Some doubts about survival analysis I'm struggling to perform a correct and unbiased survival analysis, but I  have some doubts. 
Data
I observe a population of posts on a blog within a temporal window $[T_{0}, T_{final}]$. Each post is characterized by:


*

*a $start$ date: the date in which it has been published on the blog;

*a $stop$ date: the date in which the last comment on the post has been left;

*a $event$ date: the date in which the post has been shared on Twitter for the first time.


Basically, the lifetime of each post is defined as the difference between $stop$ and $start$.
Analysis and Related Doubts
My analysis (at least in this first part) aims at quantifying the effect on the lifetime of the post being shared on Twitter. Suppose I have data organized as follows:
id  start event stop shared
 1     0   105  192      1 
 2     0   162  245      1 
 3     0     2   88      1 

that is, in the case of $id = 1$, the post is originally published in $t = 0$, it is shared on Twitter after $105$ weeks, and it stopped being commented after $192$ weeks. Note that I brought back all $start$ time to zero.
Then, I re-organized data as follows:
id  start stop shared event
 1     0  106      0     1
 1   106  194      1     1
 2     0  163      0     1
 2   163  247      1     1
 3     0    3      0     1
 3     3   90      1     1

that is, now for each id I have two rows: the first ($shared = 0$) specifies the $start$ and $stop$ times before the post is shared on Twitter; whereas the second ($shared = 1$) specifies the $start$ and $stop$ times after the post is shared on Twitter.
At this point, I would like to perform a Kaplan-Meier estimate of the survival functions before and after the post is shared on Twitter.
s = with(surv.df, Surv(start, stop, event))
KM = survfit(s ~ shared, data = surv.df)

and then apply a Cox hazard regression to model to quantify the effect on the lifetime of the post being shared on Twitter
sCox = coxph(s ~ as.factor(shared), data=surv.df)
summary(sCox)

However, I'm not convinced about such a procedure. 
Questions


*

*Do you see any sources of bias in the analysis I have just presented?

*Is it correct the way I organized data to perform my analysis?

*Am I actually observing the effect of the post being shared on Twitter?

 A: I think I've found a solution to my problem. Instead of using traditional survival analysis and Cox regression models, I used multi-state models. Here two good references:


*

*Multi-state models for the analysis of time-to-event data

*Multi-state models: a flexible approach for modelling complex event histories in epidemiology
Multi-state models allow to model complex event histories, by handling censoring and left truncation, and avoiding two common kind of bias: length bias and immortal bias.
Practically, I have three states, $S = {1,2,3}$:


*

*$S = 1 \to$ initial state: posts are published on the blog;

*$S = 2 \to$ shared state: posts are shared on Twitter;

*$S = 3 \to$ absorbing state: posts did not receive comments in the last month;


Note that $S = 1$ is the initial state, i.e. each post starts in such a state, whereas $S = 3$ is an absorbing state, so that once the post arrives there, it remains there.
A transition matrix specifies the admissible transitions from one state to another:
$$T =
 \begin{pmatrix}
  p_{1,1}(t) & p_{1,2}(t) & p_{1,3}(t) \\
  p_{2,1}(t) & p_{2,2}(t) & p_{2,3}(t) \\
  p_{3,1}(t) & p_{3,2}(t) & p_{3,3}(t)
 \end{pmatrix}$$  
In my case, I specified the following transition matrix:
$$T =
 \begin{pmatrix}
  p_{1,1}(t) & p_{1,2}(t) & p_{1,3}(t) \\
  0 & p_{2,2}(t) & p_{2,3}(t) \\
  0 & 0 & p_{3,3}(t)
 \end{pmatrix}$$ 
Note that all the probabilities are time-dependent. Such a transition matrix can be estimated by using R and the package msSurv. Once you have estimated the transition matrix, you can analyze the state entry/exit distribution in each state, the distributions of time-varying probabilities for transitions from one state to another, and the probability to be in a given state at a certain instant $t$.
In particular, by comparing the time-varying transition probabilities $p_{1,3}(t)$ and $p_{2,3}(t)$, I can understand if there is a difference between survival times of posts being or not being shared on Twitter. 
