-
Notifications
You must be signed in to change notification settings - Fork 0
/
corPFSOS.R
338 lines (308 loc) · 11.4 KB
/
corPFSOS.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
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
# survPFS ----
#' PFS Survival Function for Different Transition Models
#'
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#' @param t (`numeric`)\cr time at which the value of the PFS survival function is to be computed.
#'
#' @return The value of the survival function for the specified transition and time.
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' survPFS(transition, 0.4)
survPFS <- function(transition, t) {
UseMethod("survPFS")
}
#' @describeIn survPFS Survival Function for an exponential transition model.
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' survPFS(transition, 0.4)
survPFS.ExponentialTransition <- function(transition, t) {
ExpSurvPFS(t = t, h01 = transition$hazards$h01, h02 = transition$hazards$h02)
}
#' @describeIn survPFS Survival Function for a Weibull transition model.
#' @export
#'
#' @examples
#' transition <- weibull_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6, p01 = 2, p02 = 2.5, p12 = 3)
#' survPFS(transition, 0.4)
survPFS.WeibullTransition <- function(transition, t) {
WeibSurvPFS(
t = t, h01 = transition$hazards$h01, h02 = transition$hazards$h02,
p01 = transition$weibull_rates$p01, p02 = transition$weibull_rates$p02
)
}
#' @describeIn survPFS Survival Function for a piecewise constant transition model.
#' @export
#'
#' @examples
#' transition <- piecewise_exponential(
#' h01 = c(1, 1, 1), h02 = c(1.5, 0.5, 1), h12 = c(1, 1, 1),
#' pw01 = c(0, 3, 8), pw02 = c(0, 6, 7), pw12 = c(0, 8, 9)
#' )
#' survPFS(transition, 0.4)
survPFS.PWCTransition <- function(transition, t) {
PWCsurvPFS(t,
h01 = transition$hazards$h01, h02 = transition$hazards$h02,
pw01 = transition$intervals$pw01, pw02 = transition$intervals$pw02
)
}
# survOS ----
#' OS Survival Function for Different Transition Models
#'
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#' @param t (`numeric`)\cr time at which the value of the OS survival function is to be computed.
#'
#' @return The value of the survival function for the specified transition and time.
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' survOS(transition, 0.4)
survOS <- function(transition, t) {
UseMethod("survOS")
}
#' @describeIn survOS Survival Function for an exponential transition model.
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' survOS(transition, 0.4)
survOS.ExponentialTransition <- function(transition, t) {
ExpSurvOS(
t = t, h01 = transition$hazards$h01, h02 = transition$hazards$h02,
h12 = transition$hazards$h12
)
}
#' @describeIn survOS Survival Function for a Weibull transition model.
#' @export
#'
#' @examples
#' transition <- weibull_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6, p01 = 2, p02 = 2.5, p12 = 3)
#' survOS(transition, 0.4)
survOS.WeibullTransition <- function(transition, t) {
WeibSurvOS(
t = t, h01 = transition$hazards$h01, h02 = transition$hazards$h02,
h12 = transition$hazards$h12, p01 = transition$weibull_rates$p01,
p02 = transition$weibull_rates$p02, p12 = transition$weibull_rates$p12
)
}
#' @describeIn survOS Survival Function for a piecewise constant transition model.
#' @export
#'
#' @examples
#' transition <- piecewise_exponential(
#' h01 = c(1, 1, 1), h02 = c(1.5, 0.5, 1), h12 = c(1, 1, 1),
#' pw01 = c(0, 3, 8), pw02 = c(0, 6, 7), pw12 = c(0, 8, 9)
#' )
#' survOS(transition, 0.4)
survOS.PWCTransition <- function(transition, t) {
PWCsurvOS(
t = t, h01 = transition$hazards$h01, h02 = transition$hazards$h02,
h12 = transition$hazards$h12, pw01 = transition$intervals$pw01,
pw02 = transition$intervals$pw02, pw12 = transition$intervals$pw12
)
}
# expval ----
#' Helper Function for Computing E(PFS^2)
#'
#' @param x (`numeric`)\cr variable of integration.
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#'
#' @return Numeric results of the integrand used to calculate E(PFS^2).
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' expvalPFSInteg(0.4, transition)
expvalPFSInteg <- function(x, transition) {
x * survPFS(transition, x)
}
#' Helper Function for Computing E(OS^2)
#'
#' @param x (`numeric`)\cr variable of integration.
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#'
#' @return Numeric results of the integrand used to calculate E(OS^2).
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' expvalOSInteg(0.4, transition)
expvalOSInteg <- function(x, transition) {
x * survOS(transition = transition, t = x)
}
# p11 ----
#' Helper Function for `log_p11()`
#'
#' @param x (`numeric`)\cr variable of integration.
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#'
#' @return Hazard rate at the specified time for the transition from progression to death.
#' @keywords internal
p11Integ <- function(x, transition) {
haz(transition = transition, t = x, trans = 3)
}
#' Probability of Remaining in Progression Between Two Time Points for Different Transition Models
#'
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#' @param s (`numeric`)\cr lower time points.
#' @param t (`numeric`)\cr higher time points.
#' @return This returns the natural logarithm of the probability of remaining in progression (state 1)
#' between two time points, conditional on being in state 1 at the lower time point.
