Global associations between macronutrient supply and age-specific mortality

Significance

We compiled the most extensive dataset to date of corresponding national macronutrient supplies, survival statistics, and economic data. We show that the national macronutrient supply is a strong predictor of the pattern of mortality in different age classes. Our analyses can show how the optimum macronutrient supply that is predicted to maximize survival changes with age. In early life, equal amounts of fat and carbohydrate are predicted to improve survival. However, as we age, reducing fat in exchange for carbohydrates is associated with the lowest rates of mortality. Our results accord with published experimental and epidemiological data and can help define the mechanisms by which food supply and intake affect public health and demographic processes.

Abstract

Animal experiments have demonstrated that energy intake and the balance of macronutrients determine life span and patterns of age-specific mortality (ASM). Similar effects have also been detected in epidemiological studies in humans. Using global supply data and 1,879 life tables from 103 countries, we test for these effects at a macrolevel: between the nutrient supplies of nations and their patterns of ASM. We find that macronutrient supplies are strong predictors of ASM even after correction for time and economic factors. Globally, signatures of undernutrition are evident in the effects of low supply on life expectancy at birth and high mortality across ages, even as recently as 2016. However, in wealthy countries, the effects of overnutrition are prominent, where high supplies particularly from fats and carbohydrates are predicted to lead to high levels of mortality. Energy supplied at around 3,500 kcal/cap/d minimized mortality across ages. However, we show that the macronutrient composition of energy supply that minimizes mortality varies with age. In early life, 40 to 45% energy from each of fat and carbohydrate and 16% from protein minimizes mortality. In later life, replacing fat with carbohydrates to around 65% of total energy and reducing protein to 11% is associated with the lowest level of mortality. These results, particularly those regarding fats, accord both with experimental data from animals and within-country epidemiological studies on the association between macronutrient intake and risk of age-related chronic diseases.

Diet is a powerful determinant of health and life span (1, 2). More than a quarter of a century ago, Gage and O’Connor (3) modeled mortality as a function of the availability of macronutrients, demonstrating that supply is a powerful predictor of global variance in the pattern of age-specific mortality (ASM). They found that in countries with a high energy supply, a high ratio of fat to protein predicted inflated levels of mortality in late life. These findings were derived from just 170 life tables. Since then, the question of association between macronutrient supply and ASM has been untouched, despite the fact that global nutrient supply and mortality data are now much more widely available (4).

Furthermore, since Gage and O’Connor (3) published their work, a wealth of epidemiological and experimental research (clinical and preclinical) has explored the associations between diet, health, and longevity, and the underlying mechanisms. Numerous epidemiological studies have found that both specific macronutrient mixtures and overall energy intake predicts the probability of mortality and health status (e.g., refs. 5–7). In the shorter term, randomized controlled trials in people also demonstrate that dietary manipulations affect biomarkers in ways that might be predicted to translate into effects on life span (e.g., refs. 8–10).

Experimental biology has demonstrated a causal effect of calorie intake and dietary macronutrient composition on life span in model organisms (11, 12). For example, studies on mouse and fruit fly confined to a single diet across life show that, under energy sufficiency, restriction to diets high in protein reduces median life span relative to diets higher in carbohydrates (13, 14). The amounts and types of foods available also affect measures of variability in the age at death (15–17). For example, dietary treatments that increase the mean age at death in mice also increase its SD and the skew of the overall population distribution (18).

Results from these lifelong diet experiments in model animals imply that diet affects ASM. This is because the whole-population distribution of age at death is ultimately determined by the underlying pattern of ASM. In fact, studying how diet affects ASM is likely to be more informative than studying how diet affects either average life span or its variance in isolation. Through an understanding of ASM, one can define how the diet composition that minimizes the risk of mortality might change with age, and thus, what is “optimal” for a given age. One way to explore ASM is to use model life tables. Model life tables are representation theorems used by actuarial scientists to reduce whole patterns of ASM to a few representative parameters (19). These parameters can then be used for statistical analysis, and to rederive predicted patterns of ASM if so desired.

We recently applied model life tables to life span data from mice that were confined to one of 25 diets differing systematically in macronutrient composition and energy density (16). Using this “nutritional geometry” experimental design, it was possible to distinguish the effects of overall dietary energy density, as well as diet composition in terms of protein, carbohydrates, and fat (14, 20, 21). We found that, assuming an adequate overall energy density, low-protein, low-fat, high-carbohydrate diets reduced mortality through middle life. However, in late life, a higher ratio of dietary protein to carbohydrate reduced the risk of mortality (16).

These findings mirror epidemiological studies within human populations that also suggest a late-age benefit of increased protein intake in terms of health (22). For example, lower protein intake during middle age with increasing dietary protein in later life seems to be protective against Alzheimer’s disease (23). Some epidemiological studies have even detected late age-specific benefits of high protein intakes in terms of reduced all-cause mortality (24, 25).

