To estimate the magnitude, time trends and inequities in all-cause orphanhood and co-residing grandparent-caregiver-loss incidence and prevalence among US children, we extended a modeling methodology of COVID-19-associated orphanhood and caregiver death20,48 according to the Guidelines for Accurate and Transparent Health Estimates Reporting. The following sections summarize our methods.

Study populations

The United Nations Children’s Fund defines orphanhood as children experiencing the death of one or both parents1,2. As previously20 we considered mothers of ages 15–66 years and fathers of ages 15–94 years, so the maximum ages of parents at the birth of a child were, respectively, 49 and 77years. Mortality data were recorded among US residents, and for this reason, orphanhood estimates are restricted to children of US residents. Grandparents play indispensable roles as caregivers for children31,37,61,62,63,64; therefore, we include as previously20 minimum estimates of children who lost a primary grandparent caregiver, defined as a co-residing, custodial grandparent aged 30 years or older and providing care in the absence of a parent, or providing for most of their basic needs in the presence of a parent, and children who lost a secondary grandparent caregiver defined as a co-residing grandparent aged 30 years or older serving as head of household who owns or rents the family’s housing and provides for some but not most of the basic needs of their grandchildren32,64. Mortality data were recorded among US residents, and so grandparent caregiver death estimates are also restricted to children of US-resident grandparent caregivers.

National-level NCHS mortality data by rankable causes of death, 1983–2021

We obtained line-list mortality data on US residents from the NCHS Vital Statistics portal for each year from 1983 to 2021 (https://www.cdc.gov/nchs/data_access/vitalstatsonline.htm). Data were collected from 1983 onward because the corresponding children who lost a caregiver in 1983 at age 0 were of age 17 in 2000, and so entered our estimation of orphanhood prevalence in 2000. For each mortality record, we retained year of death, the corresponding codes of the underlying cause of death (ICD-9 code and 282 cause recode before 1999; ICD-10 code and 113 cause recode after 1999) and demographic data of the decedent including sex, age at death and information on race and Hispanic origin (https://www.cdc.gov/nchs/nvss/mortality_public_use_data.htm). Data on Hispanic origin were not available for 1983. Individuals of other races in 1984–1991 and individuals of more than one race in 2021 were not coded consistently and not included in this study (less than 0.019% (17,454) of line-list records were removed).

Information about the race and Hispanic origin of decedents in death certificates is typically self-reported by the surviving next of kin, or on the basis of observation in the absence of an informant65. Race and Hispanic origin were reported in different formats across the study period66, which we mapped to standardized race and Hispanic origin categories as described in Supplementary Table 6. Specifically, we grouped individuals of Hispanic origin and all individuals of non-Hispanic origin by their race, that is, ‘Hispanic’, ‘non-Hispanic American Indian or Alaska Native’, ‘non-Hispanic Asian or Pacific Islander’, ‘non-Hispanic Black’ and ‘non-Hispanic white’, and we refer to the resulting categories as ‘standardized race and ethnicity’ for simplicity. This approach to harmonizing race reporting over the study period did not necessarily make the primary data fully comparable. Earlier research shows inaccuracies are limited67, which indicates that the incremental implementation of multiple race reporting in the United States is unlikely to have introduced notable bias in orphanhood estimates.

