predict.coxphw: Predictions for a weigthed Cox model
In coxphw: Weighted Estimation in Cox Regression
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
View source: R/predict.coxphw.r
Description
This function obtains the effect estimates (e.g. of a nonlinear or a
time-dependent effect) at specified values of a continuous
covariable for a model fitted by coxphw. It prints the
relative or log relative hazard. Additonally, the linear predictor lp
or the risk score exp(lp) can be obtained.
Usage
1
2
3
4
Arguments
object
an output object of coxphw.
type
the type of predicted value. Choices are:
"lp" for the linear predictors,
"risk" for the risk scores exp(lp)
"shape" for visualizing a nonlinear effect of x,
"slice.x" for slicing an interaction of type fun(x)*z at values of x,
"slice.z" for slicing an interaction of type fun(x)*z at a value of z,
"slice.time" for slicing a time-by-covariate interaction of type z + fun(time):z at values of time
See details.
x
name of the continuous or time variable (use "") for type = "shape",
"slice.time", "slice.x", or "slice.z".
newx
the data values for x for which the effect estimates should be
obtained (e.g., 30:70) for type = "shape",
"slice.time", "slice.x", or "slice.z".
refx
the reference value for variable x for type = "shape" or "slice.z".
The log relative hazard at this value will be 0. (e.g., refx= 50).
z
variable which is in interaction with x (use "") for "slice.time",
"slice.x", or "slice.z".
at
if type = "slice.z" at which level ("slice") of z should the effect estimates of the
x be obtained.
exp
if set to TRUE (default), the log relative hazard is given, otherwise the relative hazard
is requested for type = "shape", "slice.time", "slice.x",
or "slice.z".
se.fit
if set to TRUE, pointwise standard errors are produced for the predictions for
type = "shape", "slice.time", "slice.x", or "slice.z".
pval
if set to TRUE add Wald-test p-values to effect estimates at values of
newx for type = "shape", "slice.time", "slice.x",
or "slice.z". Default is set to FALSE.
digits
number of printed digits. Default is 4.
verbose
if set to TRUE (default), results are printed.
...
further parameters.
Details
This function can be used to depict the estimated nonlinear or time-dependent
effect of an object of class coxphw. It supports simple nonlinear
effects as well as interaction effects of a continuous variable with a binary
covariate or with time (see examples section).
If the effect estimates of a simple nonlinear effect of x without
interaction is requested with type = "shape", then x (the usually
continuous covariate), refx (the reference value of x) and newx
(for these values of x the effect estimates are obtained) must be given.
If the effect estimates of an interaction of z with x are requested
with type = "slice.x", then x (the usually continuous variable),
z (the categorical variable) and newx (for these values of x
the effect estimates are obtained) must be given.
If the effect estimates of an interaction of z with x for one level of z
are requested with type = "slice.z"), then x (the usually continuous variable),
z (the categorical variable), at (at which level of z),
refx (the reference value of x), and newx (for these values of x
the effect estimates are obtained) must be given.
If the effect estimates of an interaction of z with time are requested
with type = "slice.time", then x (the time), z (the
categorical variable) and newx (for these values of x the effect
estimates are obtained) must be given.
Note that if the model formula contains time-by-covariate interactions, then the linear predictor
and the risk score are obtained for the failure or censoring time of each subject.
Value
If type = "shape", "slice.time", "slice.x", or "slice.z"
a list with the following components:
estimates
a matrix with estimates of (log) relative hazard and corresponding confidence limits.
se
pointwise standard errors, only if se.fit = TRUE.
p
p-value, only if pval = TRUE.
alpha
the significance level = 1 - confidence level.
exp
an indicator if log relative hazard or relative hazard was obtained.
x
name of x.
If type = "lp" or "risk", a vector.
Note
In coxphw version 4.0.0 the old plotshape function is replaced with
predict.coxphw and plot.coxphw.predict.
