Professor Kate Ren

BSc (York), MPhil (Cantab), PhD (΢Ȧ)

School of Medicine and Population Health

Professor of Statistical Health Technology Assessment

s.ren@sheffield.ac.uk
+44 114 222 0696

Full contact details

Professor Kate Ren
School of Medicine and Population Health
Regent Court (ScHARR)
30 Regent Street
΢Ȧ
S1 4DA
Profile

I joined SCHARR in 2011 after completing a PhD in Probability and Statistics, specialising in Bayesian methods in clinical trial design at the University of ΢Ȧ. My expertise lies in the development and application of Bayesian methods in Health Technology Assessment. My research interests include evidence synthesis methods (in particular indirect treatment comparisons with single-arm trials), survival extrapolation and structured expert elicitation.

I work as a member of SCHARR-TAG (an external assessment group for NICE technology appraisals). I have extensive experience in critiquing statistical methods used in NICE single technology appraisal submissions. I am also a member of NICE Appraisal Committee C.

I am an NIHR Advanced Fellow, currently working on a project titled “Improving the robustness of health technology funding decisions when evidence is from single-arm trials”.

Research interests
  • Network meta-analysis
  • Indirect treatment comparisons
  • Population-adjusted indirect comparisons
  • Survival extrapolation
  • Structured expert elicitation
  • Bayesian statistics in clinical trials and health economics
Publications

Show: Featured publications All publications

Journal articles

  • Ren S, Squires H, Hock E, Kaltenthaler E, Rawdin A & Alifrangis C (2018) . PharmacoEconomics. RIS download Bibtex download
  • Pennington B, Ren S, Barton S, Bacelar M & Edwards SJ (2018) . PharmacoEconomics. RIS download Bibtex download
  • Ren S, Bermejo I, Simpson E, Wong R, Scott D, Young A & Stevenson M (2018) . PharmacoEconomics, 36, 769-778. RIS download Bibtex download
  • Ren S, Oakley JE & Stevens JW (2018) . Medical Decision Making, 38(4), 531-542. RIS download Bibtex download
  • Ren S, Minton J, Whyte S, Latimer N & Stevenson M (2017) . PharmacoEconomics. RIS download Bibtex download
  • Bojke L, Manca A, Asaria M, Mahon R, Ren S & Palmer S (2017) . PharmacoEconomics. RIS download Bibtex download
  • Jackson C, Stevens J, Ren S, Latimer N, Bojke L, Manca A & Sharples L (2017) . Medical Decision Making, 37(4), 377-390. RIS download Bibtex download
  • Ren S & Oakley JE (2014) . Statistics in Medicine, 33(1), 31-45. RIS download Bibtex download
  • Pandor A, Thokala P, Goodacre S, Poku E, Stevens JW, Ren S, Cantrell A, Perkins GD, Ward M & Penn-Ashman J () . Health Technology Assessment, 19(42), 1-102. RIS download Bibtex download

