Estimating incidence of heroin use from treatment data presentation for TDI expert meeting

Estimating incidence of heroin use from treatment data

presentation for TDI expert meetingLucas Wiessing (EMCDDA), Lucilla Rav and Carla Rossi (Univ Rome), EMCDDA, Lisbon, 23 June 2003

BackgroundIncidence has been developed as part of the key indicator prevalence and patterns of problem drug use - one of the five EMCDDA key indicatorsSince 1997, EMCDDA (+ DG-Research-TSER / Pompidou Group) projects have resulted in estimated incidence curves for some cities and countries (Univ. Rome Tor Vergata - Prof. Carla Rossi)Guidelines have been prepared Recent project and expert meeting (May 2003) aims to obtain more data and estimates, final results expected by early 2004 -> led to request to TDI expert group

What is the difference between incidence and prevalence ?Prevalence is the total number of cases existing at a given moment in time (point prevalence), usually it is easier to estimate the cases that have existed during a one year period (one year period-prevalence)Incidence is the rate of NEW cases occurring over time, usually estimated for consecutive years (yearly incidence, either by calendar years in public health data, or by person-years-of-observation in a cohort study)

Why estimate incidence ?Incidence is much more sensitive to changes over time (trends) than prevalenceIt relates to the start of problem drug use careers and to prevention of initiationIt can provide historical information regarding the epidemic of heroin useIt can be used to forecast treatment needs in the near futureTrends can be derived from some sentinel sites, it is not essential to have complete national coverage

How to estimate incidence of first heroin use from treatment dataThe principle is simple: an observed time series of cases entering first treatment shows a certain curve (incidence of first treatment).If we know the average duration since first heroin use, we can back-project this curve to obtain the unobserved incidence curve of first heroin useAverage duration is called the latency period (LP) and its distribution needs to be estimated first

There are important limitationsWe cannot estimate total incidence from treatment data, only part of it, as a proportion of new heroin users will never enter treatment, we call this relative incidence which is a lower bound of total incidence the shape of the curve should however be unbiasedIf we include cases who started heroin use before the first year of observed treatment, we have left-truncation of LP, i.e. Some short LPs are left out.The LP is also right-truncated, i.e. we can not observe LPs which are longer than our time seriesChanges in incidence can affect LP estimation depending on the way LP is estimated

Two methods proposed in EMCDDA Guidelines1)Latency period (LP) analysis +Back-calculation method (BC)2)Reporting delay adjustment (RDA) or lag-correction method (with or without separate LP analysis)

Latency period (LP) analysis (EMCDDA/Univ. Rome pilot project)This needs to be done on individual data recordsCan be done in one or few sentinel sites only, results can then be used by BC method at national level and with aggregate dataNeed to understand biases resulting from selection of cases into the observed dataAnalysis of covariates e.g.: age of first use, gender, route of administration (time dependent, see request on age at first IDU), which are important to take into account in incidence estimationLP results not only needed for incidence, also important for own sake (treatment careers)