Here, we apply the approach from Senior et al. (16) to more than 1,800 human life tables. We assess how global patterns of macronutrient supply predict ASM. We find that nutrient availability strongly predicts patterns of ASM. After correcting for economic wealth, mortality was predicted to be lowest at around 3,500 kcal/cap/d. The ratio of fats to carbohydrates that minimizes mortality also changed dramatically with age; fats at around 40% of energy were beneficial in early life, but in late life reducing this to around 25% was predicted to be best.

Results

Available Data.

We obtained life tables from the Human Life-Table Database (HLD) (https://www.lifetable.de/cgi-bin/index.php), and macronutrient supply data from the Food and Agriculture Organization Corporate Statistical Database (FAOSTAT) (26). We also gathered historical data on gross domestic product (GDP) per capita for different countries from the Maddison project (27). After collating the different sources, we obtained 1,879 country-by-year specific estimates of macronutrient supply, GDP per capita, and corresponding life tables for each sex. The data spanned 1961 through 2016 and represent 103 countries. Fig. 1 A and B show the availability of data from different countries in early (1961 to 1990) and later (1991 to 2016) years. In early years, the United States, Russia, and certain European countries are well represented. American countries, as well as Oceania and India, are also represented, but not in every year. After 1991 more countries are present, although data from Africa and Central Asia are scarce.

Fig. 1.

Summary of available data and correlations there among. (A) Percentage of years between 1961 and 1990 and (B) 1991 and 2016 for which all data are available for each country; gray indicates an absence of data. (C) Life expectancy at birth and (D and E) proportion of a cohort surviving to 5 and 60 y of age, for males (green) and females (gold) as a function of year. (F) Supplies of carbohydrate, fat, and protein (kilocalories/capita/day) as a function of year. (G) Density of distribution of supplies of carbohydrate, fat, and protein (kilocalories/capita/day) among countries in 1970, and (H) 2010. (I) GDP per capita (in US dollars) as a function of year. (J) Correlations among variables for different countries in 1970 and (K) 2010 (sexes pooled). Temporal trends were estimated using GAMMs (spanning upper to lower 95% confidence limits) and were statistically significant (SI Appendix, Tables S1–S5). In C, F, and I, data are for 1,879 country by year estimates from 103 countries. In G, J, H, and K, data are from 42 and 66 countries, respectively.

On average, life expectancy at birth (e₀; see Table 1 for all abbreviations of mortality-related statistics) as derived from these life tables increased for both sexes across the time period covered, although variation within years (i.e., among countries) is present (Fig. 1C). Similar patterns are observed for the proportion of a cohort surviving at age 5 (l₅) and at age 60 (l₆₀; Fig. 1 D and E). On average, fat supplies increased most, with smaller increases in protein (Fig. 1F). Supplies of carbohydrates tended to fall slightly up until 1990 before stabilizing (Fig. 1F). In early years, there was a bimodality in the supply of all three macronutrients (Fig. 1G), which was less pronounced in later years (Fig. 1H). Among macronutrients, protein had the lowest average supply, but was considerably more consistent in its distribution than were fat and carbohydrate (Fig. 1 G and H). On average, the GDP per capita of the countries for which data were available increased over time (Fig. 1I). GDP per capita positively correlated with e₀ within years, at both early and late time points (e.g., Fig. 1 J and K). In earlier years there were positive correlations among all macronutrients, total energy supply, and e₀, although carbohydrate supplies were negatively associated with GDP (Fig. 1J). However, by 2010, carbohydrates were negatively correlated with e₀, as well as other macronutrient supplies and GDP (Fig. 1K). It is also worth noting that, across all observations, on average 52.8% (SD, 12.9%) of protein energy came from animal sources. Additionally, there was a positive correlation at both early and late timepoints between total protein supply, and the percentage of protein coming from animal sources (e.g., Fig. 1 J and K).

Table 1.

Notation and description of key mortality-related statistics

Notation	Name	Description
ex	Life expectancyat age x	The average number of years of life remaining for individuals entering age class x. A special case is e0, which is life expectancy at birth, or the average age at death of all individuals in a cohort.
lx	Cohort survival to age x	The proportion of a cohort surviving to age class x (1 for age class 0). For example, l60 = 0.9 indicates 90% of individuals are expected to reach age 60.
qx	Probability of mortality within age class x	Probability of dying within the age class beginning at age x. For example, q5–10 = 0.001 indicates 1% of individuals are expected to die between the moment they turn 5 y old and the moment immediately prior to turning 10.
α	Model life table parameter 1	Model life table parameter, which along with β, can be used to predict an entire pattern of ASM. Positively correlates strongly with late-life survival, and also with e0.
β	Model life table parameter 2	Model life table parameter, which along with α, can be used to predict an entire pattern of ASM. Positively correlates strongly with early-life survival, and also shares a weaker positive correlation with e0.