All publications

Journal articles

  • Harnan S, Hamilton J, Simpson E, Clowes M, Biz AN, Whyte S, Ren S, Cooper K, Ball A, Benton S , Carten R et al (2024) . International Journal of Technology Assessment in Health Care, 40(S1), S56-S57. RIS download Bibtex download
  • Biz AN, Stevenson M, Whyte S, Hamilton J, Ren S, Heathcote L, Simpson E, Cooper K, Clowes M, Ball A , Benton S et al (2024) . International Journal of Technology Assessment in Health Care, 40(S1), S7-S7. RIS download Bibtex download
  • Harnan S, Hamilton J, Simpson E, Clowes M, Biz AN, Whyte S, Ren K, Cooper K, Abulafi M, Ball A , Benton S et al (2024) . Value in Health, 27(12). RIS download Bibtex download
  • Forsyth J, Wong R & Ren K (2024) . Value in Health, 27(12), S620-S620. RIS download Bibtex download
  • Forsyth J, Mitra S, Wong R, Srivastava T & Ren K (2024) . Value in Health, 27(12), S375-S375. RIS download Bibtex download
  • Ren K & Forsyth J (2024) . Value in Health, 27(12), S636-S636. RIS download Bibtex download
  • Grand T, Thokala P, Ren K, Regnier S, Oudin Åström D, Awad SF, Bidani A & Krismer PF (2024) . Value in Health, 27(12), S120-S120. RIS download Bibtex download
  • Combe E, Jones D, Knight H, Laskier V, Ren K, Wright T, Böing EA & Trivedi P (2024) . Value in Health, 27(12), S39-S39. RIS download Bibtex download
  • Wheat H, Ren K & Stevenson MD (2024) . Value in Health, 27(12), S449-S449. RIS download Bibtex download
  • Knowles M, Kroep S & Ren K (2024) . Value in Health, 27(12), S480-S480. RIS download Bibtex download
  • Shah B, Challagulla S, Xu S, Williams R, Ren S, Srivastava T, Gautam R & Yang K (2024) . Clinical Lymphoma Myeloma and Leukemia, 24, S516-S517. RIS download Bibtex download
  • Shah B, Challagulla S, Xu S, Williams R, Ren S, Srivastava T, Gautam R & Yang K (2024) . Clinical Lymphoma Myeloma and Leukemia, 24, S227-S227. RIS download Bibtex download
  • Ren S, Essat M, Pandor A, Goodacre S, Ren S, Clowes M, Bima P, Toyofuku M, McLatchie R & Bossone E (2024) . PLOS ONE, 19(6). RIS download Bibtex download
  • Essat M, Goodacre S, Pandor A, Ren S, Ren S & Clowes M (2024) . Annals of Emergency Medicine. RIS download Bibtex download
  • Srivastava T, Gupta A, Gautam R, Hriday K & Ren S (2024) . Value in Health, 27(6), S403-S404. RIS download Bibtex download
  • Grand TS, Ren S, Hall J, Åström DO, Regnier S & Thokala P (2024) . PharmacoEconomics, 1-13. RIS download Bibtex download
  • Ren S, Ren S, Welton NJ & Strong M (2024) . Research Synthesis Methods. RIS download Bibtex download
  • Dunnewind N, Ainsworth C, Ren S & Kroep S (2023) . Value in Health, 26(12), S557-S557. RIS download Bibtex download
  • Ren S & Ren S (2023) . Value in Health, 26(12), S424-S424. RIS download Bibtex download
  • Metry A, Pandor A, Ren S, Shippam A, Clowes M, Dark P, McMullan R & Stevenson M (2023) . Health Technology Assessment, 27(14). RIS download Bibtex download
  • Zhu D, Ren S, Mills K, Hull J & Dhariwal M (2023) . Ophthalmology and Therapy, 12(2), 1157-1171. RIS download Bibtex download
  • Duro EM, Julious SA & Ren S (2022) . BMC Medical Research Methodology, 22(1). RIS download Bibtex download
  • Mandrik O, Fotheringham J, Ren S, Tice JA, Chapman RH, Stevenson MD, Pearson SD, Herron-Smith S, Agboola F & Thokala P (2022) . Clinical Journal of the American Society of Nephrology, 17(3), 385-394. RIS download Bibtex download
