Calculate probability of death (qx) from survivor data
The number of people alive at the beginning of the interval.
The number of people alive at the end of the interval.
Calculation Results
Number of Deaths (dx):–
Mortality Probability (qx):–
Survival Probability (px):–
Deaths per 1,000 Lives:–
function calculateMortality() {
// Get Input Elements
var lxStartInput = document.getElementById("lx_start");
var lxEndInput = document.getElementById("lx_end");
var errorMsg = document.getElementById("error_msg");
var resultBox = document.getElementById("result_box");
// Parse Values
var lx = parseFloat(lxStartInput.value);
var lx_n = parseFloat(lxEndInput.value);
// Reset display
errorMsg.style.display = "none";
resultBox.style.display = "none";
// Validation
if (isNaN(lx) || isNaN(lx_n)) {
errorMsg.innerText = "Please enter valid numeric values for both fields.";
errorMsg.style.display = "block";
return;
}
if (lx <= 0) {
errorMsg.innerText = "Initial survivors (lx) must be greater than zero.";
errorMsg.style.display = "block";
return;
}
if (lx_n lx) {
errorMsg.innerText = "Survivors at end (lx+n) cannot be greater than survivors at start (lx).";
errorMsg.style.display = "block";
return;
}
// Calculations
// dx = lx – lx+n
var dx = lx – lx_n;
// qx = dx / lx
var qx = dx / lx;
// px = 1 – qx (or lx+n / lx)
var px = 1 – qx;
// Per 1000
var per1000 = qx * 1000;
// Update DOM
document.getElementById("res_deaths").innerText = dx.toLocaleString();
document.getElementById("res_qx").innerText = qx.toFixed(6);
document.getElementById("res_px").innerText = px.toFixed(6);
document.getElementById("res_per1000").innerText = per1000.toFixed(2);
// Show Results
resultBox.style.display = "block";
}
How to Calculate Mortality Rate from a Life Table
Calculating the mortality rate from a life table is a fundamental skill in actuarial science, demography, and epidemiology. A life table (also known as a mortality table) tracks the mortality experience of a specific population cohort. By analyzing the reduction in the number of survivors over time, we can derive the probability of dying within a specific age interval.
Understanding Life Table Notation
Before performing the calculation, it is essential to understand the standard notation used in life tables:
Symbol
Definition
x
The specific age (e.g., 65 years).
lx
The number of persons surviving to exact age x.
dx
The number of deaths occurring between age x and age x+1.
qx
The probability that a person aged exactly x will die before reaching age x+1.
px
The probability that a person aged exactly x will survive to age x+1.
The Calculation Formula
To calculate the mortality rate (specifically the probability of dying, qx), you need two primary pieces of data: the number of survivors at the start of the age interval (lx) and the number of survivors at the end of the interval (lx+n).
Step 1: Calculate the Number of Deaths (dx)
First, determine how many people died during the interval by subtracting the survivors at the end from the survivors at the start.
dx = lx – lx+n
Step 2: Calculate the Mortality Probability (qx)
Divide the number of deaths by the initial population size (the cohort at the start of the interval).
qx = dx / lx
Step 3: Calculate the Survival Probability (px)
Conversely, the survival rate is calculated as:
px = 1 – qx
Real-World Example
Let's assume we are analyzing a cohort of 65-year-old males based on an insurance life table.
This means a 65-year-old male in this cohort has a 1.5% probability of dying before their 66th birthday.
Why is qx Important?
The variable qx is the building block for calculating life expectancy. Insurance companies use these rates to price life insurance premiums, and pension funds use them to estimate how long they will need to pay out benefits. In public health, changes in qx over time indicate improvements or deteriorations in general health conditions.
Frequently Asked Questions
What is the difference between Mortality Rate (qx) and Central Death Rate (mx)?
qx is a probability derived from the initial population at the start of the interval. mx (Central Death Rate) is typically calculated by dividing deaths by the average population during the interval (or person-years lived). While they are numerically close for single years of age, they are distinct mathematical concepts.
Can qx be greater than 1?
No. Since qx represents a probability, it must always be between 0 and 1. If your calculation results in a number greater than 1, check your input data; the number of deaths cannot exceed the number of people alive at the start.