Chapter 5

Description of categorical data

Content

Rate 、 proportion and ratio Application of relative numbers Standardization of rate Dynamic series and analysis index

Section 1 Relative Numbers

1 、 Rate 2 、 Proportion 3 、 Ratio

1 、 Rate

Rate ： To describe the frequency or intension of some phenomenon.

Number of individual occurred some thing within a period of time RateThe whole number of likely to occurred some thing in the same period

ratebase

Example1 To investigate 8589 old people in some city in 1998, and 2823 people had hypertension.

Morbidity rate ： 2823 / 8589 100% = 32.87%

2 、 Proportion

Proportion: To describe the ratio of number of one part and the whole number in the same thing.

Formula:

100%Number of individuals in one part

ProportionThe whole number of individuals

Example2 Calculate the patients proportion of 5 diseases in one hospital in 1990 and 1998.

Example2 Calculate the patients proportions of 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

Characteristics: （ 1 ） Summation of proportions in one th

ing is 100%. （ 2 ） Proportions in the same thing are i

nteractional.

3 、 Ratio

Ratio: the quotient of two related indexs Formula:

(100%)A indexRatio=

B index

Example3 There are 370 male newborns and 358 female newborns in a hospital in one year, then The sex ratio of newborn babies:

370/358×100 = 103

Section 2 Application of relative numbers

1 、 The denominator of relative number should not be too small.

2 、 Proportion should not substitute rate. 3 、 To calculate the total rate correctly. 4 、 Comparison of relative numbers 5 、 Comparison of sample

rate （ proportion ） should do hypothesis test.

Section 3 Standardization of rate

1 、 Definition To calculate standard rate by uniform interior

constitute. Standardization (or adjustment) of rates is used to

enable the valid comparison of groups that differ regarding an important health determinant (most commonly age). It is in fact a specific application of the general methods to control for confounding factors.

2 、 Calculation Method

Direct standardization

Indirect standardization

Approach 1.Choose the correct method by condition

of data. 2.Choose standard composing. 3.Calculate standard rate.

Formula Direct standardization

i iN pp

N

ii

Np p

N

Indirect standardization

i i

rp P P SMR

n P

Example4 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 53.8 400 190 47.5

Approach: 1 ） Disease cure rate of two therapeutics is

known- Direct standardization 2)Choose total patients number of two

therapeutics as standard. 3 ） Calculate anticipated cure number. 4 ） Calculate standard cure rate.

Table 3 Calculation of standard cure rate

A B

Type

（1）

Standard number （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) — 380∑ Nipi — 427∑ Nipi

380100%47.5%

800Standard cure rate of A 　

427100%53.4%

800Standard cure rate of B 　

p

p

p

Example 5 A research investigated 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.

Because the proportions of age in urban and rural areas of this investigation forms are different, so we need to standardize the two morbidity 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 Calculation of standard morbidity rate by indirect standardization

Urban Rural Age

group

（year）

（1）

Standard morbidity

rate iP

（2）

Population in

（3）

Anticipated patients

i inP (4)=(2)(3)

Population

in (5)

Anticipated patients

i inP

(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~ 71.7 41 29 58 42 合计 42.1 776 305 789 353

3221.05

305SMRUrban standard morbidity ratio

42.1% 1.05=44.2%Urban standard morbidity rate

3350.95

353SMRRural standard morbidity ratio

42.1% 0.95=40.0%Rural standard morbidity rate

After standardization, urban morbidity rate is higher than rural.

p

p

p

3 、 Application 1.The Standardization only adapt to that interior forms are

different in two groups, and may influence the comparison

of rate. 2.Because of different chosen standard population, standar

dized rates are different too. So, while comparing several standardized rates , should adopt the same standard population .

3. Standardized rate is no longer the local real level at that time, it only shows the relative level among the comparing materials.

4. 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 the sample size is small.

Section 4   Dynamic series and analysis index

Dynamic series： A series of statistical index arranged in the order of time . To observe and compare changes and development trends in time series.

The index is as follows, absolutely increasing amount , development speed and growth rate , average development speed and average growth speed.

Two important elements：

time：

Statistic index：

base line reported time the end

0 1 2, , , , ,i nt t t t t

0 1 2, , , , ,i na a a a a

Example 6 Table 6 shows the statistic data of outpatients

amount in one hospital from 1991 to 1999.To analyse by d

ynamic series.

Absolutely increasing 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 400 100 133.3 106.7 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 of 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.

0ia a

1i ia a

2 、 Development speed and growth speed

① Relative ratio with fixed base ：a1/a0 ， a2/a0 ，… ., an/a0

②  Ring ratio ：a1/a0 ， a2/a1 ，… ., an/an-1

③  Growth speed = development speed –1 （ 100% ）

0/ia a

1 /i ia a

3 、 Average development speed and average growth speed

Average development speed

a0 base line index

an index in the n period

average growth speed= average development speed-1

0/nna a