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  "Title": "Decompose Life Expectancy by Age (and Cause)",
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    "sen_lopez_ruzicka_sym",
    "sen_lopez_ruzicka_sym_instantaneous",
    "sen_lopez_ruzicka_sym_instantaneous2",
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    "sen_num",
    "sen_resid"
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      "tojson": true
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        "sex",
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        "mx"
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      "page": "abridge_mx",
      "title": "Abridge a single-year mx schedule to 0,1,5,... using lifetable quantities",
      "topics": [
        "abridge_mx"
      ]
    },
    {
      "page": "ald_to_Lx",
      "title": "Calculate the lifetable exposure",
      "topics": [
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      ]
    },
    {
      "page": "andreev",
      "title": "Andreev (1982) component decomposition of e0 difference by age",
      "topics": [
        "andreev"
      ]
    },
    {
      "page": "andreev_sym",
      "title": "Decompose using a symmetrical variant of the Andreev components approach.",
      "topics": [
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    },
    {
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      "title": "classic Arriaga decomposition",
      "topics": [
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    },
    {
      "page": "arriaga_sym",
      "title": "Decompose using a symmetrical variant of the Arriaga approach.",
      "topics": [
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      "title": "List available decomposition methods",
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        "available_methods"
      ]
    },
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      "page": "chandrasekaran_II",
      "title": "II approach of Chandrasekaran decomposition approach",
      "topics": [
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    },
    {
      "page": "chandrasekaran_III",
      "title": "Chandrasekaran III decomposition",
      "topics": [
        "chandrasekaran_III"
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    },
    {
      "page": "LEdecomp",
      "title": "Function for applying different Life-Expectancy decomposition and sensitivity methods",
      "topics": [
        "LEdecomp"
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    },
    {
      "page": "lL_to_ex",
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      "topics": [
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      ]
    },
    {
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      "title": "Lopez-Ruzicka decomposition",
      "topics": [
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    {
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      "title": "Symmetric Lopez-Ruzicka decomposition",
      "topics": [
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    },
    {
      "page": "lx_to_dx",
      "title": "Calculate the lifetable death distribution",
      "topics": [
        "lx_to_dx"
      ]
    },
    {
      "page": "mx_to_ax",
      "title": "produce single-age 'ax' values",
      "topics": [
        "mx_to_ax"
      ]
    },
    {
      "page": "mx_to_e0",
      "title": "calculate life expectancy at birth from mortality rates",
      "topics": [
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      ]
    },
    {
      "page": "mx_to_ex",
      "title": "calculate remaining life expectancy from mortality rates",
      "topics": [
        "mx_to_ex"
      ]
    },
    {
      "page": "mx_to_qx",
      "title": "produce single-age 'qx' values",
      "topics": [
        "mx_to_qx"
      ]
    },
    {
      "page": "plot.LEdecomp",
      "title": "Plot Life-Expectancy Decomposition Results (ggplot2)",
      "topics": [
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      "page": "qx_to_lx",
      "title": "Calculate the survival curve",
      "topics": [
        "qx_to_lx"
      ]
    },
    {
      "page": "rcumsum",
      "title": "top-down cumulative sums, as in the lifetable Tx",
      "topics": [
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      ]
    },
    {
      "page": "sen_andreev",
      "title": "the sensitivity implied by an Andreev decomposition",
      "topics": [
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      ]
    },
    {
      "page": "sen_andreev_instantaneous",
      "title": "Estimate sensitivity of life expectancy for a set of mortality rates",
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      ]
    },
    {
      "page": "sen_andreev_instantaneous2",
      "title": "Estimate sensitivity of life expectancy for a set of mortality rates by perturbing in the log space.",
      "topics": [
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    },
    {
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      "title": "Estimate sensitivity of life expectancy using a symmetrical Andreev approach.",
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    },
    {
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      "topics": [
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    },
    {
      "page": "sen_andreev_sym_instantaneous2",
      "title": "Estimate sensitivity of life expectancy for a set of mortality rates by perturbing in the log space.",
      "topics": [
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      ]
    },
    {
      "page": "sen_arriaga",
      "title": "the sensitivity implied by a classic Arriaga decomposition",
      "topics": [
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    },
    {
      "page": "sen_arriaga_instantaneous",
      "title": "Estimate sensitivity of life expectancy for a set of mortality rates",
      "topics": [
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    },
    {
      "page": "sen_arriaga_instantaneous2",
      "title": "Estimate sensitivity of life expectancy for a set of mortality rates by perturbing in the log space.",
      "topics": [
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    },
    {
      "page": "sen_arriaga_sym",
      "title": "Estimate sensitivity of life expectancy using a symmetrical Arriaga approach.",
      "topics": [
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    },
    {
      "page": "sen_arriaga_sym_instantaneous",
      "title": "Instantaneous sensitivity via symmetrical Arriaga decomposition",
      "topics": [
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    },
    {
      "page": "sen_arriaga_sym_instantaneous2",
      "title": "Estimate sensitivity of life expectancy for a set of mortality rates by perturbing in the log space.",
      "topics": [
        "sen_arriaga_sym_instantaneous2"
      ]
    },
    {
      "page": "sen_chandrasekaran_II",
      "title": "Sensitivity from Chandrasekaran II decomposition",
      "topics": [
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    },
    {
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      "title": "Instantaneous sensitivity via Chandrasekaran II decomposition",
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    {
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      "title": "Log-space instantaneous sensitivity via Chandrasekaran II decomposition",
      "topics": [
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    },
    {
      "page": "sen_chandrasekaran_III",
      "title": "Sensitivity from Chandrasekaran III decomposition",
      "topics": [
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    {
      "page": "sen_chandrasekaran_III_instantaneous",
      "title": "Instantaneous sensitivity via Chandrasekaran III decomposition",
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    {
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      "page": "sen_e0_mx_lt",
      "title": "A direct approximation of the sensitivity of life expectancy at birth to changes in mortality.",
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      "page": "sen_lopez_ruzicka_instantaneous2",
      "title": "Log-space instantaneous sensitivity via Lopez-Ruzicka decomposition",
      "topics": [
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    {
      "page": "sen_lopez_ruzicka_sym",
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      "topics": [
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    },
    {
      "page": "sen_lopez_ruzicka_sym_instantaneous",
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    {
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      "title": "Log-scale instantaneous sensitivity via symmetrical Lopez-Ruzicka decomposition",
      "topics": [
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      "title": "sen_min",
      "topics": [
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      ]
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      "title": "A numerical approximation of the sensitivity of life expectancy at birth to changes in mortality.",
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    },
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      "page": "US_data_CoD",
      "title": "US cause-of-death Mortality data",
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