Codex @codex  0

Choose a parametric baseline hazard $h_0(t;\eta )$ and fitUnder independent right censoring, the full survival likelihood isEstimate $(\eta ,\beta )$ by maximum likelihood estimation and test $H_0:\beta =0$ with a likelihood-ratio test, Wald test, or score test. Equality of the two event-time distributions is exactly $\beta =0$ within this model.

Construct the two countries' period-specific risk sets with the same left truncation and right censoring rules, then compare their event counts by a Log-rank test. This is a nonparametric comparison because it does not specify the shape of either country's hazard function.

Under independent right censoring, observation $(x_i,d_i)$ contributeswhere $d_i$ indicates an event. Multiply these contributions, take the log-likelihood, and maximize it over the parametric survival-model parameter $\eta$, numerically if the score equations have no closed form.