-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathMFAP4_Jump_Detection.R
214 lines (176 loc) · 6.67 KB
/
MFAP4_Jump_Detection.R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
rm(list=ls(all=TRUE))
working.dir = getwd();
setwd(".."); parent = getwd();
setwd(working.dir)
source(paste0(parent,"/MUSOLibrary.R"))
#source(paste0(parent,"/CorreCurves.R"))
library(readxl)
raw.data <- read_excel("MFAP4.xlsx")
data = cbind(raw.data$`Fibrosis Stage`, raw.data$`MFAP4 U/mL`)
X1 = sort(data[data[,1]==(1-1), 2]);
X2 = sort(data[data[,1]==(2-1), 2]);
X3 = sort(data[data[,1]==(3-1), 2]);
X4 = sort(data[data[,1]==(4-1), 2]);
X5 = sort(data[data[,1]==(5-1), 2]);
X.data = list(X1 = X1,
X2 = X2,
X3 = X3,
X4 = X4,
X5 = X5
)
k = length(X.data);
nv = array(NA,k);
for(j in 1:k){nv[j] = length(X.data[[j]])}
us = list(); cs = 0;
for(j in 1:(k-1)){
us[[j]] = seq(0,1,by=1/nv[j+1]);
cs[j] = sqrt((nv[j]*nv[j+1])/(nv[j]+nv[j+1]));
}
#nv = c(97, 176, 135, 67, 67)
nv0 = nv
set.seed(02132021)
B0 = 10000;
M1s0 = array(NA,c(B0,(k-1))); M2s0 = array(NA,c(B0,(k-1))); Mss0 = array(NA,c(B0,(k-1)));
for(b0 in 1:B0){
X0.data = list(X10 = runif(nv0[1]),
X20 = runif(nv0[2]),
X30 = runif(nv0[3]),
X40 = runif(nv0[4]),
X50 = runif(nv0[5])
)
M1s = NA; M2s = NA; Mss = NA;
us = list(); fun.Mrs = list(); cs = 0;
for(j in 1:(k-1)){
us[[j]] = seq(0,1,by=1/nv0[j+1]);
cs[j] = sqrt((nv0[j]*nv0[j+1])/(nv0[j]+nv0[j+1]));
}
for(j in 1:(k-1)){
### loading data and parameters
X = X0.data[[j]];
Y = X0.data[[j+1]];
uj = us[[j]];
cj = cs[j];
### calcuating test statistics
n.uj = length(uj); n.Y = length(Y);
emp.Rj = ecdf(X)(quantile(Y,uj));
r.emp.Rj = (1-emp.Rj[2:n.uj])/(1-uj[1:n.Y]);
Mrj = cummin(r.emp.Rj);
MRj = 1-Mrj[1:n.Y]*(1-uj[1:n.Y]); MRj[n.uj] = 1;
ubj = (1-(1:n.Y)/n.Y);
lbj = (1-(0:(n.Y-1))/n.Y);
M1j = cj*(-(sum( (1-Mrj)^1/(1+1)*(ubj^(1+1)-lbj^(1+1)))))^(1/1)
M2j = cj*(-(sum( (1-Mrj)^2/(2+1)*(ubj^(2+1)-lbj^(2+1)))))^(1/2)
Msj = cj * max((1-Mrj)*lbj)
### saving statsitics and slope function r
M1s[j] = M1j;
M2s[j] = M2j;
Mss[j] = Msj;
fun.Mrs[[j]] = approxfun(uj,c(Mrj,Mrj[n.Y]),f=1);
}
M1s0[b0,] = M1s;
M2s0[b0,] = M2s;
Mss0[b0,] = Mss;
}
Wk10 = apply(M1s0, 1, max); Sk10 = apply(M1s0, 1, sum);
Wk20 = apply(M2s0, 1, max); Sk20 = apply(M2s0, 1, sum);
Wks0 = apply(Mss0, 1, max); Sks0 = apply(Mss0, 1, sum);
jump.cv.p1 = quantile(Wk10,0.95); quantile(Sk10,0.95);
jump.cv.p2 = quantile(Wk20,0.95); quantile(Sk10,0.95);
jump.cv.ps = quantile(Wks0,0.95); quantile(Sk10,0.95);
# jump.cv.p1 # 0.8297206 for n=50 # 0.8209637 for n=100 # 0.8057219 for n=200 # 0.8164940 for n=400 # 0.8126778 for n=1000
# jump.cv.p2 # 0.9131916 for n=50 # 0.9055811 for n=100 # 0.8941796 for n=200 # 0.9013435 for n=400 # 0.8937240 for n=1000
# jump.cv.ps # 1.5000000 for n=50 # 1.4849240 for n=100 # 1.5000000 for n=200 # 1.4849240 for n=400 # 1.4758050 for n=1000
B = 1; #n = 200; n = 400;
Jump.p1 = array(NA,c(B,(k-1)));
Jump.p2 = array(NA,c(B,(k-1)));
Jump.ps = array(NA,c(B,(k-1)));
M1s.data = array(NA,c(B,(k-1)));
M2s.data = array(NA,c(B,(k-1)));
Mss.data = array(NA,c(B,(k-1)));
Jump.p11 = array(NA,c(B,(k-1)));
Jump.p21 = array(NA,c(B,(k-1)));
Jump.ps1 = array(NA,c(B,(k-1)));
M1s.data1 = array(NA,c(B,(k-1)));
M2s.data1 = array(NA,c(B,(k-1)));