The underlying cause of death is defined by the WHO as “the disease or injury which initiated the train of events leading directly to death, or the circumstances of the accident or violence which produced the fatal injury”68. For 1983–1998, underlying causes of death were in the data classified with the ICD-9 (ref. 69) and grouped further into 282 selected causes of death, termed ‘282 cause recode’70. For 1999–2021, underlying causes of death were in the data classified with the ICD-10 and grouped further into ‘113 Selected Causes of Death’71. We defined 53 non-overlapping rankable underlying causes of death that we termed ‘caregiver-loss causes of death’ and that apart from the following small modifications are identical to the 52 rankable underlying causes of death from the NCHS 113 Selected Causes of Death list71,72 (Supplementary Table 1). Specifically, we re-categorized drug-induced causes of death into ‘drug overdose’, joining the ICD-9 and ICD-10 causes of death ‘intentional self-poisoning by and exposure to nonopioid analgesics, antipyretics and antirheumatics’, ‘intentional self-poisoning by and exposure to antiepileptic, sedative–hypnotic, antiparkinsonism and psychotropic drugs, not elsewhere classified’, ‘intentional self-poisoning by and exposure to narcotics and psychodysleptics (hallucinogens), not elsewhere classified’, ‘intentional self-poisoning by and exposure to other drugs acting on the autonomic nervous system’ and ‘intentional self-poisoning by and exposure to other and unspecified drugs, medicaments and biological substances’ (E950.0–E950.5; X60–X64); ‘assault by drugs, medicaments and biological substances’ (E962.0; X85); ‘accidental poisoning by and exposure to nonopioid analgesics, antipyretics and antirheumatics’, ‘accidental poisoning by and exposure to antiepileptic, sedative–hypnotic, antiparkinsonism and psychotropic drugs, not elsewhere classified’, ‘accidental poisoning by and exposure to narcotics and psychodysleptics (hallucinogens), not elsewhere classified’, ‘accidental poisoning by and exposure to other drugs acting on the autonomic nervous system’ and ‘accidental poisoning by and exposure to other and unspecified drugs, medicaments and biological substances’ (E850–E858; X40–X44); and ‘poisoning by and exposure to nonopioid analgesics, antipyretics and antirheumatics, undetermined intent’, ‘poisoning by and exposure to antiepileptic, sedative–hypnotic, antiparkinsonism and psychotropic drugs, not elsewhere classified, undetermined intent’, ‘poisoning by and exposure to narcotics and psychodysleptics (hallucinogens), not elsewhere classified, undetermined intent’, ‘poisoning by and exposure to other drugs acting on the autonomic nervous system, undetermined intent’ and ‘poisoning by and exposure to other and unspecified drugs, medicaments and biological substances, undetermined intent’ (E980.0–E980.5; Y10–Y14). We retained these four drug overdose causes of death sub-categories as separate drug overdose subgroups for the purpose of data harmonization (see below). Correspondingly, we removed the related three drug overdose causes of death sub-categories, respectively, from ‘intentional self-harm’, ‘assault’ and ‘accidents’. We renamed these resulting three categories as ‘suicide excluding drug overdose’, ‘homicide excluding drug overdose’ and ‘unintentional injuries excluding drug overdose’. Supplementary Table 2 summarizes our aggregation of the 53 rankable causes of death into the leading parental cause-of-death groups and ‘other’ parental causes of death that we refer to in the main text and are shown in Fig. 1. The ‘other’ parental causes of death comprise the remaining 46 rankable caregiver-loss causes of death and any other causes of death that are not included in the NCHS 52 rankable causes of death.

We then mapped and aggregated line-list mortality records to the 53 rankable caregiver-loss causes of death. This was done by mapping the 1983–1998 line-list data using the 282 recodes to the 52 NCHS rankable causes of death as described in ref. 73. For drug-induced causes, we used Table 2 in ref. 74. For 1999–2021, we mapped the ICD-10 113 cause recodes to the NCHS 52 rankable causes of death based on Table A in ref. 75, and subsequently mapped the NCHS 52 rankable causes of death to the 53 rankable caregiver-loss causes of death based on the descriptions in Supplementary Table 2.

Next, we aggregated line-list death records to annualized death counts by the 53 rankable caregiver-loss causes of death for each year in 1983–2021, as well as by sex, age band (15–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, 65–69, 70–74, 75–79, 80–84 and 85+ years) and standardized race and ethnicity of the decedent. Data on race and ethnicity were not available for 1983, and for this year, we attributed mortality counts to standardized race categories according to the age-, sex- and cause-of-death-specific standardized race compositions in 1984. To harmonize cause-of-death data from 1983 to 1999 to the ICD-10 cause-of-death classifications and avoid discontinuities in our orphanhood estimates from 1998 to 1999, we used where available the comparability ratios in Table 1 of ref. 72. Thirteen comparability ratios of rankable causes of death were not provided when underlying estimations were considered imprecise72, and in these cases, we set the comparability ratios to 1.

