Chapter II. THE PREVALENCE METHOD John Bongaarts*

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1 Chpter II THE PREVALENCE METHOD John Bongrts* This chpter describes nd pplies new methodology for estimting the fertility impct of contrception obtined through fmily plnning progrmme. This pproch is clled the "prevlence method" becuse the principl dt required for its ppliction re estimtes of the prevlence of contrceptive use t given point in time. (Contrceptive prevlence is defined here s the proportion of mrried women currently using contrception.) The development nd use of the prevlence method hve become fesible in recent yers becuse prevlence dt re now routinely vilble from fertility surveys. I In contrst, in the 1960s nd erly 1970s most countries with fmily plnning progrmmes relied primrily upon service sttistics, such s the number of cceptors, for the purpose of ssessing the progress of the progrmme. Mny of the existing methods for evluting progrmme impct therefore rely upon cceptor sttistics. It is the objective ofthe prevlence method to estimte the number of births verted s well s the reduction in the crude birth rte tl)t results from the use of progrmme contrception: A single ppliction of the procedure produces these estimtes for one yer, but repeted pplictions for different yers cn yield timeseries of births verted or other impct mesures. Figure BI. Reltionlbip. between observed, potendl nd nturl fertility Dd tbe fertluty Impct ofpropmmedd non-progrmme contreepdon in popultion Nturl fertility Potentil fertility Observed fertility Fertility impct of non-progrmme contrception Fertility impct of progrmme contrception A. BASIC CONCEPTS Before proceeding with description of the methodology, it is helpful to summrize the bsic concepts nd vribles used in the prevlence procedure: () Observed fertility. This is simply the rte of childbering mesured in the yer in which the method is pplied. The principl fertility indictor used in this chpter is the ge-specific fertility rte expressed in births per 1,000 women in given ge group; (b) Ntur!fertility. This is the level of fertility tht would previl in the bsence of contrception (nd induced bortion 2 ); (c) Potentiljertility (gross3). This is the level offertility tht would previl in popultion if ll progrmme users stopped contrcepting. Since there re significnt numbers of users of non-progrmme contrception in most countries, the level of potentil fertility will be less thn the nturl level. The reltionships between these three different types of fertility re summrized in figure III. From them, the following impct mesures re obtined: Senior Associte, The Popultion Council, New York. 9 o -""'"""'-'-A () Fertility impct of progrmme contrception, which is estimted s the difference between potentil nd observed fertility; (b) Fertility impct of non-progrmme contrception, which equls the difference between nturl nd potentil fertility. Of course, the totl impct of ll contrceptionfrom both progrmme nd non-progrmme sources - is given by the difference between nturl nd observed fertility. B. METHODOLOGY The procedure for clculting births verted by progrmme users consists of five prts to obtin, consecu-

2 tively, estimtes of: () nturl fertility; (b) potentil fertility; (c) fertility impct of progrmme use; (d) births verted; (e) birth-rte impct; nd (j) method-specific results. Ech of these steps is described below in some detil. All ge-specificfertility vribles re mesured in births per 1,000 women. 1. Nturl fertility The following eqution, which reltes observed nd nturl fertility, forms the bsis for estimting nturl fertility: OF = NF (1- U E/F) (1) where =five-yer ge groups; OF =observed ge-specific fertility rte (births per 1,000 women in ge group ); NF =nturl ge-specific fertility rte; U =contrceptive prevlence, equl to the proportion of mrried women currently using contrception E =(use-) effectiveness ofcontrception' in ge group ; F =proportion of women reported fecund in ge group. Eqution (1) simply sttes tht observed fertility is lower thn nturl fertility by proportion U-E/F. As expected, this proportion increses with greter prevlence nd effectiveness. The prmeter F is included to tke ccount ofthe fct tht contrceptive use is concentrted mong the fecund women. The derivtion nd