#'
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' log_p11(transition, 1, 3)
log_p11 <- function(transition, s, t) {
assert_numeric(s, finite = TRUE, any.missing = FALSE, lower = 0)
assert_numeric(t, finite = TRUE, any.missing = FALSE, lower = 0)
assert_true(identical(length(s), length(t)))
assert_true(all(t > s))
intval <- mapply(function(s, t) {
stats::integrate(p11Integ,
lower = s,
upper = t,
transition
)$value
}, s, t)
-intval
}
# PFSOS ----
#' Helper Function for `survPFSOS()`
#'
#' @param u (`numeric`)\cr variable of integration.
#' @param t (`numeric`)\cr time at which the value of the PFS*OS survival function is to be computed.
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#'
#' @note Not all vectors `u` and `t` work here due to assertions in [log_p11()].
#'
#' @return Numeric result of the integrand used to calculate the PFS*OS survival function.
#' @keywords internal
PFSOSInteg <- function(u, t, transition) {
exp(log_p11(transition, u, t / u) + log(survPFS(transition, u)) + log(haz(transition, u, 1)))
}
#' Survival Function of the Product PFS*OS for Different Transition Models
#'
#' @param t (`numeric`)\cr time at which the value of the PFS*OS survival function is to be computed.
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#'
#' @return This returns the value of PFS*OS survival function at time t.
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' survPFSOS(0.4, transition)
survPFSOS <- function(t, transition) {
sapply(t, function(x) {
intval <- stats::integrate(PFSOSInteg, lower = 0, upper = sqrt(x), x, transition)$value
survPFS(transition, sqrt(x)) + intval
})
}
# correlation ----
#' Correlation of PFS and OS event times for Different Transition Models
#'
#' @param transition (`TransitionParameters`)\cr
#' see [exponential_transition()], [weibull_transition()] or [piecewise_exponential()] for details.
#'
#' @return The correlation of PFS and OS.
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' corTrans(transition)
corTrans <- function(transition) {
# E(PFS) & E(OS).
expvalPFS <- stats::integrate(survPFS,
lower = 0, upper = Inf,
transition = transition
)$value
expvalOS <- stats::integrate(survOS,
lower = 0, upper = Inf,
transition = transition
)$value
# Var(PFS) & Var(OS).
expvalPFS2 <- 2 * stats::integrate(expvalPFSInteg,
lower = 0, upper = Inf,
transition = transition
)$value
expvalOS2 <- 2 * stats::integrate(expvalOSInteg,
lower = 0, upper = Inf,
transition = transition
)$value
varPFS <- expvalPFS2 - expvalPFS^2
varOS <- expvalOS2 - expvalOS^2
# E(PFS*OS).
expvalPFSOS <- stats::integrate(survPFSOS,
lower = 0, upper = Inf,
transition
)$value
# Cor(PFS, OS).
(expvalPFSOS - expvalPFS * expvalOS) / sqrt(varPFS * varOS)
}
#' Correlation of PFS and OS event times for data from the IDM
#'
#' @param data (`data.frame`)\cr in the format produced by [getOneClinicalTrial()].
#' @param transition (`TransitionParameters` object)\cr specifying the assumed distribution of transition hazards.
#' Initial parameters for optimization can be specified here.
#' See [exponential_transition()] or [weibull_transition()] for details.
#' @param bootstrap (`flag`)\cr if `TRUE` computes confidence interval via bootstrap.
#' @param bootstrap_n (`count`)\cr number of bootstrap samples.
#' @param conf_level (`proportion`)\cr confidence level for the confidence interval.
#'
#' @return The correlation of PFS and OS.
#' @export
#'
#' @examples
#' transition <- exponential_transition(h01 = 1.2, h02 = 1.5, h12 = 1.6)
#' data <- getClinicalTrials(
#' nRep = 1, nPat = c(100), seed = 1234, datType = "1rowTransition",
#' transitionByArm = list(transition), dropout = list(rate = 0.5, time = 12),
#' accrual = list(param = "intensity", value = 7)
#' )[[1]]
#' corPFSOS(data, transition = exponential_transition(), bootstrap = FALSE)
#' \dontrun{
#' corPFSOS(data, transition = exponential_transition(), bootstrap = TRUE)
#' }
corPFSOS <- function(data, transition, bootstrap = TRUE, bootstrap_n = 100, conf_level = 0.95) {
assert_data_frame(data)
assert_flag(bootstrap)
assert_count(bootstrap_n)
assert_number(conf_level, lower = 0.01, upper = 0.999)
trans <- estimateParams(data, transition)
res <- list("corPFSOS" = corTrans(trans))
if (bootstrap) {
future::plan(future::multisession, workers = max(1, parallelly::availableCores() - 1))
ids <- lapply(1:bootstrap_n, function(x) sample(seq_len(nrow(data)), nrow(data), replace = TRUE))
corBootstrap <- furrr::future_map_dbl(ids, ~ {
furrr::furrr_options(
globals = list(data = data, transition = transition),
packages = c("simIDM")
)
b_sample <- data[.x, , drop = FALSE]
b_transition <- estimateParams(b_sample, transition)
corTrans(b_transition)
})
lowerQuantile <- (1 - conf_level) / 2
upperQuantile <- lowerQuantile + conf_level
c(stats::quantile(corBootstrap, lowerQuantile),
"corPFSOS" = res,
stats::quantile(corBootstrap, upperQuantile)
)
res$lower <- stats::quantile(corBootstrap, lowerQuantile)
res$upper <- stats::quantile(corBootstrap, upperQuantile)
}
res
}