estMargProbCompRisks {discSurv}

Estimated Marginal Probabilities for Competing Risks

Description

Estimates the marginal probability P(T = t,R = r|x) based on estimated discrete hazards of a competing risks model. The discrete hazards may or may not depend on covariates. The covariates have to be equal across all estimated discrete hazards. Therefore the given discrete hazards should only vary over time.

Usage

estMargProbCompRisks(hazards)

Arguments

hazards

Estimated discrete hazards ("numeric matrix"). Discrete hazards of each time interval are stored in the rows and the number of columns equal to the number of events.

Details

The argument hazards must be given for all intervals [a_0, a_1), [a_1, a_2), ..., [a_q-1, a_q), [a_q, Inf).

Value

Estimated marginal probabilities ("numeric matrix")

Note

It is assumed that all time points up to the last interval [a_q, Inf) are available. If not already present, these can be added manually. In competing risk settings the marginal probabilities of the last theoretical interval depend on the assumptions on the discrete hazards in the last theoretical interval. However the estimation of all previous discrete intervals is not affected by those assumptions.

Author(s)

Moritz Berger [e-mail]
https://www.imbie.uni-bonn.de/personen/dr-moritz-berger/

References

Tutz G, Schmid M (2016). Modeling discrete time-to-event data. Springer Series in Statistics.

See Also

estMargProb

Examples

# Example unemployment data
library(Ecdat)
data(UnempDur)

# Select subsample
subUnempDur <- UnempDur [1:100, ]

# Convert to long format
UnempLong <- dataLongCompRisks(dataShort = subUnempDur, timeColumn = "spell", 
eventColumns = c("censor1", "censor4"))
head(UnempLong)

# Estimate continuation ratio model with logit link
vglmFit <- VGAM::vglm(formula = cbind(e0, e1, e2) ~ timeInt + age + logwage, data = UnempLong,
family = VGAM::multinomial(refLevel = "e0"))

# Estimate discrete survival function given age, logwage of first person
hazards <- VGAM::predictvglm(vglmFit, newdata = subset(UnempLong, obj == 1), type = "response")[,-1]

# Estimate marginal probabilities given age, logwage of first person
# Example 1
# Assumption: Discrete hazards in last theoretical interval are equal for both event types
MarginalProbCondX <- estMargProbCompRisks(rbind(hazards, 0.5))
MarginalProbCondX
all.equal(sum(MarginalProbCondX), 1) # TRUE: Marginal probabilities must sum to 1!

# Example 2
# Assumption: Discrete hazards in last theoretical interval are event1=, event2=
MarginalProbCondX2 <- estMargProbCompRisks(rbind(hazards, c(0.75, 0.25)))
MarginalProbCondX2
all.equal(sum(MarginalProbCondX2), 1) # TRUE: Marginal probabilities must sum to 1!

# Compare marginal probabilities given X
all.equal(MarginalProbCondX[1:5, ], MarginalProbCondX2[1:5, ])
all.equal(MarginalProbCondX[6, ], MarginalProbCondX2[6, ])