LIFE TABLEDr. Priyadarshini. CI M.D.ICM, MMC

INTRODUCTION

Described as the ‘Biometer’ of the population by William Farr.

Means of describing mortality, survival and other vital events in the population.

HISTORY OF THE LIFE TABLE

HISTORY OF THE LIFE TABLE

John Graunt (1620-1674) - Natural and Political Observations Made upon the Bills of Mortality (1662)

Age interval Number surviving

0-6 1007-16 64

17-26 4027-36 2537-46 1647-56 1057-66 667-76 377-86 1>86 0

Graunt’s Life Table

HISTORY OF THE LIFE TABLE

HISTORY OF THE LIFE TABLE

Edmund Halley (1656 – 1742) - ‘An estimate of the Degree of the Mortality of Mankind drawn from the curious Table of the Births and Funerals at the city of Breslaw’

Halley’s Life TableAge (years) Expectation of life, years

0 33.55 41.55

10 39.9915 36.8620 33.6125 30.3830 27.3535 24.5140 21.7845 19.2250 16.8155 14.5160 12.0965 9.7370 7.5375 5.9980 5.74

IMPORTANCE OF LIFE TABLE

- No. of survivors

At 5 years, the no, of children likely to enter primary school

At 15 years, no. of women entering fertile period

At 21 years. no. eligible for voting

- No. likely to die after life insurance or after joining service to budget for payment towards risk or pension

IMPORTANCE OF LIFE TABLE

- Calculation of expectation of life and comparison of mortality among communities

- Population studies- Survival rate after treatment

- Analysis by causes of death

CONSTRUCTION OF A LIFE TABLE

Prerequisites

1. Population living at all individual ages in a selected period

2. No. of deaths that occurred in these ages during the selected period

Standard Notations

Px Midyear population between ages x and x+1

Dx Number of deaths between ages x and x+1

mx Age-specific death rate

ax

Average fraction of the last year of life lived by those living between x and x+1

qx Probability of dying between age x and x+1

lx Number of people surviving to age x out of the life table cohort

dx Number of deaths between age x and x+n out of the life table cohort

Lx Number of person years lived between age x and x+1

Tx Total number of person years lived after age x

ex Life expectancy at age x

Construction of Life Table

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Construction of Life Table

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DECREMENT TABLE

The column of deaths or living can be split and analysed for new characteristics.

LIFE TABLE IN CLINICAL MEDICINEKAPLAN-MEIER METHOD

Most commonly used approach to survival analysis in medicine. Also called as the Kaplan-Meier life table method or the product-limit method.

Actuarial method used if there are large numbers of subjects but the Kaplan-Meier method more advantageous if the numbers of subjects are small.

KAPLAN-MEIER METHOD

The actuarial method calculates survival rates based on fixed intervals whereas in the Kaplan-Meier method the intervals are uneven.

Here, the deaths are not conceived of as occurring during an interval. Rather, they are seen as instantaneously terminating one interval and beginning a new interval.

KAPLAN-MEIER METHOD

Data

Timing of Deaths in 4 subjects: 0.8, 3.1, 5.4, 9.2 months

Timing of loss to follow-up or censorship in four subjects: 1.0, 2.7, 7.0, 12.1 months

No. of months at time of subjects death

Survival interval

No. living just before subjects death

No. living just after subjects death

No. lost to follow up between this and next subjects death

Fraction surviving after this death

px

(proportion surviving interval)

Px

(Proportion surviving from beginning of study to end of interval)

- 0 - 0.8 - - - - 1.000 1.000

0.8 0.8 - 3.1 8 7 2 7/8 0.875 0.875

3.1 3.1- 5.4 5 4 0 4/5 0.800 0.700

5.4 5.4 – 9.2 4 3 1 3/4 0.750 0.525

9.2 9.2 – 12.1

2 1 0 1/2 0.500 0.263

No deaths >12.1 1 - 1 1/1 1.000 0.263

KAPLAN-MEIER METHODTabular Representation of Data

KAPLAN-MEIER METHODGraphic Representation of the Data

KAPLAN-MEIER METHOD Graphic Representation of comparison of two groups

TESTS OF SIGNIFICANCE

Differences between actuarial survival curve – t-test and z-test

Differences between Kaplan-Meier curves – Logrank test

LOGRANK TEST

COX REGRESSION (POPULATION HAZARDS MODEL)

Adjustment for potential confounding variables.

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