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I'm using a coxph-model (in R) to model survival time on prepayment loans. My data consists of monthly panel (longnitude) data o.v.t. to adress time-varying covariates, f.e.: loan ID 1 last for 12 months, so I got 12 rows, loan ID 2 lasts for 3,5 years, so I have 30 rows etc.

Having already a suitable standard model cox model, I'm wondering if clustered standard issues could be an serious "threat".

In usual regression, clustered standard errors are the usual way to go. Specifically, in my case, due to the panel structure the i.i.d assumption does not hold. As far as I understood, the standard errors which is provided by the coxph() regression in R only delivers homoscedactic standard errors.

Did I get this right so far? If yes, is there any possibility to get heteroscedastic ("Sandwich") Standard Errors. I read that the cluster() option might be an option, but I'm not sure if actually adresses heteroscedacity.

Note that I'm not talking about unobserved heteroscedacity, I'm concerned with the heteroscedacity of the standard errors.

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  • $\begingroup$ I am not sure about clustered standard errors, but in the terminology for clustering in survival models that I am familiar with, multilevel 'clusters' are called 'frailties'. So, for example, if you have conducted a medical randomized placebo controlled trial in 50 different hospital and want to do a survival analysis, you could add hospital as a 'frailty' to your survival model, in order to incorporate a random effect. To conclude, if this is what you were looking for, you might want to look into frailties for survival models (coxph in R has this option) $\endgroup$ – IWS Nov 15 '17 at 13:13
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Basically, this is the answer to my question. Therneau (2017) writes in his paper on Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Model

One common question with this data setup is whether we need to worry about correlated data, since a given subject has multiple observations. The answer is no, we do not. The reason is that this representation is simply a programming trick. The likelihood equations at any time point use only one copy of any subject, the program picks out the correct row of data at each time. There two exceptions to this rule:

  • When subjects have multiple events, then the rows for the events are correlated within subject and a cluster variance is needed.
  • Whena subject appears in overlapping intervals. This however is almostalways a data error, since it corresponds to two copies of the subjectbeing present in the same strata at the same time, e.g., she could meet herself at a party.

So this makes finally sense, and hence the "cluster()" or "robust" option is useless in my context, but honstely also quite missleading since standard errors are per construction robust.

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