testing ofeqution (1) re discussed elsewhere (Bongrts nd Potter, 1963) nd re not covered here. Rerrnging eqution (1) yields NF = OF/(1- U E/F). (2) From this eqution, nturl fertility cn be estimted if estimtes ofof, U, E nd F re vilble for ech ge group. In eqution (2), the vrible U mesures the prevlence of contrceptive use, including ll methods from both progrmme nd non-progrmme sources; nd E is the verge effectiveness ofthese methods. The product U-E in eqution (1) cn be clculted from method- nd sector-specific prevlence dt with U-B = U'-E' + U" E"; (3) nd trss» =IU'm E'm; (4) where tru.s» =IU"m E"m. (5) U' =prevlence of progrmme contrception E' =effectiveness of progrmme contrception U" =prevlence of non-progrmme contrception E" =effectiveness of non-progrmme contrception U'm, E'm, U'im, E"m = corresponding method-specific prevlence nd effectiveness levels (m = method). Only four methods re included in pplictions given below: steriliztion (m = 1); intr-uterine device (IUD) (m = 2); pill (m = 3); nd other (m = 4). Any number 10 of contrceptives cn be included, however, by using higher vlues for m, Furthermore, it is ssumed here for simplicity tht the use-effectiveness of ech method is similr for different ge groups nd for progrmme nd non-progrmme contrceptions, i.e., E'm = E"m = Em = Em. 2. Potentil fertility Potentil fertility is lower thn nturl fertility due to the use of non-progrmme contrception, so tht PF = NF(l- U" E"/F). (6) This eqution is similr to eqution (1) except tht now only the fertility-inhibiting effect of non-progrmme contrception hs to be tken into ccount. The clcultion of PF therefore requires only the vlues of NF, U", E" nd F. The product U" E" is estimted from eqution (5). 3. Fertility impct ofprogrmme nd non-progrmme contrception Once the levels of nturl nd potentil fertility re known, the fertility impct of progrmme nd nonprogrmme contrception is estimted s: FIP =PF - OF; (7) FIN =NF - PF. (8) Tht is, FIP, the ge-specific fertility impct of progrmme use, equls the difference between potentil nd observed fertility; nd FIN, the ge-specific fertility impct of non-progrmme contrception, equls the difference between nturl nd potentil fertility (see figure III). 4. Births verted Trnslting the fertility impct mesures, FIP nd FIN, into numbers of births verted in ech sector is ccomplished by multiplying by the number of women in the ge group to which the clcultion is pplied: BAP =FIP W/l,OOO; (9) BAN =FIN W/l,OOO (10) where BAP = births verted by progrmme contrception BAN = births verted by non-progrmme contrception W = number of women in ge group. 5. Impct ofcontrception on crude birth rte by sector Equtions (1)-(10) summrize the essentils of the methodology proposed here for the estimtion of gespecific numbers of births verted by sector. From these ge-specific results, the ggregte impct on the crude birth rte of progmme nd non-progrmme contrception re obtined from where BRIP=1,000 IBAP/POP; (11) BRIN= 1,000 IBAN/POP (12) BRIP = reduction in crude birth rte due to use of progrmme contrception; BRIN = reduction in crude birth rte due to use of non-progrmme contrception; BAP = births verted by progrmme contrception

3 BAN =births verted by non-progrmme contrception POP =totl popultion size. The clcultionof BRIP nd BRINtherefore requires tht BAP ndbanshll be clculted (with equtions (9) nd (10» for ll ge groups from to Method-specific results Since the fertility impct of ech method depends directly upon its prevlence nd effectiveness, it is cler tht in ech ge group: BAPm =BAP(U'm E'm)/(U' E'); (13) BANm =BAN(U"m E"m)/(U" E') (14) where BAPm =births verted by progrmme method m BANm =births verted by non-progrmme method m in ge group. The impct on the crude birth rte, by method nd sector, is now simply clculted s BRIPm = 1,000 fbapmipop; (15) BRINm = 1,000 IBANmlPOP (16) where BRIPm =reduction in the crude birth rte due to use of progrmme method m; BRINm =reduction in the crude birth rte due to use of non-progrmme method m. The vribles BAPm nd BANm re found by pplying equtions (13) nd (14) successively to ll ge groups from to C. REQUIRED INPUT DATA The following input dt re required for n ppliction of the prevlence method in given yer: () Contrceptive prevlence (i.e., proportion of mrried women currently