Summary. * EAA Central Facility, The University of Manchester, Faculty of Life Sciences, Manchester, UK; ** Health

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1 Screeg Computer-Asssted Dosage Programs for atcoagulato wth warfar ad other vtam K-atagosts: mmum safety requremets for dvdual programs O behalf of the Subcommttee o Cotrol of Atcoagulato of the Scetfc ad Stadardsato Commttee of the Iteratoal Socety o Thromboss ad Haemostass L Poller *, C Roberts **, S Ibrahm *, Keow M *, W Ageo+, AMHP va de Besselaar ++, D Ftzmaurce, J Hareberg, S Ktche^, G Lowe^^, M Moa &, G Palaret &&, A Trpod #, AGG Turpe##, J Jesperse ~ Summary Based o the results of the prevous Europea Acto o Atcoagulato (EAA) mult-cetre study, a smplfed mmum procedure s descrbed for screeg safety ad effectveess of marketed programs for dosage of oral atcoagulat drugs (vtam K atagosts). The am s to demostrate o-ferorty to the maual dosage at the expereced cetres the Europea Acto o Atcoagulato (EAA) study. Usg a cluster samplg procedure a mmum umber of cetres ad mmum total of patets requred to establsh o-ferorty was determed. At least four cetres each recrutg 50 patets over a perod of sx moths s show to be requred (excludg the results from the frst 3 weeks treatmet). To acheve o-ferorty the lower 95% cofdece terval of the tme target INR (Iteratoal Normalsed Rato) rage (TIR) of a marketed program must be above the TIR lmt set by the maual dosage group the EAA study.e. 57.5%. The smplfed procedure proposed although ot a absolute gude to safety s desged to scree agast gross urelablty of a test program, wthout the eed to repeat a massve clcal ed-pot study for each ad every program. Correspodece:Professor Leo Poller, EAA Cetral Faclty, Faculty of Lfe Sceces, Uversty of Machester, Oxford Road, Machester M13 9PT, UK, Tel: , Fax: , E-mal: leo.poller@machester.ac.uk * EAA Cetral Faclty, The Uversty of Machester, Faculty of Lfe Sceces, Machester, UK; ** Health Methodology Research Group, Commuty Based Medce, The Uversty of Machester, Machester, UK; +Ospedale d Crcolo d Varese, Dvso of Iteral Medce, Varese, Italy; ++ Departmet of Thromboss ad Haemostass, Lede Uversty Medcal Ceter, Lede, The Netherlads; Prmary Care, The Uversty of Brmgham, Brmgham, UK; Clcal Phamacology Mahem, Ruprecht-Karls-Uverstat Hedelberg, Mahem, Germay; ^Departmet of Coagulato, Royal Hallamshre Hosptal, Sheffeld, UK; ^^Departmet of Medce, Royal Ifrmary, Glasgow, UK; & Uversty ad IRCCS Maggore Hosptal, Magagall ad Rega Elea Foudato, Mla, Italy; && Departmet of Agology ad Blood Coagulato Maro Golell, Uversty Hosptal S Orsola-Malpgh, Bologa, Italy; # Agelo Bach Boom, Hemophla ad Thromboss Ceter, Uversty ad IRCCS Maggore Hosptal, Mla, Italy; ## McMaster Clc, Hamlto Geeral Hosptal, Hamlto, Caada; ~Departmet of Clcal Bochemstry, Hosptal of South West Demark, Departmet for Thromboss Research, Isttute of Publch Health ad Uversty of Souther Demark, Esbjerg, Demark.

