## AUC42.868331104139 3.195e+01 3.081e-13 1.037e+14 <2e-16 ***
## AUC43.7932194636857 -2.509e+02 3.081e-13 -8.143e+14 <2e-16 ***
## AUC44.8283194580273 -1.664e+02 3.418e-13 -4.868e+14 <2e-16 ***
## AUC46.7082331045888 -2.610e+02 3.418e-13 -7.636e+14 <2e-16 ***
## AUC47.2005968478153 8.213e+01 3.081e-13 2.666e+14 <2e-16 ***
## AUC48.0867954149133 3.692e+02 3.081e-13 1.199e+15 <2e-16 ***
## AUC49.3572788297169 8.289e+01 3.081e-13 2.691e+14 <2e-16 ***
## AUC5.17178029468132 -1.396e+01 3.260e-13 -4.283e+13 <2e-16 ***
## AUC5.23010988715082 2.329e+01 3.260e-13 7.143e+13 <2e-16 ***
## AUC5.25571715648467 3.111e+01 3.260e-13 9.541e+13 <2e-16 ***
## AUC5.38027981554632 1.070e+02 3.336e-13 3.207e+14 <2e-16 ***
## AUC5.79045123610611 1.436e+02 3.260e-13 4.405e+14 <2e-16 ***
## AUC53.8919126813006 -2.456e+02 3.418e-13 -7.186e+14 <2e-16 ***
## AUC54.6365877343118 -2.018e+02 3.081e-13 -6.551e+14 <2e-16 ***
## AUC54.6827117025205 9.220e+00 3.081e-13 2.993e+13 <2e-16 ***
## AUC55.225214378137 2.702e+02 3.418e-13 7.907e+14 <2e-16 ***
## AUC55.4116514712742 1.889e+02 3.081e-13 6.132e+14 <2e-16 ***
## AUC59.5200841019687 -1.637e+02 3.418e-13 -4.788e+14 <2e-16 ***
## AUC6.33588085422884 -7.427e+01 3.260e-13 -2.278e+14 <2e-16 ***
## AUC6.60787562544788 -1.652e+00 3.260e-13 -5.067e+12 <2e-16 ***
## AUC60.6462916000294 1.452e+02 3.418e-13 4.248e+14 <2e-16 ***
## AUC70.1963925244988 5.677e+01 3.418e-13 1.661e+14 <2e-16 ***
## AUC8.22375694669392 1.574e+02 3.260e-13 4.829e+14 <2e-16 ***
## AUC8.60602691525118 9.277e+00 3.260e-13 2.846e+13 <2e-16 ***
## AUC9.05250127616784 6.532e+01 3.260e-13 2.003e+14 <2e-16 ***
## AUC90.2063376387205 9.096e+01 3.418e-13 2.661e+14 <2e-16 ***
## AUC93.1111657394466 3.606e+01 3.418e-13 1.055e+14 <2e-16 ***
## AUC95.6774400095997 NA NA NA NA
## WT39.0926556253334 NA NA NA NA
## WT43.385370870966 NA NA NA NA
## WT44.1645866416275 NA NA NA NA
## WT44.4408249073636 NA NA NA NA
## WT45.1517422320562 NA NA NA NA
## WT45.6670705971498 -2.221e+01 3.418e-13 -6.499e+13 <2e-16 ***
## WT46.299742376232 NA NA NA NA
## WT46.3345640624208 NA NA NA NA
## WT46.6495409795975 NA NA NA NA
## WT46.8822393257666 7.057e+00 3.418e-13 2.065e+13 <2e-16 ***
## WT46.8973190114622 NA NA NA NA
## WT47.4826867538601 NA NA NA NA
## WT47.6143432438632 -2.122e+01 3.418e-13 -6.210e+13 <2e-16 ***
## WT47.6851482283133 NA NA NA NA
## WT48.3117070076055 4.683e+01 3.418e-13 1.370e+14 <2e-16 ***
## WT48.3446507313387 5.967e+01 3.418e-13 1.746e+14 <2e-16 ***
## WT48.4771999017763 NA NA NA NA
## WT48.5966048753623 NA NA NA NA
## WT49.1572187675018 NA NA NA NA
## WT49.2969564594932 NA NA NA NA
## WT49.8617705593529 NA NA NA NA
## WT49.868488821644 NA NA NA NA
## WT50.158878263407 NA NA NA NA
## WT50.2077352982534 NA NA NA NA
## WT50.2368325095966 NA NA NA NA
## WT50.2636476710892 1.042e+02 3.418e-13 3.048e+14 <2e-16 ***
## WT50.3494396610472 NA NA NA NA
## WT50.3915854131725 NA NA NA NA
## WT50.8289463391973 NA NA NA NA
## WT51.0472336107365 NA NA NA NA
## WT51.0793328880538 1.246e+02 3.418e-13 3.645e+14 <2e-16 ***
## WT51.5370663687331 NA NA NA NA
## WT51.8079344024178 NA NA NA NA
## WT52.4503890630421 NA NA NA NA
## WT52.9895701498835 5.699e+01 3.418e-13 1.667e+14 <2e-16 ***
## WT53.0690868837438 NA NA NA NA
## WT53.6689904718367 NA NA NA NA
## WT53.8304347347303 NA NA NA NA
## WT54.726983025146 NA NA NA NA
## WT54.8548620414376 NA NA NA NA
## WT55.0662615987696 NA NA NA NA
## WT55.0820017068382 NA NA NA NA
## WT55.189354362534 NA NA NA NA
## WT55.4661838306457 NA NA NA NA
## WT56.0331804198636 NA NA NA NA
## WT56.5706246440395 NA NA NA NA
## WT56.6217213823502 NA NA NA NA
## WT56.7464609528505 NA NA NA NA
## WT56.8341586420691 NA NA NA NA
## WT56.9941031587336 NA NA NA NA
## WT57.0349868781429 -2.992e+00 3.418e-13 -8.753e+12 <2e-16 ***
## WT57.2529607952786 NA NA NA NA
## WT57.3828325288484 NA NA NA NA
## WT57.4427679113438 NA NA NA NA
## WT57.4706335255625 NA NA NA NA
