A COMPARISON OF TWO ARRESTEE DRUG USE ESTIMATION METHODS Y. Michael Yang and Dean R. Gerstein

Transcription

1 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods A COMPARISON OF TWO ARRESTEE DRUG USE ESTIMATION METHODS Y. Mcael Yag ad Dea R. Gerste NORC at te Uversty of Ccago, 350 Coectcut Ave., N.W., Wasgto, DC KEY WORDS: Post-Samplg Stratfcato, Wegtg Adjustmet, Mea Square Error, Desg Effect, Survey Cost Sposored by te Natoal Isttute of Justce (NIJ), te Arrestee Drug Abuse Motorg program (ADAM) collects substace abuse ad oter data from arrestees 35 stes, geerally urba coutes, across te Uted States. Ts paper compares to arrestee drug use estmato metods terms of statstcal effcecy, cost effcecy, ad relevat admstratve measures. Te aalyss s based o ADAM data collected from Jauary 2000 troug September 200, t addtoal admstratve data o cost ad tmeless of data delvery troug md Secto oe reves ADAM sample desgs. Secto to descrbes te old estmato metod based o post-samplg stratfcato. Secto tree presets emprcal evdece o te defceces of te old estmato metod. Secto four proposes a e estmato metod based o a to-stage egtg sceme. Secto fve compares te statstcal effcecy, cost effcecy, ad tmeless of te to estmato metods. Fally, secto sx provdes some remarks about possble future mprovemets ADAM metodology.. ADAM Sample Desgs ADAM s desged to motor drug use treds ad provde data useful to local autortes for developg drug-cotrol polces. NIJ tally dd ot seek to make atoal estmates based o ADAM data, so t dd ot requre a probablty sample of partcpatg stes, c ere selected stead troug a oradom process. Wt eac ste, oever, sample selecto of male arrestees s carred out based o probablty prcples. Depedg o te populato structure of te ste, ADAM features a rage of sample desgs. A Sgle Jal Desg s used e a ste as oly oe arrestee bookg faclty (jal). We a ste as to to four facltes, ADAM uses a Stratfed Desg t proportoal sample ADAM collects data from adult male, adult female ad juvele arrestees. Female ad juvele data collectos are based o coveet samples, so ts aalyss oly apples to adult male estmato. Adult male arrestees comprse about 80% of all arrestees ADAM stes. allocato across jals. We tere are more ta four jals, ADAM adopts a To-Stage Stratfed Cluster Desg ere jals are sampled te frst stage ad arrestees are sampled from sampled jals te secod stage. Fally, te Feeder Jal Desg s used stes t a large cetral bookg faclty ad may small satellte facltes t varable trasportato from te satellte facltes to te cetral faclty. Wt eac sample faclty, ADAM follos a systematc samplg protocol to select arrestees. Samplg ad data collecto typcally take place over a 4-day perod usually to sequetal eeks per quarter. For ay gve day, te target populato cossts of all elgble arrestees o are booked durg te 24-our caledar day. ADAM terveers typcally ork a 8-our sft startg from 4:00PM to mdgt. Durg ay day, tere s a cotuous flo of arrestees to te jal. At ay pot tme durg tat day, tere s a accumulated stock of arrestees o ave bee booked ad are atg for processg by a judge or oter autorty. ADAM stratfes te daly populato of arrestees to stock arrestees ad flo arrestees ad selects a systematc sample of arrestees from eac stratum (Rodes, et al, 2002). Terefore, t eac stratum (stock or flo) o a gve day, samplg probabltes oly deped o te sample sze ad te total umber of elgble arrestees booked. 2. Te Old Estmato Metod ADAM curretly uses post-samplg stratfcato to adjust for potetal bas due to uequal selecto probabltes, orespose, ad ocoverage 2. Bascally, te metod s to defe post-samplg strata suc tat arrestees t te same stratum ave te same probabltes of beg selected ad terveed by ADAM. Te follog factors are used to defe te poststrata: () sze of te jal, (2) stock or flo, (3) offese carge severty, ad (4) daly case flo. Te last varable measures te umber of bookgs o a daly bass,.e., te daly populato sze. Table summarzes te post-samplg stratfcato sceme uder te old estmato metod. Eac large jal s 2 Exstg ADAM documetato oly dscusses adjustg for uequal selecto probabltes troug post-samplg stratfcato egtg (Hut ad Rodes, 200). Te egtg sceme actually adjusts for selecto probabltes, orespose ad ocoverage oe step. 4656