Grafico1

000

0.0280.0607160.046545

0.0483730.0789630.06823

0.0643220.0897060.082722

0.0768380.0964230.092791

0.0865530.100550.099746

0.0939410.102850.10437

0.0993790.103830.1072

0.103180.103810.10862

0.10560.103020.10891

0.106860.101640.10832

0.107150.0998030.10702

0.106640.0976210.10515

0.105450.0951750.10285

0.103720.0925310.1002

0.101540.0897450.097291

0.099010.0868610.094189

0.0961960.0839140.09095

0.0931680.0809360.087622

0.0899810.077950.084244

0.0866850.0749770.080848

0.0833190.0720320.077461

0.0799190.0691290.074105

0.0765130.0662790.070797

0.0731270.0634890.067553

0.0697790.0607680.064383

0.0664890.0581190.061297

0.0632680.0555470.058302

0.0601280.0530550.055404

0.0570770.0506440.052605

0.0541230.0483150.049908

0.0512690.046070.047315

0.048520.0439070.044826

0.0458780.0418270.04244

0.0433430.0398280.040157

0.0409160.0379090.037975

0.0385970.0360690.035892

0.0363830.0343060.033906

0.0342730.0326180.032015

0.0322660.0310020.030215

0.0303570.0294580.028504

0.0285460.0279820.026879

0.0268280.0265730.025337

0.02520.0252280.023874

0.023660.0239450.022487

0.0222030.0227220.021174

0.0208260.0215560.019931

0.0195270.0204450.018756

0.0183010.0193880.017644

0.0171450.0183810.016593

0.0160560.0174240.015601

0.0150310.0165130.014664

0.0140660.0156470.01378

0.0131590.0148240.012946

0.0123070.0140410.01216

0.0115060.0132980.011418

0.0107540.0125930.01072

0.0100480.0119220.010062

0.00938550.0112860.0094431

0.00876460.0106830.0088602

0.00818270.010110.0083117

0.00763740.00956680.0077957

0.00712670.00905160.0073104

0.00664870.00856310.0068542

0.00620120.00810.0064254

0.00578260.00766110.0060224

0.00539110.00724510.0056438

0.0050250.0068510.0052883

0.00468290.00647760.0049544

0.00436320.0061240.0046409

0.00406450.00578910.0043466

0.00378560.0054720.0040705

0.00352520.00517180.0038114

0.00328210.00488760.0035683

0.00305530.00461860.0033403

0.00284360.00436410.0031266

0.00264620.00412320.0029261

0.00246210.00389530.0027382

0.00229050.00367970.0025621

0.00213050.00347580.002397

0.00198140.00328290.0022424

0.00184250.00310050.0020975

0.00171310.00292810.0019617

0.00159250.0027650.0018346

0.00148020.00261080.0017155

0.00137570.00246510.0016041

0.00127840.00232740.0014997

0.00118780.00219720.001402

0.00110360.00207410.0013105

0.00102510.00195790.0012249

0.000952170.0018480.0011448

0.00088430.00174420.0010699

0.000821180.00164610.00099977

0.000762490.00155350.00093418

0.000707910.0014660.00087281

0.000657170.00138340.00081542

0.000610010.00130530.00076175

0.000566180.00123160.00071156

0.000525440.0011620.00066463

0.000487590.00109620.00062075

0.000452430.00103420.00057973

0.000452430.00103420.00057973

0.000452430.00103420.00057973

0.000452430.00103420.00057973

0.000452430.00103420.00057973

0.000452430.00103420.00057973

0.000452430.00103420.00057973

0.000452430.00103420.00057973

0.000452430.00103420.00057973

Rome

Amsterdam

London

years

frequency distribution

Latency period distributions

TABGAMM

XYZW

0000

0.30.0280.0607160.046545

0.60.0483730.0789630.06823

0.90.0643220.0897060.082722

1.20.0768380.0964230.092791

1.50.0865530.100550.099746

1.80.0939410.102850.10437

2.10.0993790.103830.1072

2.40.103180.103810.10862

2.70.10560.103020.10891

30.106860.101640.10832

3.30.107150.0998030.10702

3.60.106640.0976210.10515

3.90.105450.0951750.10285

4.20.103720.0925310.1002

4.50.101540.0897450.097291

4.80.099010.0868610.094189

5.10.0961960.0839140.09095

5.40.0931680.0809360.087622

5.70.0899810.077950.084244

60.0866850.0749770.080848

6.30.0833190.0720320.077461

6.60.0799190.0691290.074105

6.90.0765130.0662790.070797

7.20.0731270.0634890.067553

7.50.0697790.0607680.064383

7.80.0664890.0581190.061297

8.10.0632680.0555470.058302

8.40.0601280.0530550.055404

8.70.0570770.0506440.052605

90.0541230.0483150.049908

9.30.0512690.046070.047315

9.60.048520.0439070.044826

9.90.0458780.0418270.04244

10.20.0433430.0398280.040157

10.50.0409160.0379090.037975

10.80.0385970.0360690.035892

11.10.0363830.0343060.033906

11.40.0342730.0326180.032015

11.70.0322660.0310020.030215

120.0303570.0294580.028504

12.30.0285460.0279820.026879

12.60.0268280.0265730.025337

12.90.02520.0252280.023874

13.20.023660.0239450.022487

13.50.0222030.0227220.021174

13.80.0208260.0215560.019931

14.10.0195270.0204450.018756

14.40.0183010.0193880.017644

14.70.0171450.0183810.016593

150.0160560.0174240.015601

15.30.0150310.0165130.014664

15.60.0140660.0156470.01378

15.90.0131590.0148240.012946

16.20.0123070.0140410.01216

16.50.0115060.0132980.011418

16.80.0107540.0125930.01072

17.10.0100480.0119220.010062

17.40.00938550.0112860.0094431

17.70.00876460.0106830.0088602

180.00818270.010110.0083117

18.30.00763740.00956680.0077957

18.60.00712670.00905160.0073104

18.90.00664870.00856310.0068542

19.20.00620120.00810.0064254

19.50.00578260.00766110.0060224

19.80.00539110.00724510.0056438

20.10.0050250.0068510.0052883

20.40.00468290.00647760.0049544

20.70.00436320.0061240.0046409

210.00406450.00578910.0043466

21.30.00378560.0054720.0040705

21.60.00352520.00517180.0038114

21.90.00328210.00488760.0035683

22.20.00305530.00461860.0033403

22.50.00284360.00436410.0031266

22.80.00264620.00412320.0029261

23.10.00246210.00389530.0027382

23.40.00229050.00367970.0025621

23.70.00213050.00347580.002397

240.00198140.00328290.0022424

24.30.00184250.00310050.0020975

24.60.00171310.00292810.0019617

24.90.00159250.0027650.0018346

25.20.00148020.00261080.0017155

25.50.00137570.00246510.0016041

25.80.00127840.00232740.0014997

26.10.00118780.00219720.001402

26.40.00110360.00207410.0013105

26.70.00102510.00195790.0012249

279.52E-040.0018480.0011448

27.38.84E-040.00174420.0010699

27.68.21E-040.00164611.00E-03

27.97.62E-040.00155359.34E-04

28.27.08E-040.0014668.73E-04

28.56.57E-040.00138348.15E-04

28.86.10E-040.00130537.62E-04

29.15.66E-040.00123167.12E-04

29.45.25E-040.0011626.65E-04

29.74.88E-040.00109626.21E-04

304.52E-040.00103425.80E-04

300.000452430.00103420.00057973

300.000452430.00103420.00057973

300.000452430.00103420.00057973

300.000452430.00103420.00057973

300.000452430.00103420.00057973

300.000452430.00103420.00057973

300.000452430.00103420.00057973

300.000452430.00103420.00057973

TABGAMM

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

Rome

Amsterdam

London

years

frequency distribution

Latency period distributions

Latency period distribution (EMCDDA /Univ. Rome pilot project)Rome metropol.:mean 6.5, median 5 yrAmsterdam:mean 7.1, median 5 yrLondon:mean 6.7, median 5 yr

Kaplan-Meyer curves Rome: no difference by gender (EMCDDA /Univ. Rome pilot project)

Survival Functions

years

20

10

0

C

U

M

S

U

R

V

I

V

A

L

1.0

.8

.6

.4

.2

0.0

sex

women

men

Kaplan-Meyer curves Rome: strong age effect (EMCDDA /Univ. Rome pilot project)

Survival Functions

years

20

10

0

C

U

M

S

U

R

V

I

V

A

L

1.0

.8

.6

.4

.2

0.0

age at 1 use

more than 22

from 16 to 21

less than 15

Back-calculation (BC) method (Brookmeyer and Gail, Lancet 1986; Heisterkamp et al, Biometrical Journal, 1999; Downs et al, AIDS 2000)Done with a specifically developed programme that applies a deconvolution function, to back-project observed curve of treatment incidence into the unobserved curve of onset incidence of first useNo need for individual data records, aggregate time series is sufficient (but at least 8-10 years long, ideally much longer)Latency period distribution is treated as a separate input element and can come from other/ local dataVery well suited to handle large regions /national data

Observed and projected treatment incidence, Italy, BC method (EMCDDA /Univ. Rome pilot project; Rav et al submitted)

Gamma 1.51 0.30 (LT) M cov

bcfit1m3.aem lambda: 3.12e-006 abic: -111.6 prevalence codes: Onset 1: DrugsHelp 2

numbers fitted with co-variates normal approximation Fri Feb 19 19:31:16 1999 Total without new infections

TimeDrugsHelpDrugsHelpDrugsHelpDrugsHelpDrugsHelpprevprevprevprevprevprevStoppedOnset

31:12:00rep.adj.pred00Onset0+2*seDrugsHelp0+2*seann.cum inc

1986.526952695114510931200000515549175398030365

198736523652270326072800000205622009221037072426

1988842984297717762078140004644345770471200121109

1989969796971036810249104880008166280801825280173699

199011704117041293912730131500001226791216331237300221791

199113966139661543715204156720001333361322351344420233809

199220368203681769617440179540001529081516791541420233809

199321639216391939319115196720001695361681701709080233809

199418481184812054220246208400001832201817241847230233809

199520658206582100820698213200001942681926561958870233809

1996NANA1957119246198990001972051955251988910227808

1997NANA1662816268169920001901461884071918940213512

1998NANA136841332014054NANANANANANANANA




with new infections from: 1995 onwards



1986.526952695114510931200000515549175398030365

198736523652270326072800000205622009221037072426

1988842984297717762078140004644345770471200121109

1989969796971036810249104880008166280801825280173699

199011704117041293912730131500001226791216331237300221791

199113966139661543715204156720001333361322351344420233809

199220368203681769617440179540001553651541001566360257846

199321639216391939319115196720001778811763111794570281882

199418481184812054220246208400002007641987032028370305918

199520658206582100820698213200002239282211912266820329954

1996NANA2202921704223570002414372378942450070347988

1997NANA2251522155228780002509672464912554840357728





StartEndOnset /yearOnset HIV-2*seOnset +2*seCum Onset /year

198219831111

198319841112

198419856002547365316004

1985198614296137381485420300

1986198720136196092066240436

1987198820982204372152761418

1988198922021214622258183439

19891990244302385825002107869

19901991264852590127068134354

19911992269452634927541161299

19921993248052417425435186104

19931994236722292524420209776

19941995240362301625056233812

19951996257848

19961997281884

19971998305920

19981999329956

Gamma 1.51 0.30 (LT) F cov

bcfit1f3.aem lambda: 1.14e-005 abic: -23.52 prevalence codes: Onset 1: DrugsHelp 2




