Life_table_notation

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Life Tables Marie Diener-West, PhD Sukon Kanchanaraksa, PhD
Section A Clinical Life Tables, Part 1

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4 Clinical Life Table ± A fundamental technique of survival analysis that deals with “time to event” A basic example is “time to death” ± It can answer the question of the chance of survival after being diagnosed with the disease or after beginning the treatment ± The event can be any other health event—not just death It can be relapse, receiving organ transplant, pregnancy (in a study of infertility), failure of treatment, recovery, etc. ± It handles variable time of entry and (variable time of) withdrawal of individuals from the population ± It calculates cumulative event-free probabilities and generates a survival curve
5 Time since beginning of follow-up (Year) Number at beginning Deaths 1 200 20 2 30 3 40 Example ± A group of 200 subjects were followed for three years ± Deaths (events) occurred throughout the three years ± What is the chance of surviving at the end of the three years?

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6 Following a Population Patient Begin follow-up Death 1995 2000 Year Year since follow-up 1 2 3 0
7 Clinical Life Table Notation ± = number alive at the beginning of time t ± = number of deaths during the time interval l t d t

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8 Apply Notation ± Apply notation to the table in the example Time since beginning of follow-up (Year) Number at beginning l t Deaths d t 1 200 20 2 30 3 40
9 Fill in the “Number at Beginning” Column ± Fill in the missing cells Time since beginning of follow-up (Year) Number at beginning l t Deaths d t 1 200 20 2 30 3 40 200–20 = 180 200–20 = 180 180 180–30 = 150 180–30 = 150 150

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10 l t d t Clinical Life Table Notation ± = number alive at the beginning of time t ± = number of deaths during the time interval ± = probability of dying during the time interval ± = probability of surviving in the time interval q t = d t /l t p t = 1 q t
11 Interval l t d t q t p t 1 200 20 2 180 30 3 150 40 20/200 = 0.1 20/200 = 0.1 0.1 1.0–0.1 = 0.9 1.0–0.1 = 0.9 0.9 30/180 = 0.17 30/180 = 0.17 0.17 1.0–0.17 = 0.83 1.0–0.17 = 0.83 0.83 Calculate Probabilities of Dying (q) and Surviving (p) 0.27 0.73

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