2 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods stratfed separately, ereas small jals are combed before arrestees are stratfed by oter varables. Strata Table : ADAM Post-Samplg Stratfcato Wegtg Strata Faclty Sze Stock Flo Carge Severty Daly Case Flo Hg 2 Feloy Medum 3 Lo 4 Hg 5 Stock Msd. Medum 6 Lo Large 7 Hg 8 Oter Medum 9 Lo 0 Hg Flo NA Medum 2 Lo 3 Feloy 4 Stock Msd. Small NA 5 Oter 6 Flo NA Te egt for a respodet stratum s computed as, N, [] r ere N s te total umber of elgble arrestees stratum, ad r s te umber of respodets stratum 3. Te, te estmator for te populato meay s: $ Y N N r y r [2] Ad te estmator for te samplg varace of $ Y s: VY $ ( $ ) N N 2 r ( y y$ ) r r 2 [3] ere N s te total umber of arrestees per ste; N s te total umber of arrestees stratum ; r s te umber of respodets stratum ; 3 ADAM computes four egts. Our presetato ere assumes tat te total egt for terve data aalyss s of terest. Geeralzato to te oter tree egts s stragtforard. y s te observed value of Y for arrestee stratum ; ad $y s te sample mea of Y stratum. 3. A Evaluato of te Old Metod For post-samplg stratfcato estmato to be effectve, te follog assumptos ave to be true. (a) Selecto probabltes or respose rates dffer across strata; (b) Te dstrbuto of survey varables s omogeeous t strata ad eterogeeous across strata. For subsequet presetato, e defe te samplg probablty subgroup g as p g g [4] N g ere g ad N g are te sample sze ad populato sze of subgroup g, respectvely. We furter defe te respose rate of subgroup g as r g rg [5] g ere rg s te sze of te respodg sample. Wt tese deftos, e preset some results belo. Table 2: ADAM Samplg Probabltes ad Respose Rates by Stratfcato Varables Factor Subgroup ( g ) Samplg Probablty ( ) p g Respose Rate ( ) r g Faclty Sze Large Small Stock vs. Stock Flo Flo NA Carge Feloy Severty Msd Daly Case Flo Oter NA Hg Medum Lo Overall Tese are flo cases tat are ot subdvded by Carge Severty. 5 Tese are cases from small facltes tat are ot subdvded by Daly Case Flo. 4657

3 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods Table 2 sos te ma effects of te poststratfcato varables o samplg probabltes ad respose rates ere eac subgroup s defed by a sgle varable. Frst, te relatve magtudes of samplg probabltes for te subgroups are cosstet t expectatos. Arrestees from small facltes ave bee sampled at a muc ger rate ta tose from large facltes. Arrestees booked durg te flo perod ave slgtly ger probabltes of beg sampled ta tose booked earler durg te day. Tose carged t a feloy are more lkely to be sampled ta tose carged t a msdemeaor, o tur are more lkely to be te sample ta te resdual group. Te umber of arrestees booked s versely correlated t te samplg probablty. Secod, altoug all varables ave a mpact o p g, te oly drastc dfferece samplg probabltes s betee small ad large facltes. Trd, respose rate does ot seem to be affected by faclty sze ad daly case flo, but t s clearly related to stock/flo ad carge severty. I partcular, flo cases ad feloy cases ave a ger respose rate ta ter couterparts. Table 3 belo presets smlar formato but eac subgroup s a stratum uder post-samplg stratfcato. Aga, arrestees from small facltes ave far ger selecto probabltes. I addto, feloy cases, flo cases ad cases booked o lo flo days are more lkely to be selected to te sample. Te stratum t te gest samplg probablty s Small-Flo at.45, folloed by Small-Stock-Feloy at.37. Wt regard to respose rates, aga, feloy ad flo cases are more lkely to respod to te survey. Strata ( g ) Table 3: ADAM Samplg Probabltes ad Respose Rates by Wegtg Strata Faclty Sze Stock vs. Flo Carge Severty Daly Case Flo Prob. ( ) p g Resp. Rate ( ) r g Hg Feloy Medum Lo Hg Stock Msd. Medum Lo Large 7 Hg Oter Medum Lo Hg Flo NA Medum Lo Feloy Stock Msd Small NA 5 Oter Flo NA Overall Te fact tat samplg ad respose probabltes vary across strata does ot esure te effectveess of poststratfcato adjustmet. Aoter crucal codto s tat tere s sgfcat varace across strata t respect to te survey varables,.e., Y vares across strata. Assumg tat data are mssg completely at radom t strata, e use te uegted estmates per stratum $y u to approxmatey. $y u r y r, [6] Fgure presets te uegted estmates per strata for 9 ADAM drug test varables. Te most remarkable feature so Fgure s te lack of varace te uegted estmates across strata. Secodly, estmates te frst tree strata ted to be greater ta te