## WT58.0810428414755 NA NA NA NA
## WT58.3877459984707 NA NA NA NA
## WT58.3884120934077 NA NA NA NA
## WT58.6413350670283 NA NA NA NA
## WT59.0600656548766 3.323e+01 3.418e-13 9.721e+13 <2e-16 ***
## WT59.2419303221282 NA NA NA NA
## WT59.4634759747235 NA NA NA NA
## WT59.629109470457 NA NA NA NA
## WT59.7483475846391 NA NA NA NA
## WT59.8793148533197 NA NA NA NA
## WT60.1947327086809 NA NA NA NA
## WT60.6392531904703 NA NA NA NA
## WT60.9773525638669 NA NA NA NA
## WT61.0098811892406 NA NA NA NA
## WT61.2055129626385 NA NA NA NA
## WT61.2587832531637 NA NA NA NA
## WT61.323014282204 NA NA NA NA
## WT61.5125060704702 NA NA NA NA
## WT62.0082176608355 NA NA NA NA
## WT62.5588732638254 NA NA NA NA
## WT62.687184307522 NA NA NA NA
## WT62.8383015359403 NA NA NA NA
## WT62.8533647595014 9.254e+01 3.418e-13 2.708e+14 <2e-16 ***
## WT62.8954159361529 8.369e+01 3.418e-13 2.448e+14 <2e-16 ***
## WT63.1802789246418 NA NA NA NA
## WT63.2085175325467 NA NA NA NA
## WT63.74748163791 NA NA NA NA
## WT64.0513937799648 NA NA NA NA
## WT64.0845147080079 NA NA NA NA
## WT64.1953608112469 NA NA NA NA
## WT64.4887367273998 NA NA NA NA
## WT64.867603592169 NA NA NA NA
## WT66.1087736227983 NA NA NA NA
## WT66.716577146186 NA NA NA NA
## WT67.3753486626367 NA NA NA NA
## WT67.5217446512654 NA NA NA NA
## WT67.6664905819041 NA NA NA NA
## WT67.869609391395 NA NA NA NA
## WT68.2619190177503 NA NA NA NA
## WT68.310006443405 NA NA NA NA
## WT68.3772567248618 NA NA NA NA
## WT69.3704816970312 NA NA NA NA
## WT69.4238088940889 NA NA NA NA
## WT69.8916700927637 NA NA NA NA
## WT70.9081532523187 NA NA NA NA
## WT70.93283102851 NA NA NA NA
## WT71.5216041562313 NA NA NA NA
## WT71.552469405632 NA NA NA NA
## WT72.100784315348 NA NA NA NA
## WT72.1192682593673 NA NA NA NA
## WT72.5130093985331 NA NA NA NA
## WT73.8272223400376 NA NA NA NA
## WT73.8946071426946 2.569e+01 3.418e-13 7.517e+13 <2e-16 ***
## WT74.576520395053 4.582e+00 3.418e-13 1.341e+13 <2e-16 ***
## WT76.5191166392504 NA NA NA NA
## WT76.861100749222 NA NA NA NA
## WT76.8798565991695 NA NA NA NA
## WT76.9483478573463 1.014e+02 3.418e-13 2.965e+14 <2e-16 ***
## WT76.9891003678536 NA NA NA NA
## WT78.9413223689479 NA NA NA NA
## WT79.3702320383895 NA NA NA NA
## WT80.7885681864807 NA NA NA NA
## WT80.9634414352473 NA NA NA NA
## WT81.9346836005642 NA NA NA NA
## WT86.0480197659978 NA NA NA NA
## WT87.9787879168647 NA NA NA NA
## WT88.3822765460914 NA NA NA NA
## DOSE:WT39.0926556253334 NA NA NA NA
## DOSE:WT43.385370870966 NA NA NA NA
## DOSE:WT44.1645866416275 NA NA NA NA
## DOSE:WT44.4408249073636 NA NA NA NA
## DOSE:WT45.1517422320562 NA NA NA NA
## DOSE:WT45.6670705971498 NA NA NA NA
## DOSE:WT46.299742376232 NA NA NA NA
## DOSE:WT46.3345640624208 NA NA NA NA
## DOSE:WT46.6495409795975 NA NA NA NA
## DOSE:WT46.8822393257666 NA NA NA NA
## DOSE:WT46.8973190114622 NA NA NA NA
## DOSE:WT47.4826867538601 NA NA NA NA
## DOSE:WT47.6143432438632 NA NA NA NA
## DOSE:WT47.6851482283133 NA NA NA NA
## DOSE:WT48.3117070076055 NA NA NA NA
## DOSE:WT48.3446507313387 NA NA NA NA
## DOSE:WT48.4771999017763 NA NA NA NA
## DOSE:WT48.5966048753623 NA NA NA NA
## DOSE:WT49.1572187675018 NA NA NA NA
## DOSE:WT49.2969564594932 NA NA NA NA
## DOSE:WT49.8617705593529 NA NA NA NA
## DOSE:WT49.868488821644 NA NA NA NA
## DOSE:WT50.158878263407 NA NA NA NA
## DOSE:WT50.2077352982534 NA NA NA NA
## DOSE:WT50.2368325095966 NA NA NA NA
## DOSE:WT50.2636476710892 NA NA NA NA
## DOSE:WT50.3494396610472 NA NA NA NA
## DOSE:WT50.3915854131725 NA NA NA NA
## DOSE:WT50.8289463391973 NA NA NA NA
## DOSE:WT51.0472336107365 NA NA NA NA
## DOSE:WT51.0793328880538 NA NA NA NA
## DOSE:WT51.5370663687331 NA NA NA NA
## DOSE:WT51.8079344024178 NA NA NA NA
## DOSE:WT52.4503890630421 NA NA NA NA
## DOSE:WT52.9895701498835 NA NA NA NA
## DOSE:WT53.0690868837438 NA NA NA NA
## DOSE:WT53.6689904718367 NA NA NA NA
## DOSE:WT53.8304347347303 NA NA NA NA