1986.567767731728335200014241274158308285

1987856856730668795000527850035561017188

198820782078195518922020000106761031311046024819

198922752275238723222453000171871674817631033411

199024522452269825892810000243062379924818040972

199126782678298628713103000261132558626645042936

199235153515327231523394000294152883729998042936

199337043704346333383591000322083157132852042936

199432773277355934293692000345013380435205042936

199535183518353133973668000363493559837108042936

1996NANA330231653442000361833541536959041262

1997NANA279426422950000334243262734232037264








1986.567767731728335200014241274158308285

1987856856730668795000527850035561017188

198820782078195518922020000106761031311046024819

198922752275238723222453000171871674817631033411

199024522452269825892810000243062379924818040972

199126782678298628713103000261132558626645042936

199235153515327231523394000298162921630423046865

199337043704346333383591000335723279434360050794

199432773277355934293692000373693627038485054723

199535183518353133973668000411973964742777058652

1996NANA370435663843000434134132945547060907

1997NANA375636033912000433664066446155060837






198219831111

198319841112

198419851674128520631676

198519863998360843895674

1986198752264866558610900

1987198844564089482215356

1988198936673300403419023

1989199036973326406922720

1990199142013824457726921

1991199245344153491531455

1992199339153527430235370

1993199436393208407139009

1994199539293311454642938

46867

50796

54725

58654

Gamma 1.51 0.30 (LT) T cov

bcfit1t3.aem lambda: 1.47e-007 abic: -161.7 prevalence codes: Onset 1: DrugsHelp 2




1986.533723372158415061663000712767797484041753

198745084508369335493840000271682653527808091545

19881050710507100849939102300005857557728594270147743

19891197211972129131276613062000100882998391019320210863

199014156141561566415414159170001491371479051503750263655

199116644166441854918282188190001614881602001627810277072

199223883238832130521016215950001840991826711855310277072

199325343253432316222850234750002032622016772048540277072

199421758217582415223820244870002190092172682207570277072

199524176241762430923964246580002317092298282335980277072

1996NANA2261122254229710002337632318222357130268829

1997NANA1916418765195670002220482200202240840248729








1986.533723372158415061663000712767797484041753

198745084508369335493840000271682653527808091545

19881050710507100849939102300005857557728594270147743

19891197211972129131276613062000100882998391019320210863

199014156141561566415414159170001491371479051503750263655

199116644166441854918282188190001614881602001627810277072

199223883238832130521016215950001868421853601883300303904

199325343253432316222850234750002125782106582145060330737

199421758217582415223820244870002385952359062412980357570

199524176241762430923964246580002648202610592686080384403

1996NANA2535524997257150002831432781062882240402992

1997NANA2573625336261380002899452834252965390409725






198219831111

198319841112

198419858243735091358245

1985198620100192052099528345

1986198726820259952764555165

1987198824330234862517379495

19881989241052325624955103600

19891990280902722228957131690

19901991321123122732997163802

19911992331323223234032196934

19921993278652694028790224799

19931994254432439626490250242

19941995268332534728319277075

303908

330741

357574

384407

Gamma 1.51 0.30 (LT) M no cov

bcfit1m3.aem 2.36e-005 abic: -30.84 prevalence codes: Onset 1: DrugsHelp 2

numbers fitted without co-variates normal approximation Fri Feb 19 19:31:20 1999 Total without new infections