using contrception by ge nd method for both the progrmme nd nonprogrmme sectors (U'm nd U"m), t the beginning of the yer);' (b) Observed ge-specific fertility rtes (OF); (c) Number of women in ech five-yer ge group from to (W); (d) Use-effectiveness methods (Em); of different contrceptive (e) -specific proportions of fecund women (F); (j) Totl popultion size (POP). The contrceptive prevlence dt re usully vilble from fertility or contrceptive prevlence surveys. Observed ge-specific fertility rtes nd numbers of women by ge cn be obtined from surveys or other sources. Usully, the most difficult dt to obtin re estimtes of method-specific effectiveness nd proportions reported non-sterile. Fortuntely, these two vribles tend to vry reltively little mong popultions nd the estimtes of fertility impct re not sensitive to smll errors in them. The stndrd vlues given in tbles 5 nd 6 cn therefore provide good pproximtions in popultions where no direct estimtes re vilble. 6 Method m TABLE 5. STANDARD EFFECTIVENESS LEVELS OF CONTRACEPTIVE METHODS Contrceptive effectiveness Em Steriliztion 1.00 Intr-uterine device 0.95 Pill 0.90 Other" 0.70 "Other" ctegory refers to trditionl methods, such s use of condom, diphrgm, spermicidl gents, rhythm, withdrwl nd bstinence. The ltest modern methods, such s injectbles nd subderml implnts, hve much higher effectiveness levels (close to 100 per cent) nd therefore should not be included with the trditionl methods. TABLE 6. STANDARD AGE-SPECIFIC PROPORTIONS REPORTED FECUND group Proportion repone«fecund ~ D. ILLUSTRATIVE APPLICATION To illustrte the use of the prevlence method, n ppliction exmple is presented here. In this exercise, set of hypotheticl prevlence dt, given in tble 7, nd ge-specific fertility nd number of women, given in TABLE 7. CONTRACEPTIVE PREVALENCE LEVELS, BY AGE, METHOD AND SECTOR (Hypotheticl input dt) Progrtlmme contrtjcep/ion U'm Non-pro'fYlmme contrtlception U'Im Totl,roup Sterili~Q/ion IUD PIli Other TO/l Steriliztion IUD PIli Other To/l UII II (I) (2) (3) (4) (3) (6) <n (8) (9) (10) (/J) Source: Fertility surveyor contrceptive prevlence survey. Note: IUD = intr-uterine device. 11

4 tble 8, re used. This is the minimum mount of input dt tht should be ssembled before beginning the clcultions of fertility impct mesures. As lredy noted, stndrd levels of effectiveness (tble 5) nd proportions reported fecund (tble 6) cn be used. Once the input dt (tbles 5-8) re vilble, the stepby-step ppliction of the prevlence method proceeds s described below. group TABLE 8. OBSERVED AGE-SPECIFIC FERTILITY RATE AND NUMBER OF WOMEN, BY AGE GROUP (Hypotheticl input dt) Observed fertility rte OF Source: Vitl sttistics nd census dt or derived from smple surveys. m Number of women W (thousnds) (2) Estimtion of ge-specific nturl fertility rtes For ech ge group in the reproductive yers, the nturl fertility rte is clculted with eqution (2). Before using this eqution, however, it is necessry to clculte the products U-Eo, with equtions (3), (4) nd (5). To ccomplish this, the product of prevlence nd effectiveness for ech method nd ge group in both the progrmme nd non-progrmme sectors should be clculted first from the dt given in tbles 5 nd 7. The results, presented in tble 9, re obtined by multiplying the ge- nd method-specific prevlence estimtes given in tble 7 by the pproprite method-specific effectiveness levels from tble 5. The resulting ge-specific estimtes of U-B given in column (11) of tble 9 re now substituted in eqution (2), together with the gespecific proportions fecund (from tble 6) nd the observed ge-specific fertility rtes (from tble 8), to yield the ge-specific nturl fertility pttern given in the first column oftble Estimtion of ge-specific potentil fertility rtes Potentil fertility rtes re clculted with eqution (6) by substituting NF (column (1) in tble 10), U''-E' (from column (10) oftble 9) nd F (from tble 6). The results re presented in column (2) of tble 10. As expected, the potentil fertility rte in ech ge group is less thn the nturl but higher thn the observed fertility level. 