## DOSE:WT54.726983025146 NA NA NA NA
## DOSE:WT54.8548620414376 NA NA NA NA
## DOSE:WT55.0662615987696 NA NA NA NA
## DOSE:WT55.0820017068382 NA NA NA NA
## DOSE:WT55.189354362534 NA NA NA NA
## DOSE:WT55.4661838306457 NA NA NA NA
## DOSE:WT56.0331804198636 NA NA NA NA
## DOSE:WT56.5706246440395 NA NA NA NA
## DOSE:WT56.6217213823502 NA NA NA NA
## DOSE:WT56.7464609528505 NA NA NA NA
## DOSE:WT56.8341586420691 NA NA NA NA
## DOSE:WT56.9941031587336 NA NA NA NA
## DOSE:WT57.0349868781429 NA NA NA NA
## DOSE:WT57.2529607952786 NA NA NA NA
## DOSE:WT57.3828325288484 NA NA NA NA
## DOSE:WT57.4427679113438 NA NA NA NA
## DOSE:WT57.4706335255625 NA NA NA NA
## DOSE:WT58.0810428414755 NA NA NA NA
## DOSE:WT58.3877459984707 NA NA NA NA
## DOSE:WT58.3884120934077 NA NA NA NA
## DOSE:WT58.6413350670283 NA NA NA NA
## DOSE:WT59.0600656548766 NA NA NA NA
## DOSE:WT59.2419303221282 NA NA NA NA
## DOSE:WT59.4634759747235 NA NA NA NA
## DOSE:WT59.629109470457 NA NA NA NA
## DOSE:WT59.7483475846391 NA NA NA NA
## DOSE:WT59.8793148533197 NA NA NA NA
## DOSE:WT60.1947327086809 NA NA NA NA
## DOSE:WT60.6392531904703 NA NA NA NA
## DOSE:WT60.9773525638669 NA NA NA NA
## DOSE:WT61.0098811892406 NA NA NA NA
## DOSE:WT61.2055129626385 NA NA NA NA
## DOSE:WT61.2587832531637 NA NA NA NA
## DOSE:WT61.323014282204 NA NA NA NA
## DOSE:WT61.5125060704702 NA NA NA NA
## DOSE:WT62.0082176608355 NA NA NA NA
## DOSE:WT62.5588732638254 NA NA NA NA
## DOSE:WT62.687184307522 NA NA NA NA
## DOSE:WT62.8383015359403 NA NA NA NA
## DOSE:WT62.8533647595014 NA NA NA NA
## DOSE:WT62.8954159361529 NA NA NA NA
## DOSE:WT63.1802789246418 NA NA NA NA
## DOSE:WT63.2085175325467 NA NA NA NA
## DOSE:WT63.74748163791 NA NA NA NA
## DOSE:WT64.0513937799648 NA NA NA NA
## DOSE:WT64.0845147080079 NA NA NA NA
## DOSE:WT64.1953608112469 NA NA NA NA
## DOSE:WT64.4887367273998 NA NA NA NA
## DOSE:WT64.867603592169 NA NA NA NA
## DOSE:WT66.1087736227983 NA NA NA NA
## DOSE:WT66.716577146186 NA NA NA NA
## DOSE:WT67.3753486626367 NA NA NA NA
## DOSE:WT67.5217446512654 NA NA NA NA
## DOSE:WT67.6664905819041 NA NA NA NA
## DOSE:WT67.869609391395 NA NA NA NA
## DOSE:WT68.2619190177503 NA NA NA NA
## DOSE:WT68.310006443405 NA NA NA NA
## DOSE:WT68.3772567248618 NA NA NA NA
## DOSE:WT69.3704816970312 NA NA NA NA
## DOSE:WT69.4238088940889 NA NA NA NA
## DOSE:WT69.8916700927637 NA NA NA NA
## DOSE:WT70.9081532523187 NA NA NA NA
## DOSE:WT70.93283102851 NA NA NA NA
## DOSE:WT71.5216041562313 NA NA NA NA
## DOSE:WT71.552469405632 NA NA NA NA
## DOSE:WT72.100784315348 NA NA NA NA
## DOSE:WT72.1192682593673 NA NA NA NA
## DOSE:WT72.5130093985331 NA NA NA NA
## DOSE:WT73.8272223400376 NA NA NA NA
## DOSE:WT73.8946071426946 NA NA NA NA
## DOSE:WT74.576520395053 NA NA NA NA
## DOSE:WT76.5191166392504 NA NA NA NA
## DOSE:WT76.861100749222 NA NA NA NA
## DOSE:WT76.8798565991695 NA NA NA NA
## DOSE:WT76.9483478573463 NA NA NA NA
## DOSE:WT76.9891003678536 NA NA NA NA
## DOSE:WT78.9413223689479 NA NA NA NA
## DOSE:WT79.3702320383895 NA NA NA NA
## DOSE:WT80.7885681864807 NA NA NA NA
## DOSE:WT80.9634414352473 NA NA NA NA
## DOSE:WT81.9346836005642 NA NA NA NA
## DOSE:WT86.0480197659978 NA NA NA NA
## DOSE:WT87.9787879168647 NA NA NA NA
## DOSE:WT88.3822765460914 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.834e-13 on 369 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 3.461e+29 on 122 and 369 DF, p-value: < 2.2e-16step(mult_model, direction = "both")## Start: AIC=-27799.84
## Efficacy ~ DOSE + AUC + WT + DOSE * WT## Warning: attempting model selection on an essentially perfect fit is nonsense##
## Step: AIC=-27799.84
## Efficacy ~ DOSE + AUC + WT## Warning: attempting model selection on an essentially perfect fit is nonsense##
## Step: AIC=-27954.64
## Efficacy ~ DOSE + WT## Warning: attempting model selection on an essentially perfect fit is nonsense##
## Step: AIC=-27305.82
## Efficacy ~ WT##
## Call:
## lm(formula = Efficacy ~ WT, data = data_1)
##
## Coefficients:
## (Intercept) WT39.0926556253334 WT43.385370870966 WT44.1645866416275
## -24.2470 83.9280 120.4835 21.7897
## WT44.4408249073636 WT45.1517422320562 WT45.6670705971498 WT46.299742376232
## 178.3567 5.6773 -47.3732 61.1509
## WT46.3345640624208 WT46.6495409795975 WT46.8822393257666 WT46.8973190114622
## 67.2927 22.8592 -18.1030 -26.4401
## WT47.4826867538601 WT47.6143432438632 WT47.6851482283133 WT48.3117070076055
## 35.5786 -46.3851 98.1197 21.6673
## WT48.3446507313387 WT48.4771999017763 WT48.5966048753623 WT49.1572187675018
## 34.5065 13.3481 -1.0471 96.2041
## WT49.2969564594932 WT49.8617705593529 WT49.868488821644 WT50.158878263407
## -52.2592 13.5691 74.5357 332.3494
## WT50.2077352982534 WT50.2368325095966 WT50.2636476710892 WT50.3494396610472
## 7.7364 201.2226 79.0069 252.8057
## WT50.3915854131725 WT50.8289463391973 WT51.0472336107365 WT51.0793328880538
## -11.5496 -0.9083 259.4374 99.4301
## WT51.5370663687331 WT51.8079344024178 WT52.4503890630421 WT52.9895701498835
## 73.0682 42.6632 220.7004 31.8271
## WT53.0690868837438 WT53.6689904718367 WT53.8304347347303 WT54.726983025146
## 168.9951 27.2102 22.5145 439.1146
## WT54.8548620414376 WT55.0662615987696 WT55.0820017068382 WT55.189354362534
## 152.5575 -13.8097 20.8342 342.0094
## WT55.4661838306457 WT56.0331804198636 WT56.5706246440395 WT56.6217213823502
## -8.4667 212.9290 -28.7304 -42.3003
## WT56.7464609528505 WT56.8341586420691 WT56.9941031587336 WT57.0349868781429
## 60.0565 154.7642 378.0723 -28.1518
## WT57.2529607952786 WT57.3828325288484 WT57.4427679113438 WT57.4706335255625
## 12.6839 -32.1713 289.4201 100.1706
## WT58.0810428414755 WT58.3877459984707 WT58.3884120934077 WT58.6413350670283
## 15.4920 333.1081 282.1664 147.3300
## WT59.0600656548766 WT59.2419303221282 WT59.4634759747235 WT59.629109470457
## 8.0650 29.3467 612.2557 -19.1495
## WT59.7483475846391 WT59.8793148533197 WT60.1947327086809 WT60.6392531904703
## 7.1031 35.9860 13.0199 198.0215
## WT60.9773525638669 WT61.0098811892406 WT61.2055129626385 WT61.2587832531637
## 17.1741 54.1598 170.8757 53.4273
## WT61.323014282204 WT61.5125060704702 WT62.0082176608355 WT62.5588732638254
## 27.4585 81.0187 90.6040 12.6065
## WT62.687184307522 WT62.8383015359403 WT62.8533647595014 WT62.8954159361529
## 318.3391 -27.5517 67.3809 58.5248
## WT63.1802789246418 WT63.2085175325467 WT63.74748163791 WT64.0513937799648
## 419.6945 76.8721 -32.0546 25.8789
## WT64.0845147080079 WT64.1953608112469 WT64.4887367273998 WT64.867603592169
## 80.0148 -2.4079 205.4879 398.7749
## WT66.1087736227983 WT66.716577146186 WT67.3753486626367 WT67.5217446512654
## 113.7510 487.2112 432.9699 -0.6426
## WT67.6664905819041 WT67.869609391395 WT68.2619190177503 WT68.310006443405
## 380.5012 -1.0399 133.0030 -43.0889
## WT68.3772567248618 WT69.3704816970312 WT69.4238088940889 WT69.8916700927637
## 175.6295 48.9729 -50.5551 67.4484
## WT70.9081532523187 WT70.93283102851 WT71.5216041562313 WT71.552469405632
## -12.3253 155.1881 -16.2310 290.9162
## WT72.100784315348 WT72.1192682593673 WT72.5130093985331 WT73.8272223400376
## -62.7160 60.9793 65.7387 -67.6541
## WT73.8946071426946 WT74.576520395053 WT76.5191166392504 WT76.861100749222
## 0.5311 -20.5786 48.3883 96.4078
## WT76.8798565991695 WT76.9483478573463 WT76.9891003678536 WT78.9413223689479
## 23.6579 76.1908 -20.4336 -4.8243
## WT79.3702320383895 WT80.7885681864807 WT80.9634414352473 WT81.9346836005642
## -12.9927 226.7960 619.4612 34.8450
## WT86.0480197659978 WT87.9787879168647 WT88.3822765460914
## -48.9886 -25.1603 9.9046test_fit <- lm(formula = Efficacy ~ DOSE + AUC, data = data_1)
summary(test_fit)##
## Call:
## lm(formula = Efficacy ~ DOSE + AUC, data = data_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -65.58 0.00 0.00 0.00 81.22
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.03584 2.34907 -2.569 0.010563 *
