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Standardzaton Stan Becker, PhD Bloomberg School of Publc Health
Purpose of Standardzaton Purpose of Standardzaton Procedure of adjustment of crude rates to elmnate from them the effect of dfferences n populaton composton wth respect to age and/or other varables Contnued 3
Purpose of Standardzaton Ths s necessary because: Rates are affected by the demographc composton of the populaton for whch they are calculated Age composton s a key factor affectng crude rates Contnued 4
Purpose of Standardzaton For purpose of comparson of rates over tme or from area to area, t s mportant to determne the dfference between the rates after takng nto account the dfferences n the composton of the populatons Adjusted rates have no drect meanng n themselves; they must be compared wth the orgnal crude rates or wth other adjusted rates usng the same standard 5
Notaton r n n p = Rate for th group n study populaton = Number of persons n th group n study populaton = Total number of persons n study populaton = n = Proporton of persons n th group n study populaton = n /n = weght e = Number of events n study populaton = r *n Contnued 6
Notaton R = Rate for th group n standard populaton N = Number of persons n th group n standard populaton N = Total number of persons n standard populaton = N P = Proporton of persons n th group n standard populaton = N /N = weght C = Crude rate n standard populaton 7
Drect Standardzaton Smplest and most straghtforward technque Provdes the best bass for determnng the dfference between two crude rates The rates from two or more study populatons are appled to a common populaton dstrbuton (standard populaton) Contnued 8
Drect Standardzaton Often drectly standardzed rates are calculated for a seres of populatons usng the same standard The seres could be the same populaton at dfferent tme ponts 9
Standard Populaton Standard Populaton The standard populaton can be any one of the study populatons, ther average, or any other populaton dstrbuton; the choce of the standard s arbtrary Contnued 10
Standard Populaton If one of the populatons s chosen, ts crude rates = ts standardzed rates The rates from the other study populaton(s) are appled to the dstrbuton of the standard If the average s chosen, the rates from each study populaton are appled to that new standard populaton 11
Drect Standardzaton Formulas r N r N R N DSDR = r P = = = N R N N = expected events n study populaton actual events n standard populaton C = = comparatve mortalty fgure (CMF) C 12
Drect Standardzaton Example Drect Standardzaton Brth Rate (DSBR) of Maurtus Island s (M.I.) 1985 crude brth rate usng Mal's 1987 data as standard 13
Drect Standardzaton of Maurtus Island: (Study) (Standard) Expected Age group Rates M.I. per Populaton number of 1000 Mal brths, M.I. 15-19 18 725719 13063 20-24 58 574357 33313 25-29 57 536226 30565 30-34 36 443702 15973 35-39 19 379184 7204 40-44 6 325824 1955 Total 2985012 102073 Total number of brths, Mal: Total number of brths, M.I.: 375117 18247 CBR Mal: 48.7 CBR M.I. 18.5 Source: U.N. Demographc Yearbook 1986, 1992, and 1996 14
Drect Standardzaton M.I. DSBR = Expected brths n M.I. Actual brths n Mal CBR Mal = 102073 48.7= 13.3 375117 Source: U.N. Demographc Yearbook 1986, 1992, and 1996 15
Indrect Standardzaton Indrect Standardzaton The rates from a standard populaton are appled to the dstrbuton of one or more study populatons Choce of standard rates s up to the demographer 16
Indrect Standardzaton Formulas r n e IDSR = C = C = R n R n = actual events n study populaton expected events n study populaton C = = standardzed mortalty rato (SMR) * C 17
Indrect Standardzaton Standard Mortalty Rate (SMR) Notes on SMR: The absolute value of the standardzed mortalty rato depends on the chosen set of standard rates SMR has no meanng by tself t should be compared wth other SMRs (relatve values ndcate hgher or lower standardzed ncdences of events) 18