3. Estimtion ofge-specificfertility impct of progrmme nd non-progrmme contrception The ge-specific reductions in fertility rtes ttributble to progrmme contrception, FIP, re estimted directly from eqution (7) by subtrcting observed from potentil fertility rtes. This yields the vlues offip presented in column (3) oftble 10. Appliction of eqution (8) produces the estimtes of nonprogrmme effects, FIN, in column (4) of tble Estimtes ofbirths verted -specific numbers ofbirths verted by progrmme nd non-progrmme contrception estimted from equtions (9) nd (10) re presented in tble 11. A totl of 52,400 births were verted by progrmme contrception nd 27,100 births by non-progrmme contrception. 5. Estimtion ofbirth-rte effects The reductions in the crude birth rte ttributble to either progrmme or non-progrmme contrception re now directly obtined by dividing the totl number of births verted in ech sector by the totl popultion size nd multiplying by 1,000 (equtions (11) nd (12». With totl popultion, POP, of 6,125,000 persons, the birth-rte effect of progrmme contrception equls (52,400/6,125,000) x 1,000 = Similrly, the birth-rte impct of non-progrmme contrception equls From these sectorl effects, the levels of potentil nd nturl crude birth rtes cn be clculted if the observed crude birth rte is known. The popultion in this illustrtion hs crude birth rte of ' The potentil crude birth rte is therefore = 38.21, nd the nturl crude birth rte is = These results re summrized s follows: () Birth-rte impct of progrmme contrception, BRIP: 8.56; TABLE 9. ESTIMATES OF THE PRODUCT OF CONTRACEPTIVE PREVALENCE AND EFFECTIVENESS, U E, BY AGE, METHOD AND SECTOR Progrmme con/rcep/lonu'm Em Non prog1'qmme contrception U''m : Em To/l grup S/erIIIVl/ion IUD Pill Other To/l SleriJlVI/lon IUD Pill Other To/l U+E (I) (2) (3) (of) (S) (6) (7) (8) (9) (10) (11) Source: See formul in text. Note: IUD = intr-uterine device. 12

5 TABU! 10. EsTIMATED AGE-SPECIFIC NATURAL AND POTENTIAL FERTIL ITY RATES AND AGE-SPECIFIC FERTILITY EFFECTS OF PROGRAMME AND NON-PROGRAMME CONTRACEPTION (Births per J,()fX) women) Fmilily d!«t of Nlurl POlenlil conlfflceplion ferlilily fmilily role role Pro,romme Non-pro,romme,roup NF PF FIP FIN (I) (2) (3) (4) Source: Derived with equtions (2), (6), (7) nd (8). TABLE 11. ESTIMATED NUMBER OF BIRTHS AVERTED BY PROGRAMME AND NON-PROGRAMME CONTRACEPTION Births _led by Pro,romme Non pro,romme A,e conlfflceplion contrception,roup BAP BAN TOll (1) (2) (3) ()fx) to 3' TOTAL Source: Derived with equtions (9) nd (10). (b) Birth-rte impct of non-progrmme contrception, BRIN: 4.42; (c) Observed crude birth rte: 29.65; (d) Potentil crude birth rte (observed crude birth rte + BRIP): 38.21; (e) Nturl crude birth rte (observed crude birth rte + BRIP + BRIN): Estimtion ofbirths verted nd birth-rte impct by method To obtin method-specific results, it is necessry first to clculte births verted by ge nd method. This is done in tble 12. Ech cell in this tble is clculted from equtions (13) or (14) by substituting the estimtes of BAP nd BAN (from tble 11) nd the products U'm Em nd U"m E'm (from tble 9). Summing over ll ges in tble 12 yields the numbers of births verted by method in ech sector. given in the bottom row of this tble. Adding sectors yields the totl births verted by method. The results re summrized in columns (1)-(3) of tble 13. Dividing these numbers of births verted by the totl popultion size (nd multiplying by 1,(00) produces the effects on the crude birth rte, by method nd sector, given in columns (4)-(6) of tble 13. The totl birth-rte effect of progrmme contrception is 8.56, of which 1.56 is ttributble to steriliztion, 3.79 to IUD to the pill nd 1.36 to other methods. TABLE 12. ESTIMATED NUMBER OF BIRTHS AVERTED, BY AGE, METHOD AND SECTOR Births IIl1f1rted bypro,romme conlfflceplion Birlhs llf!rted by non-pro,romme conlfflcep/ion TOll TOll,roup Sterlilvllion IUD Pill Olher BAh Slerlilvllion IUD Pill OIMr BAN Totl (1) (2) (3) (4) ($) (6) (7) (8) (9) (10) (ll) SOO TOTAL Source: Derived with equtions (9) nd (10). Note: IUD = intr-uterine device. TABLE 13. ESTIMATED NUMBER OF BIRTHS AVERTED AND EFFECT OF PROGRAMME AND NON-PROGRAMME CONTRACEPTION ON CRUDE BIRTH RATES, BY METHOD Birthsllflrted CruJk birth role dfecl Progl'tlmme Non-pro.,.""". Pro'rrlmme No,,-pro,fYlmme ConlfflCeplive contf'llf.yption conlfflceplion TOIIII contrception contf'llf.yption TOllli melhod (I) (2) (3) (4) ($) (6) Steriliztion Intr-uterine device Pill l Other TOTAL Source: Derived with equtions (13)-(16). 13