1986.526952695122511651288000551552415795032460

198736523652288027662997000214712094722001073745

1988842984298016790181320004741746696481430122515

1989969796971046810341105970008327482368841850177302

199011704117041292812707131500001244291233441255190221758

199113966139661557215333158130001349041337661360470232634

199220368203681805917799183210001540541527871553260232634

199321639216391975119468200370001702671688561716840232634

199418481184812062120317209270001835821820301851400232634

199520658206582068620369210060001943161926381960020232634

1996NANA1915018821194810001966701949251984230226300

1997NANA1621315847165830001881891863731900140210765








1986.526952695122511651288000551552415795032460

198736523652288027662997000214712094722001073745

1988842984298016790181320004741746696481430122515

1989969796971046810341105970008327482368841850177302

199011704117041292812707131500001244291233441255190221758

199113966139661557215333158130001349041337661360470232634

199220368203681805917799183210001562781549681575930254386

199321639216391975119468200370001778191761531794920276138

199418481184812062120317209270001994591971932017370297890

199520658206582068620369210060002211582180632242740319641

1996NANA2137421045217050002366992326172408160335060

1997NANA2154121174219100002432302380082485090341276





StartEndHIV/yearHIV-2*seHIV+2*seCum Onset /year

198219830000

198319840000

198419856334568769806334

1985198615535148581621221869

1986198721183205552181143052

1987198820383197282103863435

1988198920622199472129684057

19891990243262363625016108383

19901991282662755928972136649

19911992285592784229276165208

19921993241922345224932189400

19931994214842060922358210884

19941995217522053022974232636

254388

276140

297892

319644

Gamma 1.51 0.30 (LT) F no cov

bcfit1f3.aem 4.17e-005 abic: -6.855 prevalence codes: Onset 1: DrugsHelp 2




1986.567767731228134400014041265155008180

1987856856721663782000522749655496017059

198820782078194218832002000105921024110948024710

198922752275236923052434000171161669017546033414

199024522452267925712790000242222372824722040695

199126782678298128673097000260072549226526042522

199235153515328031613401000292592869429829042522

199337043704347533503602000320053138132635042522

199432773277355734263689000342563357434946042522

199535183518349533613632000360693533336812042522

1996NANA325231163392000359043514736668040878

1997NANA274625952902000331743239033968036933








1986.567767731228134400014041265155008180

1987856856721663782000522749655496017059

198820782078194218832002000105921024110948024710

198922752275236923052434000171161669017546033414

199024522452267925712790000242222372824722040695

199126782678298128673097000260072549226526042522

199235153515328031613401000296332904830224046177

199337043704347533503602000332743252534032049832

199432773277355734263689000369243588437980053487

199535183518349533613632000405793913142054057142

1996NANA362634893765000426304069844606059153

1997NANA364134903796000424233993244988058863






198219830000

198319840000

198419851644130719811644

198519863945359542965589

1986198751824859550510771

1987198844934158482815264

1988198935903249393018854

1989199036963351404122550

1990199143213970467226871

1991199245914236494631462

1992199339063546426535368

1993199435013090391138869

1994199536553069424142524

46179

49834

53489

57144

Gamma 1.51 0.30 (LT) T no cov

bcfit1t3.aem 7.91e-006 abic: -34.52 prevalence codes: Onset 1: DrugsHelp 2




1986.533723372201018182212000904681839953053159

198745084508467643455018000315093022732818094700

198810507105071141811084117570006152059976630840147931

198911972119721282712614130410001060601043031078320224590

199014156141561470314387150240001540801521531560200263918

199116644166441826517958185740001662591642731682570280770

199223883238832287022552231900001886231864811907780280770

199325343253432437624033247230002076052052722099510280770

199421758217582368823313240650002232102206812257540280770

199524176241762371523331241020002357982330862385260280770

1996NANA2236421983227490002360992335052387060270823

1997NANA1898118564194040002178862151082206810244156








1986.533723372201018182212000904681839953053159

198745084508467643455018000315093022732818094700

198810507105071141811084117570006152059976630840147931

198911972119721282712614130410001060601043031078320224590

199014156141561470314387150240001540801521531560200263918

199116644166441826517958185740001662591642731682570280770

199223883238832287022552231900001920701897631943900314476

199325343253432437624033247230002193062158962227430348181

199421758217582368823313240650002478122422772534090381886

199524176241762371523331241020002773902688922860200415592

1996NANA2581125429261950002981252862153102770439349

1997NANA2723726818276580003031742872423195360446388






198219830000

198319840000

1984198599487141127559948

1985198626667241742915936615

1986198733089307423543769704

1987198817752157751973087456

19881989144881255716418101944

19891990255772359327560127521

19901991408213876642876168342

19911992472764514749405215618

19921993179451575520134233563

19931994135031129815707247066

19941995337053067036741280771

314476

348181

381886

415591

Weibul 1.28 5.33 (LT) M cov





1986.526952695130912381382000589055706218033267

198736523652291527833050000221512157522735075045

1988842984298167803483010004824747473490280123149

1989969796971055810425106900008403783079850000177667

199011704117041300312776132310001251961240631263350222545

199113966139661557615333158210001356851344991368750233817

199220368203681804017776183050001548631535521561790233817

199321639216391970319418199900001712521698021727090233817

199418481184812059820293209060001848621832731864580233817

199520658206582080620488211270001959301942151976530233817

1996NANA1917818848195110001986481968782004270227576

1997NANA1638916021167610001898841880341917430211587








1986.526952695130912381382000589055706218033267

198736523652291527833050000221512157522735075045

1988842984298167803483010004824747473490280123149

1989969796971055810425106900008403783079850000177667

199011704117041300312776132310001251961240631263350222545

199113966139661557615333158210001356851344991368750233817

199220368203681804017776183050001573691560051587390256362

199321639216391970319418199900001793611776051811250278907

199418481184812059820293209060002015601991232040120301452

199520658206582080620488211270002238972205092273110323997

1996NANA2168421354220170002401872356682447490340301

1997NANA2199221623223640002469232410802528360346856






198219831111

198319841112

198419856242543370506244

1985198615989151671681122233

1986198722073213222282444306

1987198820467197042123164773

1988198920548197762131985321

19891990240972330924884109418

19901991274672666228273136885

19911992286642784429485165549

19921993242412339725085189790

19931994214842053422435211274

19941995225452121923871233819

256364

278909

301454

323999

Weibul 1.28 5.33 (LT) F cov





1986.567767731428334600014121274155807902

1987856856689633748000517849205443017098

198820782078191018521968000105821023310937024842

198922752275236623032429000170891666417520033161

199024522452270525982814000242102371524709040750

199126782678299728843112000260092549426529042695

199235153515326931503390000292902872629859042695

199337043704345533313582000320853146632711042695

199432773277356034313692000344023372835083042695

199535183518354334103678000362833555837015042695

1996NANA328131453420000362633551937015041147

1997NANA279626452951000337213295134500037364








1986.567767731428334600014121274155807902

1987856856689633748000517849205443017098

198820782078191018521968000105821023310937024842

198922752275236623032429000170891666417520033161

199024522452270525982814000242102371524709040750

199126782678299728843112000260092549426529042695

199235153515326931503390000297222913730313046586

199337043704345533313582000334853274434234050477

199432773277356034313692000372843626838314054368

199535183518354334103678000411103970842535058259

1996NANA371335773852000434334157345333060602

1997NANA376336113917000435664117246027060710






198219831111

198319841112

198419851548121318831550

198519863782343541305332

1986198751424821546210474

1987198846654339499015139

1988198939223593425219061

1989199037633429409622824

1990199140413703437926865

1991199243313989467231196

1992199339353585428535131

1993199436763282407038807

1994199538913342444042698

46589

50480

54371

58262

Weibul 1.28 5.33 (LT) T cov





1986.5337233722069188922570009310850010156052184

198745084508453142224851000316643043832914096760

198810507105071134811035116650006247660967640040149322

