Description of enumeration data

1. Description of enumeration data Prof. Yi-xiong Lei (1021305)

2. 1. Relative Number In most situations, the absolute number can not be used for comparison between different populations. In order to compare the frequencies of occurrence in the same base number, the relative number is often used. Rate Relative number Constituent ratio Relative ratio

3. (1) Rate,the ratio of the number of events actually occurred and the total possible number of events in a defined time and area. A (+) Rate = ×K A (+) + A (-) [ K: 100%, 1000‰, 100000 per 100 thousand et al ] For example, the mortality rate of male lung cancer in Guangzhou is 43 per 100,000 per year.

4. (2) Constituent ratio, called proportion, is the percentage of a part of population in the total. A Constituent ratio = ×100 % A + B + C + … For example, Patients with hospital infection occupy 10 percent of total patients in a hospital.

5. (3) Relative ratio, a number divided by a related number. These two numbers may be the average, absolute number and relative number. A Relative ratio =×K B [ K: 100% or times ] For example, The sex ratio of students in this school is 58 % of male to female.The relative ratio oflung cancer patients in Guangzhou city is 2 times of ones in the suburb.

6. 2. Caution in the Use of Relative Number (1) In clinical practice, we need to pay attention to thedifference in the explanation of rate and ratio. Table 4-1. The explanation of rate and constituent ratio Age Population Patients Proportion Prevalance rate with tumors（%）（1/ 100000） <30 633000 19 1.3 3.0 30- 570000 171 11.4 30.0 40- 374000 486 32.0 129.9 50- 143000 574 38.5 401.4 60- 30250 242 16.2 800.0  Total 1750250 1492 100.0 85.2

7. 2. Caution in the Use of Relative Number (2) The denominator (base number) is required big enough. Table 4-2. The sample size and stable relative number No. of patients treated No. of patients cured  95% CI 2 1 1 ～ 99 % 4 2 7 ～ 93 % 50 25 36 ～ 65 % 500 250 45 ～ 54 % 5000 2500 49 ～ 51 % The bigger the sample size, the more stable the relative number

8. 2. Caution in the Use of Relative Number (3) If there are several rates with different sample size, the total numerator and total denominator should be first calculated, then calculate their average rate. (4) When two crude rates are compared, the inner cons- tituent of two populations should be similar. (5) Relative number is used to compare so that we should pay attention to the comparability. (6) Sampling error should be estimated and hypothesis testing should be done when it is a sampling study.

9. 3. Standardization of Rate (1) The meaning of rate standardization When two or more two crude rates are compared, we need to use the same standard to delete the differences of inner constituent from two or more two populations, and insure the comparability of the populations where the rates come from.

10. 3. Standardization of Rate • (2)The principle of standard selection • Selecting a representative, relative stable and bigger population as a constituent standard such as national census. • Selecting an addition of inner constituent frequencies from two groups as a co-constituent standard. • Selecting one of inner constituent frequencies from two groups as a co-constituent standard.

11. 3. Standardization of Rate (3) Calculations of standardized rate Standardized rate, called adjusted rate, is specially calculated and used for rate standardization. There are two methods: THE DIRECT METHOD THE INDIRECT METHOD

12. THE DIRECT METHOD: When knowing the original rates of sub-groups and the numbers or constituent of population in standard groups, the formula is the following:  Ni Pi P’ = ———— N P’ =  (Ni / N) × Pi P’: Standardized rate Pi: Original (death) rates each group Ni: Numbers of population in every standard group N: Total numbers of population in standard groups

13. THE INDIRECT METHOD: When unknowing the original rates of sub-groups, but knowing the observations of sub-groups and the total rates, the formula is the following: P’ = P × r /  ni ×Pi P’: Standardized rate P: total rates r: Actual positive (death) numbers  ni Pi : Expecting (death) numbers according to standard rates (Pi)

14. For example : Table 4-3. Prevalance rate of hypertension among teachers at the age of more than 35 years from A and B schools Age A school B school (Yr.) n Patients Prevalance(%) n Patients Prevalance(%) 35～ 236 16 6.78 478 33 6.90 45～ 375 27 7.20 379 28 7.39 55～ 384 38 9.90 235 24 10.21 65～ 402 59 14.68 157 24 15.29 Total 1397 140 10.02 1249 109 8.73 Standardized rate is calculated the direct method

15. Table 4-4. Calculations of standardized prevalance rate of hypertension between A and B schools with the direct method Age Standard A school B school (Yr.) population Prevalance(%) Exp. patient Prevalance(%) Exp. patient Ni Pi NiPi Pi NiPi (1) (2) (3) (4)=(2)(3) (5) (6)=(2)(6) 35～ 714 6.78 48 6.90 49 45～ 754 7.20 54 7.39 56 55～ 619 9.90 61 10.21 63 65～ 559 14.68 82 15.29 85 Total 2646 10.02 245 8.73 253 Standardized prevalance rate of hypertension among teachers in A schools Standardized prevalance rate of hypertension among teachers in B schools P’A =  Ni Pi／N = 245／2646 = 9.26% P’B =  Ni Pi／N = 253／2646 = 9.56%

16. 3. Standardization of Rate (4) Caution in standardization of rate ① Standardized rate is different if you use the same data and the same method but the different standard. ② When making comparisons among several crude rates, you should use the same standard and the same method to calculate standardized rates. ③Standardized rate can not show the actual level, it is the relative rate just for the comparability among crude rates. ④ Sampling error should be estimated and hypothesis testing should be done when standardized rate is a sampling study.

17. Thank you