Standardized Death Rates (using indirect methods) Definition and numerical questions Nadia Saeed, College of Statistical & Actuarial Sciences

SDR by Indirect Method When the age specific death rates for the given population are not available or there are fluctuations in age-specific death rates, we determine the number of deaths that would be expected in the given population, assuming that the age-specific death rates of the standard population had prevailed for one year in the given population. The ratio of the total deaths observed in the given population to expected deaths, multiplied by the CDR of the standard population yields the age-adjusted or standardized death rate by the indirect method. In other words: Nadia Saeed, College of Statistical & Actuarial Sciences

The number of expected deaths for the ith age group is computed by the formula Where denotes the number of deaths in the ith age group in the standard population during a year. denotes the midyear population figure in the ith age group of standard population during the same year denotes the midyear population figure in the ith age group of the given population of the same year. Nadia Saeed, College of Statistical & Actuarial Sciences

Where CDR (standard population is): If adjustment is also to be made with respect to sex, the expected deaths both for males and females are calculated separately in a similar way and the formula applied accordingly. In other words we use the formula Where CDR (standard population is): Nadia Saeed, College of Statistical & Actuarial Sciences

Application of SDR (indirect method) These methods can also be applied for computing the standardized accidents rates in factories when the number of employees and the accidents according to suitable age groups are available; true unemployment rates, given the number of persons and those seeking employment in a given area according to suitable age- groups. Nadia Saeed, College of Statistical & Actuarial Sciences

Example 1 Calculate the crude and standardized death rates from the following data: Nadia Saeed, College of Statistical & Actuarial Sciences

Data table Age group (years) District A Standard Population (p) Deaths (d) Population (P) Deaths (D) 0-9 20210 728 231428 6960 10-24 29875 213 302170 1972 25-44 37294 462 293149 4759 45-64 16739 741 150122 7030 65 & over 4925 823 46500 8314 Total 109043 2967 1023369 29035 Nadia Saeed, College of Statistical & Actuarial Sciences

Solution CDR for district A= (2967/109043)x1000 = 27.21 CDR for standard= (29035/1023369)x1000=28.37 The compositions for standard death rates both by Direct method is by using formula: Indirect method is by using formula Nadia Saeed, College of Statistical & Actuarial Sciences

Solution Age (years) Expected deaths in standard population (by direct method) Expected deaths in district A (indirect method) 0-9 8336 608 10-24 2154 195 25-44 3632 605 45-64 6646 784 65 & over 7770 881 Total 28538 3073 Nadia Saeed, College of Statistical & Actuarial Sciences

Solution SDR (direct)= (28538/1023369)x1000=27.89 SDR (indirect)= (2967/3073)x28.37= 27.39 Nadia Saeed, College of Statistical & Actuarial Sciences

Example 2 Calculate Crude Death Rate and Standardized Death Rates of 1964 population by (i) direct and (ii) indirect methods, using 1941 population as standard. The data are given below: Nadia Saeed, College of Statistical & Actuarial Sciences

Data Table Age-group (years) 1941 1964 Population Deaths Specific Death Rates 0-9 10,000 220 15,000 20 10-19 11,000 132 12,000 11 20-49 7,000 105 8,000 14 50 & over 2,000 90 5,000 42 Nadia Saeed, College of Statistical & Actuarial Sciences

Example 3 Calculate the CDR and SDR of the local population from the following data, using direct method Nadia Saeed, College of Statistical & Actuarial Sciences

Data table Age-group (years) Standard population No. of deaths in standard population Local population No. of deaths in local population 0-9 600 18 400 16 10-19 1000 5 1500 6 20-59 3000 24 2400 60 & over 20 700 21 Nadia Saeed, College of Statistical & Actuarial Sciences

Example 4 Calculate CDR and SDR for the following data. Nadia Saeed, College of Statistical & Actuarial Sciences

Data Table Age (years) District A Standard population (‘000) No. of deaths Male Female 0-4 2110 2010 30 27 59 55 5-14 3340 3230 6 8 109 102 15-34 7320 7310 16 20 177 180 35-59 7960 8750 70 57 121 122 60 & over 3240 4280 196 230 34 41 Nadia Saeed, College of Statistical & Actuarial Sciences

Question for Discussion Point out the differences between Crude and Standardized Death Rates? Nadia Saeed, College of Statistical & Actuarial Sciences