## DOSE 1.61899 0.04843 33.431 < 2e-16 ***
## AUC0.58137001605587 -93.96021 9.67425 -9.712 < 2e-16 ***
## AUC0.713399571742059 49.52690 9.66908 5.122 4.79e-07 ***
## AUC0.739752421579671 9.67986 9.67425 1.001 0.317660
## AUC0.798897789768316 -27.34606 9.67425 -2.827 0.004949 **
## AUC0.820112640944766 118.15642 9.66908 12.220 < 2e-16 ***
## AUC0.852877230705246 -4.51640 9.67425 -0.467 0.640874
## AUC0.966857748289669 -53.85780 9.67425 -5.567 4.87e-08 ***
## AUC1.04121735777482 -78.56532 9.67425 -8.121 6.37e-15 ***
## AUC1.08247932879118 -28.72379 9.66908 -2.971 0.003158 **
## AUC1.09649998823614 27.85371 9.67425 2.879 0.004211 **
## AUC1.1048889200803 -66.57233 9.66908 -6.885 2.37e-11 ***
## AUC1.14211088525991 -40.11582 9.67425 -4.147 4.16e-05 ***
## AUC1.25169831855773 -18.90909 9.66908 -1.956 0.051234 .
## AUC1.392955401302 94.17741 9.67425 9.735 < 2e-16 ***
## AUC1.41626834270835 -17.22701 9.66908 -1.782 0.075595 .
## AUC1.44894418903913 -38.63144 9.67425 -3.993 7.81e-05 ***
## AUC1.47963421655577 3.04062 9.67425 0.314 0.753464
## AUC1.51411821354426 -37.85573 9.67425 -3.913 0.000108 ***
## AUC1.56497850582066 -13.69959 9.67425 -1.416 0.157561
## AUC1.58114309357246 -50.59098 9.67693 -5.228 2.82e-07 ***
## AUC1.66815325160534 -66.45562 9.66908 -6.873 2.55e-11 ***
## AUC1.68362402319226 -34.77281 9.67425 -3.594 0.000368 ***
## AUC1.90250925238805 41.14232 9.67425 4.253 2.66e-05 ***
## AUC1.92683508488211 -76.70134 9.66908 -7.933 2.37e-14 ***
## AUC1.94506947759397 1.17756 9.66908 0.122 0.903132
## AUC10.385160796293 -27.73177 9.67693 -2.866 0.004389 **
## AUC102.382944918014 -89.20369 13.28837 -6.713 6.87e-11 ***
## AUC104.76071200832 -140.78678 13.28837 -10.595 < 2e-16 ***
## AUC110.735618188519 -129.08037 13.28837 -9.714 < 2e-16 ***
## AUC115.554331811852 38.49186 13.28837 2.897 0.003988 **
## AUC116.48449057737 -23.67022 13.28837 -1.781 0.075658 .
## AUC134.123620388118 -52.58931 13.28837 -3.958 9.02e-05 ***
## AUC151.024200950105 -55.57192 11.76004 -4.725 3.23e-06 ***
## AUC17.0614558420294 -287.49989 11.76004 -24.447 < 2e-16 ***
## AUC17.2623846602278 -106.29560 11.76004 -9.039 < 2e-16 ***
## AUC18.842060544626 -248.37591 11.76004 -21.120 < 2e-16 ***
## AUC2.06662704182518 2.83635 9.67693 0.293 0.769601
## AUC2.23373370853778 -21.05299 9.66908 -2.177 0.030063 *
## AUC2.2385343719125 31.33764 9.66908 3.241 0.001295 **
## AUC2.34035904397742 -47.39372 9.66908 -4.902 1.41e-06 ***
## AUC2.44895684008362 -12.73703 9.67425 -1.317 0.188761
## AUC2.52661936727981 -51.63810 9.67693 -5.336 1.63e-07 ***
## AUC2.8043453674809 0.90413 9.67425 0.093 0.925589
## AUC21.1859097363873 -253.95667 11.76004 -21.595 < 2e-16 ***
## AUC26.2165056229887 -201.00334 11.76004 -17.092 < 2e-16 ***
## AUC26.7480077583995 -251.40535 13.28837 -18.919 < 2e-16 ***
## AUC26.8308704203974 -90.18416 11.76004 -7.669 1.44e-13 ***
## AUC27.2869200564132 -187.99160 11.76004 -15.986 < 2e-16 ***
## AUC3.02738597444341 -77.48995 9.66908 -8.014 1.35e-14 ***
## AUC3.28869257986581 -28.07652 9.67693 -2.901 0.003929 **
## AUC3.34603596724053 -83.38962 9.66908 -8.624 < 2e-16 ***
## AUC3.45631507710408 -26.66472 9.66908 -2.758 0.006099 **
## AUC3.60771990074467 -1.61803 9.67693 -0.167 0.867297
## AUC3.64189318794162 -55.41526 9.67693 -5.727 2.07e-08 ***
## AUC3.67588641219015 -69.74052 9.67693 -7.207 3.06e-12 ***
## AUC3.68455430781716 26.74986 9.66908 2.767 0.005939 **
## AUC3.72753458846846 -71.02454 9.67693 -7.340 1.29e-12 ***
## AUC3.89336030249041 53.70870 9.67425 5.552 5.29e-08 ***
## AUC3.94491759229558 82.41201 9.67693 8.516 3.78e-16 ***
## AUC3.96450114665744 -35.30939 9.66908 -3.652 0.000297 ***
## AUC30.0295198010622 -370.73982 13.28837 -27.900 < 2e-16 ***
## AUC30.65231401549 -193.76711 11.76004 -16.477 < 2e-16 ***
## AUC35.2821055837656 -113.72986 11.76004 -9.671 < 2e-16 ***
## AUC35.7650663124228 -243.88964 13.28837 -18.354 < 2e-16 ***
## AUC37.9059659316011 77.68512 13.28837 5.846 1.08e-08 ***
## AUC38.051256196333 -115.21336 13.28837 -8.670 < 2e-16 ***
## AUC39.4666748158898 -63.03835 11.76004 -5.360 1.44e-07 ***
## AUC39.9098951718768 -40.35939 11.76004 -3.432 0.000665 ***
## AUC4.0114638171294 -37.57108 9.67693 -3.883 0.000122 ***
## AUC4.04346228745987 -50.63208 9.66908 -5.236 2.70e-07 ***
## AUC4.12086128770654 -84.95617 9.66908 -8.786 < 2e-16 ***
## AUC4.1460455150858 -24.71211 9.67693 -2.554 0.011044 *
## AUC4.2361832625076 61.80306 9.66908 6.392 4.76e-10 ***
## AUC4.42184383011266 -10.74319 9.66908 -1.111 0.267226
## AUC4.43899770736685 10.38830 9.67693 1.074 0.283715
## AUC4.67714240056946 -23.13250 9.67693 -2.390 0.017307 *
## AUC41.536866917836 -51.09321 13.28837 -3.845 0.000141 ***
## AUC42.0707560534761 -267.47371 13.28837 -20.128 < 2e-16 ***
## AUC42.83521470782 -228.25842 13.28837 -17.177 < 2e-16 ***
## AUC42.868331104139 21.10654 11.76004 1.795 0.073477 .
