1019_Homework Exercise 1
Pei-Yun,Li
2020-10-26
1 Description
The new drug Novafylline is developed to reduce the symptoms of intermittent claudication, which is a medical term for pain caused by too little blood flow,
usually during exercise.Patients were randomly assigned to receive either Novafylline (active treatment) or a placebo in a double-blind study.
A total of 38 patients (20 for treatment, 18 for placebo) underwent treadmill testing at baseline and at each of 4 monthly follow-up visits.
Patients were stratified by gender (17 females, 21 males).
The primary measurement of efficacy is the walking distance on a treadmill until discontinuation due to claudication pain.
Is there any distinction in exercise tolerance profiles between patients who receive Novafylline and those on placebo?
Column 1: Treatment ID
Column 2: Patient ID
Column 3: Gender ID
Column 4: Walking distance at baseline (month 0)
Column 5: Walking distance at month 1
Column 6: Walking distance at month 2
Column 7: Walking distance at month 3
Column 8: Walking distance at month 4
2 Input Data
## 'data.frame': 38 obs. of 8 variables:
## $ Treatment: chr "ACT" "ACT" "ACT" "ACT" ...
## $ PID : chr "P101" "P105" "P109" "P112" ...
## $ Gender : chr "M" "M" "M" "M" ...
## $ D0 : int 190 98 155 245 182 140 196 162 195 167 ...
## $ D1 : int 212 137 145 228 205 138 185 176 232 187 ...
## $ D2 : int 213 185 196 280 218 187 185 192 199 228 ...
## $ D3 : int 195 215 189 274 194 195 227 230 185 192 ...
## $ D4 : int 248 225 176 260 193 205 180 215 200 210 ...## Treatment PID Gender D0 D1 D2 D3 D4
## 1 ACT P101 M 190 212 213 195 248
## 2 ACT P105 M 98 137 185 215 225
## 3 ACT P109 M 155 145 196 189 176
## 4 ACT P112 M 245 228 280 274 260
## 5 ACT P117 M 182 205 218 194 193
## 6 ACT P122 M 140 138 187 195 2053 Wide to long format
## 'data.frame': 190 obs. of 5 variables:
## $ Treatment: Factor w/ 2 levels "ACT","PBO": 1 1 1 1 1 1 1 1 1 1 ...
## $ PID : Factor w/ 38 levels "P101","P102",..: 1 5 9 12 17 22 23 28 29 32 ...
## $ Gender : Factor w/ 2 levels "F","M": 2 2 2 2 2 2 2 2 2 2 ...
## $ Month : Factor w/ 5 levels "D0","D1","D2",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Distance : int 190 98 155 245 182 140 196 162 195 167 ...## Treatment PID Gender Month Distance
## 1 ACT P101 M D0 190
## 2 ACT P105 M D0 98
## 3 ACT P109 M D0 155
## 4 ACT P112 M D0 245
## 5 ACT P117 M D0 182
## 6 ACT P122 M D0 1404 make ellipses in pairwise plot (by Treatment)
scatterplotMatrix(~ D0 + D1 + D2 + D3 + D4 | Treatment,
data = dta1,
smooth = F,
by.group = TRUE,
regLine = F,
ellipse = T,
diagonal = T,
pch = c(1, 20))
5 Line chart(By treatment,By Gender)
ggplot(dta1L, aes(Month, Distance,
group = Treatment,
shape = Treatment,
linetype = Treatment,
color = Treatment)) +
stat_summary(fun = mean, geom = "line") +
stat_summary(fun = mean, geom = "point") +
stat_summary(fun.data = mean_se, geom = "errorbar", width = 0.2) +
scale_shape_manual(values = c(1, 2)) +
labs(x = "TIME (in months)",
y = "Walking distance (in meters)",
linetype = "Treatment", shape = "Treatment") +
theme(legend.justification = c(1, 1),
legend.position = c(1, 1),
legend.background = element_rect(fill = "white",color = "black"))
treatment是ACT的組別，其每月行走距離會比PBO組別來的多。
ggplot(dta1L, aes(Month, Distance,
group = Treatment,
shape = Treatment,
linetype = Treatment,
color = Treatment)) +
geom_point() +
stat_summary(fun = mean, geom = "line") +
stat_summary(fun = mean, geom = "point") +
stat_summary(fun.data = mean_se, geom = "errorbar", width = 0.3) +
scale_shape_manual(values = c(1, 2)) +
facet_wrap( ~ Gender)+
