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11

Including cluster(ID) does not change the point estimates of the parameters. It does change the way that the standard errors are computed however. More details can be found in Therneau & Grambsch's book Extending the Cox Model, chapter 8.2. Note that in their example, they use method = "breslow" as correction for ties, but also with the default (method ...


11

This subject is covered by a number of papers including: Modelling clustered survival data from multicentre clinical trials The shared frailty model and the power for heterogeneity tests in multicenter trials The Frailty Model, Chapter 3 Proportional hazards models with frailties and random effects. Here is a very brief (and non-exhaustive) summary of the ...


6

coxph() actually implements a penalised log-likelihood approach which turns out to return the same estimates as the EM algorithm in the case of gamma frailties when method="em"; see Therneau and Grambsch (2000, Section 9.6). (method actually refers to the method used to select a solution for theta, the heterogeneity parameter, not to the estimation procedure)...


5

This is an interesting question. In a survival setting, where we are typically concerned with studying the time to "failure", there are two types of frailties: 1. Individual frailties and 2. Shared frailties. ("Failure" could be death, transplant failure, etc.) Individual frailties are specific to each subject in the target population being studied, ...


3

If your intervals that you divide things up with do not overlap (for example, all response variable end up in disjoint bins, such as [0,2.5), [3.5,4.5), [4.5,5.5), etc), I would actually suggest you disregard the interval censored aspect of your data, and merely treat it as ordinal/discrete. And my bias is toward using interval censored methods! The reason ...


3

The answer seems to be that the resampling process needs to take account of the structure of the data. There is a nice explanation here (along with some R code to implement this). http://biostat.mc.vanderbilt.edu/wiki/Main/HowToBootstrapCorrelatedData Thanks to the pointer from the UCLA Statistical Consulting Group. I have written a speedier (but less ...


2

The problem here is the same as would be obtained trying to predict outcomes from a linear mixed effects model. Since the survival curve is non-collapsible, each litter in your example has a litter-specific survival curve according to the model you fit. A frailty as you may know is the same as a random intercept indicating common levels of confounding and ...


2

Some background Using standard notations, the Cox model is defined as $$h(t) = h_0(t) \exp(\mathbf{x}^\prime \mathbf{\beta})$$ and the associated likelihood is \begin{align*} L(\mathbf{\beta}, h_0; \textrm{data}) & = \prod_{j=1}^n h_j(y_j)^{\delta_j} S_j(y_j) \\ & = \prod_{j=1}^n \left(h_0(t) \exp(\mathbf{x}^\prime_j \mathbf{\beta})\right)^{\...


2

When events recur they are called recurrent events. There is a theory that has been developed for recurrent events and even two books. One by Richard Cook and Jerald Lawless and the other by Wayne Nelson.


2

Imagine that you conducted a study about children educational achievements. You took a random sample of schools from some area and from each school one class was included in the study. You conducted analysis and now want to use bootstrap to obtain confidence intervals for your estimates. How to do it? First, notice that your data is hierarchical, it has ...


2

You may find useful a relatively new type of model, which is a combination of mixed and relative risk models: "Joint Models for Longitudinal and Survival Data". Here are some links: link1, link2, link3, link4, link5, link6.


2

The short answer is that yes, you can do that. However, frailty models (i.e. survival models with random effects) are quite speculative when dealing only with survival data (non-shared). The short explanation would go like this: if you do not have any covariates in the model, then the baseline hazard and the frailty would be confounded, and then the frailty ...


1

Here's an answer from a survival package vignette I found helpful - it's linked in the first answer to the first question you linked to: Best packages for Cox models with time varying covariates They're referring to the long form data setup, or data with repeated entries for subjects. One common question with this data setup is whether we need to worry ...


1

It depends on what you want to model. Survival analysis tools would be useful if: You know the inter-event times (it is not clear if you have just the number of visits / 14 days or if you have the times of these visits). In other words, the structure of the data should be put into a (Tstart, Tstop, status) for Survival tools. If the data is in the format I ...


1

This seems like a recurrent events situation. Some possible modelling approaches include negative binomial regression. In that case the between visit waiting times follow an exponential distribution for each patient (and a gamma distribution across patients).


1

I am not sure understanding your question, but I suggest you looking at the statistical model details of parfm in the companion paper Munda M, Rotolo F, Legrand C. (2012) parfm: Parametric Frailty Models in R. J Stat Soft, 51(12). http://www.jstatsoft.org/v51/i11 Hope this helps


1

In SAS, you can use "proc phreg" and there is a "random" statement where you can assign your random effect. for example: if variable (dish) is your cluster then proc phreg data=survGeno2; class dish geno; model Time*Status(0)=geno; random dish; <- to assign the cluster effect here hazardratio 'Frailty Model Analysis' geno; run; reference ...


1

Yes, these data are correlated survival data. You could use a Cox model on this data and a simple variance adjustment to deal with correlation, i.e., add "+ cluster(id)" to the coxph model, where "id" is a variable that identifies individual mothers.


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