rest of te strata for most varables. It appears tat arrestees large facltes ad arrestees t more serous carges ted to abuse drugs more frequetly ta ter couterparts. Percet Postve Fgure : Uegted Ure Estmates by Strata Strata MJ COC OP PCP VAL AEMIT METH ANYDRUG MULTIDRUG Furter aalyss dcates tat ts patter s largely drve by Carge Severty c s te oly egtg varable tat s correlated t te survey varables. Clearly, f Y does ot so apprecable varato across strata, adjustg to W ll ot ave a sgfcat mpact o $ Y. To assess te effectveess of post-samplg stratfcato estmato terms of reducg mea square error (MSE), e follo Ks s advce to compare te egted ad uegted estmates ad ter relatve MSEs (Ks, 992). A total of 42 ADAM varables are volved te comparsos. We frst defe te egted, uegted ad bas estmates as follos. 4658

4 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods $y $y u y, [7] y, [8] B$ y$ y$, [9] u ere represets te total respodg sample. We assume tat te egted estmates are ubased relatve to te uegted estmates. Tus, $B represets a estmate of te bas of te uegted estmates 6. Fgure 2 compares te egted ad uegted estmates of 0 drug test varables over all stes ad quarters ere ADAM data are avalable at te tme of ts evaluato. It sos tat te dffereces betee egted ad uegted estmates are extremely small. Percet Postve Fgure 2: Wegted ad Uegted Ure Estmates MJ COC OP PCP VAL METH AEMIT METH ANYDRUG MULTIDRUG Dr ug U egted Wegted Smlar aalyss o oter varables ad at te ste level reveals te same patter. Across all stes ad all quarters, tere are 200 depedet data fles. For te 5 most mportat statstcs derved from drug test data, e computed te follog statstcs from eac fle: uegted estmate $y u, egted estmate $y, estmated bas B $, stadard error of te uegted estmate $ σ yu $, stadard error of te egted estmate $ σ y $, bas rato of te uegted estmate BS, mea square error of te uegted estmate 6 As oted earler, $y s ot strctly ubased f W s ot accurate. MSE yu $, mea square error of te egted estmate MSE y $, ad te rato of te to mea square errors MSE MSE y $ y $. I addto, e computed te u desg effects troduced by uequal egtg. Due to space lmtato, e oly provde te follog summares ere. Frst, te egted ad uegted estmates are remarkably close per ste per quarter, gvg lttle evdece of sgfcat bas te uegted estmates eve at te ste level. Secod, te poststratfcato estmator teds to ave greater MSE ta te uegted estmator. Of te reported MSE ratos, to trds of tem are greater ta. Obvously, bas s geerally small relatve to stadard error t small samples at te ste level. Fally, te average desg effect due to uequal egtg s about.4 for bot questoare egts ad ure egts. For detals about ste level aalyss, please see Yag ad Gerste, I cocluso, te old estmato metod as ot bee effectve terms of reducg bas or varace. Altoug some stratfcato varables fluece selecto ad respose probabltes, te populato sos lttle varace across post-strata t respect to te survey varables. As Cocra (977) pots out, te ga precso from a stratfed sample over a radom sample ll be small uless te survey varables vary greatly across strata. Te same geeral prcple apples to poststratfcato. Te curret estmato metod s ot oly statstcally effcet, t also causes delays data dssemato because te collecto ad processg of populato data ( N []) are expesve ad tme cosumg. Besdes, te populato data collected, typcally retrospectvely, are ofte accurate due to defceces of te record keepg systems at te stes. I te ext secto, e descrbe a alteratve estmato metodology tat as superor statstcal effcecy, cost effcecy, tmeless, ad accuracy. 4. Te Ne Estmato Metod Te post-samplg stratfcato egt uder te old metod may be decomposed to to compoets: te base egt ad te orespose egt. Tat s, equato [] may be rtte as, N N r r, [0] Notce tat te frst term o te rgt ad sde s te verse of selecto probablty ad te secod term s te verse of respose rate of post stratum. Sample sze cacels out because te egtg classes for 4659

