1. Epidemiology and Global Health
  2. Microbiology and Infectious Disease
Download icon

Global divergence in critical income for adult and childhood survival: analyses of mortality using Michaelis–Menten

  1. Ryan J Hum  Is a corresponding author
  2. Prabhat Jha
  3. Anita M McGahan
  4. Yu-Ling Cheng
  1. University of Toronto, Canada
  2. St Michael's Hospital, Canada
Research Article
Cite this article as: eLife 2012;1:e00051 doi: 10.7554/eLife.00051
6 figures, 4 tables, 9 data sets and 1 additional file

Figures

(A) The original ‘Preston curve’ (plotted as a logistic function) demonstrating an upward shift from 1930 to 1960. Source: Preston (1975). (B) A hypothetical Michaelis–Menten plot with kinetic parameters vmax and Km.

https://doi.org/10.7554/eLife.00051.003

(A) The graphical similarity between the logistic, log-linear, and Michaelis–Menten model fits of life expectancy for the year 1990. (B) Preston curve plotted as an enzyme kinetics reaction with coefficients critical income and maximum life expectancy for the years 1970 and 2007.

https://doi.org/10.7554/eLife.00051.004

Trends for maximum survival (A) and critical income (B) for children and adults from 1970 to 2007.

https://doi.org/10.7554/eLife.00051.007

Adult male (A) and female (B) survival regression curves for the years 1970 and 2007. Adult survival in 2007 is lower than in 1970 for countries under the income threshold of $10.95 (for men) and $5.93 (for women).

https://doi.org/10.7554/eLife.00051.009

Impact of smoking and HIV on critical income for adult males in 2000.

https://doi.org/10.7554/eLife.00051.010

Child, adult male and adult female maximum survival (A) and critical income (B) curves from 1970 to 2005 using two different data sources (IHME and UN Population Division). Maximum survival and critical income values were calculated using 5-year averages where the national income per capita and country survival rates for year i was an average for the years i to i + 4.

https://doi.org/10.7554/eLife.00051.012

Tables

Table 1

Maximum life expectancy, critical income, and regression coefficients (95% confidence intervals) for all countries at 5-year intervals from 1970 to 2007

https://doi.org/10.7554/eLife.00051.005
YearnR2MaxLife expectancy (LEmax, years)5% trimmed mean LE for high-income countriesIncome require for varying levels of LEmax
Full sample95% random sampleCritical income (Kinc, 50%)66.70%80%90%
Full sample95% random sample
19701480.53567.8 (65.4–70.1)67.666.71.48 (1.18–1.78)1.432.965.9213.32
19751480.57469.3 (67.2–71.4)69.270.31.50 (1.22–1.77)1.533.006.0013.50
19801490.66871.3 (69.6–73.0)71.171.81.51 (1.28–1.74)1.463.026.0413.59
19851520.71673.2 (71.8–74.8)73.173.21.50 (1.29–1.70)1.463.006.0013.50
19901640.73574.6 (73.2–75.9)73.574.31.45 (1.27–1.63)1.342.905.8013.05
19951770.67775.0 (73.6–76.4)74.875.41.31 (1.13–1.49)1.272.625.2411.79
20001780.6475.2 (73.8–76.7)75.376.21.27 (1.08–1.46)1.272.545.0811.43
20051770.53275.3 (73.6–76.9)75.676.51.19 (0.97–1.41)1.232.384.7610.71
20071720.52175.5 (73.9–77.1)75.776.41.21 (0.98–1.44)1.222.424.8410.89
  1. Note: All model parameters were found to be significant, p<0.0001.

Table 2

Comparison of the logistic adapted Michaelis–Menten and log-linear models for the year 1990

https://doi.org/10.7554/eLife.00051.006
ModelFormR2Parameters
LogisticLE=LEmaxa+e(b×GDP)0.745LEmax = 73.6 (72.1–75.1)a = 0.642 (0.546–0.739)b = 0.129 (0.159–0.100)Inflection point = −3.43
Adapted Michaelis–MentenLE=LEmax×GDP(kinc+GDP)0.735LEmax = 74.6 (73.2–75.9)kinc = 1.50 (1.29–1.70)
Log-linearLE = a + b × ln(GDP)0.731a = 44.1 (42.0–46.2)b = 7.65 (6.93–8.37)
Table 3

Maximum survival, critical income, and regression coefficients (95% confidence intervals) from 1970 to 2005

https://doi.org/10.7554/eLife.00051.008
YearChildFemaleFemale (with HIV covariate)MaleMale (with HIV covariate)
R2Max%Kinc, $R2Max%Kinc, $R2Max%Kinc, $HIVR2Max%Kinc, $R2Max%Kinc, $HIV
19700.44494.5 (92.7–96.2)0.58 (0.46–0.70)0.37685.9 (84.1–87.7)0.57 (0.43–0.70)0.25377.7 (75.6–79.7)0.54 (0.38–0.71)
19800.56996.9 (95.7–98.2)0.57 (0.48–0.66)0.44888.3 (86.7–89.9)0.62 (0.49–0.74)0.28679.5 (77.5–81.6)0.65 (0.46–0.83)
19900.62998.3 (97.4–99.2)0.48 (0.42–0.55)0.48290.2 (88.7–91.8)0.68 (0.55–0.81)0.59590.4 (88.8–91.4)0.54 (0.41–0.67)−1.8 (−1.2 to −2.4)0.38082.1 (80.2–84.1)0.81 (0.62–0.99)0.49881.8 (79.8–83.8)0.60 (0.42–0.79)−2.2 (−1.3 to −2.8)
20000.53097.9 (97.2–98.7)0.30 (0.25–0.34)0.37790.2 (88.0–92.4)0.86 (0.65–1.06)0.78792.1 (90.5–93.6)0.69 (0.55–0.82)−1.8(−1.6 to −2.0)0.28481.9 (79.0–84.8)1.10 (0.77–1.43)0.72083.5 (81.4–85.6)0.79 (0.57–1.00)−2.2 (−1.9 to −2.5)
20050.46698.0 (97.3–98.6)0.25 (0.20–0.29)0.32390.1 (87.8–92.3)0.86 (0.63–1.12)0.80392.4 (90.9–93.8)0.68 (0.54–0.81)−2.2(−1.8 to −2.5)0.25482.0 (79.0–85.0)1.14 (0.81–1.58)0.73984.2 (82.1–86.3)0.82 (0.59–1.04)−2.6 (−3.0 to −2.2)
  1. Note: All model parameters were found to be significant, p<0.0001.

Table 4

First differences analysis for HIV prevalence and cigarette consumption on country-specific critical income from 1990 to 2000

https://doi.org/10.7554/eLife.00051.011
NR2HIV α ($ per HIV %)Standardized αSmoking β ($ per cigarette per person per day)Standardized β
Adult male920.2400.70 (0.27–1.13)0.3021.70 (0.96–2.43)0.425
Adult female920.5040.40 (0.31–0.49)0.6550.38 (0.23–0.54)0.366
  1. Note: All model parameters were found to be significant, p<0.0001.

Data availability

The following data sets were generated
  1. 1
  2. 2
  3. 3
    Estimated HIV Prevalence (Ages 15–49)
    1. UNAIDS
    (2010)
    Publicly available.
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9

Additional files

Supplementary file 1

Country specific critical incomes for adult male, adult female and children (in constant $2005 with purchasing price parity) for the years 1970, 1990 and 2007.

https://doi.org/10.7554/eLife.00051.013

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)