312 PART 6 Analyzing Survival Data

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» ^{The intervals are often the same size for all the rows in a life table like in the}

example, but they don’t have to be. You may choose these on the basis of the

probabilities in your data.»

» ^{The hazard rate obtained from a life table for each time slice is equal to the}

Probability of Dying (Column F) divided by the width of the slice. Therefore,

the hazard rate for the first year would be expressed as 0.105 per year, or

10.5 percent per year.»

» ^{The Cumulative Survival probability, in Column H, is the probability of surviving}

from the start date through to the end of the interval. It has no units, and it

can be expressed as a fraction or as a percentage. The value for any time slice

applies to the moment in time at the end of the interval.»

» ^{The cumulative survival probability is always 1.0 (or 100 percent) at time 0,}

whenever you designate that time 0 is (in the example, date of surgery), but

it’s not included in the table.»

» ^{The cumulative survival function decreases only at the end of an interval that}

has at least one observed death, because censored observations don’t cause

a decrease in the estimated survival. Censored observations however

influence the size of the decreases when subsequent events occur. This is

because censoring reduces the number at risk, which is used in the denomi-

nator in the calculation of the death and survival probabilities.»

» ^{If an interval contains no events and no censoring, like in the 1–2 years row in}

the table in Figure 21-4, it has no impact on the calculations. Notice how all

subsequent values for Column B and for Columns E through H would remain

identical if that row were removed.

Graphing hazard rates and survival

probabilities from a life table

Graphs of hazard rates and cumulative survival probabilities (Columns F and H

from Figure  21-4, respectively) can be prepared from life-table results using

Microsoft Excel or another spreadsheet or statistical program with graphing

capabilities. Figure 21-5 illustrates the way these results are typically presented.»

» ^{Figure 21-5a is a graph of hazard rates. Hazard rates are often graphed as}

bar charts, because each time slice has its own hazard rate in a life table.»

» ^{Figure 21-5b is a graph of cumulative survival probabilities, also known as}

the survival function. Survival values are usually graphed as stepped line charts,