Extended Data Fig. 2 illustrates the aggregated annual mortality data among US residents by standardized race categories and Extended Data Fig. 3 by leading parental causes of death as relevant for caregiver loss and orphanhood.

National-level live birth data, 1969–2021

We required live birth data before 1983 to calculate fertility rates and attribute children experiencing orphanhood to descendants between 1983 and 2021. This is because the children who lost a caregiver in 1983 at age 1–17 years were born between 1966 and 1982. However, due to limitations in publicly available population size data, we considered only live birth data from 1990 in the central analysis and assumed constant fertility rates before 1990. We investigated the sensitivity of our orphanhood estimates to this assumption using live birth records since 1980 together with corresponding population size estimates, and found that orphanhood prevalence estimates since 2008 were not affected by our assumptions on historic fertility, while in the sensitivity analysis, orphanhood prevalence estimates for 2000–2007 were slightly lower due to overall lower fertility rates in the 1980s (Extended Data Fig. 10a). Line-list live births with demographic data on both mothers and fathers were available and downloaded from the NCHS Vital Statistics portal (https://www.cdc.gov/nchs/data_access/vitalstatsonline.htm) for each year between 1969 and 2021. We considered only live birth records to US-resident mothers for consistency with the mortality data available. Information on residency status of fathers was not available, and we assumed fathers were also US residents in the retained birth records associated with US-resident mothers. For each live birth, we retained the year of birth, the age of mothers and fathers, and information on race and Hispanic ethnicity (https://www.cdc.gov/nchs/data_access/vitalstatsonline.htm). The age of mothers and fathers was reported by single year of age. Following ref. 20, we considered live births to women aged 15–49 years and men aged 15–77 years, to match the mortality data of women aged 15–66 years and men aged 15–94 years. In total, less than 0.012% (19,367) of line-list records were removed from further analysis because parents were outside of these age ranges or demographic information was unreported or not stated. Age information was mapped to 5 year age bands 15–19 years, …, 45–49 years for mothers and age bands 15–19 years, …, 50–54 years and 55–77 years for fathers. Information about the race and Hispanic origin of mothers and fathers was between 1969 and 2021 self-reported in different standards due to the revision of the US certificates of live births on race in 1989 and 200376. Information on the race of mothers and fathers has been publicly available since 1969, and information on their ethnicity since 1978. For 1978–2021, we mapped available information on race and ethnicity to the same standardized race and ethnicity categories used to stratify the mortality data, according to Supplementary Table 7. Individuals of multiple races were excluded (less than 0.23% (398,424) of line-list natality records were removed).

Next, we aggregated line-list live birth records to annualized live birth counts to mothers (in age bands 15–19, …, 45–49 years) and fathers (in age bands 15–19, …, 55–77 years) for each year in 1969–1977, and stratified further by standardized race and ethnicity categories for each year in 1978–2021. Before 1985, data reporting was incomplete for some US states and we used NCHS sampling weights reported in each year (see Appendix A of ref. 77 to extrapolate reported live birth counts to state populations.

National-level population size data, 1990–2021

We further required population size data of US residents in the age, sex and standardized race and ethnicity categories of the live birth data to calculate fertility rates. We obtained CDC WONDER Vintage bridged-race postcensal and ethnicity population size estimates for each year in 1990–1999 and 2000–2020 (https://wonder.cdc.gov/wonder/help/bridged-race.html#About%201990-2020) and single race population size estimates for 2021 (https://wonder.cdc.gov/wonder/help/single-race.html#About%202020-2021). Data were extracted by 5 year age bands (15–19 years, …, 85+ years) and single years of age from 75 to 77 years, and data for individuals aged 55–77 years were summed into a single age band as required for the purposes of our analyses. Information about race and Hispanic origin was self-reported during the US Census. Race-specific population size estimates were aggregated to the standardized race and ethnicity categories described in Supplementary Table 8.

For sensitivity analyses (see below), we also obtained national-level population size estimates by 5 year age bands, sex and US states without race and ethnicity stratification for each year in 1969–1989 from the US National Cancer Institute Surveillance, Epidemiology, and End Results Program (https://population.un.org/wpp/Download/Standard/Mortality/).

