# Racial and Ethnic Disparities in Years of Potential Life Lost Attributable to COVID-19 in the United States: An Analysis of 45 States and the District of Columbia

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Estimation Procedure for YPLL-Based Estimands from Administratively Interval Censored Ages at Death

#### 2.3. Procedure Modification to Account for Suppression of Low Death Counts

#### 2.4. Procedure Modification to Further Account for a Subset of Deaths with Unknown Race/Ethnicty

#### 2.5. Computational Savings by Omitting Unnecessary Mortality Datasets

#### 2.6. Complete Monte Carlo Simulation Procedure for Estimation of YPLL-Based Estimands

- Calculate the difference between the total number of deaths as provided by the NCHS Sex Data and the total number of deaths contained in intervals with non-suppressed death counts; this is the number of deaths contained in the union of intervals with suppressed death counts.
- Let $\mathcal{B}$ denote the total number of MC iterations, and let $b=1,\dots ,\mathcal{B}$ index the MC iterations. For the task of obtaining a maximum MC point estimate of the estimand of interest that primarily concerns racial/ethnic group r at each MC iteration b, combine the Unknown racial/ethnic group with racial/ethnic group r into a combined r-Unknown racial/ethnic group whose constituents we all assume to be in racial/ethnic group r, combine the remaining racial/ethnic groups that are not included in the definition of the estimand into a single “other” racial/ethnic group, and enumerate all possible mortality datasets, omitting those that would yield a maximum MC point estimate with probability 0. For the task of obtaining a minimum MC point estimate of the estimand of interest, combine all of the racial/ethnic groups not included in the definition of the estimand (including the Unknown racial/ethnic group) and enumerate all possible mortality datasets, omitting those that would yield a minimum MC point estimate with probability 0. Let ${J}_{s}^{\left(\mathrm{max}\right)}$ denote the number of mortality datasets considered for the maximization task in state s, and let ${J}_{s}^{\left(\mathrm{min}\right)}$ denote the number of mortality datasets considered for the minimization task in state s.
- Specify a YPLL upper reference age $\mathcal{A}$ less than or equal to 85 years. We view age group <1 as equivalent to the singular age 0, and the remaining numeric NCHS age group endpoints represent integer age at last birthday so that there is a 1-year gap between the endpoints of two chronologically consecutive age groups (e.g., 35–44 and 45–54). We treat age as a continuous variable, and as a consequence, we mathematically interpret the <1 age group (age 0) as the right half-open interval $[0,1)$, the $85+$ age group as the half-bounded interval $[85,\infty )$, and the remaining NCHS age groups as right half-open intervals with lower limit equal to the lower endpoint of the corresponding NCHS age group and upper limit equal to the upper endpoint of the corresponding NCHS age group plus one (e.g., age group 5–14 is viewed as $[5,15)$). At each MC iteration b and for each mortality dataset $j=1,\dots ,{J}_{s}^{\left(\mathrm{max}\right)}+{J}_{s}^{\left(\mathrm{min}\right)}$ considered for the maximization and minimization tasks, independently simulate an age at death ${\tilde{a}}_{ijs}^{\left(b\right)}$ for each individual fatality i corresponding to age interval $({L}_{ijs},{U}_{ijs})$, where $\mathcal{A}>{L}_{ijs}$, from the corresponding continuous uniform distribution:$$\begin{array}{c}\hfill {\tilde{a}}_{ijs}^{\left(b\right)}\stackrel{ind}{\sim}\mathcal{U}({L}_{ijs},{U}_{ijs}).\end{array}$$Observe that $\mathcal{A}$ is intentionally and necessarily chosen to be less than or equal to 85 years to obviate the simulation of ages at death corresponding to the 85+ age group, thereby avoiding potential analytic difficulties because each fatality corresponding to the 85+ age group contributes nothing to YPLL.
- At each MC iteration b and for each mortality dataset j, calculate a point estimate of the estimand of interest. In particular, for the estimation of the percentage of total YPLL for racial/ethnic group r, first calculate total YPLL for racial/ethnic group r (which includes the Unknown racial/ethnic group for the maximization task) and the remaining racial/ethnic groups from the simulated ages at death, which are ${\widehat{\mathrm{YPLL}}}_{rjs}^{\left(b\right)}={\displaystyle \sum _{i\in r}}\mathrm{max}\left(\right)open="\{"\; close="\}">\mathcal{A}-{\tilde{a}}_{ijs}^{\left(b\right)},0$ and ${\widehat{\mathrm{YPLL}}}_{\overline{r}js}^{\left(b\right)}={\displaystyle \sum _{i\notin r}}\mathrm{max}\left(\right)open="\{"\; close="\}">\mathcal{A}-{\tilde{a}}_{ijs}^{\left(b\right)},0$, respectively. Then, the percentage of total YPLL for racial/ethnic group r, which we denote ${\widehat{\pi}}_{rjs}^{\left(b\right)}$, is given by:$$\begin{array}{c}\hfill {\widehat{\pi}}_{rjs}^{\left(b\right)}=\frac{{\widehat{\mathrm{YPLL}}}_{rjs}^{\left(b\right)}}{{\widehat{\mathrm{YPLL}}}_{rjs}^{\left(b\right)}+{\widehat{\mathrm{YPLL}}}_{\overline{r}js}^{\left(b\right)}}\times 100\%.\end{array}$$For estimation of the age-adjusted r-to-NH White YPLL RR, first estimate the age-adjusted YPLL rates for racial/ethnic group r and NH Whites, using the 2019 CDC WONDER age distribution estimate of the overall U.S. population as the standard population. The age-adjusted YPLL rate for racial/ethnic group r (which includes the Unknown racial/ethnic group for the maximization task) is calculated using direct age adjustment [54] from the simulated ages at death, which we denote ${\widehat{\mathrm{R}}}_{\mathrm{YPLL},rjs}^{\left(b\right)}$. Since the simulated ages at death are continuous and the CDC WONDER age distribution estimates are defined over integer ages from 0 to 84, we aggregate the corresponding simulated YPLL values with respect the 1-year intervals implied by these integer ages (i.e., age $a\in \{0,1,\dots ,84\}$ implies age interval $[a,a+1)$) to calculate the age-specific YPLL rates, which are subsequently applied to the standard population to obtain the age-adjusted YPLL rate for racial/ethnic group r:$$\begin{array}{c}\hfill {\widehat{\mathrm{R}}}_{\mathrm{YPLL},rjs}^{\left(b\right)}=\frac{{\displaystyle \sum _{a=0}^{84}}\left(\right)open="("\; close=")">{n}_{a}\times \frac{{\widehat{\mathrm{YPLL}}}_{rjsa}^{\left(b\right)}}{{n}_{rsa}}}{}{\displaystyle \sum _{a=0}^{84}}{n}_{a}+{n}_{85+},\end{array}$$$$\begin{array}{c}\hfill {\widehat{\mathrm{RR}}}_{\mathrm{YPLL},r,\mathrm{NH}\phantom{\rule{4.pt}{0ex}}\mathrm{White},js}^{\left(b\right)}=\frac{{\widehat{\mathrm{R}}}_{\mathrm{YPLL},rjs}^{\left(b\right)}}{{\widehat{\mathrm{R}}}_{\mathrm{YPLL},\mathrm{NH}\phantom{\rule{4.pt}{0ex}}\mathrm{White},js}^{\left(b\right)}}.\end{array}$$
- At each MC iteration b, store the maximum of the ${J}_{s}^{\left(\mathrm{max}\right)}$ MC point estimates of the estimand of interest calculated from the set of ${J}_{s}^{\left(\mathrm{max}\right)}$ mortality datasets considered for the maximization task, and store the minimum of the ${J}_{s}^{\left(\mathrm{min}\right)}$ MC point estimates calculated from the set of ${J}_{s}^{\left(\mathrm{min}\right)}$ mortality datasets considered for the minimization task.
- A conservative $(1-\alpha )\times 100\%$ interval estimate of the estimand of interest is given by the $\frac{\alpha}{2}$ quantile of the $\mathcal{B}$ minimum MC point estimates and the $1-\frac{\alpha}{2}$ quantile of the $\mathcal{B}$ maximum MC point estimates.