198911972119721299412791131990001066381048871084030224210

199014156141561516914852154890001551981532281571800265466

199116644166441846218147187780001673231652821693760279646

199223883238832258522257229150001894281872171916510279646

199325343253432432323973246750002082592058592106720279646

199421758217582403523656244170002238582212702264620279646

199524176241762388123483242840002365202337562392990279646

1996NANA2210521706225080002369282342742395960269776

1997NANA1883118395192730002195682167612223930244062








1986.5337233722069188922570009310850010156052184

198745084508453142224851000316643043832914096760

198810507105071134811035116650006247660967640040149322

198911972119721299412791131990001066381048871084030224210

199014156141561516914852154890001551981532281571800265466

199116644166441846218147187780001673231652821693760279646

199223883238832258522257229150001925801902171949570308006

199325343253432432323973246750002184592151242218190336366

199421758217582403523656244170002448632396812501010364726

199524176241762388123483242840002717002639162795960393086

1996NANA2525724858256600002891812784133001540411576

1997NANA2587925442263200002913192769703060300414222






198219831111

198319841112

1984198598717302124399873

1985198625713233932803435586

1986198733199310753532468785

1987198819867182192151588652

19881989162191453017909104871

19891990260242427427774130895

19901991368573515438559167752

19911992443264247746174212078

19921993242682221626321236346

19931994149421316516719251288

19941995283602573330987279648

308008

336368

364728

393088

Weibul 1.28 5.33 (LT) M no cov





1986.526952695168815071879000759567828455043198

198736523652377534644098000258422463527078078136

1988842984299253893995730005085049390523310122705

1989969796971045610261106530008869287030903690190958

199011704117041221811926125140001296941278711315300222191

199113966139661534515061156320001399871381091418780235810

199220368203681953419238198320001587921567761608200235810

199321639216392086420545211870001748341726581770250235810

199418481184812013419784204870001881371857941904930235810

199520658206582025819899206200001989421964432014560235810

1996NANA1880418450191620002001211977692024880228228

1997NANA1604315656164350001857471832001883110206720








1986.526952695168815071879000759567828455043198

198736523652377534644098000258422463527078078136

1988842984299253893995730005085049390523310122705

1989969796971045610261106530008869287030903690190958

199011704117041221811926125140001296941278711315300222191

199113966139661534515061156320001399871381091418780235810

199220368203681953419238198320001618191596401640130263048

199321639216392086420545211870001846311814461878430290286

199418481184812013419784204870002083112032112134740317524

199520658206582025819899206200002327302249562406350344762

1996NANA2183221477221890002503082394722613830364418

1997NANA2281222424232030002546592401632695800370149






198219830000

198319840000

1984198575824957102077582

1985198621507191442387029089

1986198728217260503038457306

1987198814635128211644871941

1988198912389106581412084330

19891990214031961423192105733

19901991339433207635809139676

19911992425244057544472182200

19921993175161550519526199716

199319948856683310879208572

19941995272382455929917235810

263048

290286

317524

344762

Weibul 1.28 5.33 (LT) F no cov





1986.567767728325930700012711166138207091

1987856856620578662000477845654996016213

19882078207817721730181400010098979110409024454

198922752275227222162328000166011621516991032672

199024522452266725692767000236972323924159040114

199126782678299528873105000254792500025963041953

199235153515326531503383000287252819829258041953

199337043704344933273573000314893090932074041953

199432773277355334263682000337773314634414041953

199535183518352333933656000356343495636318041953

1996NANA324631123384000357083500536418040521

1997NANA276326162915000335933287134322037189








1986.567767728325930700012711166138207091

1987856856620578662000477845654996016213

19882078207817721730181400010098979110409024454

198922752275227222162328000166011621516991032672

199024522452266725692767000236972323924159040114

199126782678299528873105000254792500025963041953

199235153515326531503383000291342859229682045632

199337043704344933273573000328123215233479049310

199432773277355334263682000365023565037363052989

199535183518352333933656000401973908241328056668

1996NANA365535203792000424864105743940058914

1997NANA367835303829000429004110844730059261






198219830000

1983198400480

198419851432122316411432

198519863332310135634764

198619874654443148779418

1987198846844458491114102

1988198942213986445618323

1989199040543814429422377

1990199141523909439526529

1991199241973951444330726

1992199338913632415134617

1993199436573345396838274

1994199536793262409641953

45632

49311

52990

56669

Weibul 1.28 5.33 (LT) T no cov





1986.533723372179416981893000807576418520045459

198745084508396337814148000290592831329816094090

198810507105071062410441108080006017759219611430148235

198911972119721294512783131090001032821021271044420216502

199014156141561539615127156670001517191503801530630263117

199116644166441853818261188170001637681623771651650274943

199223883238832182921535221260001856951841701872260274943

199325343253432370923390240310002043522026722060390274943

199421758217582422023876245660002197962179572216430274943

199524176241762387723519242380002323252303392343200274943

1996NANA2192721564222930002339722319452360060266444

1997NANA1865718252190660002199412178042220880244202








1986.533723372179416981893000807576418520045459

198745084508396337814148000290592831329816094090

198810507105071062410441108080006017759219611430148235

198911972119721294512783131090001032821021271044420216502

199014156141561539615127156670001517191503801530630263117

199116644166441853818261188170001637681623771651650274943

199223883238832182921535221260001883241867261899280298596

199325343253432370923390240310002128592107352149940322248

199421758217582422023876245660002373152342362404130345901

199524176241762387723519242380002616662572512661170369554

1996NANA2455624193249220002775522715552836140384708

1997NANA2453524130249440002797822719272877490386119






198219830000

198319840000

198419858499734496548499

1985198622242210842340030741

1986198729436283953047760177

1987198823604225382467083781

19881989206191955421685104400

19891990264442535827531130844

19901991347813366535897165625

19911992372243608238365202849

19921993273062615128461230155

19931994211361988422387251291

19941995236532186625439274944

298597

322250

345903

369556

DUs inc M - with-without cov

1010

1010

6002633462427582

14296155351598921507

20136211832207328217

20982203832046714635

22021206222054812389

24430243262409721403

26485282662746733943

26945285592866442524

24805241922424117516

2367221484214848856

24036217522254527238

Gamma 1.51 0.30 - with cov

Gamma 1.51 0.30 - without cov

Weibull 1.28 5.33 - with cov

Weibull 1.28 5.33 - without cov

Year

DUs Incidence

Incidence of DUs - Male

DUs inc M - with cov

11

11

60026242

1429615989

2013622073

2098220467

2202120548

2443024097

2648527467

2694528664

2480524241

2367221484

2403622545

Gamma 1.51 0.30 - with cov - (LT)

Weibull 1.28 5.33 - with cov - (LT)

Year

DUs Incidence

Incidence of DUs - Male - With "Age at first treatment" covariate

DUs inc M - without cov

00

00

63347582

1553521507

2118328217

2038314635

2062212389

2432621403

2826633943

2855942524

2419217516

214848856

2175227238

Gamma 1.51 0.30 - without cov - (LT)

Weibull 1.28 5.33 - without cov - (LT)

Year

DUs Incidence

Incidence of DUs - Male - Without "Age at first treatment" covariate

tr DUs inc M - with-without cov

11451225130916882695

27032880291537753652

77178016816792538429

103681046810558104569697

1293912928130031221811704

1543715572155761534513966

1769618059180401953420368

1939319751197032086421639

2054220621205982013418481

2100820686208062025820658

220292137421684218321996

225152154121992228121997

228842164022199236801998

231642169922337244191999

233332168822385249822000

234032160722349253532001





Observed incidence

Year

DUs under treatment Incidence

Incidence of DUs under treatment - Male

tr DUs inc M - with cov

114513092695

270329153652

771781678429

10368105589697

129391300311704

154371557613966

176961804020368

193931970321639

205422059818481

210082080620658

22029216841996

22515219921997

22884221991998

23164223371999

23333223852000

23403223492001



Observed incidence

Year


Incidence of DUs under treatment - Male - With "Age at first treatment" covariate