In summary, the available data span a period of demographic, nutritional, and socioeconomic change. Life expectancy at birth and macronutrient supplies display substantial variation both among countries within years, and across years.

Model Life Tables.

We used the Brass relational system to condense each life table to two representative parameters for analysis (28, 29). With this method, the pattern of cohort survival to age x (l_x) in a life table is reduced to the parameters, α and β, via its relationship to a “standard life table.” At its most basic, the Brass method proposes l_x for a life table of interest can be found as follows:

$$\text{logit}\left(l_x\right)=\alpha +\beta \times \text{logit}\left(l_x^s\right),$$

where logit is a logit transformation, α and β are life table-specific parameters, and $l_x^s$ is the pattern of cohort survival in the standard life table. Wherever a common series of $l_x^s$ is used, the α and β values of different life tables are comparable summaries of the pattern of survival therein. We used a variant of the Brass method that has been slightly modified to model human life tables specifically (30). For each life table in each sex, we estimated values of α and β (Fig. 2 A and B). Rederiving each life table from its estimated α and β values generated patterns of l_x that correlated very strongly with the observed data (males, r² = 0.997; females, r² = 0.997), suggesting that the approach captures the underlying life tables well. Within this dataset, α associates with life expectancy at birth, e₀, very strongly, and β also shares a positive but weaker correlation with e₀ (Fig. 2 C and D). α predicts late life survival most strongly (l₆₀), and β, early life survival (l₅; Fig. 2 E–H).

Fig. 2.

Distributions of life table parameters and their associations. Density of distribution of life table-specific values of (A) α and (B) β. Association between life expectancy at birth (e₀) as derived from life tables and life table-specific values of (C) α and (D) β. Association between α and (E) proportional survival at age 5 (l₅) and (F) age 60 (l₆₀). Association between β and (G) l₅ and (H) l₆₀. On all panels, males are shown in green and females in gold. On C and D, r² is the coefficient of determination estimated as the square of the Pearson’s correlation coefficient between variables within each sex.

Macronutrients and Mortality.

To quantify the association between macronutrient supply and ASM, we stratified the dataset by sex and analyzed α and β as responses in a series of multiresponse generalized additive mixed models (GAMMs). The GAMMs explored the effects of macronutrient supply space as a three-dimensional (3D) effect, along with effects of time and GDP (for a full list of models see SI Appendix, Table S6). We highlight here that we have not further separated macronutrients into subtypes (e.g., animal vs. plant proteins) because we are already dealing with a highly multidimensional dataset that contains complex covariances. We do, however, return to this issue in our discussion of the results. All models corrected for idiosyncratic differences among countries through the repeated temporal observations via a random effect. Models were compared using Akaike information criterion (AIC) and Akaike weights. For both sexes, a model that considered an interactive effect of time and supply, and an additive effect of GDP was favored (SI Appendix, Table S6). These results suggest that 1) macronutrient supply is predictive of patterns of ASM independently of its covariance with wealth, and 2) the association between macronutrient supply and ASM has changed over time. The AIC-favored model has captured this changing association between supply and ASM over time, although from hereon we focus on predictions for the most recent year for which all data are available, 2016. A complete description of the predicted temporal effect has been provided in SI Appendix, Text S1 and Figs. S1–S4.

For females, the α value (which strongly correlates with survival to late age, and life expectancy at birth) is maximized with high protein (400 to 450 kcal/cap/d) and carbohydrate (1,800 to 2,000 kcal/cap/d) supplies, and moderate fat supplies (1,200 kcal/cap/d) (Fig. 3 A–C). The β parameter (which correlates most strongly with early life survival) shows almost the obverse association, and is maximized at a low carbohydrate, low protein supply, and at high fat supplies (Fig. 3 D–F). The same pattern is seen in males (Fig. 3 G–L).

Fig. 3.

Predicted effects of protein, carbohydrate, and fat supply (kilocalories/capita/day) on life table parameters. The first column shows the effects of protein and carbohydrate, the second shows protein and fat, while the final column shows carbohydrate and fat. On each panel, the third macronutrient is held at the median for the dataset (value shown). Colors denote the value of the outcome, where red is the maximal and blue is the minimal, with the scale common across panels on the same row. The outer hull of the displayed prediction is determined by the distribution of the observed data. (A–C) α in females. (D–F) β in females. (G–I) α in males. (J–L) β in males. Surfaces were predicted using a GAMM. Predictions are shown for a “typical country” in 2016 and assume a GDP per capita of 31,322 (2011 USD; median GDP for 2016). Effects of macronutrient supply on α and β were statistically significant in both sexes (SI Appendix, Table S7).

