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I'm analyzing 2 groups where all of the subjects in one group are still alive, i.e. one group is entirely right-censored. The other group is a mix of censored and uncensored. Is a Cox proportional hazards model valid to use here? I suspect it fails the proportional hazards assumption, plus Matlab's coxphfit function fails in this case, saying it can't calculate the baseline cumulative hazard. Is there a better alternative? Any insight would be appreciated.

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It is not so much that proportional hazards fails in this case, but rather, proportional hazards becomes an untestable assumption if all the data is censored. As a general principle, you estimate the hazard function by looking at failures over time; if there are no failures in the observation period then it is not possible to make robust inferences about the "shape" of the hazard function with respect to the explanatory variables, and thus it is not possible to robustly diagnose whether the proportional hazards assumption holds.

In relation to the secondary matter you mention, the absence of any failures in the observation period means that the MLE for the hazard function occurs in an edge case --- i.e., hazard being zero for that group, or equivalently, coefficients for the explanatory variables being infinite. This is probably what is leading to the failure of convergence of the fitting function. There are a number of ways you could deal with this; either you could change your fitting method (e.g., to Bayesian estimation) or you could consider the properties of the fitted function at the edge case.

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