tr DUs inc M - without cov

122516882695

288037753652

801692538429

10468104569697

129281221811704

155721534513966

180591953420368

197512086421639

206212013418481

206862025820658

21374218321996

21541228121997

21640236801998

21699244191999

21688249822000

21607253532001



Observed incidence

Year


Incidence of DUs under treatment - Male

DUs inc F - with-without cov

1010

1010

1674164415481432

3998394537823332

5226518251424654

4456449346654684

3667359039224221

3697369637634054

4201432140414152

4534459143314197

3915390639353891

3639350136763657

3929365538913679





Year

DUs Incidence

Incidence of DUs - Female

DUs inc F - with cov

11

11

16741548

39983782

52265142

44564665

36673922

36973763

42014041

45344331

39153935

36393676

39293891



Year

DUs Incidence

Incidence of DUs - Female - With "Age at first treatment" covariate

DUs inc F - without cov

00

00

16441432

39453332

51824654

44934684

35904221

36964054

43214152

45914197

39063891

35013657

36553679



Year

DUs Incidence

Incidence of DUs - Female - Without "Age at first treatment" covariate

tr DUs inc F - with-without

317312314283677

730721689620856

19551942191017722078

23872369236622722275

26982679270526672452

29862981299729952678

32723280326932653515

34633475345534493704

35593557356035533277

35313495354335233518

37043626371336551996

37563641376336781997

37973650379936901998

38283655382636951999

38403646383536882000

38333622382736682001





Observed incidence

Year

DUs Incidence in treatment

Incidence of DUs under treatment - Female

tr DUs inc F - with cov

317314677

730689856

195519102078

238723662275

269827052452

298629972678

327232693515

346334553704

355935603277

353135433518

370437131996

375637631997

379737991998

382838261999

384038352000

383338272001



Observed incidence

Year


Incidence of DUs under treatment - Female - With "Age at first treatment" covariate

tr DUs inc F - without cov

312283677

721620856

194217722078

236922722275

267926672452

298129952678

328032653515

347534493704

355735533277

349535233518

362636551996

364136781997

365036901998

365536951999

364636882000

362236682001



Observed incidence

Year


Incidence of DUs under treatment - Female

DUs inc T - with-without cov

1010

1010

8243994898718499

20100266672571322242

26820330893319929436

24330177521986723604

24105144881621920619

28090255772602426444

32112408213685734781

33132472764432637224

27865179452426827306

25443135031494221136

26833337052836023653





Year

DUs Incidence

Incidence of DUs - Male & Female

DUs inc T - with cov

11

11

82439871

2010025713

2682033199

2433019867

2410516219

2809026024

3211236857

3313244326

2786524268

2544314942

2683328360



Year

DUs Incidence

Incidence of DUs - Male & Female - With "Age at first treatment" covariate

DUs inc T - without cov

00

00

99488499

2666722242

3308929436

1775223604

1448820619

2557726444

4082134781

4727637224

1794527306

1350321136

3370523653



Year

DUs Incidence

Incidence of DUs - Male & Female - Without "Age at first treatment" covariate

tr DUs inc T - with-without

15842010206917943372

36934676453139634508

1008411418113481062410507

1291312827129941294511972

1566414703151691539614156

1854918265184621853816644

2130522870225852182923883

2316224376243232370925343

2415223688240352422021758

2430923715238812387724176

253552581125257245561996

257362723725879245351997

260172850626405244561998

262252957826836243511999

263223038927120241852000

263093092727247239502001





Observed incidence

tr DUs inc T - with cov

158420693372

369345314508

100841134810507

129131299411972

156641516914156

185491846216644

213052258523883

231622432325343

241522403521758

243092388124176

25355252571996

25736258791997

26017264051998

26225268361999

26322271202000

26309272472001



Observed incidence

Year


Incidence of DUs under treatment - Male & Female - With "Age at first treatment" covariate

tr DUs inc T - without cov

201017943372

467639634508

114181062410507

128271294511972

147031539614156

182651853816644

228702182923883

243762370925343

236882422021758

237152387724176

25811245561996

27237245351997

28506244561998

29578243511999

30389241852000

30927239502001



Observed incidence

Year


Incidence of DUs under treatment - Male & Female

CUM inc M - with-without cov

30365324603326743198

72426737457504578136

121109122515123149122705

173699177302177667190958

221791221758222545222191

233809232634233817235810

257846254386256362263048

281882276138278907290286

305918297890301452317524

329954319641323997344762

347988335060340301364418

357728341276346856370149





Year

DUs Cumulative Incidence

Cumulative Incidence of DUs - Male

CUM inc M - with cov

3036533267

7242675045

121109123149

173699177667

221791222545

233809233817

257846256362

281882278907

305918301452

329954323997

347988340301

357728346856



Year


Cumulative Incidence of DUs - Male - With "Age at first treatment" covariate

CUM inc M - without cov

3246043198

7374578136

122515122705

177302190958

221758222191

232634235810

254386263048

276138290286

297890317524

319641344762

335060364418

341276370149



Year


Cumulative Incidence of DUs - Male - Without "Age at first treatment" covariate

CUM inc F - with-without cov

8285818079027091

17188170591709816213

24819247102484224454

33411334143316132672

40972406954075040114

42936425224269541953

46865461774658645632

50794498325047749310

54723534875436852989

58652571425825956668

60907591536060258914

60837588636071059261





Year


Cumulative Incidence of DUs - Female

CUM inc F - with cov

82857902

1718817098

2481924842

3341133161

4097240750

4293642695

4686546586

5079450477

5472354368

5865258259

6090760602

6083760710



Year


Cumulative Incidence of DUs - Female - With "Age at first treatment" covariate

CUM inc F - without cov

81807091

1705916213

2471024454

3341432672

4069540114

4252241953

4617745632

4983249310

5348752989

5714256668

5915358914

5886359261



Year


Cumulative Incidence of DUs - Female - Without "Age at first treatment" covariate

CUM inc T - with-without cov

41753531595218445459

91545947009676094090

147743147931149322148235

210863224590224210216502

263655263918265466263117

277072280770279646274943

303904314476308006298596

330737348181336366322248

357570381886364726345901

384403415592393086369554

402992439349411576384708

409725446388414222386119





Year


Cumulative Incidence of DUs - Male & Female

CUM inc T - with cov

4175352184

9154596760

147743149322

210863224210

263655265466

277072279646

303904308006

330737336366

357570364726

384403393086

402992411576

409725414222



Year



CUM inc T - without cov

5315945459

9470094090

147931148235

224590216502

263918263117

280770274943

314476298596

348181322248

381886345901

415592369554

439349384708

446388386119



Year


Cumulative Incidence of DUs - Male & Female - Without "Age at first treatment" covariate

CUM inc M - with-without c (2)

1010

2020

6004633462447582

20300218692223329089

40436430524430657306

61418634356477371941

83439840578532184330

107869108383109418105733

134354136649136885139676

161299165208165549182200

186104189400189790199716

209776210884211274208572

233812232636233819235810

257848254388256364263048

281884276140278909290286

305920297892301454317524

329956319644323999344762





Year


Cumulative Incidence of DUs - Male

CUM inc M - with cov (2)

11

22

60046244

2030022233

4043644306

6141864773

8343985321

107869109418

134354136885

161299165549

186104189790

209776211274

233812233819

257848256364

281884278909

305920301454

329956323999



Year


Cumulative Incidence of DUs - Male - With "Age at first treatment" covariate

CUM inc M - without cov (2)