Using these predicted values for α and β, it is possible to estimate an entire life table and associated statistics for a given nutrient supply. As shown in SI Appendix, Fig. S5, doing so reveals that the patterns for α shown in Fig. 3 reflect almost exactly the patterns for the effect of macronutrient supply on e₀, which is unsurprising given the strength of correlation between these parameters (Fig. 2C). We can also assess how the probability of mortality within each age class (q_x) is affected by macronutrient supply. Fig. 4 shows the q_x in childhood (q_5–10), and at the onset of late life (q_60–65) as derived from the predicted α and β values in Fig. 3. For females between ages 5 and 10, the q_x is lowest on high fat and protein supplies, with carbohydrates at around 1,500 kcal/cap/d. In contrast, q_5–10 is high with low supplies of all macronutrients (i.e., low total energy; Fig. 4 A–C). As age increases, the predicted association changes, with low fat and low protein supplies having a much less detrimental effect (Fig. 4 D–F). In males, low fat in concert with low protein is predicted to be particularly detrimental at younger ages, although for the most part the patterns in the sexes are similar (Fig. 4 G–L).

Fig. 4.

Predicted effects of protein, carbohydrate, and fat supply (kilocalories/capita/day) on the probability of mortality at different age classes. Derived from life tables estimated using the predicted values of α and β in Fig. 3. The first column shows the effects of protein and carbohydrate, the second shows protein and fat, while the final column shows carbohydrate and fat. On each panel, the third macronutrient is held at the median for the dataset (value shown). (A–C) Age class 5 to 10 in females. (D–F) Age class 50 to 55 in females. (G–I) Age class 5 to 10 in males. (J–L) Age class 50 to 55 in males.

Fig. 5 A and B shows the total energy supply and macronutrient composition that is predicted to minimize q_x for every age class. The total energy supply that minimizes mortality is relatively stable at around 3,500 kcal/cap/d, but the optimal composition of that energy changes with age (Fig. 5 A and B). Below the age of 20, lowest mortality is associated with around 16% of energy from protein and approximately equal proportions of carbohydrates and fat (Fig. 5 A and B). With age, the composition minimizing mortality changes gradually, before going through a more sudden transition. By age 60 in males and 80 in females, mortality is predicted to be lowest at around 67% of energy from carbohydrates and 11% protein.

Fig. 5.

Effects of nutrient supply on mortality at different age classes. (A) Composition of total energy supply in terms of protein, carbohydrates, and fat (percentage), as well as total energy supply (kilocalories/capita/day) associated with the lowest probability mortality at each age (q_x) for females in 2016. (B) As in A for males. (C) Predicted effect of increasing (red) and decreasing (blue) all three macronutrient supplies by 10% on mortality at each age class (q_x) in the sexes relative to the median supply (values shown). The black horizontal line indicates no effect. (D–F) As in C, but for protein, carbohydrate, and fat individually. Predictions are derived from the AIC-favored GAMM and are shown for a “typical country” in 2016 and assume a GDP per capita of 31,322 (2011 USD; median GDP for 2016).

Using these models, we can also ask how mortality might be expected to respond to changes in supply. In Fig. 5 C–F, we have tested the sensitivity of mortality in each age class to a 10% change from the median supplies (median protein, carbohydrate, and fat: 402, 1,554, and 1,159 kcal/cap/d, or 13%, 50%, and 37%). Decreasing the total energy supply increases q_<90 in both sexes although the effect is stronger in males (at ages 90+, nutrient supply is predicted to have little effect; Fig. 5C). Increasing total energy relative to the median reduces mortality in middle age (40 to 85), but at other ages either has little effect or is detrimental (Fig. 5C). Increasing the protein supply by 10% while holding the other supplies constant (and thus altering their ratio) reduces q_<90 in both sexes, while decreasing protein increases mortality (Fig. 5D). Decreases in carbohydrate are predicted to increase mortality at ages above 25 in both sexes (Fig. 5E). Increases in carbohydrate are associated with higher mortality prior to age 25 but decrease it above the age of 40 (Fig. 5E). Prior to the age of 25, we again see a beneficial effect of fats, whereby increasing fat decreases mortality and vice versa (Fig. 5F).

The 14-Wealthy Country Subset.

In their recent analyses of dietary macronutrient intake, Lieberman et al. (31) identified 14 countries with a high GDP per capita where protein intakes were relatively stable and comparable. Those countries were as follows: Australia, Canada, Czech Republic, Finland, France, Germany, Ireland, Japan, Korea, Netherlands, Norway, Poland, the United Kingdom, and the United States. For these countries, the average percentage of protein energy from animal sources is higher than in the complete dataset (mean, 58.8%; SD, 9.8%). We repeated our life table analyses on this same subset of countries using the FAOSTAT supply data.

