The Kaplan-Meier estimator is a product of survival probabbilities. It gives an estimate of the survival rate at various intervals, but it doesn't take into consideration variables or covariates that might affect survival. A semi-parametric model that permits the addition of variables is the Cox-Oakes model. Hazard ratios, which indicate the relative probability of an event occurring (such as a death) for varying amounts of the variables, are provided by this model. If you're only interested in estimating survival rates and you don't have any covariates to consider, the Kaplan-Meier method might be the better choice. But if you have covariates that you think might influence survival, the Cox-Oakes model would be more appropriate. In this case I think the Cox-Oakes model is the best since we are estimating daily survival rates. SInce it takes the daily survival rate it will have a larger sample size and lower confidence intervals