2 Itroducto Greatly creased use of oral atcoagulat drugs (vtam K atagosts) worldwde has resulted from proof of ther value a wdeg rage of clcal dsorders cludg atral fbrllato (AF). May patets wth AF ad other thrombotc dsorders have bee uable to receve ths treatmet or have oly bee treated for a restrcted perod due to ther large umbers ad lmted resources for atcoagulat admstrato. Hosptals ad clcs have as a result bee oblged to tur creasgly to computer-assstace to facltate dosage by urses, pharmacsts ad laboratory techologsts assstg medcal staff usg a rage of commercal ad o-commerca l computer-asssted dosage programs. However, the safety ad effectveess of such computer assstace requres clcal valdato for each ad every program. Utl recetly the promoto of computer-assstace dosage has bee based o clams of success achevg the laboratory ed-pot of tme target INR (Iteratoal Normalsed Rato) rage (TIR) but wthout evdece of clcal safety or of effectveess preveto of clcal evets of thromboss or bleedg 1. The uproved assumpto was that adequate TIR cotrol wth computer-dosage would be reflected clcal safety ad effectveess. Thrty two cetres the Europea Acto o Atcoagulato (EAA) cluded the study gave a overall total recrutmet maual ad computer dosage groups of 18,617 patet-years 13,219 patets 2. TIR success wth the two dfferet programs cluded the study was tme-depedet, creasg wth durato of treatmet ad mprovg TIR up to 22 weeks. The safety of the two studed computer programs wth three dfferet drugs (warfar, coumaloe, ad pheprocoumo) was also cofrmed by the fact that the overall clcal ga dd ot reach the statstcal sgfcace. I the 3209 patets wth establshed DVT ad/or PE, the reducto of clcal evets was statstcally sgfcat (p=0 001). Ths demostrated the safety of two dfferet wdely used commercal programs, DAWN AC (UK) ad PARMA 5 (Italy). The oly covcg way to demostrate safety ad effectveess of other computer-asssted dosage programs would be to perform smlar radomsed clcal ed-pot studes of suffcet sze ad durato to provde a statstcally sgfcat result wth each ad every program. To requre smlar large-scale clcal vestgatos for every avalable program would be mpractcal. A smplfed mmum procedure for screeg safety ad effectveess of other marketed programs based o the EAA study results s therefore descrbed employg a much smaller represetatve clcal sample. The am s to demostrate o-ferorty to the maual dosage results at the expereced cetres the prevous EAA study. 2

3 Method Computer-dosage programs vary cosderably desg ad cotet but typcally calculate whether dose adjustmet s ecessary from a user-defed table of tred rules for each therapeutc rage ad each oral atcoagulat drug. If dose adjustmet s recommeded, the curret INR s compared wth the target INR, ad the dfferece s used a propretary equato for each program ad drug to calculate the ext dose. I the varous computer programs the tme-terval to the ext INR test s also set by the computer usg a set of varables comparg the curret INR, the terval from the last test, the umber of prevous chages, ad the umber of prevous INR values wth the target rage. The am of the preset report s to esure mmum stadards of safety ad effectveess of test programs (o-ferorty) compared wth laboratory edpot TIR establshed the large maual dosage group at the expereced cetres the EAA study 2. To acheve ths, a suffcet sample sze of patets for a mmum study perod of 6 moths each patet has bee determed. I the EAA study the percetage TIR progressvely creased to the levels of stable patets at the 6 moths stage. The mportat cosderato the proposed screeg evaluato s the mea TIR compared wth the EAA maual dosage results. The cdece of falure to dose (see below) ad the mmum durato of treatmet requred by the computer to provde a relable atcoagulat dose for a dvdual patet s recorded but would ot be crtcal crtera. Falure to dose The ablty of computer-asssted dosage programs to provde a atcoagulat dose s largely depedet o the prevous hstory of dose respose a gve patet. Some computer dosage programs have fxed INR lmts beyod whch they wll ot provde a dosage. The success of a test program dosage durg the frst 3-week ducto perod vares cosderably betwee programs. Ths was show to be the case wth both DAWN ad PARMA, the two programs the EAA study, wth greater dfferece betwee them the rate of falure to dose durg the frst 3 weeks, especally ew patets startg treatmet. The rate was comparable however after 3 weeks. Results durg the frst 3 weeks are therefore to be excluded the proposed screeg assessmet. Safety evaluato Ideally evaluato of the safety of a caddate program should be based o the cdece of clcal evets of bleedg ad/or thromboss. Ths s ot feasble route practce owg to the large umber of patets requred for adequate statstcal evaluato of such clcal ed-pots ad because of the possble creased dager of clcal evets to patets should the program prove usatsfactory. Istead t s proposed for ths screeg procedure that the TIR be used to assess the safety of dosage cotrol wth a test program compared to the results of the two clcally valdated programs the EAA study 2. The TIR s the proporto of tme the INR s wth the target INR rage set for the patet 3