5 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods base egt ad orespose egt are detcal. Hoever, our evaluato reveals tat samplg probablty ad orespose probablty are affected by dfferet factors. Te former s prmarly determed by te sze of te faclty, t addtoal t-faclty varato by date ad betee stock ad flo. Te latter s maly affected by stock/flo ad carge severty. To closely represet tese to processes, e adjust for selecto probabltes ad orespose separately. 4. Stage Oe: Base Wegt If e stratfy te sample by day ad stock/flo t eac day, e ca reasoably assume tat selecto probabltes are te same t strata. We use te follog otato. samplg stratum defed by data collecto date ad stock/flo. Te total umber of strata s determed by te umber of jals per ste ad te legt of data collecto perod eac jal. N umber of arrestees stratum sample sze of stratum Te, te base egt for a sample arrestee of stratum s: N [] Notce tat te N [] s defed by date ad stock/flo oly t eac faclty. Carge severty, c cotrbutes te most to cost ad does ot affect selecto probablty, drops out from te defto of populato data. 4.2 Stage To: Norespose Adjustmet Wegt Carge severty, togeter t stock/flo, does affect orespose. We make te follog assumptos regardg te mecasm of orespose, te populato dstrbuto of survey varables, ad te patter of mssg data. a) Te probablty of orespose s affected by stock/flo ad carge severty (feloy ad oter); b) Te meas of survey varables are omogeeous t adjustmet classes; c) Data are mssg at radom t adjustmet classes. Let s defe te follog otato: c orespose adjustmet class defed by stock/flo ad severty (feloy ad oter) c sample sze of class c rc umber of respodets class c Te, te orespose adjustmet egt for respodet class c s: c c [2] rc Te fal egt of samplg stratum ad orespose adjustmet class c s * c* R [3] ere R s for respodets ad 0 for orespodets. Sce carge severty s oly volved orespose adjustmet, te requred data are already avalable from te ADAM samples. Ts cage as sgfcat cost mplcatos for ADAM. Notce tat expresso [3] oly addresses t-jal samplg ad respose probabltes. Uder multstage desgs ere jals clusters or PSUs are sampled te frst stage, sould be multpled by te frst stage samplg egt approprate for te desg Estmator of Y ad V( Y $ ) To preset geeral estmators tat are applcable to all ADAM desgs, e troduce te follog otato. 2,,..., H s te stratum umber 2,,..., s te cluster jal or PSU umber t stratum j 2,,..., m s te case umber t cluster of stratum f s te frst stage samplg rate for stratum j s te egt for observato j cluster of stratum y j s te observed value of varable y for observato j cluster of stratum 7 We cose ot to formally troduce te frst stage samplg egt to te e egtg sceme due to te lack of populato data about jals tat are ot cluded te ste sample. 4660

6 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods Te H strata sould ot be cofused t te tjal samplg or post-samplg strata defed earler. Tese H strata are te frst stage samplg strata uder stratfed to-stage cluster desgs. For a multstage sample desg, te varace estmato metod depeds oly o te frst stage of te sample desg. So, te requred put cludes oly frst-stage cluster ad frst-stage stratum detfcato. For a desg tout stratfcato, e ll set H ; for a desg tout clusters, e ll let m for all combatos of ad. Te survey egt j corporates selecto probabltes of all samplg stages as ell as adjustmets for orespose. Here, e assume tat j s te product of te cluster egt ad as computed expresso [3]. Te estmator of te populato mea s $ Y H m j H m j y j Te estmator of te varace of $ Y s j j ( f) ( ) H $ ( $ VY ) ( e e ) ere e. e.. m j H j ( yj Y $ ) m e j. j 2... [7] [4] [6) [5] SAS PROC SURVEYMEANS may be used to carry out tese estmatos (SAS IsttuteIc., 999). For varace estmato, ts metod obtas a lear approxmato for te estmator ad te uses te varace estmate for ts approxmato to estmate te varace of te estmate tself (Woodruff, 97). 5. Comparsos of te To Estmato Metods 5. Statstcal Propertes We coducted parallel tests t a sample of 0 ADAM stes to compare te propertes of te postsamplg stratfcato estmator (OLD) ad te alteratve estmator (NEW). We compared te pot estmates, stadard errors, ad overall desg effects t respect to seve drug test varables. Te old ad e estmates are remarkably close; most of te dffereces are t to percetage pots, ad tey rarely exceed fve percetage pots. Te stadard errors estmates are also very close, but te dffereces ere are more systematc, as te e stadard errors ted to be smaller ta te old oes. Fgure 3 compares te pot estmates ad stadard errors betee te to estmato metods for te Acorage ADAM ste. Te oter e testg stes (ot preseted) so te same patter. Percet Postve Fgure 3: Pot ad SE Estmates uder te To Estmators ANYDRUG COC MJ DRUG OP METH PCP Old Est. Ne Est. Old s.e. Ne s.e. MULTIDRUG Te comparso of overall desg effects depcts a smlar pcture, t te e estmator avg smaller desg effects ta te old estmator. We te defe to MSE ratos to compare te estmated total samplg errors uder te to estmators. Te frst MSE rato s te MSE of te old estmator dvded by te MSE of te uegted estmator, ad te secod MSE rato s te MSE of te e estmator dvded by te MSE of te uegted estmator. 