Author(s)
Georg Heinze, Meinhard Ploner, Daniela Dunkler
References
Royston P and Altman D (1994). Regression Using Fractional Polynomials of Continuous
Covariates: Parsimonious Parametric Modelling. Applied Statistics 43, 429-467.
Royston P and Sauerbrei W (2008). Multivariable Model-building. A pragmatic approach to regression
analysis based on fractional polynomials for modelling continuous variables. Wiley, Chichester, UK.
See Also
Examples
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### Example for type = "slice.time"
data("gastric")
gastric$yrs <- gastric$time / 365.25
# check proportional hazards
fitcox <- coxph(Surv(yrs, status) ~ radiation + cluster(id), data = gastric, x = TRUE,
method = "breslow")
fitcox.ph <- cox.zph(fit = fitcox, transform = "identity")
## compare and visualize linear and log-linear time-dependent effects of radiation
fit1 <- coxphw(Surv(yrs, status) ~ yrs * radiation, data = gastric, template = "PH")
summary(fit1)
predict(fit1, type = "slice.time", x = "yrs", z = "radiation", newx = c(0.5, 1, 2),
verbose = TRUE, exp = TRUE, pval = TRUE)
fit2 <- coxphw(Surv(yrs, status) ~ log(yrs) * radiation, data = gastric, template = "PH")
summary(fit2)
predict(fit2, type = "slice.time", x = "yrs", z = "radiation", newx = c(0.5, 1, 2),
verbose = TRUE, exp = TRUE, pval = TRUE)
plotx <- seq(from = quantile(gastric$yrs, probs = 0.05),
to = quantile(gastric$yrs, probs = 0.95), length = 100)
y1 <- predict(fit1, type = "slice.time", x = "yrs", z = "radiation", newx = plotx)
y2 <- predict(fit2, type = "slice.time", x = "yrs", z = "radiation", newx = plotx)
plot(x = fitcox.ph, se = FALSE, xlim = c(0, 3), las = 1, lty = 3)
abline(a = 0, b = 0, lty = 3)
lines(x = plotx, y = y1$estimates[, "coef"], col = "red", lty = 1, lwd = 2)
lines(x = plotx, y = y2$estimates[, "coef"], col = "blue", lty = 2, lwd = 2)
legend(x = 1.7, y = 1.6, title = "time-dependent effect", title.col = "black",
legend = c("LOWESS", "linear", "log-linear"), col = c("black", "red", "blue"),
lty = c(3, 1:2), bty = "n", lwd = 2, text.col = c("black", "red", "blue"))
### Example for type = "shape"
set.seed(512364)
n <- 200
x <- 1:n
true.func <- function(x) 2.5 * log(x) - 2
x <- round(runif(x) * 60 + 10, digits = 0)
time <- round(100000 * rexp(n= n, rate = 1) / exp(true.func(x)), digits = 1)
event <- rep(x = 1, times = n)
my.data <- data.frame(x,time,event)
fit <- coxphw(Surv(time, event) ~ log(x) + x, data = my.data, template = "AHR")
predict(fit, type = "shape", newx = c(30, 50), refx = 40, x = "x", verbose = TRUE)
plotx <- seq(from = quantile(x, probs = 0.05),
to = quantile(x, probs = 0.95), length = 100)
plot(predict(fit, type = "shape", newx = plotx, refx = 40, x = "x"))
### Example for type = "slice.x" and "slice.z"
set.seed(75315)
n <- 200
trt <- rbinom(n = n, size = 1, prob = 0.5)
x <- 1:n
true.func <- function(x) 2.5 * log(x) - 2
x <- round(runif(n = x) * 60 + 10, digits = 0)
time <- 100 * rexp(n = n, rate = 1) / exp(true.func(x) /
4 * trt - (true.func(x) / 4)^2 * (trt==0))
event <- rep(x = 1, times = n)
my.data <- data.frame(x, trt, time, event)
fun<-function(x) x^(-2)
fit <- coxphw(Surv(time, event) ~ x * trt + fun(x) * trt , data = my.data,