00

00

63347582

2186929089

4305257306

6343571941

8405784330

108383105733

136649139676

165208182200

189400199716

210884208572

232636235810

254388263048

276140290286

297892317524

319644344762



Year


Cumulative Incidence of DUs - Male - Without "Age at first treatment" covariate

CUM inc F - with-without co (2)

1010

2020

1676164415501432

5674558953324764

1090010771104749418

15356152641513914102

19023188541906118323

22720225502282422377

26921268712686526529

31455314623119630726

35370353683513134617

39009388693880738274

42938425244269841953

46867461794658945632

50796498345048049311

54725534895437152990

58654571445826256669





Year


Cumulative Incidence of DUs - Female

CUM inc F - with cov (2)

11

22

16761550

56745332

1090010474

1535615139

1902319061

2272022824

2692126865

3145531196

3537035131

3900938807

4293842698

4686746589

5079650480

5472554371

5865458262



Year


Cumulative Incidence of DUs - Female - With "Age at first treatment" covariate

CUM inc F - without cov (2)

00

00

16441432

55894764

107719418

1526414102

1885418323

2255022377

2687126529

3146230726

3536834617

3886938274

4252441953

4617945632

4983449311

5348952990

5714456669



Year


Cumulative Incidence of DUs - Female - Without "Age at first treatment" covariate

CUM inc T - with-without co (2)

1010

2020

8245994898738499

28345366153558630741

55165697046878560177

79495874568865283781

103600101944104871104400

131690127521130895130844

163802168342167752165625

196934215618212078202849

224799233563236346230155

250242247066251288251291

277075280771279648274944

303908314476308008298597

330741348181336368322250

357574381886364728345903

384407415591393088369556





Year


Cumulative Incidence of DUs - Male & Female

CUM inc T - with cov (2)

11

22

82459873

2834535586

5516568785

7949588652

103600104871

131690130895

163802167752

196934212078

224799236346

250242251288

277075279648

303908308008

330741336368

357574364728

384407393088



Year



CUM inc T - without cov (2)

00

00

99488499

3661530741

6970460177

8745683781

101944104400

127521130844

168342165625

215618202849

233563230155

247066251291

280771274944

314476298597

348181322250

381886345903

415591369556



Year


Cumulative Incidence of DUs - Male & Female - Without "Age at first treatment" covariate

Back-calculated incidence of first heroin use, Italy, BC method (EMCDDA /Univ. Rome pilot project; Rav et al submitted)