8 Te old estmator as greater MSEs ta te uegted estmator for te vast majorty of ADAM statstcs, but 8 Te MSE of te egted estmators are smply ter respectve varaces, sce e assume tat te egted estmators are ubased. Tere are to ubased estmators ad tey are very close. Te sze of te bas of te uegted estmator depeds o c ubased estmator t s evaluated agast. 466

7 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods te e estmator ted to ave smaller MSEs ta te uegted estmator. Ts provdes strog evdece tat te e estmato metod s superor terms of bas reducto. Overall, te parallel tests so tat te e estmato metod produces smlar pot estmates but smaller stadard errors, MSEs, ad desg effects. 5.2 Cost Effcecy Te e estmator s also more cost effcet because t does ot requre detaled populato data as postsamplg stratfcato does. To estmate base egts all e eed s te total umber of elgble bookgs by stock ad flo per day, ad te formato eeded for estmatg te orepose adjustmet egt s already cluded te sample. Te cost of populato data collecto ad processg as to compoets: ste costs ad cetral costs. Approxmately, te former s te data collecto costs ad te latter data processg costs. ADAM stes take eter of to approaces to provdg populato data: () submttg electroc fles produced by te arrestg ageces, or (2) submttg prted outputs or potocopes of bookg logs, dvdual case seets, or smlar records. Altoug te dfferece ste costs betee te to approaces ould slgtly favor te e metod, ts comprses a relatvely small ad eglgble sum compared t te cetral costs. ADAM cetral data processg costs dffer dramatcally for te to estmato metods. Table 4 compares te estmated aualzed costs related to populato data processg for 35 ADAM stes, based o FY2003 loaded ourly rates for eac labor category, actual ours per ste durg te last alf of 2002 to process te curret populato data, ad actual ours per ste durg early 2003 to process te populato data from te test stes. Table 4. Comparso of Cetral Costs of Old Versus Ne Cesus Metods Labor OLD NEW Category Hours Costs($) Hours Costs($) Programmg,280 43, Supervso ,337 2,96 Clercal ,282 0 Data Edt/Etry 3,660 07, ,050 Statstcal , ,239 Total 6,78 385, ,205 Dfferece -6,04-325,207 Oce te e estmato metod s fully mplemeted, te estmated cost savgs ll total approxmately $325,000 per year; tese savgs derve large part from reductos data etry ad programmg costs. Data etry ad assocated support ad supervso are eglgble uder te e metod, ad statstcal costs are someat less. Te large commtmet of programmer tme to fully process bot forms of te curret populato data dsappear uder te e metod, t tasks suc as trasformg te electroc fles to te stadard format, rug ad cleag te results of te programs tat recode arrest carges from te may put formats to ADAM carge codes ad ceck for matcg betee populato ad questoares, obtag e populato fles e tose provded prove to be flaed, ad so fort, are o loger ecessary. 5.3 Tmeless Oe of te major objectves of ADAM s to motor treds substace abuse ad elp form local agecy operatos ad polces. Terefore, tmely data processg ad dssemato are mportat goals. Uder te curret desg, t as take a average of 49 caledar days for eac ste to delver ts populato data to cetral processg after completo of quarterly data collecto 2002, t apprecable varato by ste, from a mmum of day to early 5 mots. Ts average fell to about 40 days by te secod quarter of 2003, ad t does ot seem possble to reduce ts terval ay furter. Moreover, t as take a average of 76 caledar days durg 2002 from recept of te tal populato data to te pot tat bot te populato ad questoare data are fully processed, cleaed, ad ready to merge. Ts s te pot at c e tate te statstcal estmato process, c tself s geerally qute rapd (oe to four days, depedg o load factors), produce egted data ad post reports. Ts umber