Statistical analysisEstimating national-level fertility rates, 1990–2021

We calculated age-, sex- and standardized race and ethnicity-specific fertility rates in each year in 1990–2021 for women in one of the age bands a ∈  years and men in one of the age bands a ∈  years according to

where the number of live births and population sizes in each strata are denoted by By,a,s,r and Py,a,s,r, respectively. Calculations were done for each of the five standardized race categories ‘Hispanic’, ‘non-Hispanic American Indian or Alaska Native’, ‘non-Hispanic Asian or Pacific Islander’, ‘non-Hispanic Black’ and ‘non-Hispanic white’. In the central analysis, we assumed the same fertility rates in each year in 1966–1989 as in 1990 as shown in Extended Data Fig. 4, and considered alternative assumptions in several sensitivity analyses (see below). We calculated mortality rates in analogy to equation (1) and found correlations by standardized race and ethnicity between fertility and mortality rates that changed primarily by age of mothers and fathers, and less so over calendar years. These correlations prompted us to estimate national-level incidence and prevalence of orphanhood by standardized race and ethnicity and then sum the standardized race and ethnicity-specific estimates to obtain national-level estimates.

Estimating national-level orphanhood, 1983–2021

We estimated the number of children who newly experienced orphanhood in year y, y = 1983, …, 2021, from the population-level mortality records of US residents in year y and the number of children each decedent was expected to leave behind. We obtained the expected number of children per US resident of age a years, sex s and standardized race and ethnicity r in year y who are of age b = 0, 1, …, 17 years (denoted by Cy,a,s,r,b) by multiplying the corresponding fertility rates of equation (1) with pediatric survival probabilities of children born in year y − b and surviving until age b + 1 (denoted with \(_^}}\)). Specifically

$$_=}}_\times _^}},$$

(2)

where y ranges from 1983 to 2021, the single year of age of mothers ranges from a ∈  years, the single year of age of fathers ranges from a ∈  years, the standardized race and ethnicity categories are as described before, and b = 0, 1, …, 17 years. We obtained the pediatric survival probabilities from child mortality data (https://population.un.org/wpp/Download/Standard/Mortality/) and use in equation (2) the fertility rates of the age band that includes age a − b. We then estimated the number of children aged b who newly experienced in year y the death of a parent s of age specified in 5 year age bands \(^ }\in }\) = , and standardized race and ethnicity r who died of caregiver-loss cause of death c by

$$_^ },s,r,b,c}^}\,}\,}}=_^ },s,r,b}\times _^ },s,r,c},$$

(3)

assuming that parents and their children have the same standardized race and ethnicity and where the expected number of children of parents in age bracket \(^ }\), \(_^ },s,r,b}\), is calculated as the mean over the expected number of children of parents aged \(a\in ^ }\) in equation (2). Due to the correlations between standardized race and ethnicity-specific fertility and mortality rates, we calculated equation (3) for each standardized race and ethnicity. In equation (3), we assumed that population-level fertility rates are not correlated with population-level mortality rates, which may lead to upward or downward bias in orphanhood estimates that we explored in several sensitivity analyses (see below and Extended Data Fig. 10a–c).

As orphanhood considers children who experienced the death of their mother, father or both, we are interested in the sum of equation (3) for both mothers and fathers, but need to subtract children who lost their other parent in the previous b − 1 years, or who lost their other parent in the same year y. We assumed that the other parent 1 − s is in the same age band \(^ }\) and of the same standardized race and ethnicity as parent s. The probability that the other biological parent of the children in equation (3) died in the same year y is based on standard life table calculations78, specifically the probability that an individual of sex 1 − s and standardized race and ethnicity r died in year y between (continuous) age a and a + n conditional on survival up to age a, where n = 5 corresponds to the width of the 5 year age bands considered. This mortality hazard is approximated using midpoints x = (a + a + 5)/2 in each age interval, through

$$}}_=}}f(x)}}=}}}_S(a)}}}},$$

(4a)

$$=\frac\frac}_S(a)}(S(a)+(1-__)S(a))}=\frac\frac__}_}=\frac\frac}_}}_},$$

(4b)