Gamma 1.51 0.30 (LT) M cov





1986.526952695114510931200000515549175398030365

198736523652270326072800000205622009221037072426

1988842984297717762078140004644345770471200121109

1989969796971036810249104880008166280801825280173699

199011704117041293912730131500001226791216331237300221791

199113966139661543715204156720001333361322351344420233809

199220368203681769617440179540001529081516791541420233809

199321639216391939319115196720001695361681701709080233809

199418481184812054220246208400001832201817241847230233809

199520658206582100820698213200001942681926561958870233809

1996NANA1957119246198990001972051955251988910227808

1997NANA1662816268169920001901461884071918940213512








1986.526952695114510931200000515549175398030365

198736523652270326072800000205622009221037072426

1988842984297717762078140004644345770471200121109

1989969796971036810249104880008166280801825280173699

199011704117041293912730131500001226791216331237300221791

199113966139661543715204156720001333361322351344420233809

199220368203681769617440179540001553651541001566360257846

199321639216391939319115196720001778811763111794570281882

199418481184812054220246208400002007641987032028370305918

199520658206582100820698213200002239282211912266820329954

1996NANA2202921704223570002414372378942450070347988

1997NANA2251522155228780002509672464912554840357728






198219831111

198319841112

198419856002547365316004

1985198614296137381485420300

1986198720136196092066240436

1987198820982204372152761418

1988198922021214622258183439

19891990244302385825002107869

19901991264852590127068134354

19911992269452634927541161299

19921993248052417425435186104

19931994236722292524420209776

19941995240362301625056233812

19951996257848

19961997281884

19971998305920

19981999329956

Gamma 1.51 0.30 (LT) F cov





1986.567767731728335200014241274158308285

1987856856730668795000527850035561017188

198820782078195518922020000106761031311046024819

198922752275238723222453000171871674817631033411

199024522452269825892810000243062379924818040972

199126782678298628713103000261132558626645042936

199235153515327231523394000294152883729998042936

199337043704346333383591000322083157132852042936

199432773277355934293692000345013380435205042936

199535183518353133973668000363493559837108042936

1996NANA330231653442000361833541536959041262

1997NANA279426422950000334243262734232037264








1986.567767731728335200014241274158308285

1987856856730668795000527850035561017188

198820782078195518922020000106761031311046024819

198922752275238723222453000171871674817631033411

199024522452269825892810000243062379924818040972

199126782678298628713103000261132558626645042936

199235153515327231523394000298162921630423046865

199337043704346333383591000335723279434360050794

199432773277355934293692000373693627038485054723

199535183518353133973668000411973964742777058652

1996NANA370435663843000434134132945547060907

1997NANA375636033912000433664066446155060837






198219831111

198319841112

198419851674128520631676

198519863998360843895674

1986198752264866558610900

1987198844564089482215356

1988198936673300403419023

1989199036973326406922720

1990199142013824457726921

1991199245344153491531455

1992199339153527430235370

1993199436393208407139009

1994199539293311454642938

46867

50796

54725

58654

Gamma 1.51 0.30 (LT) T cov





1986.533723372158415061663000712767797484041753

198745084508369335493840000271682653527808091545

19881050710507100849939102300005857557728594270147743

19891197211972129131276613062000100882998391019320210863

199014156141561566415414159170001491371479051503750263655

199116644166441854918282188190001614881602001627810277072

199223883238832130521016215950001840991826711855310277072

199325343253432316222850234750002032622016772048540277072

199421758217582415223820244870002190092172682207570277072

199524176241762430923964246580002317092298282335980277072

1996NANA2261122254229710002337632318222357130268829

1997NANA1916418765195670002220482200202240840248729








1986.533723372158415061663000712767797484041753

198745084508369335493840000271682653527808091545

19881050710507100849939102300005857557728594270147743

19891197211972129131276613062000100882998391019320210863

199014156141561566415414159170001491371479051503750263655

199116644166441854918282188190001614881602001627810277072

199223883238832130521016215950001868421853601883300303904

199325343253432316222850234750002125782106582145060330737

199421758217582415223820244870002385952359062412980357570

199524176241762430923964246580002648202610592686080384403

1996NANA2535524997257150002831432781062882240402992

1997NANA2573625336261380002899452834252965390409725






198219831111

198319841112

198419858243735091358245

1985198620100192052099528345

1986198726820259952764555165

1987198824330234862517379495

19881989241052325624955103600

19891990280902722228957131690

19901991321123122732997163802

19911992331323223234032196934

19921993278652694028790224799

19931994254432439626490250242

19941995268332534728319277075

303908

330741

357574

384407

Gamma 1.51 0.30 (LT) M no cov





1986.526952695122511651288000551552415795032460

198736523652288027662997000214712094722001073745

1988842984298016790181320004741746696481430122515

1989969796971046810341105970008327482368841850177302

199011704117041292812707131500001244291233441255190221758

199113966139661557215333158130001349041337661360470232634

199220368203681805917799183210001540541527871553260232634

199321639216391975119468200370001702671688561716840232634

199418481184812062120317209270001835821820301851400232634

199520658206582068620369210060001943161926381960020232634

1996NANA1915018821194810001966701949251984230226300

1997NANA1621315847165830001881891863731900140210765








1986.526952695122511651288000551552415795032460

198736523652288027662997000214712094722001073745

1988842984298016790181320004741746696481430122515

1989969796971046810341105970008327482368841850177302

199011704117041292812707131500001244291233441255190221758

199113966139661557215333158130001349041337661360470232634

199220368203681805917799183210001562781549681575930254386

199321639216391975119468200370001778191761531794920276138

199418481184812062120317209270001994591971932017370297890

199520658206582068620369210060002211582180632242740319641

1996NANA2137421045217050002366992326172408160335060

1997NANA2154121174219100002432302380082485090341276






198219830000

198319840000

198419856334568769806334

1985198615535148581621221869

1986198721183205552181143052

1987198820383197282103863435

1988198920622199472129684057

19891990243262363625016108383

19901991282662755928972136649

19911992285592784229276165208

19921993241922345224932189400

19931994214842060922358210884

19941995217522053022974232636

254388

276140

297892

319644

Gamma 1.51 0.30 (LT) F no cov





1986.567767731228134400014041265155008180

1987856856721663782000522749655496017059

198820782078194218832002000105921024110948024710

198922752275236923052434000171161669017546033414

199024522452267925712790000242222372824722040695

199126782678298128673097000260072549226526042522

199235153515328031613401000292592869429829042522

199337043704347533503602000320053138132635042522

199432773277355734263689000342563357434946042522

199535183518349533613632000360693533336812042522

1996NANA325231163392000359043514736668040878

1997NANA274625952902000331743239033968036933








1986.567767731228134400014041265155008180

1987856856721663782000522749655496017059

198820782078194218832002000105921024110948024710

198922752275236923052434000171161669017546033414

199024522452267925712790000242222372824722040695

199126782678298128673097000260072549226526042522

199235153515328031613401000296332904830224046177

199337043704347533503602000332743252534032049832

199432773277355734263689000369243588437980053487

199535183518349533613632000405793913142054057142

1996NANA362634893765000426304069844606059153

1997NANA364134903796000424233993244988058863






198219830000

198319840000

198419851644130719811644

198519863945359542965589

1986198751824859550510771

1987198844934158482815264

1988198935903249393018854

1989199036963351404122550

1990199143213970467226871

1991199245914236494631462

1992199339063546426535368

1993199435013090391138869

1994199536553069424142524

46179

49834

53489

57144

Gamma 1.51 0.30 (LT) T no cov





1986.533723372201018182212000904681839953053159

198745084508467643455018000315093022732818094700

198810507105071141811084117570006152059976630840147931

198911972119721282712614130410001060601043031078320224590

199014156141561470314387150240001540801521531560200263918

199116644166441826517958185740001662591642731682570280770

199223883238832287022552231900001886231864811907780280770

199325343253432437624033247230002076052052722099510280770

199421758217582368823313240650002232102206812257540280770

199524176241762371523331241020002357982330862385260280770

1996NANA2236421983227490002360992335052387060270823

1997NANA1898118564194040002178862151082206810244156








1986.533723372201018182212000904681839953053159

198745084508467643455018000315093022732818094700

198810507105071141811084117570006152059976630840147931

198911972119721282712614130410001060601043031078320224590

199014156141561470314387150240001540801521531560200263918

199116644166441826517958185740001662591642731682570280770

199223883238832287022552231900001920701897631943900314476

199325343253432437624033247230002193062158962227430348181

199421758217582368823313240650002478122422772534090381886

199524176241762371523331241020002773902688922860200415592

1996NANA2581125429261950002981252862153102770439349

1997NANA2723726818276580003031742872423195360446388






198219830000

198319840000

1984198599487141127559948

1985198626667241742915936615

1986198733089307423543769704

1987198817752157751973087456

19881989144881255716418101944

19891990255772359327560127521

19901991408213876642876168342

19911992472764514749405215618

19921993179451575520134233563

19931994135031129815707247066

19941995337053067036741280771

314476

348181

381886

415591

Weibul 1.28 5.33 (LT) M cov





1986.526952695130912381382000589055706218033267

198736523652291527833050000221512157522735075045

1988842984298167803483010004824747473490280123149

1989969796971055810425106900008403783079850000177667

199011704117041300312776132310001251961240631263350222545

199113966139661557615333158210001356851344991368750233817

199220368203681804017776183050001548631535521561790233817

199321639216391970319418199900001712521698021727090233817

199418481184812059820293209060001848621832731864580233817

199520658206582080620488211270001959301942151976530233817

1996NANA1917818848195110001986481968782004270227576

1997NANA1638916021167610001898841880341917430211587








1986.526952695130912381382000589055706218033267

198736523652291527833050000221512157522735075045

1988842984298167803483010004824747473490280123149

1989969796971055810425106900008403783079850000177667

199011704117041300312776132310001251961240631263350222545

199113966139661557615333158210001356851344991368750233817

199220368203681804017776183050001573691560051587390256362

199321639216391970319418199900001793611776051811250278907

199418481184812059820293209060002015601991232040120301452

199520658206582080620488211270002238972205092273110323997

1996NANA2168421354220170002401872356682447490340301

1997NANA2199221623223640002469232410802528360346856






198219831111

198319841112

198419856242543370506244

1985198615989151671681122233

1986198722073213222282444306

1987198820467197042123164773

1988198920548197762131985321

19891990240972330924884109418

19901991274672666228273136885

19911992286642784429485165549

19921993242412339725085189790

19931994214842053422435211274

19941995225452121923871233819

256364

278909

301454

323999

Weibul 1.28 5.33 (LT) F cov





1986.567767731428334600014121274155807902

1987856856689633748000517849205443017098

198820782078191018521968000105821023310937024842

198922752275236623032429000170891666417520033161

199024522452270525982814000242102371524709040750

199126782678299728843112000260092549426529042695

199235153515326931503390000292902872629859042695

199337043704345533313582000320853146632711042695

199432773277356034313692000344023372835083042695

199535183518354334103678000362833555837015042695

1996NANA328131453420000362633551937015041147

1997NANA279626452951000337213295134500037364





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Estimating incidence of heroin use from treatment data presentation for TDI expert meeting

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Transcript of Estimating incidence of heroin use from treatment data presentation for TDI expert meeting