4 expressed as a percetage e.g. target rage of INR The falure to dose rate s also to be recorded as a supplemetary gude. I the EAA study, the two computer programs were foud to acheve a small but sgfcat mprovemet TIR compared to expereced maual dosage at cetres wth a specal terest oral atcoagulato. The EAA maual dosage group appeared to provde a far ad reasoable comparso basele for all programs ad has bee used as the referece bechmark. A caddate software program should acheve oferorty relatve to the EAA maual dosage ad ths report explas the procedure. Method of aalyss for Evaluato of Safety To establsh safety ad effectveess for a ew computer-dosage program, t would be approprate to use a covetoal statstcal testg procedure as falure to reject the ull hypothess does ot establsh equalty. Nor s t adequate to compare a mea agast the proposed stadard T (T = target) as ths takes o accout of samplg varato. The recommeded statstcal method by whch o-ferorty relatve to a target value T s establshed s to cosder a value T-D where D s a clcally umportat reducto the stadard. No-ferorty would be based o comparso to results wth maual dosage the EAA study provded the lower 95% cofdece terval of the mea TIR s above the specfed lmt. Ths s the geeral approach take o-ferorty clcal trals where the am s to demostrate that a ew treatmet s as good as a exstg treatmet 3. The study should cotue for a maxmum 26 weeks each patet. Patets selected for the study are to have a target INR of , the most commoly used therapeutc terval used oral atcoagulato ad the EAA study. I the early stages of therapy, partcularly ew patets, the computer program may requre dose adjustmet ad INR results va maual terveto before t ca beg to provde a dose. Therefore the frst 3 weeks of therapy are to be excluded. Selecto crtera Over 40% of all adverse clcal evets the EAA study occurred the frst 6 moths of therapy whch s therefore the crtcal perod for the proposed screeg. I the EAA study, mea TIR progressvely creased over the frst 6 moths durg whch perod ew patets were at greater rsk of clcal evets (thromboss ad/or haemorrhage). INR of ew patets therefore eeds to be wth the target rage as quckly as possble. The safety of a computer program should therefore be assessed by ts ablty to provde a relable dose as soo as possble ad esure mateace wth the recommeded target INR rage. For these reasos the group of patets from the EAA results selected for comparso the screeg procedure; (1) were ot prevously o oral atcoagulato; (2) had target INR wth the 2.0 to 3.0 rage; (3) were o treatmet for at least 24 weeks; (4) had INR results excluded from the frst 3 weeks of treatmet. 4

5 A breakdow of the basele characterstcs of the patets selected as the referece group s show Table 1. Statstcal Aalyss Betwee-cetre varablty eeds to be cosdered whe calculatg stadard errors ad cofdece tervals ad the statstcal measure of ths s kow as the Itra-cluster correlato coeffcet (ICC) deoted as the symbol ρ (rho). The ICC s descrbed as the proporto of varato the data that ca be explaed by the varato betwee cetres. Mathematcally t s wrtte as ICC( ) varb /(varb varw ) where var b = varace betwee-cetres ad var w = varace wth-cetres 4. The ICC s to be used as part of a correcto factor for the sample sze calculato whch s commoly termed the varace flato factor or the desg effect sample survey research 3. The desg effect s calculated as the followg: desg effect 1 ( 1) where ρ s the ICC estmated from the data the EAA study ad s the umber of patets requred each cetre. The desg effect ca be used as part of a adjustmet factor to determe a adjusted varace : s 2 (1 ( 1) ) /(1 ) where s 2 s the total uadjusted varace. Thus, a adjusted stadard error ca be determed for calculato of a acceptable 95% cofdece terval lmt. A lear mxed model was ftted to the referece maual group of EAA study data wth TIR as the depedet varable ad o covarates. Itally, the clcal dagoss group was added as a covarate to the model but ths was ot sgfcat ad excluded from the model. The aalyss was carred out usg the STATA software package. The ICC was estmated from the mxed model ad thus a desg effect was estmated for a varety of combatos of patet umbers ad cetres, wth sample sze of patets ragg from 50 to 200 ad umber of cetres ragg from Adjusted stadard devatos ad lower 95% CI s of TIR were calculated for each combato of patet umbers ad cetres ad examed to see whether TIR was above the acceptable lmt. Addtoally, examples were show usg a suffcet sample sze of patets from the computer group the EAA study to llustrate how a caddate program would be tested for acceptablty. The eed for multcetre screeg Eve though cetres the EAA study were expereced atcoagulato there was betwee-cetre varablty ther INR cotrol. It s mportat therefore that valdato of ew computer programs cludes patets from several dfferet cetres to cotrol the effects of betwee-cetre varablty. A suffcet umber of 5