where for ease of readability we have suppressed y, s and r, and nPa and nDa are respectively the estimated population sizes and observed death counts by the end of the corresponding calendar year in each 5 year age band \(^ }=\left[a,a+5\right)\). The intermediate quantities in equation (4) are the approximated (unknown) mortality probability density function nf(x) at age midpoint x and (unknown) survival function S(a) up to age a, which can be expressed in terms of the age-specific mortality rate nqa defined as the proportion of individuals alive at age a and who die before reaching age a + n in the corresponding calendar year. It is standard to estimate nqa with \((}_)/(}_+\frac}_)\), from which equation (4) follows78. Using equation (4), we estimated the number of children aged b who newly experienced in year y the death of one parent due to cause-of-death c and the death of the other parent due to any cause with

$$_^ },s,r,b,c}^}\,}}=__\times _^ },s,r,b}\times _^ },s,r,c},$$

(5)

where x is the midpoint age in age band \(^ }\). In equation (5), we assumed that deaths among parents occurred independently of each other and ignored correlations of deaths among parents by the same cause of death such as COVID-19 (ref. 20), as well as correlations of deaths among parents who died of different causes of death. Following the same rationale, we estimated the number of children aged b who newly experienced in year y the death of one parent s due to cause-of-death c and the death of their other parent 1 − s due to any cause in any of the previous i = 1, …, b − 1 years with

$$_^},s,r,b,c}^}}=\left(\frac\sum _^ }}\mathop\limits_^}_\right)\times _^ },s,r,b}\times _^ },s,r,c}.$$

(6)

With these considerations, we estimated the number of children aged b who newly experienced orphanhood in year y = 1983, …, 2021, by the death of one or both parents of age \(^ }\) and standardized race and ethnicity r who died of cause-of-death c with

$$_^ },r,b,c}^}}=\quad _^ },s,r,b,c}^}\,}\,}}+_^ },1-s,r,b,c}^}\,}\,}}$$

(7a)

$$-\left(_^ },s,r,b,c}^\,}}+_^ },1-s,r,b,c}^\,}}\right)/2$$

(7b)

$$-_^ },s,r,b,c}^}}-_^ },1-s,r,b,c}^}}.$$

(7c)

Equation (7b) subtracts the children who lost in year y a parent owing to cause c and the other parent owing to any cause, which are counted twice in equation (7a). Without line-list family data and working from individual-level live birth and death statistics, the two terms \(_^ },s,r,b,c}^\,}}\) and \(_^ },1-s,r,b,c}^\,}}\) are not identical, and for this reason, we subtracted the average of both. Equation (7c) subtracts the children who already lost the other parent in previous years. In previous studies on COVID-19-associated orphanhood20, we did not consider the possibility of reinfection with COVID-19 and for this reason did not subtract children who already lost the other parent owing to COVID-19 in previous years in these studies. Further arguments show that across ages, standardized race and ethnic groups, and caregiver-loss causes of death, the values in equations (7b) and (7c) are approximately equal to orphanhood prevalence divided by four, and in the US context remain below 1% of the average values in equation (7a).

To estimate the prevalence of orphanhood in year y = 2000, …, 2021, we accrued the number of children who newly experienced orphanhood in the previous 17 years and current year y, while accounting for aging. Specifically, for each calendar year since 2000, we estimated the total number of children aged b = 0, …, 17 years in calendar year y and of race and ethnicity r who experienced orphanhood and survived in their lifetime by cause-of-death c in one or both parents with

$$_^}}=\mathop\limits_^\left(\sum _^ }}_^ },r,b-i,c}^}}\times \mathop\limits_^(1-__)\right),$$

(8)

which sums over children who newly experienced orphanhood at younger ages in previous years conditional on survival up to the time point y + 1, where 1hy,r,b is as described in equation (4). In equation (8), j does not start at 0 because we already conditioned on survival up to the current year in the incidence calculations via equation (2). For 2021, the downward adjustments in equation (8) accounting for survival amounted to less than 1.5% of the prevalence count.