template = "AHR", verbose = FALSE)
# plots the interaction of trt with x (the effect of trt dependent on the values of x)
plotx <- quantile(x, probs = 0.05):quantile(x, probs = 0.95)
plot(predict(fit, type = "slice.x", x = "x", z = "trt",
newx = plotx, verbose = FALSE), main = "interaction of trt with x")
# plot the effect of x in subjects with trt = 0
y0 <- predict(fit, type = "slice.z", x = "x", z = "trt", at = 0, newx = plotx,
refx = median(x), verbose = FALSE)
plot(y0, main = "effect of x in subjects with trt = 0")
# plot the effect of x in subjects with trt = 1
y1 <- predict(fit, type = "slice.z", x = "x", z = "trt", at = 1, newx = plotx,
refx = median(x), verbose = FALSE)
plot(y1, main = "effect of x in subjects with trt = 1")
# Example for type = "slice.time"
set.seed(23917)
time <- 100 * rexp(n = n, rate = 1) / exp((true.func(x) / 10)^2 / 2000 * trt + trt)
event <- rep(x = 1, times = n)
my.data <- data.frame(x, trt, time, event)
plot.x <- seq(from = 1, to = 100, by = 1)
fun <- function(t) { PT(t)^-2 * log(PT(t)) }
fun2 <- function(t) { PT(t)^-2 }
fitahr <- coxphw(Surv(time, event) ~ fun(time) * trt + fun2(time) * trt + x,
data = my.data, template = "AHR")
yahr <- predict(fitahr, type = "slice.time", x = "time", z = "trt", newx = plot.x)
fitph <- coxphw(Surv(time, event) ~ fun(time) * trt + fun2(time) * trt + x,
data = my.data, template = "PH")
yph <- predict(fitph, type = "slice.time", x = "time", z = "trt", newx = plot.x)
plot(yahr, addci = FALSE)
lines(yph$estimates$time, yph$estimates$coef, lty = 2)
legend("bottomright", legend = c("AHR", "PH"), bty = "n", lty = 1:2,
inset = 0.05)
Example output
Loading required package: survival
coxphw(formula = Surv(yrs, status) ~ yrs * radiation, data = gastric,
template = "PH")
Model fitted by unweighted estimation (PH template)
coef se(coef) exp(coef) lower 0.95 upper 0.95 z
radiation 1.2699606 0.4334889 3.5607124 1.5224762 8.3276657 2.929627
yrs:radiation -0.9652886 0.3409321 0.3808733 0.1952444 0.7429892 -2.831322
p
radiation 0.003393692
yrs:radiation 0.004635608
Wald Chi-square = 9.047941 on 2 df, p = 0.01084588
Covariance-Matrix:
radiation yrs:radiation
radiation 0.1879126 -0.1241715
yrs:radiation -0.1241715 0.1162347
Generalized concordance probability: Estimates may be biased!
concordance prob. lower 0.95 upper 0.95
radiation 0.7807 0.6036 0.8928
yrs:radiation 0.2758 0.1634 0.4263
yrs HR HR lower 0.95 HR upper 0.95 p
1 0.5 2.1975 1.2096 3.9924 0.0098
2 1.0 1.3562 0.8536 2.1547 0.1971
3 2.0 0.5165 0.2381 1.1207 0.0946
coxphw(formula = Surv(yrs, status) ~ log(yrs) * radiation, data = gastric,
template = "PH")
Model fitted by unweighted estimation (PH template)
coef se(coef) exp(coef) lower 0.95 upper 0.95
radiation 0.03766302 0.2367992 1.0383813 0.6528193 1.651660
log(yrs):radiation -0.66924556 0.4821178 0.5120948 0.1990540 1.317437
z p
radiation 0.1590504 0.8736291
log(yrs):radiation -1.3881370 0.1650953
Wald Chi-square = 1.97312 on 2 df, p = 0.372857
Covariance-Matrix:
radiation log(yrs):radiation
radiation 0.056073853 0.004581723
log(yrs):radiation 0.004581723 0.232437577
Generalized concordance probability: Estimates may be biased!