## AUC43.7932194636857 -261.70242 11.76004 -22.254 < 2e-16 ***
## AUC44.8283194580273 -166.37988 13.28837 -12.521 < 2e-16 ***
## AUC46.7082331045888 -260.99065 13.28837 -19.641 < 2e-16 ***
## AUC47.2005968478153 71.28956 11.76004 6.062 3.21e-09 ***
## AUC48.0867954149133 358.40139 11.76004 30.476 < 2e-16 ***
## AUC49.3572788297169 72.04826 11.76004 6.127 2.23e-09 ***
## AUC5.17178029468132 -52.99888 9.67693 -5.477 7.84e-08 ***
## AUC5.23010988715082 -15.74600 9.67693 -1.627 0.104521
## AUC5.25571715648467 -7.92782 9.67693 -0.819 0.413152
## AUC5.38027981554632 65.76956 9.66908 6.802 3.97e-11 ***
## AUC5.79045123610611 104.59713 9.67693 10.809 < 2e-16 ***
## AUC53.8919126813006 -245.60161 13.28837 -18.482 < 2e-16 ***
## AUC54.6365877343118 -212.67154 11.76004 -18.084 < 2e-16 ***
## AUC54.6827117025205 -1.62242 11.76004 -0.138 0.890344
## AUC55.225214378137 270.24635 13.28837 20.337 < 2e-16 ***
## AUC55.4116514712742 178.05478 11.76004 15.141 < 2e-16 ***
## AUC59.5200841019687 -163.65272 13.28837 -12.315 < 2e-16 ***
## AUC6.33588085422884 -113.30701 9.67693 -11.709 < 2e-16 ***
## AUC6.60787562544788 -40.68642 9.67693 -4.204 3.26e-05 ***
## AUC60.6462916000294 145.20182 13.28837 10.927 < 2e-16 ***
## AUC70.1963925244988 56.76551 13.28837 4.272 2.45e-05 ***
## AUC8.22375694669392 118.40412 9.67693 12.236 < 2e-16 ***
## AUC8.60602691525118 -29.75682 9.67693 -3.075 0.002255 **
## AUC9.05250127616784 26.28114 9.67693 2.716 0.006909 **
## AUC90.2063376387205 90.96048 13.28837 6.845 3.04e-11 ***
## AUC93.1111657394466 36.06298 13.28837 2.714 0.006950 **
## AUC95.6774400095997 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.79 on 384 degrees of freedom
## Multiple R-squared: 0.9863, Adjusted R-squared: 0.9824
## F-statistic: 257.5 on 107 and 384 DF, p-value: < 2.2e-16#nonlinear model
emax_model <- function(DOSE, Emax, EC50, Hill) {
Emax * (DOSE^Hill) / (EC50^Hill + DOSE^Hill)
}
start_params <- list(Emax = max(data_1$Efficacy, na.rm = TRUE),
EC50 = median(data_1$DOSE, na.rm = TRUE),
Hill = 1)
fit <- nlsLM(Efficacy ~ emax_model(DOSE, Emax, EC50, Hill),
data = data_1,
start = start_params,
lower = c(Emax = 0, EC50 = 0, Hill = 0.1),
upper = c(Emax = Inf, EC50 = Inf, Hill = 10))
# Show result
summary(fit)##
## Formula: Efficacy ~ emax_model(DOSE, Emax, EC50, Hill)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## Emax 951.296 2536.472 0.375 0.708
## EC50 390.626 958.825 0.407 0.684
## Hill 1.700 1.038 1.638 0.102
##
## Residual standard error: 102.6 on 489 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 1.49e-08#Optimized parameters
params <- coef(fit)
print(params)## Emax EC50 Hill
## 951.296099 390.626491 1.700326#plot linear+nonlinear models
ggplot(data=data_1, aes(x=DOSE,y=Efficacy)) +
geom_point() +
geom_smooth(method="lm")+
stat_function(fun = function(x) emax_model(x, params["Emax"], params["EC50"], params["Hill"]),
color = "blue") +
labs(title = "Efficacy-Dose dependency")
#Calculate Dose for MED
DOSE <- ((194 * params["EC50"]^params["Hill"]) / (params["Emax"] - 194))^(1/params["Hill"])
#Any side effects with increasing dose?
Sidis <- lm(side_effect ~ DOSE,
data = data_1)
summary(Sidis)##
## Call:
## lm(formula = side_effect ~ DOSE, data = data_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.06619 -0.05639 -0.03092 -0.02798 0.97202
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0269960 0.0116749 2.312 0.0212 *
## DOSE 0.0001960 0.0001086 1.805 0.0717 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1972 on 490 degrees of freedom
## Multiple R-squared: 0.006603, Adjusted R-squared: 0.004576
## F-statistic: 3.257 on 1 and 490 DF, p-value: 0.07173The model chosen to calculate MED was the Emax model with optimuzed parameters: Emax=951.31, EC50=390.63 and hill koafficient= 1.70. With these parameters MED was computed to 175 mg. It was then evaluated whether side effects might occur for 175 mg more frequently than for placebo. This can be extracted directly from the dataset since the number of side effects at high doses is not particularly higher than for placebo, but this was also statistically tested with the null hypothesis that there are no change in side effect frequency between these dose groups.The p-value was 0.07 indicating that the null hypothesis cannot be rejected. In conclusiion there is no indication that the rate of side effects will increase with 175 mg, which is our MED.
Part B
#Explore solubility
summary(data_1_B$Solubility)## Length Class Mode
## 2000 character charactersd_sol <- sd(data_1_B$Solubility)
#Explore weight
summary(data_1_B$MolWt)## Length Class Mode
## 2000 character charactersd_Mw <- sd(data_1_B$MolWt)
#Explore logP
summary(data_1_B$MolLogP)## Length Class Mode
## 2000 character charactersd_logP <- sd(data_1_B$MolLogP)
#Explore H-acceptors
summary(data_1_B$NumHAcceptors)## Length Class Mode
## 2000 character charactersd_HA <- sd(data_1_B$NumHAcceptors)
#Explore H-donors
summary(data_1_B$NumHDonors)## Length Class Mode
## 2000 character charactersd_HD <- sd(data_1_B$NumHDonors)The distribution with respect to solubility is within the range of -11.999 and 2.138, with a mean of -3.501 and standard deviation of 2.253. The distribution with respect to molecular weight is within the range of 17.03 and 5299.46, with a mean of 310.42 and standard deviation of 274.41. The distribution with respect to LogP is within the range of -29.1 and 68.5, with a mean of 2.62 and standard deviation of 5.03. The distribution with respect to H-donors is within the range of 0 and 21, with a mean of 0.90 and standard deviation of 1.49. The distribution with respect to H-acceptors is within the range of 0 and 86, with a mean of 3.68 and standard deviation of 4.61.