Fig. 6 shows the associations between macronutrient supply and α and β in this subset. There are two key points of contrast evident from comparisons between Figs. 3 and 6. First, the region of the nutrient space inhabited by these countries is a subregion of that in Fig. 3. In this subset, low protein, low fat, and high carbohydrate supplies are not as well represented. Second, the shape of the association between macronutrient supplies and mortality differs for this subset of countries. For example, in the subset, simultaneously abundant supplies of all three macronutrients tend to decrease α, especially so for high fat supplies (Fig. 6). Again, as shown in SI Appendix, Fig. S6, the surface for the α parameter also reflects the association between supply and life expectancy at birth. The 14 countries identified by Lieberman et al. (31) therefore represent a fairly wealthy group of countries with greater access to proteins and fats, but lower supplies of carbohydrates than the complete cases analyses. In this subset, the effects of “overnutrition” on life expectancy are evident.

Fig. 6.

As in Fig. 3 but for the 14-country subset. (A–C) α in females. (D–F) β in females. (G–I) α in males. (J–L) β in males. Predictions are shown for a “typical country” in 2016 and assume a GDP per capita of 39,162 (2011 USD; median GDP for 2016 in this subset). Effects of macronutrient supply on α and β were statistically significant in both sexes (SI Appendix, Table S8).

In these countries, the composition of macronutrient supply associated with the lowest level of mortality changes very little with age in either sex. Mortality is lowest at just under 3,000 kcal/cap/d with around 50% energy from carbohydrates, 35 to 40% energy from fat, and 10 to 15% energy from protein (Fig. 7 A and B). Like the complete cases analysis above, beyond age 90 altering the macronutrient supply is predicted to have little effect on mortality (Fig. 7 C–F). Increasing total energy, energy from carbohydrates, and energy from fats relative to the median is predicted to heavily increase mortality across ages in both sexes, although males most strongly (Fig. 7 C, E, and F). Either increasing or decreasing protein supplies is predicted to reduce mortality across all ages (Fig. 7D).

Fig. 7.

Effects of nutrient supply on mortality at different age classes in the 14-country subset. (A) Composition of total energy supply in terms of protein, carbohydrates, and fat (percentage), as well as total energy supply (kilocalories/capita/day) associated with the lowest probability mortality at each age (q_x) for females in 2016. (B) As in A for males. (C) Predicted effect of increasing (red) and decreasing (blue) all three macronutrient supplies by 10% on mortality at each age class (q_x) in the sexes relative to the median supply (values shown). The black horizontal line indicates no effect. (D–F) As in C, but for protein, carbohydrate, and fat individually. Predictions are derived from the AIC-favored GAMM and are shown for a “typical country” in 2016 and assume a GDP per capita of 39,162 (2011 USD; median GDP for 2016 in this data subset).

Discussion

Here, we have presented the first analysis of associations between patterns of national ASM and macronutrient supply since Gage and O’Connor (3) over 25 y ago (4). We have been able to make several advances over the earlier analysis. First, owing to the greater availability of data, we have considered an order of magnitude more life tables than did Gage and O’Connor (3). Second, thanks to advances in statistical modeling we were able to model nutrient supply without relying heavily on dimension reduction (e.g., nutrient ratios and principal components). This approach has allowed us to separate the potential effects of total energy and supply composition, as well as nonlinear associations. Third, we made statistical corrections for time, economic wealth, and stochastic differences in overall mortality among countries.

We found that the supply of macronutrients available to a population is predictive of observed patterns of ASM. The overall energy supply that is associated with minimal mortality is relatively stable at (∼3,500 kcal/cap/d) with age, but composition of energy in terms of macronutrients is not. In early life, around 40 to 45% energy from each of fat and carbohydrates and 16% from protein minimizes mortality. However, for later life, lower fat and protein supplies at 22% and 11%, respectively, and replacing these with carbohydrates is associated with the lowest rate of mortality; these changes also constitute a drop in the ratio of protein to carbohydrate (P:C), and an increase in protein to fat (P:F) with age. For reference, the United States recommends that protein contribute 10 to 35% of energy; carbohydrate, 45 to 65%; and fat, 20 to 35% for adults (32).

The benefit of increasing P:F with age that we saw was also noted by Gage and O'Connor (3). Numerous other studies have also observed an association between fat (at the levels of supply and intake) and the risk of specific age-related diseases (e.g., refs. 33–39). Considering cancers alone, in women there are positive correlations between national fat supplies and the risk of mortality due to breast cancer (35). This pattern also seems present at the level of fat intake and the risk of developing breast cancer (40). Ecological studies find similar associations between fat supplies/intake and prostate cancer (34, 41), as well as non–sex-specific cancers (41, 42).