  • Thokala P, Fuller GW, Goodacre S, Keating S, Herbert E, Perkins GD, Rosser A, Gunson I, Miller J, Ward M , Bradburn M et al (2021) . BMC Emergency Medicine, 21. RIS download Bibtex download
  • Thokala P, Stevenson M, Kumar VM, Ren S, Ellis AG & Chapman RH (2020) . Cost Effectiveness and Resource Allocation, 18. RIS download Bibtex download
  • Hart R, Burns D, Ramaekers B, Ren S, Gladwell D, Sullivan W, Davison N, Saunders O, Sly I, Cain T & Lee D (2020) . PharmacoEconomics. RIS download Bibtex download
  • Kearns B, Stevens J, Ren S & Brennan A (2020) . PharmacoEconomics, 38(2), 193-204. RIS download Bibtex download
  • Laskier V, Guy H, Fisher M, Neuman WR, Bucior I, Cohen AT & Ren S (2019) . Journal of Medical Economics. RIS download Bibtex download
  • Simpson EL, Ren S, Hock ES, Stevens JW, Binard A, Pers Y-M, Archer R, Paisley S, Stevenson MD, Herpin C & Ghabri S (2019) . International Journal of Technology Assessment in Health Care. RIS download Bibtex download
  • Ren S, Squires H, Hock E, Kaltenthaler E, Rawdin A & Alifrangis C (2018) . PharmacoEconomics. RIS download Bibtex download
  • Pennington B, Ren S, Barton S, Bacelar M & Edwards SJ (2018) . PharmacoEconomics. RIS download Bibtex download
  • Ren S, Bermejo I, Simpson E, Wong R, Scott D, Young A & Stevenson M (2018) . PharmacoEconomics, 36, 769-778. RIS download Bibtex download
  • Bermejo I, Ren S, Simpson E, Clowes M, Scott DL, Young A & Stevenson M (2018) . Pharmacoeconomics, 36(12), 1427-1437. RIS download Bibtex download
  • Ren S, Oakley JE & Stevens JW (2018) . Medical Decision Making, 38(4), 531-542. RIS download Bibtex download
  • Uttley L, Bermejo I, Ren S, Martyn-St James M, Wong R, Scott DL, Young A & Stevenson M (2018) . PharmacoEconomics, 36(9), 1063-1072. RIS download Bibtex download
  • Ren S, Minton J, Whyte S, Latimer N & Stevenson M (2017) . PharmacoEconomics. RIS download Bibtex download
  • Sadler S, Holmes M, Ren S, Holden S, Jha S & Thokala P (2017) . BJGP Open, 1(3). RIS download Bibtex download
  • Uttley L, Whyte S, Gomersall T, Ren S, Wong R, Chambers D & Tappenden P (2017) . PharmacoEconomics, 35(7), 717-726. RIS download Bibtex download
  • Bojke L, Manca A, Asaria M, Mahon R, Ren S & Palmer S (2017) . PharmacoEconomics. RIS download Bibtex download
  • Jackson C, Stevens J, Ren S, Latimer N, Bojke L, Manca A & Sharples L (2017) . Medical Decision Making, 37(4), 377-390. RIS download Bibtex download
  • Cooper KL, Martyn-StJames M, Kaltenthaler E, Dickinson K, Cantrell A, Ren S, Wylie K, Frodsham L & Hood C (2017) . Sexual Medicine, 5(1), e1-e18. RIS download Bibtex download
  • Martyn-St James M, Cooper K, Ren S, Kaltenthaler E, Dickinson K, Cantrell A, Wylie K, Frodsham L & Hood C (2017) . European Urology Focus, 3(1), 119-129. RIS download Bibtex download
  • Tappenden P, Harnan S, Ren S, Thokala P, Wong R, Mukuria C, Green C, Pledge S & Tidy J (2017) . PharmacoEconomics, 35(1), 97-109. RIS download Bibtex download
  • Tappenden P, Ren S, Archer R, Harvey R, Martyn-St James M, Basarir H, Stevens J, Lobo A & Hoque S (2016) . PharmacoEconomics, 34(10), 1023-1038. RIS download Bibtex download
  • Harnan S, Ren S, Gomersall T, hock , sutton A, Dhanasiri S & Kulasekararaj A (2016) . Acta Haematologica, 136(1), 23-42. RIS download Bibtex download
