Unlike wikipedia, the linear predictor (LP) in coxph is made dependent from the baseline hazard function $\lambda$. For example, if a model has two predictors x1, x2 stratified by sex, the linear predictor would be like:
$$LP = log ( \lambda _{sex}) + \beta _{1}x _{1}+\beta _{2}x _{2}$$
Where the $log(\lambda _{sex})$ can be obtained by predict() with x1=x2=0.
We could calculate the LP without strata information (sex) by hand using the $\beta _{1} \, \beta _{2}$ provided by coef(fit) and a customised $\lambda _{unkown \, sex}$.
Below is a simulation comparing the results from predict() and by hand coef(fit).
## Toy data
df <- list(time=c(4,3,1,1,2,2,3),
status=c(1,1,1,0,1,1,0),
x1=c(0,2,1,1,1,0,0),
x2 = 1x2=1:7,
sex=c(0,0,0,0,1,1,1))
## Fit a stratified model
fit <- coxph(Surv(time, status) ~ x1 + x2 + strata(sex), df)
coef(fit)
# x1 x2
# 0.79451881 -0.01917633
## Baseline linear predictor
lambda_sex1 <- predict(fit, newdata=list(x1=0, x2=0, sex=0))
# -0.746578
lambda_sex2 <- predict(fit, newdata=list(x1=0, x2=0, sex=1))
# -0.1497816
## by predict function
predict(fit, newdata=list(x1=1, x2=2, sex=0))
# 0.009588167
predict(fit, newdata=list(x1=1, x2=2, sex=1))
# 0.6063845
## by hand
lambda_sex1 + coef(fit)[1]*1 + coef(fit)[2]*2
# 0.009588167
lambda_sex2 + coef(fit)[1]*1 + coef(fit)[2]*2
# 0.6063845
Finally, to calculate "a" linear predictor for an unknown sex:
# prevented by predict function
predict(fit, newdata=list(x1=1, x2=2, sex=2))
#Error in model.frame.default(data = list(x1 = 1, x2 = 2, sex = 2), formula = ~x1 + :
# factor strata(sex) has new level sex=2
# by hand, assuming lambda for sex 2 is 0
0 + coef(fit)[1]*1 + coef(fit)[2]*2
# 0.7561661