Mss.data1 = array(NA,c(B,(k-1)));
M21p1s.data1 = array(NA,c(B,(k-1)));
M21p2s.data1 = array(NA,c(B,(k-1)));
M21pss.data1 = array(NA,c(B,(k-1)));
set.seed(02142021)
for(b in 1:B){
us = list(); fun.Mrs = list(); cs = 0;
for(j in 1:(k-1)){
us[[j]] = seq(0,1,by=1/nv[j+1]);
cs[j] = sqrt((nv[j]*nv[j+1])/(nv[j]+nv[j+1]));
}
for(j in 1:(k-1)){
### loading data and parameters
X = X.data[[j]];
Y = X.data[[j+1]];
uj = us[[j]];
cj = cs[j];
### calcuating test statistics
n.uj = length(uj); n.Y = length(Y);
emp.Rj = ecdf(X)(quantile(Y,uj));
r.emp.Rj = (1-emp.Rj[2:n.uj])/(1-uj[1:n.Y]);
Mrj = cummin(r.emp.Rj);
MRj = 1-Mrj[1:n.Y]*(1-uj[1:n.Y]); MRj[n.uj] = 1;
ubj = (1-(1:n.Y)/n.Y);
lbj = (1-(0:(n.Y-1))/n.Y);
M1j = cj*(-(sum( (1-Mrj)^1/(1+1)*(ubj^(1+1)-lbj^(1+1)))))^(1/1)
M2j = cj*(-(sum( (1-Mrj)^2/(2+1)*(ubj^(2+1)-lbj^(2+1)))))^(1/2)
Msj = cj * max((1-Mrj)*lbj)
### saving statsitics and slope function r
M1s.data[b,j] = M1j;
M2s.data[b,j] = M2j;
Mss.data[b,j] = Msj;
rmn = 0; rmn = Rmn(X,Y);
LSRmn = 0; LSrmn = LSMRmn(rmn);
M21p1s.data1[b,j] = Mp21(rmn,LSrmn,m=length(X),n=length(Y),p=1)
M21p2s.data1[b,j] = Mp21(rmn,LSrmn,m=length(X),n=length(Y),p=2)
M21pss.data1[b,j] = Ms21(rmn,LSrmn,m=length(X),n=length(Y))
}
Jump.p1[b,] = c(M1s.data[b,]>jump.cv.p1);
Jump.p2[b,] = c(M2s.data[b,]>jump.cv.p2);
Jump.ps[b,] = c(Mss.data[b,]>jump.cv.ps);
delta.p1 = c(0,sort(M1s.data[b,]));
delta.p2 = c(0,sort(M2s.data[b,]));
delta.ps = c(0,sort(Mss.data[b,]));
JP1 = array(,c(k,k-1)); QP1 = array(,k);
JP2 = array(,c(k,k-1)); QP2 = array(,k);
JPs = array(,c(k,k-1)); QPs = array(,k);
constp1 = log(log(cs))*2/3 #0.652; #log(log(cs)); #log(log(cs)) #1/2#sqrt(log(log(cs))/2) # 0.652/0.585#log(log(cs))/2; #log(log(cs))/2
constp2 = log(log(cs))*3/4#log(log(cs)) #0.725; #log(log(cs)); #log(log(cs)) #1/2#sqrt(log(log(cs))/2) # 0.725/0.676#log(log(cs))/2; #log(log(cs))/2
constps = log(log(cs))*1#log(log(cs)) #1.201; #log(log(cs)); #log(log(cs)) #1/2#sqrt(log(log(cs))/2) # 1.201/1.353#log(log(cs))/2; #log(log(cs))/2
for(j in 1:k){
JP1[j,] = c(M1s.data[b,]>delta.p1[j]);
JP2[j,] = c(M2s.data[b,]>delta.p2[j]);
JPs[j,] = c(Mss.data[b,]>delta.ps[j]);
QP1[j] = sum( (1-JP1[j,])*(M1s.data[b,]/1) + (JP1[j,])*((M21p1s.data1+log(cs)*constp1)/1));
QP2[j] = sum( (1-JP2[j,])*(M2s.data[b,]/1) + (JP2[j,])*((M21p2s.data1+log(cs)*constp2)/1));
QPs[j] = sum( (1-JPs[j,])*(Mss.data[b,]/1) + (JPs[j,])*((M21pss.data1+log(cs)*constps)/1));
}
delta.p1.star = delta.p1[which.min(QP1)]
delta.p2.star = delta.p2[which.min(QP2)]
delta.ps.star = delta.ps[which.min(QPs)]
Jump.p11[b,] = c(M1s.data[b,]>delta.p1.star);
Jump.p21[b,] = c(M2s.data[b,]>delta.p2.star);
Jump.ps1[b,] = c(Mss.data[b,]>delta.ps.star);
}
JP1comp = rbind(Jump.p1, Jump.p11)
rownames(JP1comp) = c("original", "+delta")
colnames(JP1comp) = c("12", "23", "34", "45")
JP2comp = rbind(Jump.p2, Jump.p21)
rownames(JP2comp) = c("original", "+delta")
colnames(JP2comp) = c("12", "23", "34", "45")
JPscomp = rbind(Jump.ps, Jump.ps1)
rownames(JPscomp) = c("original", "+delta")
colnames(JPscomp) = c("12", "23", "34", "45")
JP1comp
JP2comp
JPscomp
par(mfrow=c(1,3))
plot(delta.p1,QP1,type="s")
plot(delta.p2,QP2,type="s")
plot(delta.ps,QPs,type="s")
par(mfrow=c(1,1))