6 patets should be cluded such a screeg evaluato. Optmally ths would be at 10 cetres for adequate modellg of betwee- ad wth-cetre varato. Istead as a compromse the formato from the EAA study regardg the betwee-cetre varablty, termed the desg effect sample survey research was used 5. Ths provded the ecessary correcto factor. The magtude of the desg effect depeded o the umber of patets each cetre. Results Based o a lear mxed model the mea TIR for the sample cluded the EAA study was 62.7% (sd = 22.4%), the betwee-cetre varato was 5.6% ad the wth cetre varato was 21.7%. Thus, the ICC (ρ) was 6.25%. For smplcty the 62.7% mea TIR was take to be 62.5%. The sample sze requred to demostrate o-ferorty depeds o the choce of D wth D beg a clcally umportat reducto. A D value of 5% was arbtrarly suggested ad so the lmt of TIR o-ferorty was therefore set as 57.5% (5% below the mea TIR). I the EAA study as stated earler, there was also evdece of betwee-cetre varato. After exclusos, 3,089 patets remaed for aalyss the EAA maual dosage group ad form the bass of the preset recommedatos. The varace of the 3089 patets used to determe a sample sze was estmated usg the adjustmet va the desg effect. Ths was a adjustmet to take to accout the betwee-cetre varato the 3089 patets used to determe the sample sze. The desg effect vares depedg o the umber of patets sampled from each cetre. Table 2 llustrates how the desg effect chages whe we sample successvely patets from 4, 5 ad 6 cetres to obta the requred total sample sze to demostrate acceptable TIR. Ths calculato assumes that the sample has a equal umber of patets each cetre. If a ew caddate program were tested by 4 cetres, a mmum of 200 patets (50 per cetre) would be requred to acheve satsfactory results. I ths way f 5 cetres were used, a mmum of 150 patets would suffce ad wth 6 cetres, oly 100 patets. A total of less tha 4 cetres s ot recommeded because of the varablty of maual ad computer-asssted dosage betwee cetres ad the very large umber of patets overall whch would be requred. The valdato procedure The mea % target TIR the EAA study maual dosage group was 62.7% (sd = 22.4%). Assumg a clcally umportat reducto of 5% below the mea target % TIR, the umber of patets requred to obta satsfactory results would be 200 (100 patet-years) f patets are chose from 4 cetres. The valdato should: (1) be multcetre, wth a mmum of 4 cetres recrutg 50 patets per cetre; (2) be sx moths durato for each patet; (3) exclude the frst 3 weeks of therapy; 6

7 (4) show that the lower 95% CI of the TIR of a caddate program s above the TIR lmt of 57.5% set by the EAA study maual group to acheve satsfactory valdato (see examples below). Example 1 As a example of how a computer-dosage program may be valdated, a sample of 200 patets was radomly chose from 4 cetres from the EAA study (Table 3). These were all ew patets wth a target INR rage of I the lear mxed model, the ICC was 6.2%. The mea TIR wth SD was calculated ad the lower 95% Cofdece Iterval was examed to determe whether the sample of patets was above the acceptable TIR lmt of 57.5%. The resultg mea TIR was 63.8% ad the lower 95% CI = 57.7% whch was satsfactory beg above the mmum TIR acceptable lmt. Example 2 Aother example wth uequal umber of patets at each cetre Table 4 showed the mea TIR was 64.1% wth the lower 95% CI = 58.6% whch was above the acceptable TIR lmt of 57.7%.e. a satsfactory result. Table 5 gves further examples of valdatos of the two test programs DAWN AC ad PARMA 5 based o results wth 4, 5 ad 6 cetres respectvely. The Table shows all the results of these examples were satsfactory but the umber of patets requred s see to be markedly reduced wth the crease of partcpat cetres from 4 to 6 wth the two computer programs. Supplemetary observato o falure to dose Ths would be a supplemetary but ot a essetal gude to sutablty. The mea overall cdece of falure to dose by the two referece programs the EAA study was 6.1% from 3 weeks up to 6 moths (95% CI : 5.6% - 6.6%). Dscusso Although warfar s the most popular oral atcoagulat drug there are other types of oral vtam K atagosts wth dfferet speeds ad durato of acto. Most avalable marketed computer programs ca prescrbe for ay of these but a dfferet dosage schedule s requred for each dvdual drug. Clcal experece wth computer-asssted dosage of oral vtam K atagost drugs has bee descrbed may reports the last 25 years, e.g. Wlso ad James 6, Rya et al 7, Mara et al 8, Whte ad Mugall 9, Vsser 10, Ageo ad Turpe 11, Hatte et al 12, Poller et al 13, Ageo et el 14, Ftzmaurce et al 15, Maott et al 16 ad Yousef et al 17. I two studes Poller et al 13, Maott et 16, the clc doctors were more coservatve ther dosage at hgher target INR ( ) tha the computers. Most of the above publshed reports o computer-asssted dosage have bee from cetres wth a specal terest oral atcoagulato ad therefore assumed greater expertse clcal dosage. 7

