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
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
|
/*
** The code for start-stop data
** this is the essentially the first iteration of agfit4.c
*/
#include <math.h>
#include "survS.h"
#include "survproto.h"
SEXP zph2(SEXP gt2, SEXP y2,
SEXP covar2, SEXP eta2, SEXP weights2,
SEXP strata2,SEXP method2, SEXP sort12, SEXP sort22) {
int i,j, k, kk, person, p, p1;
int cstrat; /* current stratum*/
int indx1, nrisk;
double temp, temp2, tmean, etasum;
double *dtemp, timewt=1;
double *a, *a2, **cmat, **cmat2;
int *keep;
double denom, dtime=0, ndead, denom2;
double risk, meanwt, recenter;
int nprotect;
/* scalar input arguments and counts*/
int nused, nvar, nevent, nstrat;
int method;
/* input vectors */
double *start, *tstop, *gt, *eta, *weights, *status;
int *strata, *sort1, *sort2;
double **covar;
/* returned objects */
SEXP rlist;
double *u, **imat, **schoen;
int **used;
static const char *rnames[]={"u", "imat", "schoen", "used", ""};
/* get local copies of input args */
nused = nrows(y2);
nvar = ncols(covar2);
method = asInteger(method2);
start = REAL(y2);
tstop = start + nused;
status = tstop + nused;
weights = REAL(weights2);
strata = INTEGER(strata2);
gt = REAL(gt2);
eta = REAL(eta2);
sort1= INTEGER(sort12);
sort2= INTEGER(sort22);
/*
** count up the number of events and the number of strata
*/
nevent =0;
nstrat =1;
for (i=0; i< nused; i++) {
nevent += status[i];
if (strata[i] >= nstrat) nstrat= strata[i] + 1;
}
/*
** Set up the ragged arrays and scratch space
*/
nprotect =0;
if (MAYBE_REFERENCED(covar2)) {
nprotect =1;
covar = dmatrix(REAL(PROTECT(duplicate(covar2))), nused, nvar);
}
else covar = dmatrix(REAL(covar2), nused, nvar);
nprotect++;
PROTECT(rlist = mkNamed(VECSXP, rnames));
u = REAL(SET_VECTOR_ELT(rlist, 0, allocVector(REALSXP, 2*nvar)));
dtemp = REAL(SET_VECTOR_ELT(rlist, 1, allocMatrix(REALSXP, 2*nvar, 2*nvar)));
imat = dmatrix(dtemp, 2*nvar, 2*nvar); /* information matrix */
dtemp = REAL(SET_VECTOR_ELT(rlist, 2, allocMatrix(REALSXP, nevent, nvar)));
schoen = dmatrix(dtemp, nevent, nvar); /* schoenfeld residuals */
used = imatrix(INTEGER(SET_VECTOR_ELT(rlist, 3,
allocMatrix(INTSXP, nstrat, nvar))),
nstrat, nvar);
/* scratch vectors */
a = (double *) R_alloc(2*nvar*nvar + 2*nvar, sizeof(double));
a2 = a + nvar;
cmat = dmatrix(a2+ nvar, nvar, nvar);
cmat2= dmatrix(a2+ nvar +nvar*nvar, nvar, nvar);
keep = (int *) R_alloc(nused, sizeof(int));
/* zero variables */
for (i=0; i<2*nvar; i++) {
u[i] =0;
for (j=0; j<2*nvar; j++) imat[i][j] =0 ;
}
for (i=0; i<nvar; i++) {
a[i] =0;
a2[i] =0;
for (j=0; j<nvar; j++) {
cmat[i][j] =0;
cmat2[i][j] =0;
}
for (j=0; j<nstrat; j++) used[i][j] =0;
}
for (i=0; i<nused; i++) keep[i] =0;