Such results have typically been interpreted as evidence for a detrimental effect of fat on health. As we describe for our data above, however, changes in energy from fats are often also accompanied by changes in other dietary metrics such as P:C. In experimental systems where the causal effects of macronutrients have been separated, P:C has emerged as one the primary determinants of life span independently of fat (11, 13, 14). In mice, for example, being constrained to low P:C diet throughout life (excluding very early ages for very low-protein, low-energy diets) extends life expectancy by minimizing mortality throughout middle age (16). Similarly, the longest-lived human populations have a low P:C diet, such as the traditional Okinawan diet (11, 43).

Whereas a low P:C diet reduces midlife mortality (a pattern evident in the global supply data), epidemiological and experimental data suggest increasing protein intake in late life may improve health and minimize mortality (16, 22–24). In contrast, we found that the protein supply associated with minimal mortality falls monotonically with age. Three nonexclusive factors must be considered when interrogating why trends differ at the two levels. First, we have modeled risk of mortality as a function of concurrent nutrient supply. However, health in old age (and therefore risk of death) is likely to be influenced by nutritional intake over many preceding years. Indeed, the physiological footprint of former nutritional intakes can be detected later within an individual’s lifetime and even intergenerationally via epigenetic changes (44–46). The historical trajectory of a country’s nutrient supply therefore contains additional information when trying to assess mortality risk in the elderly. Second, studies that argue the case for elevated protein intake in old age, do so on the basis that high protein helps to offset the costs of disease burden and prevents lean muscle loss (22). If, however, one reaches old age in relatively good health (e.g., due to a lifetime on a low P:C diet), then there may not necessarily be any benefit to elevated dietary protein.

Finally, the epidemiological results that suggest benefits of increased protein in old age are typically based on intracountry variation in protein intake, rather than intercountry variation in supply. Supply sets the upper limits to nutrient intake (47), and consequently the two are positively correlated, but not always strongly so (48). The food balance sheets used here misestimate intakes depending on intermediaries that vary as a function of food group, geographical region, and even age itself (38, 49–51). It is these intermediaries that transform the relationship between supply and ASM (which we report), into that between intake and health (as described elsewhere; e.g., ref. 23). With the more widespread release of national nutritional surveys, it will be possible to assess how international variation in protein intake (rather than supply) predicts variation in ASM (e.g., ref. 51). Furthermore, where possible, contrasts between subpopulations within countries may also allow for better control of international confounders.

A further analysis that may also provide a supplementary perspective is at the level of food groups. In the case of protein supply, for example, we observed that there is a positive correlation between total protein and percentage of protein from animal sources. Thus, while we found a lower protein supply is associated with minimal mortality in older age, it is difficult to separate this from the potential benefits of moving to a supply richer in plant-based foods (e.g., ref. 52). An analysis at the level of food groups could help separate these effects.

For observational studies such as ours, there will always be the issue of confounding. We have attempted to correct for confounding by including economic data, and repeated measures. We also report results where we confined our analyses to wealthy countries, many of which exhibit characteristics of what is sometimes labeled a “western diet pattern” (e.g., elevated intake of animal-based foods and increased reliance on industrially processed, energy-dense foods) (53). The results of the 14-country subset showed some interesting contrasts with those for the complete data. The subset analysis clearly reflects the detrimental effects of overnutrition; increasing total energy as well as supplies of fats and carbohydrates was associated with increased mortality at all ages. This is in stark contrast to the results of the more inclusive analysis where the effects of undernutrition on life expectancy appear dominant [also noted by Gage and O’Connor (3)]. For those countries considered in the complete cases analysis, the median protein supply was 402 kcal/cap/d (13% of total energy) in 2016. At this level, increasing national protein supplies by just 10% is associated with reductions in mortality in all age classes and both sexes.

Our study has shown that national supplies of macronutrients associate with patterns of ASM. The supply that minimizes mortality in early life is substantially higher in fats than the supply that minimizes mortality in late life. This finding correlates with other ecological studies that find associations between dietary fat and the risk of noncommunicable age-related diseases (e.g., refs. 33–39). The global patterns also reflect the effects of undernutrition on life expectancy even as recently as 2016. As national/subnational survey data become more widely available, it will be possible to repeat our analyses at a level that allow for more robust inference about nutrient intake rather than supply.

Materials and Methods

Data.

We obtained life tables from the Human Mortality Database’s HLD (https://www.lifetable.de/cgi-bin/index.php). The HLD is a collection of national and subnational population life tables, which were collected from official statistical and scientific publications, national reports, and datasets collected by individual researchers. The HLD is highly inclusive and accepts data from a range of sources. Our aim was to obtain life tables from as broad a spectrum of countries and years as was available, and we therefore downloaded the entire HLD on February 4, 2020. We only consider life tables designated as being for a whole population, and in the event that a source reported multiple life tables for the same country and year, we preferred life tables derived from whole life table, or else data from abridged life tables were used. Where several sources reported whole life tables for the same country and year, we averaged ASM statistics.