8 A smplfed procedure for screeg computer-asssted dosage programs s descrbed the preset report. Ths s related to the comparatve results obtaed the maual dosage group the EAA mult-cetre clcal ed-pot study 2. The umber of patets requred for the valdato of a satsfactory program s see to be reduced cosderably from 200 to 100 whe the umber of partcpat cetres s creased from 4 to 6. For the proposed o-ferorty screeg method, a mmum TIR ad patet-years requred for the frst 6 moths of treatmet has bee defed based o a mea value for 4-6 cetres. Other programs should coform to these crtera for mmum stadards of safety ad effectveess. The smplfed procedure although ot a absolute gude to safety s desged to be a safety procedure agast gross urelablty of a gve program. The am s to avod the eed to repeat a massve mult-cetre vestgato wth every dvdual computer-asssted dosage program. The TIR of 57.5% s recommeded as the mmum target ad should at least be equalled f ot exceeded by the test program. I practce, both of the referece programs used the EAA study acheved better results tha the recommeded mmum value ther large maual dosage groups at the expereced cetres. Patets wth a INR of was selected as the referece because ths s the rage gvg the largest value for the TIR the EAA study ad the majorty of patets were ths target INR rage. However, there s o reaso why caddate computer program caot be compared wth the values establshed wth the referece INR rage. Approval of mauscrpt All authors have see ad approved ths mauscrpt. Coflcts of Iterests Noe of the authors has ay facal terest the computer-asssted dosage programs. Role of fudg source The work was supported by Grat No QLG4-CT from the Europea Commuty Qualty of Lfe Programme ad wth added facal assstace from the Machester Thromboss Research Foudato, a UK regstered charty. The fudg sources had o volvemet the study desg, the collecto, aalyss ad terpretato of data, the wrtg of the report ad the decso to submt the paper for publcato other tha gvg ther formal approval to the project uder the terms of ther EC grats. 8

9 Refereces 1. Rosedaal FR, Caegeter SC, va der Meer FJM, Brët E. A method to determe the optmal testy of oral atcoagulat therapy. Thromb Haemost 1993;69: Poller L, Keow M, Ibrahm S, Lowe G, Moa M, Turpe AG, Roberts C, va de Besselaar AMHP, va der Meer FJM, Trpod A, Palaret G, Shach C, Brya S, Samama M, Burgess-Wlso M, Heagerty A, MacCallum P, Wrght D, Jesperse J. A teratoal multcetre radomsed study of Computer- Asssted Oral Atcoagulat Dosage versus Medcal Staff Dosage. JTH 2008;6: Paggo G, Elboure DR, Altma DG, Pocock SJ, Evas SJW. Reportg of o-ferorty ad equvalece radomzed trals: A exteso of the CONSORT statemet. JAMA. 2006; 295: S Kllp, Z Mahfoud, K Pearce. What Is a Itracluster Correlato Coeffcet? Crucal Cocepts for Prmary Care Researchers. Aals of Iteral Medce. 2004:2: Doer A, Klar N. Desg ad Aalyss of Cluster Radomzato Trals Health Research. Amerca ed, New York, NY: Oxford Uversty Press, Wlso R, James AH. Computer asssted maagemet of warfar treatmet. BMJ 1984;289: Rya PJ, Glbert M, Rose PE. Computer cotrol of atcoagulat dose for therapeutc maagemet. BMJ 1989;299: Mara G, Maott C, Dettor AG. A Computerzed regulato of dosage oral atcoagulat therapy. Rcerca Clca e Laboratoro 1990;20: Whte RH ad Mugall D. Out patet maagemet of warfar therapy comparso of computer-predcted dosage adjustmet to sklled professoal care. Ther Drug Mot 1991;13: Vsser J. Twety-fve years of computer-asssted atcoagulato therapy. Nederlads Tjdschrft voor Geeeskude 1997;141: Ageo W, Johso J, Nowack B, Turpe AGG. A computer geerated ducto system for hosptalzed patets startg o oral atcoagulat therapy. Thromb Haemost 2000;83:

10 12. Hatte BA, Prs MH, Redekop WK. Comparso of three methods to assess qualty cotrol of treatmet wth vtam K atagosts. J Thromb Thrombolyss 1999;82: Poller L, Shach CR, MacCallum PK, Johase AM, Müster AM, Magalhães A, Jesperse J. The Europea Cocerted Acto o Atcoagulato (ECAA). Multcetre radomsed study of computersed atcoagulat dosage. The Lacet 1998;352: Ageo W, Johso J, Nowack B, Turpe AGG. A computer geerated ducto system for hosptalzed patets startg o oral atcoagulat therapy. Thromb Haemost 2000;83: Ftzmaurce DA, Hobbs FD, Murray ET, Bradley CP. Holder R. Evaluato of computerzed decso support for oral atcoagulato maagemet based prmary care. Brtsh Joural of Geeral Practce 1996;46: Maott C, Moa M, Palaret G, Pego V, Ra L, Dettor AG. Effect of computer aded maagemet o the qualty of treatmet atcoagulated patets: a prospectve, radomzed, multceter tral of APROAT. Haematologca 2001;86: Yousef ZR, Tady SC, Tudor V, Jsh F, Tret RJ, Watso DK ad Cowell RPW. Warfar for o-rheumatc atral fbrllato: fve year experece a dstrct geeral hosptal. Heart 2004:90:

11 Number of Patets 3,089 Patet-years 1,478.4 Number of INR tests (frequecy of clc vsts) 30,055 Percetage dose chages 13.1% Number of patets by geder Male 1,636 Female 1,426 Not formed 27 Mea age at etry years (SD) 67.8 (13.5) Number of patets by age group at etry Less tha 50 years years years years 1, years or above 481 Number of patets by clcal dcatos Atral Fbrllato 1,730 Deep ve thromboss/pulmoary embolsm 798 Mechacal heart valve 143 Other dcatos 376 Table 1. Basele characterstcs of the 3,089 patets used to determe TIR lmt 11

12 4 Cetres Total sample sze Number per cetre Desg Effect Lower C.I. 55.9% 56.9% 57.3% 57.5% 5 Cetres Total sample sze Number per cetre Desg Effect Lower C.I. 56.2% 57.3% 57.7% 57.9% 6 Cetres Total sample sze Number per cetre Desg Effect Lower C.I. 56.4% 57.5% 58.0% 58.2% Table 2. Estmato of lower 95% CI of TIR usg dfferet sample szes based o the EAA maual group. 12

13 Cetre Mea for each Cetre x Stadard Devato for Each Cetre s Sample each cetre Adjusted Varace ( ) for each cetre [ICC^ (ρ= )] s (1 ( 1) ) /(1 ) % 19.30% % 23.10% % 24.00% % 16.70% Total Patets 200 Pooled Mea, Uadjusted stadard error (assumg ρ=0 ), Adjusted stadard error, X x 63.80% 1.48% 3.09% ^ Itra-cluster Correlato Coeffcet * result satsfactory 2 s ( 1)} /( Lower 95% C.I. Table 3. Example 1 - calculato of TIR for a valdato study wth 4 cetres. SE uadj { 4) SE v / adj X 1.96SEadj 57.7% * 13

14 Cetre Mea for each Cetre Stadard Devato for Each Cetre Sample each cetre Adjusted Varace ( ) for each cetre [ICC^ (ρ= )] x s s (1 ( 1) )/(1 ) % 19.50% % 16.30% % 19.20% % 23.10% % 19.70% Total Patets 160 Pooled Mea, Uadjusted stadard error (assumg ρ=0 ), Adjusted stadard error, X x 64.10% 1.57% 2.82% ^ Itra-cluster Correlato Coeffcet * result satsfactory SE uadj { 2 s ( 1)} /( Lower 95% C.I. 5) SE v / adj X 1.96SEadj 58.6% * Table 4: Example 2 - TIR results from a further example wth 5 cetres where there could be uequal umber of patets each cetre ad how a acceptable TIR lmt ca stll be determed. 14

15 Program Number of cetres Number of total patets Mea TIR Lower 95% CI* DAWN AC % 60.7% Yes DAWN AC % 62.1% Yes DAWN AC % 57.9% Yes PARMA % 58.9% Yes PARMA % 59.1% Yes PARMA % 58.0% Yes Above satsfactory lmt of 57.5%? * Lower 95% CI calculated usg the adjusted stadard error as show Tables 3 ad 4 Table 5: Further example of satsfactory valdatos of the two test programs DAWN AC ad PARMA 5 at four, fve ad sx cetres respectvely. 15