/* count the number of events, per covariate per strata
** if a covariate is constant in the stratum it gets a 0, otherwise
** the number of events in the stratum. The algorithm is fairly
** simple but the code is ugly. Count the number of deaths, then at
** the end of each stratum set used[][] to the number of events or
** to zero for each covariate.
*/
k = 0; /* first obs of the stratum */
ndead=0;
cstrat = strata[sort2[0]];
for (i=0; i<nused; i++) {
person= sort2[i];
if (cstrat == strata[person]) ndead += status[person];
else { /* end of a stratum */
p1 = sort2[k]; /* first obs of the stratum */
for (j=0; j<nvar; j++) {
used[j][cstrat] =0; /* start pessimistic */
for (kk =k; kk<i; kk++) {
person = sort2[kk];
if (covar[j][person] != covar[j][p1]) {
used[j][cstrat] = ndead;
break;
}
}
}
k = i;
ndead = status[sort2[i]];
cstrat = strata[sort2[i]];
}
}
/* Deal with the last strata */
p1 = sort2[k];
for (j=0; j<nvar; j++) {
used[j][cstrat] =0; /* start pessimistic */
for (kk =k; kk<i; kk++) {
person = sort2[kk];
if (covar[j][person] != covar[j][p1]) {
used[j][cstrat] = ndead;
break;
}
}
}
/*
** Recenter the X matrix to make the variance computation more stable
*/
for (i=0; i<nvar; i++) {
tmean =0;
for (j=0; j<nused; j++) tmean += covar[i][j];
tmean /= nused;
for (j=0; j<nused; j++) covar[i][j] -= tmean;
}
/*
** 'person' walks through the the data from 1 to n,
** sort1[0] points to the largest stop time, sort1[1] the next, ...
** 'dtime' is a scratch variable holding the time of current interest
** 'indx1' walks through the start times.
*/
person =0;
indx1 =0;
denom=0;
nrisk=0;
etasum =0;
cstrat = -1;
recenter =0;
while (person < nused) {
/* find the next death time */
for (k=person; k< nused; k++) {
if (strata[sort2[k]] != cstrat) {
/* hit a new stratum; reset temporary sums */
cstrat = strata[sort2[k]];
denom = 0;
nrisk = 0;
etasum =0;
for (i=0; i<nvar; i++) {
a[i] =0;
for (j=0; j<nvar; j++) cmat[i][j] =0;
}
person =k; /* skip to end of stratum */
indx1 =k;
}
p = sort2[k];
if (status[p] == 1) {
dtime = tstop[p];
timewt = gt[p]; /* time weight for this event time */
break;
}
}
if (k == nused) person =k; /* no more ndead to be processed */
else {
/* remove any subjects no longer at risk */
/*
** subtract out the subjects whose start time is to the right
** If everyone is removed reset the totals to zero.
*/
for (; indx1<nused; indx1++) {
p1 = sort1[indx1];
if (strata[p1] != cstrat || start[p1] < dtime) break;
if (keep[p1] == 0) continue; /* skip any never-at-risk rows */
nrisk--;
if (nrisk ==0) {
etasum =0;
denom =0;
for (i=0; i<nvar; i++) {
a[i] =0;
for (j=0; j<=i; j++) cmat[i][j] =0;
}
}
else {
etasum -= eta[p1];
risk = exp(eta[p1] - recenter) * weights[p1];
denom -= risk;
for (i=0; i<nvar; i++) {
a[i] -= risk*covar[i][p1];
for (j=0; j<=i; j++)
cmat[i][j] -= risk*covar[i][p1]*covar[j][p1];
}
}
}
/*
** add any new subjects who are at risk
** denom2, a2, cmat2, meanwt and ndead count only the ndead
*/
denom2= 0;
