医学统计学英文课件CH05-description-of-categorical-data.ppt

1、Chapter 5Description of categorical dataContentnRate、proportion and ratio nApplication of relative numbers nStandardization of rate nDynamic series and analysis index Section 1 Relative Numbersn1、Raten2、Proportionn3、Ratio1、RateRate：To describe the frequency or intension of some phenomenon.=Number of

2、 individual occurred some thing within a period of time RateThe whole number of likely to occurred some thing in the same periodratebasenExample1 To investigate 8589 old people in some city in 1998,and 2823 people had hypertension.nMorbidity rate：n2823/8589 100%=32.87%2、ProportionnProportion:To desc

3、ribe the ratio of number of one part and the whole number in the same thing.nFormula:100%=Number of individuals in one partProportionThe whole number of individualsExample2 Calculate the patients proportion of 5 diseases in one hospital in 1990 and 1998.Example2 Calculate the patients proportions of

4、 5 diseases in one hospital in 1990 and 1998.Table1 Proportions of 5 diseases in one hospital in 1990 and 1998 Diseases 1990 1998 Number Proportion（%）Number Proportion（%）1 58 30.53 40 26.85 2 44 23.16 44 29.53 3 37 19.47 29 19.46 4 19 10.00 18 12.08 5 32 16.84 18 12.08 total 190 100.00 149 100.00 nC

5、haracteristics:n（1）Summation of proportions in one thing is 100%.n（2）Proportions in the same thing are interactional.3、RationRatio:the quotient of two related indexsnFormula:(100%)A indexRatio=B indexnExample3 There are 370 male newborns and 358 female newborns in a hospital in one year,then The sex

6、 ratio of newborn babies:n370/358100=103Section 2 Application of relative numbers n1、The denominator of relative number should not be too small.n 2、Proportion should not substitute rate.n 3、To calculate the total rate correctly.n 4、Comparison of relative numbers n 5、Comparison of sample rate（proport

7、ion）should do hypothesis test.Section 3 Standardization of rate n1、DefinitionnTo calculate standard rate by uniform interior constitute.nStandardization(or adjustment)of rates is used to enable the valid comparison of groups that differ regarding an important health determinant(most commonly age).It

8、 is in fact a specific application of the general methods to control for confounding factors.n2、CalculationnMethod Direct standardization Indirect standardization nApproachn1.Choose the correct method by condition of data.n2.Choose standard composing.n3.Calculate standard rate.nFormula nDirect stand

9、ardization iiN ppN=iiNppN=nIndirect standardizationiirpPPSMRn P=nExample4 To calculate standard cure rate of two therapeutics.Table2 Comparison of two therapeutics A B Type Number Cure Cure rate（%）Number Cure Cure rate（%）Common 300 180 60.0 100 65 65.0 Severe 100 35 35.0 300 125 41.7 Total 400 215 5

10、3.8 400 190 47.5 nApproach:n1）Disease cure rate of two therapeutics is known-Direct standardizationn2)Choose total patients number of two therapeutics as standard.n3）Calculate anticipated cure number.n4）Calculate standard cure rate.Table 3 Calculation of standard cure rate A B Type （1）Standard numbe

11、r（Ni）（2）Former rate Anticipated（pi）（Nipi）（3）（4）=(2)(3)Former rate Anticipated （pi）(Nipi)（5）(6)=(2)(5)Common 400 60.0 240 65.0 260 Ssevere 400 35.0 140 41.7 167 合计 800(N)380Nipi 427Nipi 380100%47.5%800=Standard cure rate of A427100%53.4%800=Standard cure rate of B pppnExample 5 A research investigate

12、d old women,776 in the city and 789 in Countryside.Among them,322 and 335 suffered from primary osteoporosis.The total morbidity rates are 41.5 and 42.5 respectively.nBecause the proportions of age in urban and rural areas of this investigation forms are different,so we need to standardize the two m

13、orbidity rate.Table4 Comparison of Morbidity Rate Urban Rural Age group（year）（1）Number of Investigation（2）Number of patients（3）Morbidity rtae（%）（4）Number of Investigation（5）Number of patients（6）Morbidity rtae（%）（7）50 354 241 60 251 315 70 130 175 80 41 58 Total 776 322 41.5 789 335 42.5 Table5 Calcu

14、lation of standard morbidity rate by indirect standardization Urban Rural Age group （year）（1）Standard morbidity rate iP（2）Population in（3）Anticipated patients iin P(4)=(2)(3)Population in (5)Anticipated patients iin P(6)=(2)(5)50 21.3 354 75 241 51 60 46.1 251 116 315 145 70 65.5 130 85 175 115 80 7

15、1.7 41 29 58 42 合计 42.1 776 305 789 353 3221.05305SMR=Urban standard morbidity ratio42.1%1.05=44.2%=Urban standard morbidity rate3350.95353SMR=Rural standard morbidity ratio42.1%0.95=40.0%=Rural standard morbidity rateAfter standardization,urban morbidity rate is higher than rural.ppp3、Applicationn1

16、.The Standardization only adapt to that interior forms are different in two groups,and may influence the comparison of rate.n2.Because of different chosen standard population,standardized rates are different too.So,while comparing several standardized rates,should adopt the same standard population.

17、n3.Standardized rate is no longer the local real level at that time,it only shows the relative level among the comparing materials.n4.The standardized rates of two samples are sample values,the sampling error exists.When comparing the standardized rates of two samples,we should do hypothesis test if

18、 the sample size is small.Section 4 Dynamic series and analysis index nDynamic series：A series of statistical index arranged in the order of time.To observe and compare changes and development trends in time series.nThe index is as follows,absolutely increasing amount,development speed and growth ra

19、te,average development speed and average growth speed.Two important elements：time：Statistic index：base line reported time the end012,inttttt012,ina a aaaExample 6 Table 6 shows the statistic data of outpatients amount in one hospital from 1991 to 1999.To analyse by dynamic series.Absolutely increasi

20、ng amount Development speed%Increase speed%Year Index sign Patients amount Add up Year after year Relative ratio with fixed base Ring ratio Relative ratio with fixed base Ring ratio（1）（2）（3）（4）（5）（6）（7）（8）（9）1991 0a 1200 100.0 100.0 1992 1a 1500 300 300 125.0 125.0 25.0 25.0 1993 2a 1600 400 100 133

21、.3 106.7 33.3 6.7 1994 3a 1670 470 70 139.2 104.4 39.2 4.4 1995 4a 1750 550 80 145.8 104.8 45.8 4.8 1996 5a 1820 620 70 151.7 104.0 51.7 4.0 1997 6a 2210 1010 390 184.2 121.4 84.2 21.4 1998 7a 2680 1480 470 223.3 121.3 123.3 21.3 1999 8a 3450 2250 770 287.5 128.7 187.5 28.7 Table 6 Dynamic changes o

22、f outpatients amount 1、Absolutely increasing amount the increasing amount totally the increasing amount year by year Absolutely increasing amount explains the absolute value that the thing increases in a regular period.0iaa1iiaa2、Development speed and growth speed Relative ratio with fixed base：a1/a0，a2/a0，.,an/a0 Ring ratio：a1/a0，a2/a1，.,an/an-1 Growth speed=development speed 1（100%）0/iaa1/iiaa3、Average development speed and average growth speedAverage development speeda0 base line indexan index in the n periodaverage growth speed=average development speed-10/nnaa