#### 2.7. Monte Carlo Simulation Procedure for Estimation of Age-Adjusted Mortality Rates and Rate Ratios

#### 2.8. Computation

`R`version 3.6.0 programming language [71]. The code used in our analysis is available upon reasonable request from the corresponding author.

## 3. Results

#### 3.1. Results for Non-Hispanic Whites

#### 3.2. Results for Non-Hispanic Blacks

#### 3.3. Results for Hispanics

#### 3.4. Results for Non-Hispanic Asians

#### 3.5. Results for Non-Hispanic American Indian or Alaska Natives

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CDC | Centers for Disease Control and Prevention |

COVID-19 | Coronavirus Disease 2019 |

D.C. | District of Columbia |

MC | Monte Carlo |

NCHS | National Center for Health Statistics |

NH AIAN | Non-Hispanic American Indian or Alaska Native |

NH Asian | Non-Hispanic Asian |

NH Black | Non-Hispanic Black |

NH White | Non-Hispanic White |

RR | Rate Ratio |

U.S. | United States |

YPLL | Years of Potential Life Lost |

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**Figure 1.**Conservative 95% interval estimates of the percentage of total COVID-19-attributable YPLL before age 75, intervals denoting the entire plausible range for the percentage of total COVID-19 deaths, and the percent population shares for NH Whites in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020.