# linear regression
exclude_cols <- c(1:5, 9)
# Convert all other columns to numeric
data_1_B[, -exclude_cols] <- lapply(data_1_B[, -exclude_cols], as.numeric)
# Split the data into training and testing sets
train_index <- sample(1:nrow(data_1_B), 0.7 * nrow(data_1_B))
train_set <- data_1_B[train_index, ]
test_set <- data_1_B[-train_index, ]
test_set$ID <- factor(test_set$ID, levels = levels(train_set$ID))
test_set$Name <- factor(test_set$Name, levels = levels(train_set$Name))
test_set$InChI <- factor(test_set$InChI, levels = levels(train_set$InChI))
test_set$InChIKey <- factor(test_set$InChIKey, levels = levels(train_set$InChIKey))
test_set$SMILES <- factor(test_set$SMILES, levels = levels(train_set$SMILES))
# Fit the linear regression model
model_lin <- lm(Solubility ~ ., data = train_set)
# random forest
X <- data_1_B[, !names(data_1_B) %in% c("Solubility")]
y <- data_1_B$Solubility
set.seed(200)
train_indices <- sample(1:nrow(data_1_B), size = 0.7 * nrow(data_1_B))
train_data <- data_1_B[train_indices, ]
test_data <- data_1_B[-train_indices, ]
rf_model <- randomForest(Solubility ~ ., data = train_data, ntree = 100, importance = TRUE)
predictions <- predict(rf_model, newdata = test_data)
residuals_rf <- (test_data$Solubility - predictions)^2
#Evaluate RF
mse <- mean((test_data$Solubility - predictions)^2)
rmse_rf <- sqrt(mse)
mae_rf <- mean(abs(test_data$Solubility - predictions))
r2_rf <- 1 - sum((test_data$Solubility - predictions)^2) / sum((test_data$Solubility - mean(test_data$Solubility))^2)
#Support vector regression
set.seed(200)
train_indices <- sample(1:nrow(data_1_B), size = 0.7 * nrow(data_1_B))
train_data <- data_1_B[train_indices, ]
test_data <- data_1_B[-train_indices, ]
svr_model <- svm(Solubility ~ MolLogP, data = train_data, type = "eps-regression", kernel = "radial")
predictions <- predict(svr_model, newdata = test_data)
#Evaluate SVR
test_data$residuals <- test_data$Solubility - predictions
rmse_svr <- sqrt(mean((test_data$Solubility - predictions)^2))
mae_svr <- mean(abs(test_data$Solubility - predictions))
r2_svr <- 1 - (sum((test_data$Solubility - predictions)^2) / sum((test_data$Solubility - mean(test_data$Solubility))^2))
#Hyperparameters for SVR
tuned_model <- tune(svm, Solubility ~ MolLogP, data = train_data,
ranges = list(cost
= 2^(2:4), epsilon = seq(0.1, 1, 0.1),
gamma = 2^(-3:1)))
# Best parameters
best_model <- tuned_model$best.model
summary(best_model)##
## Call:
## best.tune(METHOD = svm, train.x = Solubility ~ MolLogP, data = train_data,
## ranges = list(cost = 2^(2:4), epsilon = seq(0.1, 1, 0.1), gamma = 2^(-3:1)))
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 8
## gamma: 2
## epsilon: 0.4
##
##
## Number of Support Vectors: 655#We see that SD Ocurrences NumSaturatedRings and NumAliphaticRings contributes least to Solubility and hence we remove them
data_1_B <- data_1_B%>%
select(-c(1:5,7,8,20,21))The models tested were linear regression (rmse=1.88, R2=0.12), random forest (rmse=1.73, mae=1.31, R2=0.42) and support vector machine (rmse=1.64, mae=1.18, R2=0.47). Out of these, SVM had better metrics evaluation and the hyperparameters for this model were determined to be as follows; type=eps-regression, kernel= radial, cost=8, gamma=2, epsilon=0.4. The parameters affecting the solubility the most were MolLogP (with coefficient 0.03) and MolMR (with coefficient 0.23) wich makes sense considering logP and molecular refraction should affect solubility. logP reflects chemical properties (i.e partition coefficient of octanol and water) and MR reflects physical properties (i.e refractivity).
data_1_B$Group <- as.numeric(data_1_B$Group)## Warning: NAs introduced by coercioncor_matrix <- cor(data_1_B)
cor_matrix_melted <- melt(cor_matrix)
# Create heatmap using ggplot2
ggplot(cor_matrix_melted, aes(Var1, Var2, fill = value)) +
geom_tile() +
scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0) +
theme_minimal() +
labs(title = "Correlation Heatmap", x = "", y = "") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Heat map was created to clearly visualize whether descriptors correlate,
where bright red areas correspond to high correlation. We then see that
for example weight and number of valence electrons correlate as well as
weight and number of heavy atoms, which both are logical.
ggplot(test_data, aes(x=Solubility, y = residuals)) +
geom_point() +
geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
labs(title = "Residualplot", x = "Faktiska värden", y = "Residualer")
test_data$abs_residuals <- abs(test_data$residuals)
# Sortera efter största residualerna
poor_performance <- test_data[order(-test_data$abs_residuals), ]
head(poor_performance)## # A tibble: 6 × 28
## ID Name InChI InChIKey SMILES Solubility SD Ocurrences Group MolWt
## <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <chr> <dbl>
## 1 A-2771 1H-Pyraz… InCh… BHAUFRO… [H+].… -7.75 0 1 G1 564.
## 2 A-2295 oxygen(-… InCh… QRTRRDM… [O--]… -7.71 0 1 G1 203.
## 3 A-2766 hafnium … InCh… WIHZLLG… [O--]… -7.24 0 1 G1 210.
## 4 A-2292 palladiu… InCh… PLYDYQG… [Pd++… -7.44 0 1 G1 305.
## 5 A-2309 potassiu… InCh… NGNZTXN… [K+].… -8.15 3.87 3 G4 323.
## 6 A-2781 aluminiu… InCh… OJMOMXZ… [Al+3… -6.93 0 1 G1 85.8
## # ℹ 18 more variables: MolLogP <dbl>, MolMR <dbl>, HeavyAtomCount <dbl>,
## # NumHAcceptors <dbl>, NumHDonors <dbl>, NumHeteroatoms <dbl>,
## # NumRotatableBonds <dbl>, NumValenceElectrons <dbl>, NumAromaticRings <dbl>,
## # NumSaturatedRings <dbl>, NumAliphaticRings <dbl>, RingCount <dbl>,
## # TPSA <dbl>, LabuteASA <dbl>, BalabanJ <dbl>, BertzCT <dbl>,
## # residuals <dbl>, abs_residuals <dbl>To test where the model performs poorly, the residuals were plotted against the actual solubility values. The plot shows largest residuals in the beginning and the end, indicating that these spots were poorly predicted. Could be due to the fexer data points in these areas.