Food balance datasheets were taken from the FAOSTAT (26) on February 4, 2020. The FAOSTAT provides food balance sheets as far back as 1961, and any life table data going back further than that were discarded. From the food balance sheets, we extracted data on total food (kilocalories), protein (grams), fat (grams), and alcohol (kilocalories) supply per capita per day. We calculated carbohydrate supply in kilocalories/capita/day as the residual of total supplies less protein (assuming 4 kcal/g), fat (assuming 9 kcal/g), and alcohol supplies. We obtained historical data on GDP per capita in 2011 US dollars from the Maddison project (27). After collating mortality, nutrition, and GDP data across sources, we were left with 1,879 life tables in each sex from 103 countries spanning 1961 to 2017. All data were processed and analyzed using R (54), and in the event that we report correlation coefficients, r refers to a Pearson’s correlation coefficient.

Model Life Tables.

Model life tables are representation theorems that allow whole patterns of ASM as given within a cohort life table to be summarized using a few parameters. The Brass relational logit life table system is one such representation theorem, which relates life tables based on the logit transformation of the proportion of a cohort surviving to specific age classes (l_x) (28, 29).

Applied to human populations, Murray et al. (30) demonstrate that the Brass system can be used to unbiasedly model the proportion of a cohort (i) surviving to age x (l_x) as follows:

$$\text{logit}\left(l_x^i\right)={\alpha }_i+{\beta }_i\times \text{logit}\left(l_x^s\right)+{\gamma }_x\left(1-\frac{\text{logit}\left(l_5^i\right)}{\text{logit}\left(l_5^s\right)}\right)+{\theta }_x\left(1-\frac{\text{logit}\left(l_{60}^i\right)}{\text{logit}\left(l_{60}^s\right)}\right),$$ [1]

where logit is a logit transformation, $l_x^i$ is the proportion of cohort i surviving at age x, α_i and β_i are coefficients specific to cohort i, $l_x^s$ is the proportion of a “standard” cohort surviving to age x (which captures the general shape of survival to each age-class), and γ_x and θ_x are standard-specific constants for age x (0 for ages 5 and 60) specifically derived for human survival. Based on Eq. 1, a whole human life table can be reconstituted using the two population-specific coefficients α_i and β_i and the corresponding standard life table pattern (comprising the series of $l_x^s$, γ_x, and θ_x). Using a common standard, a whole series of life tables can be summarized by their α and β coefficients, which can themselves then be modeled as a function of some predictor (e.g., time, economic indicators, or nutrient supply). Murray et al. (30), who originally describe the method, do provide a standard pattern for ages 0 through 85, although here we used the updated standard pattern provided by Wilmoth et al. (55), which includes ages 0 through 110.

For a population of life tables, one may estimate the distribution of α and β in Eq. 1 from a sample of life tables using a linear mixed-effects model (LMM) as in Eqs. 2 and 3:

$$\text{logit}\left(l_x^i\right)=\alpha +{\delta }_{\alpha }^i+\left(\beta +\hspace{1em}{\delta }_{\beta }^i\right)\times \text{logit}\left(l_x^s\right)\hspace{1em}+{\tau }_x+{\eta }_x+{\epsilon }_x^i\text{,}$$ [2]

$${\delta }_{\alpha }^i\sim \text{N}\left(0,{\sigma }_{\alpha }\right),{\delta }_{\beta }^i\sim \text{N}\left(0,{\sigma }_{\beta }\right),{\epsilon }_x^i\sim \text{N}\left(0,{\sigma }_{\epsilon }\right),$$ [3]

where $l_x^i$ and $l_x^s$ are as above, α and β give the life table coefficients for a “typical” cohort, ${\delta }_{\alpha }^i$ and ${\delta }_{\beta }^i\hspace{1em}$are random-regression coefficients for the deviation of cohort i from the typical values of α and β, which are assumed to be normally distributed with mean 0 and SDs σ_α and σ_β , τ_x and η_x are age-specific constants derived from the standard pattern as in Eqs. 4 and 5, and ${\epsilon }_x^i$ is the residual for cohort i at age class x. τ_x and η_x are calculated as follows:

$${\tau }_x=\hspace{1em}{\gamma }_x\left(1-\frac{\text{logit}\left(l_5^i\right)}{\text{logit}\left(l_5^s\right)}\right),$$ [4]

$${\eta }_x={\theta }_x\left(1-\frac{\text{logit}\left(l_{60}^i\right)}{\text{logit}\left(l_{60}^s\right)}\right)\text{.}$$ [5]