**Figure 2.**Conservative 95% interval estimates of the percentage of total COVID-19-attributable YPLL before age 75, intervals denoting the entire plausible range for the percentage of total COVID-19 deaths, and the percent population shares for NH Blacks in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020.

**Figure 3.**Conservative 95% interval estimates of the age-adjusted NH Black-to-NH White YPLL and mortality RR’s in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020. States are ordered from top to bottom in descending order of the signed difference between the lower limit of the YPLL RR interval and the upper limit of the mortality RR interval. Values are displayed on the base 10 logarithmic scale. Interval endpoints above 20.0 and below 0.30 are truncated, with the actual values numerically annotated.

**Figure 4.**Conservative 95% interval estimates of the percentage of total COVID-19-attributable YPLL before age 75, intervals denoting the entire plausible range for the percentage of total COVID-19 deaths, and the percent population shares for Hispanics in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020.

**Figure 5.**Conservative 95% interval estimates of the age-adjusted Hispanic-to-NH White YPLL and mortality RR’s in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020. States are ordered from top to bottom in descending order of the signed difference between the lower limit of the YPLL RR interval and the upper limit of the mortality RR interval. Values are displayed on the base 10 logarithmic scale. Interval endpoints above 20.0 and below 0.30 are truncated, with the actual values numerically annotated.

**Figure 6.**Conservative 95% interval estimates of the percentage of total COVID-19-attributable YPLL before age 75, intervals denoting the entire plausible range for the percentage of total COVID-19 deaths, and the percent population shares for NH Asians in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020.

**Figure 7.**Conservative 95% interval estimates of the age-adjusted NH Asian-to-NH White YPLL and mortality RR’s in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020. States are ordered from top to bottom in descending order of the signed difference between the lower limit of the YPLL RR interval and the upper limit of the mortality RR interval. Values are displayed on the base 10 logarithmic scale. Interval endpoints above 20.0 and below 0.30 are truncated, with the actual values numerically annotated.

**Figure 8.**Conservative 95% interval estimates of the percentage of total COVID-19-attributable YPLL before age 75, intervals denoting the entire plausible range for the percentage of total COVID-19 deaths, and the percent population shares for NH AIAN’s in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020.

**Figure 9.**Conservative 95% interval estimates of the age-adjusted NH AIAN-to-NH White YPLL and mortality RR’s in the U.S. and in each examined state with respect to cumulative COVID-19 deaths according to data from the National Center for Health Statistics as of 30 December 2020. States are ordered from top to bottom in descending order of the signed difference between the lower limit of the YPLL RR interval and the upper limit of the mortality RR interval. Values are displayed on the base 10 logarithmic scale. Interval endpoints above 20.0 and below 0.30 are truncated, with the actual values numerically annotated.

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**MDPI and ACS Style**

Xu, J.J.; Chen, J.T.; Belin, T.R.; Brookmeyer, R.S.; Suchard, M.A.; Ramirez, C.M.
Racial and Ethnic Disparities in Years of Potential Life Lost Attributable to COVID-19 in the United States: An Analysis of 45 States and the District of Columbia. *Int. J. Environ. Res. Public Health* **2021**, *18*, 2921.
https://doi.org/10.3390/ijerph18062921

**AMA Style**

Xu JJ, Chen JT, Belin TR, Brookmeyer RS, Suchard MA, Ramirez CM.
Racial and Ethnic Disparities in Years of Potential Life Lost Attributable to COVID-19 in the United States: An Analysis of 45 States and the District of Columbia. *International Journal of Environmental Research and Public Health*. 2021; 18(6):2921.
https://doi.org/10.3390/ijerph18062921

**Chicago/Turabian Style**

Xu, Jay J., Jarvis T. Chen, Thomas R. Belin, Ronald S. Brookmeyer, Marc A. Suchard, and Christina M. Ramirez.
2021. "Racial and Ethnic Disparities in Years of Potential Life Lost Attributable to COVID-19 in the United States: An Analysis of 45 States and the District of Columbia" *International Journal of Environmental Research and Public Health* 18, no. 6: 2921.
https://doi.org/10.3390/ijerph18062921