## 2 Materials and Methods
### Computational Savings by Omitting Unnecessary Mortality Datasets  
For each state and estimand of interest, the modified version of [PERSON] et al.'s MC simulation procedure described in Section 2.4--in theory--comprises simulating ages at death for each individual in \(\mathcal{B}\times\int_{ms}\times\int_{fs}\) male-female mortality dataset pairs, where \(\mathcal{B}\) denotes the number of specified MC iterations, \(J_{ms}\) denotes the number of male mortality datasets in state \(s\), and \(J_{fs}\) denotes the number of female mortality datasets in state \(s\). As such, the total number of male-female mortality dataset pairs to simulate from can be enormous for sufficiently large values of either \(J_{ms}\) or \(J_{fs}\) (or both), potentially making it a computationally prohibitive endeavor. However, substantial computational savings can be achieved by identifying male-female mortality dataset pairs that we do not need to simulate ages at death from because they would yield a maximum or minimum MC point estimate of the estimand of interest with probability 0.  
We describe an example of identifying such superfluous male-female mortality dataset pairs we can omit from our analysis when the estimand of interest is the male percentage of total YPLL. This is achieved by separately considering which male-female mortality dataset pairs will yield a maximum or minimum point estimate. To obtain a maximum point estimate at each MC iteration, only one male-female mortality dataset pair needs to be considered. The only male mortality dataset that needs to be considered is the one that contains the maximum possible number of deaths in the youngest age groups corresponding to suppressed death counts, and the only female mortality dataset that needs to be considered is the one that contains the maximum possible number of deaths in the oldest age groups corresponding to suppressed death counts. Any other male-female mortality dataset pair would yield a maximum MC point estimate with probability 0. A similar result applies when obtaining a minimum point estimate at each MC iteration. For that task, the only male mortality dataset that needs to be considered is the one that contains the maximum possible number of deaths in the oldest age groups corresponding to suppressed death counts, and the only female mortality dataset that needs to be considered is the one that contains the maximum possible number of deaths in the youngest age groups corresponding to suppressed death counts. Any other male-female mortality dataset pair would yield a minimum MC point estimate with probability 0. Hence, when the estimand of interest is the male percentage of total YPLL, only 2 male-female mortality dataset pairs need to be simulated from at each MC iteration.  
For estimation of the age-adjusted YPLL-based estimands of interest (i.e., age-adjusted male and female YPLL rate, age-adjusted male-to-female YPLL RR), identifying male-female mortality dataset pairs that can be omitted is less straightforward. However, inequality conditions can be established computationally to identify meaningful numbers of male-female mortality dataset pairs that can validly be omitted, thereby attaining computational savings.