This subject is covered by a number of papers including:
Here is a very brief (and non-exhaustive) summary of the differences between the two approaches.
For each pair, there is an unspecified baseline hazard function. The partial likelihood idea is readily adapted by multiplying the partial likelihoods specific to each stratum.
- It does not provide any information about heterogeneity between pairs;
- Pairs in which both members shared the same covariate information or which provide only censoring observations do not contribute to the likelihood; this is because no between-pair comparisons are attempted.
Within-pair association is accounted for by a random effect common to both members from the same pair. Hence, there is again a different baseline hazard for each pair, but they are not totally unspecified; there is some structure. Estimation is based on the marginal likelihood.
- Parsimony: heterogeneity is described by a single parameter;
- Summary measures about heterogeneity are available (Understanding heterogeneity...);
- It is possible to study the effect of variables common within the pairs.
- software availability (in R, you can look at
parfm(); in SAS, you can look at
- research is still ongoing.
As a conclusion, the choice depends on your research. However, the last reference from the list gives some guideline:
For situations where group size is five or greater, it is difficult to justify use of the random
effects model over that of the stratified model, this latter model being very much more
readily implemented. The story changes for group sizes less than five and, for twin studies in
particular, the efficiency gains are such that we would prefer to use a random effects model
over a stratified model. The stratified model remains valid but can required from 20 per cent
to 30 per cent more observations to achieve the same precision.