Following equations (7) and (8), we derived additional key quantities such as the number of children aged b in calendar year y = 1983, …, 2021 and standardized race and ethnicity r who newly experienced orphanhood in year y by parental sex s and cause-of-death c

$$_^}}=\sum _^ }}_^ },s,r,b,c}^}\,}\,}}-_^ },s,r,b,c}^}};$$

(9)

so maternal and paternal orphanhood incidence estimates each include children who experience the death of both parents20,79. Furthermore, we derived the number of children aged b in calendar year y = 2000, …, 2021 and standardized race and ethnicity r who experienced orphanhood in their lifetime by parent sex s and cause-of-death c by

$$_^}}=\mathop\limits_^\left(_^}}\times \mathop\limits_^(1-__)\right);$$

(10)

the number of children of standardized race and ethnicity r who experienced orphanhood in calendar year y = 2000, …, 2021 in their lifetime by cause-of-death c in one or both parents by

$$_^}}=\sum _^ }}\mathop\limits_^\mathop\limits_^\left(_^ },r,b,c}^}}\times \mathop\limits_^(1-__)\right).$$

(11)

All other total numbers reported in this paper are aggregations of equations (7)–(11).

Estimating national-level grandparent caregiver loss, 1983–2021

We estimated the number of children who newly experienced grandparent caregiver death in year y, y = 1983, …, 2021, from the population-level mortality records in year y of US residents aged 30 years and above (30+). Starting from 2010, ACS32 collected data on the proportion \(_^}}\) of adults aged 30+ years living with their grandchildren of age 17 or under in the United States, and proportions of these by sex, and separately by bridged-race and Hispanic origin (https://data.census.gov/cedsci/table?tid=ACSST5Y2019.S1002). Information about the bridged-race and Hispanic origin was self-reported. In addition, the ACS derive data on the proportion \(_^\,\text}}\) of those who provide most of the care to any of their grandchildren through the question, ‘Is this grandparent currently responsible for providing most of the basic needs of any children under the age of 18 years and living in this house or apartment?’, and further derive information on the proportion \(_^}}\) of those who are responsible for children in the absence of parents through column ‘Householder or spouse responsible for grandchildren with no parent of grandchildren present’ in Table S1002. From these data, we estimated the sex- and race and ethnicity-specific proportions of adults aged 30+ years who respectively are most responsible for the basic needs of grandchildren in the absence of a parent, who are most responsible for the basic needs of grandchildren in the presence of a parent and, finally, who serve as head of household who own or rent the family’s housing and provide for some but not most of the basic needs of their grandchildren31,32 by

$$_^}}=_^}}\times _^}}\times _^\,\text}}}\times _^}}$$

(12a)

$$_^}}}=_^}}\times _^}}\times _^}}\times \left(1-_^}}\right)$$

(12b)

$$_^}}=_^}}\times _^}}\times \left(1-_^}}\right).$$

(12c)

From 2010 to 2021, the proportions of grandparent caregivers providing for most of the basic needs of their grandchildren with or without a parent present (respectively \(_^}\) and \(_^}}\)) declined over time, whereas the proportions of grandparent caregivers providing housing and for some but not most of the needs of their grandchildren (\(_^}}\)) increased, and so we expected different trends in grandparent caregiver loss across these categories. We then assumed that each grandparent caregiver leaves upon death a minimum of one child behind (corresponding to equation (2)) and estimated the minimum number of grandchildren who newly experienced grandparent caregiver death in year y = 1983, …, 2021, with a US-resident grandparent caregiver aged 30+ years, sex s and standardized race and ethnicity category r who died of leading cause c by

$$_^=1\times _^\times \sum _^ }\ge 30}_^ },s,r,c},$$

(13)

where x represents the three types of grandparent caregivers in equation (12), and assuming that \(_^\) is for y = 1983, …, 2009 the same as in 2010. As illustrated in Extended Data Fig. 1, we then estimated the number of grandchildren who newly experienced the death of respectively a primary or secondary grandparent caregiver of sex s and race and ethnicity r due to caregiver-loss cause-of-death c in year y = 1983, …, 2021 by