concordance prob. lower 0.95 upper 0.95
radiation 0.5094 0.395 0.6229
log(yrs):radiation 0.3387 0.166 0.5685
yrs HR HR lower 0.95 HR upper 0.95 p
1 0.5 1.6513 0.7514 3.6290 0.2119
2 1.0 1.0384 0.6528 1.6517 0.8736
3 2.0 0.6530 0.2882 1.4793 0.3070
x coef coef lower 0.95 coef upper 0.95
1 30 -0.7201 -0.8582 -0.5821
2 50 0.5655 0.4235 0.7075
coxphw documentation built on July 8, 2020, 6:52 p.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/predict.coxphw.r
Description
This function obtains the effect estimates (e.g. of a nonlinear or a
time-dependent effect) at specified values of a continuous
covariable for a model fitted by coxphw. It prints the
relative or log relative hazard. Additonally, the linear predictor lp
or the risk score exp(lp) can be obtained.
Usage
1 2 3 4 |
Arguments
object |
an output object of |
type |
the type of predicted value. Choices are:
|
x |
name of the continuous or time variable (use "") for |
newx |
the data values for |
refx |
the reference value for variable |
z |
variable which is in interaction with |
at |
if |
exp |
if set to TRUE (default), the log relative hazard is given, otherwise the relative hazard
is requested for |
se.fit |
if set to TRUE, pointwise standard errors are produced for the predictions for
|
pval |
if set to TRUE add Wald-test p-values to effect estimates at values of
|
digits |
number of printed digits. Default is 4. |
verbose |
if set to TRUE (default), results are printed. |
... |
further parameters. |
Details
This function can be used to depict the estimated nonlinear or time-dependent
effect of an object of class coxphw. It supports simple nonlinear
effects as well as interaction effects of a continuous variable with a binary
covariate or with time (see examples section).
If the effect estimates of a simple nonlinear effect of x without
interaction is requested with type = "shape", then x (the usually
continuous covariate), refx (the reference value of x) and newx
(for these values of x the effect estimates are obtained) must be given.
If the effect estimates of an interaction of z with x are requested
with type = "slice.x", then x (the usually continuous variable),
z (the categorical variable) and newx (for these values of x
the effect estimates are obtained) must be given.
If the effect estimates of an interaction of z with x for one level of z
are requested with type = "slice.z"), then x (the usually continuous variable),
z (the categorical variable), at (at which level of z),
refx (the reference value of x), and newx (for these values of x
the effect estimates are obtained) must be given.
If the effect estimates of an interaction of z with time are requested
with type = "slice.time", then x (the time), z (the
categorical variable) and newx (for these values of x the effect
estimates are obtained) must be given.
Note that if the model formula contains time-by-covariate interactions, then the linear predictor and the risk score are obtained for the failure or censoring time of each subject.
Value
If type = "shape", "slice.time", "slice.x", or "slice.z"
a list with the following components:
estimates |
a matrix with estimates of (log) relative hazard and corresponding confidence limits. |
se |
pointwise standard errors, only if |
p |
p-value, only if |
alpha |
the significance level = 1 - confidence level. |
exp |
an indicator if log relative hazard or relative hazard was obtained. |
x |
name of |
If type = "lp" or "risk", a vector.
Note
In coxphw version 4.0.0 the old plotshape function is replaced with
predict.coxphw and plot.coxphw.predict.
Author(s)
Georg Heinze, Meinhard Ploner, Daniela Dunkler
References
Royston P and Altman D (1994). Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling. Applied Statistics 43, 429-467.
Royston P and Sauerbrei W (2008). Multivariable Model-building. A pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables. Wiley, Chichester, UK.