  • Morrell CJ, Sutcliffe P, Booth A, Stevens J, Scope A, Stevenson M, Harvey R, Bessey A, Cantrell A, Dennis C-L , Ren S et al (2016) . Health Technology Assessment, 20(37), 1-414. RIS download Bibtex download
  • Archer R, Tappenden P, Ren S, Martyn-St James M, Harvey R, Basarir H, Stevens J, Carroll C, Cantrell A, Lobo A & Hoque S (2016) . Health Technology Assessment, 20(39), 1-326. RIS download Bibtex download
  • Essat M, Tappenden P, Ren S, Bessey A, Archer R, Wong R, Lobo A & Hoque S (2016) . PharmacoEconomics, 34(3), 245-257. RIS download Bibtex download
  • Martyn-St James M, Cooper K, Ren K, Kaltenthaler E, Dickinson K, Cantrell A, Wylie K, Frodsham L & Hood C (2016) . Sexual Health, 13(2), 114-123. RIS download Bibtex download
  • Goodacre S, Stevens JW, Pandor A, Poku E, Ren S, Cantrell A, Bounes V, Mas A, Payen D, Petrie D , Roessler MS et al (2014) . Academic Emergency Medicine, 21(9), 960-970. RIS download Bibtex download
  • Carroll C, Hummel S, Leaviss J, Ren S, Stevens JW, Cantrell A & Michaels J (2014) . Br J Surg, 101(9), 1040-1052. RIS download Bibtex download
  • Leaviss J, Hummel S, Carroll C, Ren S, Stevens JW, Everson-Hock E, Cantrell A, Stevenson M & Michaels J (2014) Clinical and cost-effectiveness of minimally invasive techniques for the treatment of varicosis: Systematic review and economic evaluation. Vasomed, 26(4), 210-211. RIS download Bibtex download
  • Ren S & Oakley JE (2014) . Statistics in Medicine, 33(1), 31-45. RIS download Bibtex download
  • Leaviss J, Sullivan W, Ren S, Everson-Hock E, Stevenson M, Stevens JW, Strong M & Cantrell A (2014) . Health Technol Assess, 18(33), 1-120. RIS download Bibtex download
  • Uttley L, Kearns B, Ren S & Stevenson M (2013) . Pharmacoeconomics, 31(11), 981-990. RIS download Bibtex download
  • Carroll C, Hummel S, Leaviss J, Ren S, Stevens JW, Everson-Hock E, Cantrell A, Stevenson M & Michaels J (2013) . Health Technol Assess, 17(48), i-141. RIS download Bibtex download
  • Woods B, Kearns B, Schmitt L, Jankovic D, Rothery C, Harnan S, Hamilton J, Scope A, Ren S, Bojke L , Wilcox M et al () . Applied Health Economics and Health Policy. RIS download Bibtex download
  • Harnan S, Hamilton J, Simpson E, Clowes M, Navega Biz A, Whyte S, Ren S, Cooper K, Abulafi M, Ball A , Beton S et al () Faecal Immunochemical Tests For Patients With Symptoms Suggestive Of Colorectal Cancer: An Updated Systematic Review And Multiple-Threshold Meta-Analysis of Diagnostic Test Accuracy Studies. Colorectal Disease. RIS download Bibtex download
  • Harnan S, Kearns B, Scope A, Schmitt L, Jankovic D, Hamilton J, Srivastava T, Hill H, Ku CC, Ren S , Rothery C et al () . Health Technology Assessment, 1-230. RIS download Bibtex download
  • Woods B, Schmitt L, Jankovic D, Kearns B, Scope A, Ren S, Srivastava T, Ku CC, Hamilton J, Rothery C , Bojke L et al () . Health Technology Assessment, 1-238. RIS download Bibtex download
  • Thokala P, Srivastava T, Smith R, Ren S, Whittington MD, Elvidge J, Wong R & Uttley L () . PharmacoEconomics. RIS download Bibtex download
  • Pandor A, Thokala P, Goodacre S, Poku E, Stevens JW, Ren S, Cantrell A, Perkins GD, Ward M & Penn-Ashman J () . Health Technology Assessment, 19(42), 1-102. RIS download Bibtex download
  • Leaviss J, Davis S, Ren S, Hamilton J, Scope A, Booth A, Sutton A, Parry G, Buszewicz M, Moss-Morris R & White P () . Health Technology Assessment, 24(46), 1-490. RIS download Bibtex download