ndead=0; meanwt=0;
for (i=0; i<nvar; i++) {
a2[i]=0;
for (j=0; j<nvar; j++) {
cmat2[i][j]=0;
}
}
for (; person<nused; person++) {
p = sort2[person];
if (strata[p] != cstrat || tstop[p] < dtime) break; /* no more to add */
etasum += eta[p];
nrisk++;
if (fabs(etasum/nrisk - recenter) > 200) {
temp = etasum/nrisk - recenter;
recenter = etasum/nrisk;
if (denom > 0) {
/* we can skip this if there is no one at risk */
if (fabs(temp) > 709) error("exp overflow due to covariates\n");
temp = exp(-temp);
denom *= temp;
for (i=0; i<nvar; i++) {
a[i] *= temp;
for (j=0; j<nvar; j++) {
cmat[i][j]*= temp;
}
}
}
}
risk = exp(eta[p] - recenter) * weights[p];
if (status[p] ==1) {
nevent--;
keep[p] =1;
ndead++;
denom2 += risk;
meanwt += weights[p];
for (i=0; i<nvar; i++) {
u[i] += weights[p] * covar[i][p];
u[i+nvar] += weights[p]*covar[i][p] * timewt;
a2[i]+= risk*covar[i][p];
schoen[i][nevent] = covar[i][p];
for (j=0; j<=i; j++)
cmat2[i][j] += risk*covar[i][p]*covar[j][p];
}
}
else if (start[p] < dtime) {
keep[p] =1;
denom += risk;
for (i=0; i<nvar; i++) {
a[i] += risk*covar[i][p];
for (j=0; j<=i; j++)
cmat[i][j] += risk*covar[i][p]*covar[j][p];
}
}
}
/*
** Add results into u and imat for all events at this time point
*/
if (method==0 || ndead ==1) { /*Breslow */
denom += denom2;
for (i=0; i<nvar; i++) {
a[i] += a2[i];
temp = a[i]/denom; /*mean covariate at this time */
u[i] -= meanwt*temp;
u[i+nvar] -= meanwt*temp * timewt;
for (j=0; j<=i; j++) {
cmat[i][j] += cmat2[i][j];
temp2 = meanwt*((cmat[i][j]- temp*a[j])/denom);
imat[j][i] += temp2;
imat[j][i+nvar] += temp2* timewt;
imat[j+nvar][i+nvar] += temp2*timewt * timewt;
}
for (j=0; j<ndead; j++)
schoen[i][nevent+j] -= temp;
}
}
else {
meanwt /= ndead;
/* compute the mean x, for Schoenfeld residuals */
for (i=0; i<nvar; i++) {
tmean =0;
for (k=0; k<ndead; k++) {
temp = (k+1)/ndead;
tmean += (a[i] + a2[i]*temp)/(denom + denom2*temp);
}
for (j=0; j<ndead; j++)
schoen[i][nevent+j] -= tmean/ndead;
}
for (k=0; k<ndead; k++) {
denom += denom2/ndead;
for (i=0; i<nvar; i++) {
a[i] += a2[i]/ndead;
temp = a[i]/denom;
u[i] -= meanwt*temp;
u[i+nvar] -= meanwt*temp* timewt;
for (j=0; j<=i; j++) {
cmat[i][j] += cmat2[i][j]/ndead;
temp2 = meanwt*((cmat[i][j]- temp*a[j])/denom);
imat[j][i] += temp2;
imat[j][i+nvar] += temp2* timewt;
imat[j+nvar][i+nvar] += temp2*timewt * timewt;
}
}
}
}
if (fabs(etasum/nrisk) > 200) {
temp = etasum/nrisk;
for (i=0; i<nused; i++) eta[i] -= temp;
temp = exp(-temp);
denom *= temp;
for (i=0; i<nvar; i++) {
a[i] *= temp;
for (j=0; j<nvar; j++) {
cmat[i][j]*= temp;
}
}
etasum =0;
}
}
} /* end of accumulation loop */
/* fill in the rest of the information matrix */
for (i=0; i<nvar; i++) {
for (j=0; j<i; j++) {
imat[i][j] = imat[j][i];
imat[i][j+nvar]= imat[j][i+nvar];
imat[i+nvar][j+nvar] = imat[j+nvar][i+nvar];
}
}
for (i=0; i<nvar; i++) {
for (j=0; j<nvar; j++) /* upper right */
imat[i+nvar][j] = imat[j][i+nvar];
}
UNPROTECT(nprotect);
return(rlist);
}
|