fell to approxmately 50 days by te secod quarter of 2003, ad ts average also seems mpossble to reduce furter, ve of stubbor outlers ad te cotug stream of cages local persoel ad procedures, t assocated e problems to be solved, amog te 35 ADAM stes. Overall, te, completg te collecto ad processg of te old populato data requred a average of slgtly more ta 4 mots from te ed of te feld perod troug te ed of te estmato process. Based o egt quarters of experece, e ave bee able to reduce ts by o more ta aoter mot. Based o te parallel testg, e ca delver data apprecably faster uder te e metod. Uder ts estmato metod, populato data are to be collected o a daly bass durg quarterly data collecto. Terefore, te stes sould be able to delver te e 4662

8 2003 Jot Statstcal Meetgs - Secto o Survey Researc Metods populato data to cetral processg at te same tme as tey delver te questoare data, c o averages rougly 0 caledar days after completo of data collecto. Wt te muc reduced processg requremets (ad reduced eed for resubmsso) of te e populato data, e estmate tat t ll requre a average of o more ta 28 days to completely process te populato, questoare, ad uralyss data from eac ste ad beg to egt te data. We terefore estmate tat te average tme to produce fal egted data usg te e cesus ll be o more ta 6 eeks, c s alf of te mmum average tme tat ca be aceved uder te old metodology. 6. Cocludg Remarks Wt te accumulato of ADAM data, e ave gaed mportat sgt to te structure of te arrestee populato at eac ste ad te propertes of te post-samplg stratfcato estmator. Te e estmato metod represets te frst frut of tegratg ts formato to a more effcet desg tat eaces te overall qualty of ADAM data at reduced costs. Te e metod ll be mplemeted te fourt quarter of A major lmtato of te curret ADAM metodology s assocated t te populato data ad ts role estmato. ADAM produces ste level estmates o a quarterly bass, but te so called populato data are ot true populato data because () tey are lmted oly to tose arrestees o are booked to sampled facltes, ad (2) tey are lmted to te to-eek data collecto perod. Tus, te old estmato metod does ot accout for te frst stage samplg of jals uder stratfed cluster desg, or does t accout for te etre quarterly populato of arrestees t a ste. Ts as at least tree mplcatos: () te curret ADAM egts are ot approprate for estmatg populato totals beyod te sample facltes ad te data collecto perod, (2) strog assumptos about betee faclty varaces are eeded to derve ubased populato estmates of meas ad proportos cluster stes, ad (3) te reported varaces of populato meas or proportos for cluster stes are uderestmated. Addressg ts lmtato requres expadg populato data collecto to all jals t a ste trougout te quarter, c s probtvely expesve, especally for tose stes t very large umbers of jals. Oe less expesve alteratve ould be to collect populato data from all jals at oe pot tme so te frst stage samplg egts may be estmated. We ave coducted lmted but promsg researc to explore te possblty of usg Uform Crme Report (UCR) data to model ad predct ADAM populato data per faclty. Oter aspects of te ADAM desg tat may be mproved clude te sample allocato amog stes, samplg of female arrestees, orespose ad ocoverage adjustmets, ad so o. I some ADAM stes, a probablty sample of jals s ot feasble gve budgetary ad operatoal costrats. Ivestgatos o te betee-jal varace structure t respect to mportat ADAM varables ll be of great value. REFERENCES Cocra, W. G. (977). Samplg Tecques. Trd Edto. Ne York: Jo Wley. Hut, D. ad Rodes, W. (200). Metodology Gude for ADAM. Wasgto, D.C.: Natoal Isttute of Justce. Ks, L. (965). Survey Samplg. Ne York: Jo Wley. Ks, L. (992). Wegtg for Uequal P. Joural of Offcal Statstcs, Vol. 8. No. 2, Rodes, W. et al. (2002). Arrestee Drug Abuse Motorg System: Samplg Desg ad Aalyss, Upublsed paper. SAS Isttute, Ic. (999). SAS/STAT User's Gude, Verso 8, Volumes 2, Cary, NC: SAS Isttute, Ic. Yag, M. ad Gerste, D. (2003). Respose to Reves of A Alteratve To-Stage ADAM Wegtg Sceme, Report submtted to te Natoal Isttute of Justce. Yag, M. ad Gerste, D. (2002). A Alteratve To-Stage ADAM Wegtg Sceme, Report submtted to te Natoal Isttute of Justce. Woodruff, R.S. (97). A Smple Metod for Approxmatg te Varace of a Complcated Estmate, Joural of te Amerca Statstcal Assocato, 66,