ACS did not collect data on whether both grandparents are alive and live with their grandchildren of age 17 or under, and for this reason, we did not adjust equation (14) further for loss of other grandparents. We investigated in sensitivity analyses our assumption that \(_=__^\) was approximately constant from 1983 to 2010 using longitudinal United Nations Population Division data on Households and Living Arrangements of Older Persons for the United States, which suggested that the proportion of older persons who live with children or who are the primary caregivers of children has in the United States remained fairly constant since 1990 (see below). To estimate the minimum number of children who experienced grandparent caregiver death in their lifetime, we additionally need disaggregations of equation (14) by single year of age b = 0, …, 17 years. For the central analysis, we assumed that the age composition of \(_^\) is the same as the age composition of children who lost parents older than 30 years

$$_^=_^\times \frac_^ }\ge 30}_^ },s,r,b,c}^}}}\nolimits_^_^ }\ge 30}_^ },s,r,b,c}^}}},$$

(15)

where x represents primary or secondary grandparent caregiver loss and \(_^ },s,r,b,c}^}}\) are obtained from equation (7) by summing over the years y = 2000, …, 2021, and c is one of the leading parental causes of death; these age compositions differ across causes of death while they are relatively more stable across standardized race and ethnicity. It is plausible that the age composition of \(_^\) may differ from the age composition of children who lost parents older than 30 years, and we explored alternative approaches to equation (15) in sensitivity analyses; none of these had a considerable impact on our overall estimates.

Estimating national-level caregiver loss, 1983–2021

To estimate the total number of children experiencing caregiver loss defined as either orphanhood or grandparent caregiver loss, we finally sought to subtract from equation (14) those grandchildren who previously experienced orphanhood or who experienced the death of their mother or father in the same year. For the proportion pboth parents present of grandchildren who co-resided with their grandparent and both parents at the start of year y, we assumed that either or both of the parents may have died in the remainder of the year after the ACS survey. For the latter, we considered age-, sex- and race and ethnicity-specific mortality rates and aggregated these using parent age compositions as weights to obtain the mortality rate \(_^}}\) of a parent of sex s and race and ethnicity r in year y. Then, we subtracted from grandchildren who co-resided with their grandparent and both parents at the start of year y the proportion \((_^}}+_^}}-_^}}_^}})\times 6/12\) that we expected to additionally experience the loss of one or both of their parents in the 6 months on average after the ACS survey. For the proportion 1 − pboth parents present of grandchildren who co-resided with their grandparent and one parent at the start of year y, we assumed that in a proportion pother parent died the other parent had died previously and removed these children experiencing grandparent caregiver loss from the caregiver loss count. In the remaining proportion, we assumed again that either or both of the parents may have died in the remainder of the year after the ACS survey. Finally, for grandchildren who lived in skip generation households at the start of year y, we assumed a proportion pskip gen parent died previously lost either their mother, their father or both, and removed these children experiencing grandparent caregiver loss from the caregiver loss count. In the remaining proportion, we assumed again that either or both of the parents may have died in the remainder of the year after the ACS survey. We thus obtained for each year y = 1983, …, 2021 the estimated number of US children aged 0–17 years newly experiencing the loss of a caregiver of sex s and race and ethnicity r due to caregiver-loss cause-of-death c through

$$_^}=_^}}\times (1-^}})\times$$

(16b)

$$\left(1-\left(_^}}+_^}}-_^}}_^}}\right)\frac\right)$$

(16c)

$$+\left[_^}}+_^}}\right]\times$$

(16d)

$$\left(^}}+(1-^}})\left(1-^}}\right)\right)\times$$

(16e)

$$\left(1-\left(_^}}+_^}}-_^}}_^}}\right)\frac\right).$$

(16f)

In equation (16), we specified pskip gen parent died = 11% and pother parent died = 11% based on US data indicating that the large majority of grandparent caregivers provide care owing to child maltreatment, and/or parents experiencing substance misuse or incarceration31,37. We set pboth parents present = 70% based on UN data on US household composition and living arrangements of persons aged 60 or over (https://www.un.org/development/desa/pd/data/living-arrangements-older-persons), and further supported by ref. 31.

To estimate caregiver-loss prevalence, we noted that the grandparent caregiver-loss estimates are derived from cross-sectional data, and we therefore summed the orphanhood prevalence estimates in equation (8) and the de-duplicated annual grandparent-caregiver-loss contributions in equation (