See Also
Examples
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 | ### Example for type = "slice.time"
data("gastric")
gastric$yrs <- gastric$time / 365.25
# check proportional hazards
fitcox <- coxph(Surv(yrs, status) ~ radiation + cluster(id), data = gastric, x = TRUE,
method = "breslow")
fitcox.ph <- cox.zph(fit = fitcox, transform = "identity")
## compare and visualize linear and log-linear time-dependent effects of radiation
fit1 <- coxphw(Surv(yrs, status) ~ yrs * radiation, data = gastric, template = "PH")
summary(fit1)
predict(fit1, type = "slice.time", x = "yrs", z = "radiation", newx = c(0.5, 1, 2),
verbose = TRUE, exp = TRUE, pval = TRUE)
fit2 <- coxphw(Surv(yrs, status) ~ log(yrs) * radiation, data = gastric, template = "PH")
summary(fit2)
predict(fit2, type = "slice.time", x = "yrs", z = "radiation", newx = c(0.5, 1, 2),
verbose = TRUE, exp = TRUE, pval = TRUE)
plotx <- seq(from = quantile(gastric$yrs, probs = 0.05),
to = quantile(gastric$yrs, probs = 0.95), length = 100)
y1 <- predict(fit1, type = "slice.time", x = "yrs", z = "radiation", newx = plotx)
y2 <- predict(fit2, type = "slice.time", x = "yrs", z = "radiation", newx = plotx)
plot(x = fitcox.ph, se = FALSE, xlim = c(0, 3), las = 1, lty = 3)
abline(a = 0, b = 0, lty = 3)
lines(x = plotx, y = y1$estimates[, "coef"], col = "red", lty = 1, lwd = 2)
lines(x = plotx, y = y2$estimates[, "coef"], col = "blue", lty = 2, lwd = 2)
legend(x = 1.7, y = 1.6, title = "time-dependent effect", title.col = "black",
legend = c("LOWESS", "linear", "log-linear"), col = c("black", "red", "blue"),
lty = c(3, 1:2), bty = "n", lwd = 2, text.col = c("black", "red", "blue"))
### Example for type = "shape"
set.seed(512364)
n <- 200
x <- 1:n
true.func <- function(x) 2.5 * log(x) - 2
x <- round(runif(x) * 60 + 10, digits = 0)
time <- round(100000 * rexp(n= n, rate = 1) / exp(true.func(x)), digits = 1)
event <- rep(x = 1, times = n)
my.data <- data.frame(x,time,event)
fit <- coxphw(Surv(time, event) ~ log(x) + x, data = my.data, template = "AHR")
predict(fit, type = "shape", newx = c(30, 50), refx = 40, x = "x", verbose = TRUE)
plotx <- seq(from = quantile(x, probs = 0.05),
to = quantile(x, probs = 0.95), length = 100)
plot(predict(fit, type = "shape", newx = plotx, refx = 40, x = "x"))
### Example for type = "slice.x" and "slice.z"
set.seed(75315)
n <- 200
trt <- rbinom(n = n, size = 1, prob = 0.5)
x <- 1:n
true.func <- function(x) 2.5 * log(x) - 2
x <- round(runif(n = x) * 60 + 10, digits = 0)
time <- 100 * rexp(n = n, rate = 1) / exp(true.func(x) /
4 * trt - (true.func(x) / 4)^2 * (trt==0))
event <- rep(x = 1, times = n)
my.data <- data.frame(x, trt, time, event)
fun<-function(x) x^(-2)
fit <- coxphw(Surv(time, event) ~ x * trt + fun(x) * trt , data = my.data,
template = "AHR", verbose = FALSE)
# plots the interaction of trt with x (the effect of trt dependent on the values of x)
plotx <- quantile(x, probs = 0.05):quantile(x, probs = 0.95)
plot(predict(fit, type = "slice.x", x = "x", z = "trt",
newx = plotx, verbose = FALSE), main = "interaction of trt with x")
# plot the effect of x in subjects with trt = 0
y0 <- predict(fit, type = "slice.z", x = "x", z = "trt", at = 0, newx = plotx,
