## 1 Introduction  
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [1], the beta-coronavirus that causes what is known as coronavirus disease 2019 (COVID-19), was first identified in an outbreak in Wuhan, Hubei province, China, in December 2019. The virus rapidly spread throughout the world, and on 11 March 2020, the World Health Organization officially declared the international COVID-19 situation a pandemic [2]. In the United States (U.S.), the first confirmed case was identified on 20 January 2020 [3,4] in Washington state, although evidence suggests COVID-19 may have arrived in the U.S. as early as December 2019 [5; 6]. The number of infected individuals and subsequent deaths quickly grew, and as of 31 March 2021--slightly past the one-year anniversary of the pandemic--the U.S. had over 30.5 million cumulative confirmed COVID-19 cases and over 560,000 COVID-19 deaths according to the Centers for Disease Control and Prevention (CDC) [7], both figures the highest among every country in the world [8].  
Clinical studies on COVID-19 patients conducted early in the pandemic found that men were dying at markedly higher rates relative to women [9; 10; 11; 12; 13]. At the population level, males comprise the majority of COVID-19 deaths in the overwhelming majority of countries that report sex-disaggregated COVID-19 mortality data [14]. Here, we focus on the U.S., where the majority of COVID-19 deaths also occur among males [15]. Standard analyses and commentaries contrasting the male and female population level COVID-19 mortality burdens typically involve calculating the percentage of total deaths by sex--contrasting them with their respective percent population shares--and/or calculating male and female (age-adjusted) mortality rates [16; 17; 18]. For example, the Gender-Sci Lab COVID Project at Harvard University [18] tracks the number of male and female COVID-19 deaths by state, calculating the percentage of total deaths by sex as well as crude and age-adjusted male and female mortality rates for each state. However, because COVID-19 case fatality rates are considerably higher among individuals in older age groups, COVID-19 death counts and mortality rates for both males and females are predominantly determined by data from COVID-19 decedents in older age groups. Younger individuals, however, are also susceptible to death from COVID-19, which in principle represent greater unrealized years of life, economic productivity, and broader contributions to society compared to decedents of greater age.  
Years of potential life lost (YPLL) is a widely used epidemiological measure of mortality burden that emphasizes deaths that occur at younger ages by explicitly weighting such deaths more heavily [19]. The mathematical formula for YPLL for an individual decedent \(i\) is defined as the difference between an upper reference age \(\mathcal{A}\) (typically close to a widely applicable life expectancy) and age at death \(a_{i}\) if the difference is positive and zero otherwise:  
\[\text{YPLL}_{i}=\text{max}\{\mathcal{A}-a_{i},0\}. \tag{1}\]  
Here, we quantified disparities in YPLL attributable to COVID-19 in the U.S. by sex at the state level to examine both their magnitudes and their state-to-state variation. Specifically, we characterized the disparities by estimating (a) percentages of total YPLL by sex and (b) age-adjusted male-to-female YPLL rate ratios (RRs), both nationally and for each of the 50 states and the District of Columbia (D.C.). For comparison, we also calculated the corresponding percentages of total deaths by sex and estimated the corresponding age-adjusted male-to-female mortality RRs to examine potential differences in the characterization of the disparities when measuring mortality burden in terms of YPLL compared to (age-irrespective) death counts. To perform estimation and uncertainty quantification of the estimands of interest, we used novel Monte Carlo (MC) simulation techniques to obtain interval estimates for them.