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Formal experiments: randomisation + study size

Formal experiments: randomisation + study size. Concept of randomisation. Biology, 1926: Sir Ronald Fisher Medicine, 1947: Sir Austin Bradford Hill R andomised C ontrolled T rial Criminal justice ?. Randomisation in medicine.

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Formal experiments: randomisation + study size

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  1. Formal experiments: randomisation + study size

  2. Concept of randomisation • Biology, 1926: Sir Ronald Fisher • Medicine, 1947: Sir Austin Bradford Hill Randomised Controlled Trial • Criminal justice ?

  3. Randomisation inmedicine • Toss of coin determines experimental or control treatment RCT assignment unpredictable • Fair [=> ethical] allocation of scarce resource • Balance treatment numbers overall, in each hospital, and for major prognostic factors

  4. RCTTelephone Randomisation

  5. Licensing of pharmaceuticals: requires efficacy in RCTs • Patients’ informed consent [ethics] • Sufficiently-large [precise answer] • Randomised [unbiassed: like with like]

  6. “What works” in UK criminal justice? Large RCTs essentially untried . . . (bar restorative justice)

  7. Judges prescribe sentence on lesser evidence than doctors prescribe medicines Is public aware?

  8. Drug Treatment &Testing Orders (DTTOs) • England & Wales: 210 clients • Scotland: 96 clients • Targets for DTTO clients in E&W: 6,000+ per annum • DTTO clients: 21,000+ by end 2003

  9. RSS Court DTTO-eligible offenders:do DTTOs work ? • Off 1DTTO • Off 2 DTTO • Off 3 alternative = • Off 4 DTTO • Off 5 alternative = • Off 6alternative = Count offenders’ deaths, re-incarcerations etc . . .

  10. UK courts’ DTTO-eligible offenders: ? guess • Off 7 DTTO [ ? ] • Off 8 DTTO [ ? ] • Off 9 DTTO [ ? ] • Off10 DTTO [ ? ] • Off11 DTTO [ ? ] • Off12 DTTO [ ? ] • Off13 DTTO [ ? ] • Off14 DTTO [ ? ] (before/after) Interviews versus . . . [ ? ]

  11. Evaluations-charade • Failure to randomise • Failure to find out about major harms • Failure evento elicit alternative sentence  funded guesswork on relative cost-effectiveness • Volunteer-bias in follow-up interviews • Inadequate study size re major outcomes . . .

  12. Power (study size) matters! Back-of-envelope sum for 80% power e. g. Percentages If MPs/social scientists don’t know, UK plc keeps hurting

  13. For 80% POWER, 5% significance: compare failure (re-conviction) rates Randomise pertreatment group, 8times STEP 1 answer STEP 1: Success * fail rate + Success * fail rate for new disposal for control ------------------------------------------------------------ (new success rate – control success rate)2

  14. DTTOs:target 60% versus control 70% re-conviction rate? Randomise per ‘CJ disposal’ group, 8times STEP 1 answer = 8times45 = 360 STEP 1 answer: 40 * 60 + 30 * 70 2400 + 2100 DTTOs control --------------------------------- = --------------- (40 – 30)2100

  15. Four PQs for every CJ initiative • PQ1: Minister, why no randomised controls? • PQ2:Minister, whyhave judgesnot evenbeen asked to document offender’salternative sentencethat this CJ initiative supplants? {cf electronic tagging} • PQ3:What statistical powerdoes Ministerial pilot have rewell-reasonedtargets? {or, just kite flying . . .} • PQ4:Minister, cost-effectivenessis driven bylonger-term health & CJ harms, how are these ascertained?{ database linkage}

  16. Randomised controlled trials to police Policy by Home Office Prisons & Criminal Justice

  17. HMP Peterborough PILOT: Kalyx prison, Social Finance run, & payment by results.

  18. HMP Peterborough PILOT: Kalyx prison, Social Finance run, & payment by results. Per SF-release, comparators are? 10 same-sex ‘matched’ prisoners who also served less than 12 months & were released on same day but from other prisons {All Kalyx-run? Where? Functionality? Locality? De-selections & transfers?} Reduce convictions in 1st year post-release by 7.5% . . . Conviction costed how . . . ??? {eg 60% to 55.5% convicted within 1 year of release ~ or reduce conviction-count by 7.5%}

  19. Guardian Society: 17 Nov. 2004 “Some statisticians are so severe that they would stop social policy making in its tracks. For example, Birdwould forbid the government to introduce any policy that had not been assessed through controlled trials. . . ”

  20. SIMPLE RANDOMISATION STEP 1:Correspondence between random number (see tables) & CJ disposal: EVEN random number (0)  DTTO ODD random number  alternative STEP 2: Document starting point in tables & direction of reading: SMB = down 03(row) 07 (column)

  21. RANDOM NUMBER tables 72137 73850 32733 48083 50731 50584 • 26772 81250 row 3, column 7: 55480 29910 89693 read down 77708 83761 47184 • 54432 65664 73669

  22. SIMPLE RANDOMISATION: down

  23. Randomisation by minimisation: next client = Cambridge, male,18-24 years, >5 prison terms ClientRCT assignments characteristicso far to DTTO alternative Cambridge20 15* male 205 190 * 18-24 years100 * 108 >5 in-prison180 * 185 SUM points:505 498 ** RANDOMISE this client preferentially (eg 80:20) to** because lower on points

  24. Critical reading: BMJ, Lancet etc Statistical guide-lines for contributors to medical journals (20+ years): beware “bars” Structured ABSTRACT: essential design & primary outcome (s) CONSORT flowchart for reporting RCTs: beware i) post-randomization exclusions from analysis; ii) post-hoc subgroups. STROBE guide-lines for reporting observational studies: beware bias in many guises (especially: how explanatory variable is coded at analysis - eg binary!! & retrospective classification: deaths on transplant waiting list ~ count survival contribution on the waiting list of transplantees beofre operation)

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