[R] Joint modelling of survival data

[Terry Therneau]

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Assume that we collect below data : -
subjects  = 20 males + 20 females, every single individual is
independence,
and difference
events = 1, 2, 3... n
covariates = 4 blood types A, B, AB, O

http://r.789695.n4.nabble.com/file/n4245397/CodeCogsEqn.jpeg 

?m = hazards rates for male
?n = hazards rates for female
Wm = Wn x ?, frailty for males, where ? is the edge ratio of male
compare to
female
Wn = frailty for females
X = covariates, blood types effects
? = coefficients of blood types

I would like to apply frailty model to get below results:-
1) 1 edge ratio between male and female ?
2) 4 coefficient values of blood types ?

Under this situation, shall I use which package (coxme or frailtypack)?
 will coxme function able to cope with it?

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 Could you clarify your question?  First, the above is rather hard to
read with all the misisng symbols.

 Now coxme fits the model  
   \lambda_i(t) = \lambda_0(t) exp(X beta + Z b)
    b ~ N(0, A)
    beta = fixed effects coef X = covariate matrix for fixed effects
    b= random effects coefs, Z= covariate matrix for random effects

(Bear with the latex-like notation, at least it's simple text for a
mailer).
   
 There are several possible models of interest for your data:
  No random effect: coxph(Surv(time, status) ~ bloodtype + sex)
  Random sex effect: coxme(Surv(time, status) ~ bloodtype + (1|sex))  

 But does your data set have multiple events per subject?  (I'm not sure
what you mean by "difference events".)  If it does then neither of the
above is good, since they do not account for correlation within subject.
The simple Cox model is easy to correct by adding "+ cluster(id)" to the
model where id is a variable that identifies individual subjects.  The
random effect model needs to have a per-subject random effect.

  That leads to two more models
     fixed sex effect + random subject effect
     random subject effect, but with different variance for the males &
females.

 What are you trying to do?

Terry Therneau