refx = median(x), verbose = FALSE)
plot(y0, main = "effect of x in subjects with trt = 0")
# plot the effect of x in subjects with trt = 1
y1 <- predict(fit, type = "slice.z", x = "x", z = "trt", at = 1, newx = plotx,
refx = median(x), verbose = FALSE)
plot(y1, main = "effect of x in subjects with trt = 1")
# Example for type = "slice.time"
set.seed(23917)
time <- 100 * rexp(n = n, rate = 1) / exp((true.func(x) / 10)^2 / 2000 * trt + trt)
event <- rep(x = 1, times = n)
my.data <- data.frame(x, trt, time, event)
plot.x <- seq(from = 1, to = 100, by = 1)
fun <- function(t) { PT(t)^-2 * log(PT(t)) }
fun2 <- function(t) { PT(t)^-2 }
fitahr <- coxphw(Surv(time, event) ~ fun(time) * trt + fun2(time) * trt + x,
data = my.data, template = "AHR")
yahr <- predict(fitahr, type = "slice.time", x = "time", z = "trt", newx = plot.x)
fitph <- coxphw(Surv(time, event) ~ fun(time) * trt + fun2(time) * trt + x,
data = my.data, template = "PH")
yph <- predict(fitph, type = "slice.time", x = "time", z = "trt", newx = plot.x)
plot(yahr, addci = FALSE)
lines(yph$estimates$time, yph$estimates$coef, lty = 2)
legend("bottomright", legend = c("AHR", "PH"), bty = "n", lty = 1:2,
inset = 0.05)
|
Example output
Loading required package: survival
coxphw(formula = Surv(yrs, status) ~ yrs * radiation, data = gastric,
template = "PH")
Model fitted by unweighted estimation (PH template)
coef se(coef) exp(coef) lower 0.95 upper 0.95 z
radiation 1.2699606 0.4334889 3.5607124 1.5224762 8.3276657 2.929627
yrs:radiation -0.9652886 0.3409321 0.3808733 0.1952444 0.7429892 -2.831322
p
radiation 0.003393692
yrs:radiation 0.004635608
Wald Chi-square = 9.047941 on 2 df, p = 0.01084588
Covariance-Matrix:
radiation yrs:radiation
radiation 0.1879126 -0.1241715
yrs:radiation -0.1241715 0.1162347
Generalized concordance probability: Estimates may be biased!
concordance prob. lower 0.95 upper 0.95
radiation 0.7807 0.6036 0.8928
yrs:radiation 0.2758 0.1634 0.4263
yrs HR HR lower 0.95 HR upper 0.95 p
1 0.5 2.1975 1.2096 3.9924 0.0098
2 1.0 1.3562 0.8536 2.1547 0.1971
3 2.0 0.5165 0.2381 1.1207 0.0946
coxphw(formula = Surv(yrs, status) ~ log(yrs) * radiation, data = gastric,
template = "PH")
Model fitted by unweighted estimation (PH template)
coef se(coef) exp(coef) lower 0.95 upper 0.95
radiation 0.03766302 0.2367992 1.0383813 0.6528193 1.651660
log(yrs):radiation -0.66924556 0.4821178 0.5120948 0.1990540 1.317437
z p
radiation 0.1590504 0.8736291
log(yrs):radiation -1.3881370 0.1650953
Wald Chi-square = 1.97312 on 2 df, p = 0.372857
Covariance-Matrix:
radiation log(yrs):radiation
radiation 0.056073853 0.004581723
log(yrs):radiation 0.004581723 0.232437577
Generalized concordance probability: Estimates may be biased!
concordance prob. lower 0.95 upper 0.95
radiation 0.5094 0.395 0.6229
log(yrs):radiation 0.3387 0.166 0.5685
yrs HR HR lower 0.95 HR upper 0.95 p
1 0.5 1.6513 0.7514 3.6290 0.2119
2 1.0 1.0384 0.6528 1.6517 0.8736
3 2.0 0.6530 0.2882 1.4793 0.3070
x coef coef lower 0.95 coef upper 0.95
1 30 -0.7201 -0.8582 -0.5821
2 50 0.5655 0.4235 0.7075
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