We fitted a LMM equivalent to Eqs. 2 and 3 in the R package lme4 using the “lmer” function (56). In the model, the response was logit transformed proportion of a cohort surviving to age x (l_x; at age classes 1, 5, 10, 15 … 110) for all life tables. The corresponding survival in the standard pattern $\left(l_x^s\right)$ was a fixed effect; the cohort (country and year from which the life table data came) was a random effect with a random intercept and slope for $l_x^s$ (i.e., ${\delta }_{\alpha }^i$ and ${\delta }_{\beta }^i$ in Eq. 2). Importantly, because we had life tables for each sex, we also included sex (male or female) in the model as an interaction with the fixed and random terms for $l_x^s$ giving us sex-specific estimates for the coefficients; these could also be obtained by subsetting the data and estimating the model for each sex separately. τ_x and η_x for each age class and sex in each cohort were calculated following Eqs. 4 and 5 and included in the LMM as “offset” terms (i.e., a fixed effect with a coefficient fixed at 1). The standard pattern used to derive the predictors was taken from SI Appendix, table S2 in Wilmoth et al. (55). All estimates of terms from the LMM can be found in SI Appendix, Table S9. From the LMM, we extracted the random effect estimates for each cohort life table (${\delta }_{\alpha }^i$ and ${\delta }_{\beta }^i$) and calculated cohort-specific estimates of the model life table coefficients as ${\alpha }_i=\alpha +{\delta }_{\alpha }^i$ and ${\beta }_i+\mathrm{\beta }+{\delta }_{\beta }^i$ (with the addition of the coefficients for sex where necessary).

Where we needed to compute life tables from a pair of α and β values, we first estimated l_x based on Eq. 1. The series of l_x was then used to derive the complete life table including life-expectancies in each age class (e_x) using the “LifeTable” function in the R package, MortalityLaws (57).

GAMMs.

GAMMs were used to assess changes in variables of interest over time, and effects of macronutrient supply and GDP. GAMMs are similar to generalized linear mixed models (GLMMs) in that they contain a mix of random and fixed effects. However, in addition to the usual linear fixed effects that appear in GLMMs, GAMMs can include nonlinear terms as nonparametric smoothed functions. These smooth functions are usually a form of spline, which provide a flexible approach for estimating nonlinear associations. All models were implemented using the R package, mgcv using the “gam” function (58, 59). All GAMMs included the country for which data refer as a random effect. In all models, the gamma term, which specifies the degree to which the estimated effect is smoothed was specified as log(n)/2 (59) (where n is the sample size; here number of estimates of model life table parameters). For the temporal trends in Fig. 1, year was fitted as a smooth predictor (with separate smooth terms for each sex where relevant). Life expectancy at birth (e₀) and GDP per capita were modeled using a Gaussian family with a log-link function, macronutrient supply using Gaussian family with an identity-link function, and survival at ages 5 (l₅) and 60 (l₆₀) as a beta family with a logit-link function.

To assess effects of macronutrient supply on the life table parameters α and β, we used multiresponse GAMMs, where the two parameters were treated as response variables. We stratified the dataset by sex and for each sex built a series of models. The models included a null model that contained only the country as a random effect. Further models then included all combinations of the individual, additive and two-way interactions between macronutrient supply, year, and GDP per capita. Macronutrient supply was modeled as a 3D thin-plate spline. GDP and year were modeled as single-dimensional cubic-regression splines [“s()” function in mgcv]. Where we allowed interactions between smooth terms that exist on different scales (e.g., year and macronutrient supply), tensor product smoothers were used [“te()” function in mgcv]. Models were compared via AIC, and models with lower AIC values were favored (60). We calculated Akaike weights following Eq. 3 in Wagenmakers and Farrell (61), and the Akaike weight is a conditional probability that reflects the relative weight of evidence in support of each model (1 = complete support; 0 = no support). In places we found the protein, carbohydrate, and fat supplies predicted to have the lowest level of mortality for a specific age class as given by a GAMM. This was done using a general-purpose optimizer (“optim” function in Base R and default settings). For each age class, the optimizer was initiated with 500 different sets of starting values drawn from a random multivariate normal distribution with population statistics based on the observed supplies.

To test the sensitivity of our results to biases in the available data, we performed two sets of sensitivity analyses. In the first set of sensitivity analyses, we repeated our analyses using imputation to estimate missing data for some countries and years. We used the function “mice” in the R packages mice and miceadds (62, 63). In the second set of sensitivity analyses, we randomly split the complete cases dataset into two random halves and reapplied the AIC-favored model to these subsets. The conclusions drawn from all sensitivity analyses concur with those from the analyses in the main text, as shown in SI Appendix, Text S2 and S3.

Data Availability.

All analyses are performed on publicly available data with sources stated explicitly in text. For any future analyses, it is recommended that up-to-date data be obtained from the cited sources. All code and data for the current analyses can be found at GitHub, https://github.com/AlistairMcNairSenior/ASM_HumanLT.