Question

6. A study exploring the lives of Canadian males in various states of health presents an interesting application of the life table [14]. When constructing their table, the authors divided the person-years lived during a given age interval, n^x, into person- years lived inside institutions and person-years lived outside institutions. The life table can now be used to determine the average remaining years of life outside nstitutions Number Rate of Person-Years of Life Lived Person-Years in Institutions Alive Institutionalization 100,000 98,004 96,408 92,509 72,274 1,475,419 972,823 1,896,306 1,699,064 1,037,206 0.0020387 0.002917:3 0.002739:5 0.0059150 0.0526520 3008 2838 5195 10,050 54,611 15 25 65 Person-Years Outside Institutions Total Person-Years Outside Institutions from Age x on Average Remaining Years Outside Institutions 1,472,411 969,985 1,891,111 1,689,014 982,595 Columns 2 and 3 list the values of l, and ,Lx from the 1978 life table for Canadian males. The rates of institutionalization displayed in column 4 were obtained from the Canadian Health Survey. (a) Explain how columns 5 and 6 are derived (b) Complete columns 7 and 8 of the table. Note that column 8 represents the aver- age remaining years of life outside institutions for all men involved in the study

Answer 1

Part a) For column 5

The Column is person-years in the institution. So it will be the product of person-years of life lived and Rate of institutionalization. That is the product of column 3 and column 4.

For column 6

The Column is person-years outside the institution. So it will be the difference between person-years of life lived and person-years in the institution.   That is the difference between column 3 and column 5.

Part b) For column 7

We need total person-years outside institutions from age x on. It will be the sum of all 5 data of column 6 for 0 years, sum of last 4 data for 15 years and so on.

For column 8

Average remaining years will be column 6 divided by column 1

Age	column 7	column 8
0	7005116	14.72
15	5532705	9.89
25	4562720	19.61
45	2671609	18.25
65	982595	13.59