Indrect Standardzaton Crude Brth Rate Example Indrect Standardzaton Brth Rate (ISBR) of Maurtus Island s (M.I.) 1985 crude brth rate usng Mal's 1987 data as standard 19
Indrect Standardzaton of Maurtus Island: (Standard) (Study) Expected Age group Rates Mal Populaton number of per 1000 M.I. brths, M.I. 15-19 79 105764 8355 20-24 159 109914 17476 25-29 171 94576 16172 30-34 140 81144 11360 35-39 107 60063 6427 40-44 50 45825 2291 Total 497286 62082 Total number of brths, Mal: 375117 Total number of brths, M.I.: 18247 CBR Mal: 48.7 CBR M.I. 18.5 Source: U.N. Demographc Yearbook 1986, 1992, and 1996 20
Indrect Standardzaton Formulas M.I. ISBR = Observed brths n M.I. Expected brths n M.I. CBR Mal = 18247 62082 48.7 = 14.3 Source: U.N. Demographc Yearbook 1986, 1992, and 1996 21
Indrect Standardzaton Indrect standardzaton can be deceptve It s to be used f: There are no rates avalable for study populatons,.e., only counts avalable Rates for study populatons are not relable because of small numbers of events or populaton Contnued 22
Indrect Standardzaton Example Comparson of crude and ndrectly standardzed rates for four populatons, usng England and Wales or Mexco as standard Contnued 23
Indrect Standardzaton Study Populaton Indrectly standardzed rates CDR 1962 England and Wales Mexco Rate Rank Rate Rank Rate Rank Czechoslovaka 10.38 3 12.27 1 8.97 2 Iceland 14.78 4 22.84 3 13.52 4 Poland 8.15 1 14.35 2 8.56 1 Thaland 9.15 2 23.90 4 10.49 3 Contnued 24
Indrect Standardzaton Example Comparson of drectly and ndrectly standardzed crude death rates for four countres, usng the U.S. populaton and crude death rate as standard (U.S. CDR = 8.75) Contnued 25
Indrect Standardzaton Standardzed Death Rates Country Crude Drect Indrect CMF SMR Kuwat 5.15 11.7 13.64 1.34 1.56 New Zealand 7.93 9.16 9.13 1.04 1.04 Sngapore 5.18 9.46 9.10 1.07 1.05 Sr Lanka 6.00 11.6 11.80 1.27 1.34 26
27 Comparng the Two Methods C N R N r SDR D = C N R n r IDSR = Contnued
Comparng the Two Methods In drect standardzaton, the weghts are constant across study populatons In ndrect standardzaton, the weghts (n ) are nfluenced by the dstrbutons of the study populatons 28
Exercse Drect and Indrect Standardzaton Calculate drectly and ndrectly standardzed crude death rates for populatons one and two by usng the standard populaton Populaton1 Populaton2 Standard Pop. Age group Rate Prop. n group Rate Prop. n group Rate Prop. n group ( ) ( r ) ( n/n ) ( r ) ( n/n ) ( R ) ( N/N ) 1 30 0.8 32 0.3 20 0.6 2 15 0.2 16 0.7 35 0.4 CDR: 30*0.8+15*0.2=27 32*0.3+16*0.7=20.8 20*0.6+35*0.4=26 You have 15 seconds to calculate the answer. You may pause the presentaton f you need more tme. Source: Vtal Statstcs of the Unted States, 1989 1991 29
Exercse Answer Drect and Indrect Standardzaton The correct answers are as follows: Drectly standardzed crude death rate: 30*0.6+15*0.4=24.0 32*0.6+16*0.4=25.6 Indrectly standardzed crude death rate: Populaton 1 Populaton 2 (27/(20*0.8+35*0.2))*26=30.5 (20.8/(20*0.3+35*0.7)*26=17.7 30
Adjustment for Two Factors Dstrbuton of mongolods and total lve brths by maternal age and brth order. Adapted from Joseph L. Fless, Statstcal methods for rates and proportons, Second Edton, John Wley and Sons, Inc. 1981. Data from Stark and Mantel (1966) 31
Smultaneous Drect Adjustment Incdence rates of dscovered mongolsm by maternal age and brth order Adapted from Joseph L. Fless, Statstcal methods for rates and proportons, Second Edton, John Wley and Sons, Inc. 1981. Data from Stark and Mantel (1966) 32
Summary Both methods of adjustment are used, but t s preferable to use the drect method (when possble) An adjusted rate has no meanng by tself; t s only used for purpose of comparson The drect and the ndrect methods can lead to dfferent nterpretatons: Be Careful 33