labs(x = "TIME (in months)",
y = "Walking distance (in meters)",
linetype = "Treatment", shape = "Treatment") +
theme(legend.justification = c(1, 1),
legend.position = c(1, 1),
legend.background = element_rect(fill = "white",color = "black"))
若以性別分組會發現，行走距離增加的趨勢依然是ACT會高於PBO。
6 Analysis
# means & sd of differ Treatment and gender
dta1_nid <- dta1 %>% select(-2)
# mean
aggregate(.~ Treatment + Gender, data = dta1_nid, mean, na.rm=T)## Treatment Gender D0 D1 D2 D3 D4
## 1 ACT F 180.3750 193.3750 207.8750 196.7500 208.5000
## 2 PBO F 165.5556 170.1111 175.7778 168.1111 171.2222
## 3 ACT M 163.1667 179.5000 195.5833 204.0833 207.6667
## 4 PBO M 178.3333 165.5556 173.3333 193.6667 194.2222## Treatment Gender D0 D1 D2 D3 D4
## 1 ACT F 42.18306 33.10994 58.21006 41.65762 57.10892
## 2 PBO F 41.52743 39.13261 47.25404 33.43443 45.34252
## 3 ACT M 42.34669 34.51350 40.14623 28.40441 28.04001
## 4 PBO M 45.00556 45.53051 43.68352 55.37824 47.351827 Correlation(Gender&treatment ACT)
## D0 D1 D2 D3 D4
## D0 1.0000000 0.8021966 0.8724733 0.8483852 0.8757233
## D1 0.8021966 1.0000000 0.8645096 0.7073820 0.9054398
## D2 0.8724733 0.8645096 1.0000000 0.8937510 0.9159571
## D3 0.8483852 0.7073820 0.8937510 1.0000000 0.9251102
## D4 0.8757233 0.9054398 0.9159571 0.9251102 1.0000000## D0 D1 D2 D3 D4
## D0 1.0000000 0.8624819 0.8052568 0.5928303 0.4068980
## D1 0.8624819 1.0000000 0.6464277 0.3498338 0.4496799
## D2 0.8052568 0.6464277 1.0000000 0.6704930 0.6323603
## D3 0.5928303 0.3498338 0.6704930 1.0000000 0.5941441
## D4 0.4068980 0.4496799 0.6323603 0.5941441 1.00000008 Correlation(Gender&treatment PBO)
## D0 D1 D2 D3 D4
## D0 1.0000000 0.9269134 0.6057892 0.8657560 0.7776916
## D1 0.9269134 1.0000000 0.6826171 0.7707920 0.7579993
## D2 0.6057892 0.6826171 1.0000000 0.3713199 0.4846551
## D3 0.8657560 0.7707920 0.3713199 1.0000000 0.7931043
## D4 0.7776916 0.7579993 0.4846551 0.7931043 1.0000000## D0 D1 D2 D3 D4
## D0 1.0000000 0.9271229 0.8530641 0.8833606 0.9202039
## D1 0.9271229 1.0000000 0.7036016 0.7846666 0.9031326
## D2 0.8530641 0.7036016 1.0000000 0.8292800 0.8073104
## D3 0.8833606 0.7846666 0.8292800 1.0000000 0.9197535
## D4 0.9202039 0.9031326 0.8073104 0.9197535 1.00000009 m1
summary(m1 <- gls(Distance ~ Month + Gender*Treatment + Month:Treatment,
weights = varIdent(form = ~ 1 | Month),
correlation = corSymm(form = ~ 1 | PID),
data = dta1L))## Generalized least squares fit by REML
## Model: Distance ~ Month + Gender * Treatment + Month:Treatment
## Data: dta1L
## AIC BIC logLik
## 1749.506 1835.414 -847.7529
##
## Correlation Structure: General
## Formula: ~1 | PID
## Parameter estimate(s):
## Correlation:
## 1 2 3 4
## 2 0.878
## 3 0.781 0.718
## 4 0.770 0.635 0.673
## 5 0.746 0.736 0.715 0.837
## Variance function:
## Structure: Different standard deviations per stratum
## Formula: ~1 | Month
## Parameter estimates:
## D0 D1 D2 D3 D4
## 1.0000000 0.8915599 1.0795057 0.9486381 1.0287427
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 170.03789 13.440748 12.650925 0.0000
## MonthD1 15.00000 4.607348 3.255669 0.0014
## MonthD2 30.45000 6.661777 4.570852 0.0000
## MonthD3 31.10000 6.377944 4.876180 0.0000
## MonthD4 37.95000 6.955426 5.456172 0.0000
## GenderM 0.02018 15.640507 0.001290 0.9990
## TreatmentPBO 1.79485 18.675206 0.096109 0.9235
## GenderM:TreatmentPBO 0.20322 22.484646 0.009038 0.9928
## MonthD1:TreatmentPBO -19.11111 6.694322 -2.854824 0.0048
## MonthD2:TreatmentPBO -27.83889 9.679338 -2.876115 0.0045
## MonthD3:TreatmentPBO -22.15556 9.266937 -2.390817 0.0179
## MonthD4:TreatmentPBO -27.17222 10.106000 -2.688722 0.0079
##
## Correlation:
## (Intr) MnthD1 MnthD2 MnthD3 MnthD4 GendrM TrtPBO GM:TPB
## MonthD1 -0.325
## MonthD2 -0.162 0.195
## MonthD3 -0.291 0.076 0.252
## MonthD4 -0.230 0.360 0.366 0.665
## GenderM -0.698 0.000 0.000 0.000 0.000
## TreatmentPBO -0.720 0.234 0.117 0.210 0.165 0.503
## GenderM:TreatmentPBO 0.486 0.000 0.000 0.000 0.000 -0.696 -0.660
## MonthD1:TreatmentPBO 0.223 -0.688 -0.134 -0.052 -0.248 0.000 -0.340 0.000
## MonthD2:TreatmentPBO 0.112 -0.134 -0.688 -0.174 -0.252 0.000 -0.170 0.000
## MonthD3:TreatmentPBO 0.200 -0.052 -0.174 -0.688 -0.457 0.000 -0.305 0.000
## MonthD4:TreatmentPBO 0.158 -0.248 -0.252 -0.457 -0.688 0.000 -0.240 0.000
## MD1:TP MD2:TP MD3:TP
## MonthD1
## MonthD2
## MonthD3
## MonthD4
## GenderM
## TreatmentPBO
## GenderM:TreatmentPBO
## MonthD1:TreatmentPBO
## MonthD2:TreatmentPBO 0.195
## MonthD3:TreatmentPBO 0.076 0.252
## MonthD4:TreatmentPBO 0.360 0.366 0.665
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -1.8562836 -0.6190432 -0.1082266 0.5224223 3.5519928
##
## Residual standard error: 43.03221
## Degrees of freedom: 190 total; 178 residual10 m2
summary(m2<- gls(Distance ~ Month + Treatment,
weights = varIdent(form = ~ 1 | Month),
correlation = corSymm(form = ~ 1 | PID),
data = dta1L))## Generalized least squares fit by REML
## Model: Distance ~ Month + Treatment
## Data: dta1L
## AIC BIC logLik
## 1789.923 1857.437 -873.9617
##
## Correlation Structure: General
## Formula: ~1 | PID
## Parameter estimate(s):
## Correlation:
## 1 2 3 4
## 2 0.865
## 3 0.740 0.708
## 4 0.752 0.633 0.666
## 5 0.710 0.728 0.711 0.833
## Variance function:
## Structure: Different standard deviations per stratum
## Formula: ~1 | Month
## Parameter estimates:
## D0 D1 D2 D3 D4
## 1.0000000 0.8438931 1.0134753 0.8938903 0.9657476
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 184.69912 8.902720 20.746368 0.0000
## MonthD1 5.94737 3.651185 1.628887 0.1050
## MonthD2 17.26316 5.286598 3.265457 0.0013
## MonthD3 20.60526 4.913125 4.193922 0.0000
## MonthD4 25.07895 5.454259 4.598049 0.0000
## TreatmentPBO -29.03147 10.819479 -2.683260 0.0080
##
## Correlation:
## (Intr) MnthD1 MnthD2 MnthD3 MnthD4
## MonthD1 -0.440
## MonthD2 -0.282 0.345
## MonthD3 -0.398 0.223 0.371
## MonthD4 -0.343 0.473 0.478 0.715
## TreatmentPBO -0.576 0.000 0.000 0.000 0.000
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -1.9320355 -0.5706269 -0.1401018 0.5628160 3.7326441
##
## Residual standard error: 44.87449
## Degrees of freedom: 190 total; 184 residual## Contrasts set to contr.sum for the following variables: Treatment| Effect | df | MSE | F | ges | p.value |
|---|---|---|---|---|---|
| Treatment | 1, 36 | 6925.36 | 2.06 | .043 | .160 |
| Month | 3.18, 114.49 | 584.58 | 8.49 *** | .048 | <.001 |
| Treatment:Month | 3.18, 114.49 | 584.58 | 2.63 + | .015 | .050 |
## Treatment = ACT:
## Month emmean SE df lower.CL upper.CL
## D0 171 9.57 55.8 151 190
## D1 186 9.57 55.8 166 205
## D2 201 9.57 55.8 182 220
## D3 202 9.57 55.8 182 221
## D4 208 9.57 55.8 189 228
##
## Treatment = PBO:
## Month emmean SE df lower.CL upper.CL
## D0 172 9.68 58.1 153 192
## D1 168 9.68 58.1 149 188
## D2 175 9.68 58.1 156 194
## D3 181 9.68 58.1 162 201
## D4 183 9.68 58.1 164 203
##
## Warning: EMMs are biased unless design is perfectly balanced
## Confidence level used: 0.95dta1_b <- gather(dta1, Month, Distance, D1:D4, factor_key=TRUE)
xyplot(Distance ~ D0 | as.factor(Month), groups=Treatment, data=dta1_b,
type=c("p","r","g"), layout=c(5,1),
xlab="Baseline distance (in meters)",
ylab="Distance (in meters)",
auto.key = TRUE)