Survival Data • simstudy

Time-to-event data, including both survival and censoring times, are created using functions defSurv and genSurv. The survival data definitions require a variable name as well as a specification of a scale value, which determines the mean survival time at a baseline level of covariates (i.e. all covariates set to 0). The Weibull distribution is used to generate these survival times. In addition, covariates (which have been defined previously) that influence survival time can be included in the formula field. Positive coefficients are associated with longer survival times (and lower hazard rates). Finally, the shape of the distribution can be specified. A shape value of 1 reflects the exponential distribution.

# Baseline data definitions

def <- defData(varname = "x1", formula = 0.5, dist = "binary")
def <- defData(def, varname = "x2", formula = 0.5, dist = "binary")
def <- defData(def, varname = "grp", formula = 0.5, dist = "binary")

# Survival data definitions

set.seed(282716)

sdef <- defSurv(varname = "survTime", formula = "1.5*x1", scale = "grp*50 + (1-grp)*25", 
    shape = "grp*1 + (1-grp)*1.5")
sdef <- defSurv(sdef, varname = "censorTime", scale = 80, shape = 1)

sdef

##       varname formula               scale               shape
## 1:   survTime  1.5*x1 grp*50 + (1-grp)*25 grp*1 + (1-grp)*1.5
## 2: censorTime       0                  80                   1

The data are generated with calls to genData and genSurv:

# Baseline data definitions

dtSurv <- genData(300, def)
dtSurv <- genSurv(dtSurv, sdef)

head(dtSurv)

##    id x1 x2 grp survTime censorTime
## 1:  1  0  0   1    9.206     95.976
## 2:  2  0  1   0   25.525     46.754
## 3:  3  0  1   0  604.203     31.620
## 4:  4  1  1   0   23.631    338.427
## 5:  5  1  0   0  108.276    287.553
## 6:  6  0  1   1    8.122     53.406

# A comparison of survival by group and x1

dtSurv[, round(mean(survTime), 1), keyby = .(grp, x1)]

##    grp x1    V1
## 1:   0  0 156.2
## 2:   0  1  19.0
## 3:   1  0  43.3
## 4:   1  1  14.1

Observed survival times and censoring indicators can be generated by defining new fields:

cdef <- defDataAdd(varname = "obsTime", formula = "pmin(survTime, censorTime)", dist = "nonrandom")
cdef <- defDataAdd(cdef, varname = "status", formula = "I(survTime <= censorTime)", 
    dist = "nonrandom")

dtSurv <- addColumns(cdef, dtSurv)

head(dtSurv)

##    id x1 x2 grp survTime censorTime obsTime status
## 1:  1  0  0   1    9.206     95.976   9.206   TRUE
## 2:  2  0  1   0   25.525     46.754  25.525   TRUE
## 3:  3  0  1   0  604.203     31.620  31.620  FALSE
## 4:  4  1  1   0   23.631    338.427  23.631   TRUE
## 5:  5  1  0   0  108.276    287.553 108.276   TRUE
## 6:  6  0  1   1    8.122     53.406   8.122   TRUE

# estimate proportion of censoring by x1 and group

dtSurv[, round(1 - mean(status), 2), keyby = .(grp, x1)]

##    grp x1   V1
## 1:   0  0 0.51
## 2:   0  1 0.13
## 3:   1  0 0.37
## 4:   1  1 0.17

Here is a Kaplan-Meier plot of the data by the four groups: