Survmspline_wane {survextrap} | R Documentation |
M-spline survival distribution under treatment effect waning
Description
This defines the CDF, cumulative hazard and hazard of a survival distribution defined by combining the hazards of two different groups (e.g. "treated" and "untreated") each defined by a standard M-spline model. The log hazards of one group and the other are interpolated over a defined period of time. This may be used for models where the treatment effect wanes, over a period of time, between an estimated hazard ratio and zero.
Usage
Hsurvmspline_wane(
x,
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
wane_period,
wane_nt = 10,
pcure1 = 0,
pcure0 = 0,
offsetH = 0,
backhaz = NULL,
bsmooth = TRUE,
log = FALSE
)
psurvmspline_wane(
q,
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
bsmooth = TRUE,
wane_period,
wane_nt = 10,
lower.tail = TRUE,
pcure1 = 0,
pcure0 = 0,
offsetH = 0,
backhaz = NULL,
log.p = FALSE
)
hsurvmspline_wane(
x,
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
bsmooth = TRUE,
wane_period,
wane_nt = 10,
pcure1 = 0,
pcure0 = 0,
offseth = 0,
backhaz = NULL,
log = FALSE
)
dsurvmspline_wane(
x,
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
bsmooth = TRUE,
wane_period,
wane_nt = 10,
pcure1 = 0,
pcure0 = 0,
offseth = 0,
offsetH = 0,
backhaz = NULL,
log = FALSE
)
qsurvmspline_wane(
p,
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
bsmooth = TRUE,
lower.tail = TRUE,
log.p = FALSE,
pcure1 = 0,
pcure0 = 0,
offsetH = 0,
backhaz = NULL,
wane_period,
wane_nt = 10
)
rsurvmspline_wane(
n,
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
bsmooth = TRUE,
pcure1 = 0,
pcure0 = 0,
offsetH = 0,
backhaz = NULL,
wane_period,
wane_nt = 10
)
rmst_survmspline_wane(
t,
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
pcure1 = 0,
pcure0 = 0,
offsetH = 0,
backhaz = NULL,
bsmooth = TRUE,
wane_period,
wane_nt = 10,
disc_rate = 0,
method = "gl",
gl_nodes = 100
)
mean_survmspline_wane(
alpha1,
alpha0,
coefs1,
coefs0,
knots,
degree = 3,
pcure1 = 0,
pcure0 = 0,
backhaz = NULL,
bsmooth = TRUE,
wane_period,
wane_nt = 10,
disc_rate = 0
)
Arguments
x , q , t |
Vector of times. |
alpha1 , coefs1 , pcure1 |
log hazard intercept, spline coefficients and cure probability before the start of the waning period ("treated") |
alpha0 , coefs0 , pcure0 |
log hazard intercept, spline coefficients and cure probability after the end of the waning period ("untreated") |
knots |
Locations of knots on the axis of time, supplied in increasing order. These include the two boundary knots. In vectorised usage of these functions, the knots and degree must be the same for all alternative times and parameter values. |
degree |
Spline polynomial degree. Can only be changed from
the default of 3 if |
wane_period |
vector of two components giving start and stop of waning period |
wane_nt |
time resolution for piecewise constant hazard approximation in the waning period. If this is not specified, defaults to dividing the waning period into 10 pieces. |
offsetH |
Constant to be added to the cumulative hazard. |
backhaz |
A data frame that defines the background hazard as a piecewise-constant function of time.
This should have two columns, named |
bsmooth |
If |
log , log.p |
Return log density or probability. |
lower.tail |
logical; if |
offseth |
Constant to be added to the hazard, e.g. representing a "background" risk of death from causes other than the cause of interest. |
p |
Vector of probabilities. |
n |
Number of random numbers to simulate. |
disc_rate |
Discounting rate used to calculate the discounted mean or restricted mean survival time, using an exponential discounting function. |
method |
Method of numerical integration to obtain the restricted mean survival time from the survival function. The default is
|
gl_nodes |
Number of nodes for the Gauss-Legendre method. |
Details
This distribution is defined as follows.
Between time 0 and
wane_period[1]
, the "treated" hazard is used, as defined by an M-spline with interceptalpha1
.Between
wane_period[1]
andwane_period[2]
, the log hazard is defined by linear interpolation. The waning period is divided into a number of discrete pieces in which the hazard is assumed to be constant, defined by the hazard at the start of the piece. These hazard values are obtained from the spline model, using an intercept parameteralpha
(log scale parameter) defined by linearly interpolating betweenalpha1
andalpha0
over the waning period. The cumulative hazard at any time can then be deduced by adding up contributions on each piece.After
wane_period[2]
, the "untreated" hazard is used, as defined by an M-spline with interceptalpha0
.
See the methods vignette for more details and examples.
This can be used to predict the hazard of a person treated with a treatment whose short-term effect is estimated from shorter-term data, but we wish to extrapolate this model over a longer period where the effect is assumed to diminish.
This may not work if the hazard is zero or infinite at any point in the waning period (thus the log hazard is indeterminate). This might typically happen at time 0.
Value
psurvmspline_wane
gives the CDF, Hsurvmspline_wane
gives the cumulative
hazard, hsurvmspline_wane
gives the hazard, dsurvmspline_wane
gives the PDF,
qsurvmspline_wane
gives the quantiles, and rsurvmspline_wane
generates random
numbers from the distribution.