6 CONCLUSION The preceding overview of the prevlence method indictes tht this new pproch provides simple nd strightforwrd lterntive to existing methods for estimting the gross fertility impct ofprogrmme contrception. In contrst to severl of the other procedures, the prevlence method does not require detiled input dt on numbers of pst cceptors nd continution rtes. Insted, estimtes of the prevlence of progrmme nd non-progrmme contrception by ge nd method re required s principl input dt. While such dt were rrely vilble in the pst, prevlence estimtes re now routinely obtined from ntionl surveys in mny developing countries, thus mking the ppliction of the prevlence method possible. NOTES I Exmples of ntionl smple surveys conducted in lrge numbers of countries re the World Fertility Survey (WFS) nd the Contrceptive Prevlence Survey (CPS). 2 Nturl fertility is defined s fertility in the bsence of ny deliberte prity-specific birth control prctices, such s the use of contrception or induced bortion. In the pplictions of the prevlence method given here, the term "nturl fertility" is used s the fertility previling in the bsence of contrception. This yieldsthe nturl fertility only if there is no induced bortion, but results of the prevlence method re not ffected becuse births verted re clculted only s result ofcontrceptive use. 3 Potentil fertility is generlly defined s the fertility tht would previl in the bsence of fmily plnning progrmme. At lest two types of potentil fertility cn be distinguished. Gross potentil fertility is the level tht would be observed if ll progrmme users stopped contrcepting (without substituting). Net potentil fertility is the level tht would be observed if progrmme hd never existed. The differencebetweengross nd net fertility is tht the ltter tkes into ccount substitution nd ctlytic or spill-overeffectsofthe progrmme. Further discussion of the definition of potentil fertility nd its use in vrious methodologies cn be found in Bongrts (1985). 4 The use-effectiveness of contrceptive method equls the proportionl reduction in the monthly probbility of conception chieved while using the method. A discussion of this nd other mesures of contrceptive performnce (such s filure rte, Perl rte nd continution rte) is given in Bongrts nd Potter (1983). The mesurement of use-effectiveness is difficult nd requires specil complex surveys. For further detils, see Ling (1978 nd 1984)., For simplicity, it is ssumed here tht there is six-month dely between contrceptive use nd its effect on fertility. A nine-month dely would theoreticlly be preferble, but the error is negligible in prctice. In fct, this dely cn be ignored ltogether in most cses without significnt error, unless contrceptive prevlence is chnging very rpidly. 6 These stndrd ptterns of use-effectiveness nd reported proportions fecund re proposed in Bongrts nd Potter (1983). For simplicity, method-specific effectiveness levels re ssumed to be the sme for ll ge groups in the pplictions presented in this chpter. Where considered pproprite, n incresing trend with ge could be used. 7 The crude birth rte of the hypotheticl popultion used in this illustrtion is equl to the observed number of births divided by the totl popultion (x 1,(00):1,000 x 181,625/6,125,000 = The observed totl number of births is clculted by summing over ll ge groups the product of the observed fertility rte, OF, nd the number of women, W, given in tble 8. REFERENCES Bongrts, John (1985). The concept of potentil fertility in evlution of the fertility impct of fmily plnning progrmmes. In Studies to Enhnce the Evlution of Fmily Plnning Pr0 grmmes. New York: United Ntions, Sles No. E.84.XIII.9. nd Robert G. Potter (1983). Fertility, Biology nd Behvior:An Anlysis ofthe Proximte Determinnts. New York: Acdemic Press. Ling, John E. (1978). Estimting the effects of contrceptive use on fertility: techniques nd findings from the 1974 Philippine Ntionl Acceptor Survey. Studies in Fmily Plnning 9(6): (1984). Mesurement of contrceptive protection for fertility nlysis. Pper submitted to the Interntionl Union for the Scientific Study of Popultion/World Fertility Survey Seminr on Integrting Proximte Determinnts into the Anlysis of Fertility Levels nd Trends, London, April