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 Tumbleweed
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  • 11 votes cast
Mar
22
awarded  Tumbleweed
Mar
15
asked Missing survival probability estimates and times using R using an Anderson-Gill model for recurrent events
Mar
15
comment Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
To follow on from above: we might fit dynamic covariates to help understand the true nature of the dependence of the outcomes on the outcome history, but for understanding the effect of a non-dynamic covariate (say the effect of treatment in a clinical trial) we would not want the non-dynamic covariate effect underestimated, nor would we want to risk introducing bias into the estimate, and so we would fit an AG model without dynamic covariates - strictly not an AG model but a "rate" model as proposed by Lin et al 2000.
Mar
15
comment Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
In terms of your general comments @Theodor on the AG model, I am not saying you are wrong since I am no expert, but I believe time-varying covariates can be used which depend on the outcome history since this ensures conditional independence of all the recurrent events within a subject. I believe this is in the spirit of the original model proposed by Andersen and Gill, 1982. Even though there are reasons why we would not wish to include these in the model (i.e. they "steal strength" from non-dynamic covariates, and in designed experiments they are post-randmoisation) they are "allowed".
Mar
15
comment Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Even though @Theodor your equation $S_i(t|s) = \exp \left( -\int_s^t \lambda_0(u) \exp(\beta'x_i(u)) du \right)$ does not use the product form as mine does in the question (not important) is your equation not similar in principle to equation (1) - i.e. path of the covariate vector through time from $T=0$ to $T=t$ is not taken into account? Does this makes sense? Should I be using something like my equation (2)? Furthermore I see your R code call to "survfit" does not use the "id" statment. Is it true that using the "id" statement gives equation (2) and not using it gives (1) or your equation?
Mar
15
revised Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Updating R code due to errors in previous code
Mar
15
revised Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Clarifying how the survival probabilities should be calculated
Mar
14
comment Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Thanks @Theodor for your answer - I really appreciate this but will need some time to digest your comments. For now I have updated my original question to clarify the recurrent event model I am using. I will get back to you ASAP.
Mar
14
revised Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Explained in more detail the model I am using
Mar
12
comment Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Yes where I wish to calculate $S[t|x(t)]:=P[T>t|x(t)]$ which is the probability of the time of the next event being greater than $t$. Thus as $t$ varies the covariate vector also varies, but nonetheless I we should still end up with a "survival" curve that decreases towards zero as $t$ increases - just like we do when we have covariates that do not vary with time?
Mar
11
comment Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Thanks for your comment @Theodor, I have no terminal event other than censoring, and yes as you describe I have recurrent events at t1, t2, t3, .. for a subject. What I wish to do is to calculate the survival probability at time $T=t$ conditional on the time varying covariates. So say $t2< t<t3$ then the covariates recorded at t2 will be the most up to date covariates before $t$, call these $x(t)$, and I wish to calculate the survival probability at time $T=t|x(t)$
Mar
9
awarded  Promoter
Mar
7
revised Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Clarified the question
Mar
6
asked Using R to calculate survival probabilities with time-varying covariates using an Andersen-Gill model
Jan
12
comment Error in the design of an experiment
It sounds as though what you are proposing to do is some sort of resampling scheme which sometimes people call a bootstrap. Can you give an example of your groups - for example do you want to sample different groups, or different "units" (people perhaps) within the same groups? If within-group observations are expected to be correlated then I think this can be exploited in particular bootstrap methods - like the cluster bootstrap. Perhaps you could give a detailed example?
Jan
11
comment Error in the design of an experiment
Are you talking about sampling from an observed dataset - i.e. you have some sort of test scores for individual people and select N1 groups from the whole dataset and then N2 groups from a subset of the whole dataset (your subpopulation) where N1=N2. You then compute maybe the mean score for each group so you want to compare the distribution of the N1 whole population means to the N2 subpopulation means? Furthermore I imagine your whole dataset can be viewed as a sample from some larger population?
Jan
4
accepted Basic question regarding construction of likelihood function from a Cox PH model
Jan
4
comment Basic question regarding construction of likelihood function from a Cox PH model
Thank-you very much @StatNoodle - I didn't realise that the definition of the likelihood function (that says $L(\theta|X)\equiv cL(\theta|X)$) permits densities to be used instead of probabilities
Jan
4
asked Basic question regarding construction of likelihood function from a Cox PH model
Oct
7
awarded  Yearling