pca_facto <- PCA(data_1_B[, 3:17], scale.unit = TRUE, ncp = 5, graph = TRUE)
# Summary of PCA
summary(pca_facto)##
## Call:
## PCA(X = data_1_B[, 3:17], scale.unit = TRUE, ncp = 5, graph = TRUE)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
## Variance 9.246 2.438 1.251 0.797 0.701 0.163 0.124
## % of var. 61.638 16.255 8.342 5.313 4.674 1.086 0.825
## Cumulative % of var. 61.638 77.892 86.234 91.548 96.221 97.307 98.132
## Dim.8 Dim.9 Dim.10 Dim.11 Dim.12 Dim.13 Dim.14
## Variance 0.083 0.066 0.058 0.039 0.021 0.009 0.004
## % of var. 0.552 0.437 0.388 0.259 0.138 0.062 0.028
## Cumulative % of var. 98.684 99.122 99.510 99.769 99.907 99.969 99.997
## Dim.15
## Variance 0.001
## % of var. 0.003
## Cumulative % of var. 100.000
##
## Individuals (the 10 first)
## Dist Dim.1 ctr cos2 Dim.2 ctr cos2
## 1 | 2.625 | -0.258 0.000 0.010 | 1.259 0.033 0.230 |
## 2 | 1.822 | -0.964 0.005 0.280 | -0.194 0.001 0.011 |
## 3 | 2.065 | -1.886 0.019 0.835 | 0.159 0.001 0.006 |
## 4 | 5.957 | 5.294 0.152 0.790 | 0.286 0.002 0.002 |
## 5 | 2.887 | 1.829 0.018 0.401 | 0.094 0.000 0.001 |
## 6 | 2.321 | -2.086 0.024 0.807 | 0.447 0.004 0.037 |
## 7 | 1.567 | -1.485 0.012 0.898 | 0.123 0.000 0.006 |
## 8 | 2.814 | 1.250 0.008 0.197 | -1.138 0.027 0.163 |
## 9 | 1.514 | -0.896 0.004 0.350 | 0.216 0.001 0.020 |
## 10 | 1.183 | 0.636 0.002 0.289 | 0.260 0.001 0.048 |
## Dim.3 ctr cos2
## 1 0.558 0.012 0.045 |
## 2 -1.322 0.070 0.527 |
## 3 -0.581 0.013 0.079 |
## 4 -2.307 0.213 0.150 |
## 5 -1.336 0.071 0.214 |
## 6 -0.761 0.023 0.107 |
## 7 0.064 0.000 0.002 |
## 8 0.297 0.004 0.011 |
## 9 -1.130 0.051 0.557 |
## 10 -0.428 0.007 0.131 |
##
## Variables (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3
## MolWt | 0.953 9.833 0.909 | 0.097 0.383 0.009 | 0.100
## MolLogP | 0.349 1.314 0.122 | 0.881 31.847 0.776 | -0.162
## MolMR | 0.922 9.186 0.849 | 0.366 5.499 0.134 | -0.023
## HeavyAtomCount | 0.974 10.257 0.948 | 0.211 1.823 0.044 | 0.014
## NumHAcceptors | 0.847 7.753 0.717 | -0.380 5.927 0.145 | 0.188
## NumHDonors | 0.459 2.279 0.211 | -0.325 4.330 0.106 | 0.295
## NumHeteroatoms | 0.791 6.768 0.626 | -0.448 8.230 0.201 | 0.245
## NumRotatableBonds | 0.582 3.666 0.339 | 0.615 15.493 0.378 | 0.445
## NumValenceElectrons | 0.950 9.768 0.903 | 0.279 3.200 0.078 | 0.084
## NumAromaticRings | 0.741 5.946 0.550 | -0.166 1.136 0.028 | -0.563
## ctr cos2
## MolWt 0.802 0.010 |
## MolLogP 2.086 0.026 |
## MolMR 0.041 0.001 |
## HeavyAtomCount 0.016 0.000 |
## NumHAcceptors 2.824 0.035 |
## NumHDonors 6.936 0.087 |
## NumHeteroatoms 4.802 0.060 |
## NumRotatableBonds 15.822 0.198 |
## NumValenceElectrons 0.564 0.007 |
## NumAromaticRings 25.342 0.317 |# Plot the eigenvalues
fviz_eig(pca_facto)
# Plot the variables (e.g., first two principal components)
fviz_pca_var(pca_facto)
#Selecting MolWt, MolLogP, MolMR and HeavyAtomCount based on pca to perform pcr
data_pcr <- data_1_B%>%
select(1,3:6)
model_lin <- lm(Solubility ~ MolWt + MolLogP + MolMR + HeavyAtomCount, data = data_pcr)
summary(model_lin)##
## Call:
## lm(formula = Solubility ~ MolWt + MolLogP + MolMR + HeavyAtomCount,
## data = data_pcr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.6483 -1.2366 -0.0033 1.1901 12.8839
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.7427608 0.0647683 -42.347 < 2e-16 ***
## MolWt -0.0034484 0.0005476 -6.298 3.7e-10 ***
## MolLogP -0.2819950 0.0155973 -18.080 < 2e-16 ***
## MolMR 0.0122688 0.0044885 2.733 0.00632 **
## HeavyAtomCount 0.0041882 0.0192747 0.217 0.82800
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.89 on 1995 degrees of freedom
## Multiple R-squared: 0.2978, Adjusted R-squared: 0.2964
## F-statistic: 211.5 on 4 and 1995 DF, p-value: < 2.2e-16# Evaluate
residuals <- model_lin$residuals
r_squared <- summary(model_lin)$r.squared
mse <- mean(residuals^2)
rmse <- sqrt(mse)
mae=mean(abs(residuals))A PCA was done choosing MolWt, MolLogP, MolMR and Heavy AtomCount, which together accounted for 91,5% of the variance. However, when a line.ar model was fitted to these parameters it performed worse than SVM with rmse=1.88, mae=1.48 and r2= 0.30