Conference proceedings papers

  • Goodacre S, Ren S, Essat M, Pandor A, Ren S, Clowes M, Bima P, Toyofuku M, McLatchie R, Bossone E & Wilson S (2024) . RCEM Annual Scientific Conference 2024 Abstracts (pp A9.1-A9) RIS download Bibtex download
  • Combe E, Jones D, Knight H, Laskier V, Ren K, Wright T, Boing EA & Trivedi P (2024) COMPARATIVE EFFICACY OF ELAFIBRANOR AND SELADELPAR IN PATIENTS WITH PRIMARY BILIARY CHOLANGITIS: A NETWORK META-ANALYSIS. VALUE IN HEALTH, Vol. 27(12) RIS download Bibtex download
  • Srivastava T, Gupta A, Gautam R, Hriday K & Ren S (2024) ARE WE DEALING WITH HETEROGENEITY IN NETWORK META-ANALYSIS APPROPRIATELY? A REVIEW OF NICE SUBMISSIONS. VALUE IN HEALTH, Vol. 27(6) (pp S403-S404) RIS download Bibtex download
  • Shah B, Challagulla S, Xu S, Williams R, Ren S, Srivastava T, Gautam R & Yang K (2024) Indirect Comparison of Efficacy of Zanubrutinib Versus Acalabrutinib in the Treatment of Relapsed/Refractory (R/R) Mantle Cell Lymphoma (MCL). CLINICAL LYMPHOMA MYELOMA & LEUKEMIA, Vol. 24 (pp S516-S517) RIS download Bibtex download
  • Ren K & Forsyth J (2024) ENHANCING EXPERT ELICITATION IN HEALTH TECHNOLOGY ASSESSMENT: PRACTICAL INSIGHTS AND RECOMMENDATIONS. VALUE IN HEALTH, Vol. 27(12) RIS download Bibtex download
  • Knowles M, Kroep S & Ren K (2024) COMPARATIVE EFFICACY OF TREATMENTS IN ADVANCED/METASTATIC PANCREATIC CANCER: DEMONSTRATING THE POWER OF MULTI-LEVEL NETWORK META REGRESSION. VALUE IN HEALTH, Vol. 27(12) RIS download Bibtex download
  • Grand T, Thokala P, Ren K, Regnier S, Astroem OD, Awad SF, Bidani A & Krismer PF (2024) USE OF DISEASE ANALOGUES TO INFORM HEALTH-ECONOMIC PARAMETERS FOR ECONOMIC EVALUATIONS OF RARE DISEASES: A CASE-STUDY OF MULTIPLE SYSTEM ATROPHY. VALUE IN HEALTH, Vol. 27(12) (pp S120-S120) RIS download Bibtex download
  • Forsyth J, Mitra S, Wong R, Srivastava T & Ren K (2024) CAN EXCESS HAZARD MODELS ENHANCE SURVIVAL ANALYSIS IN HEALTH TECHNOLOGY ASSESSMENTS?. VALUE IN HEALTH, Vol. 27(12) (pp S375-S375) RIS download Bibtex download
  • Forsyth J, Wong R & Ren K (2024) ARE WE MAKING EXPERT USE OF EXPERTS? A SCOPING REVIEW OF EXPERT ELICITATION IN SURVIVAL EXTRAPOLATION. VALUE IN HEALTH, Vol. 27(12) (pp S620-S620) RIS download Bibtex download
  • Wheat H, Ren K & Stevenson MD (2024) INVESTIGATING THE USE OF THE DIFFERENCE METHOD FOR SAMPLING MORE THAN TWO ORDERED VARIABLES. VALUE IN HEALTH, Vol. 27(12) RIS download Bibtex download
  • Dunnewind N, Ainsworth C, Ren S & Kroep S (2023) PRIORS ON BETWEEN- STUDY HETEROGENEITY IN BAYESIAN META-ANALYSIS MODELS: A SIMULATION STUDY USING HAMILTONIAN MONTE CARLO SAMPLING. VALUE IN HEALTH, Vol. 26(12) (pp S557-S557) RIS download Bibtex download
  • Ren S (2023) A NOVEL UNANCHORED SIMULATED TREATMENT COMPARISON APPROACH FOR TIME-TO-EVENT DATA. VALUE IN HEALTH, Vol. 26(12) (pp S424-S424) RIS download Bibtex download
  • Sultana N & Ren S (2022) REVIEW OF METHODS USED TO ESTIMATE TREATMENT EFFECTS AGAINST RELEVANT COMPARATORS USING EVIDENCE FROM SINGLE-ARM STUDIES IN NICE SINGLE TECHNOLOGY APPRAISALS. VALUE IN HEALTH, Vol. 25(12) (pp S10-S10) RIS download Bibtex download
  • Zhu D, Ren S, Mills K, Lemp-Hull J, Dhariwal M & Srivastava T (2022) RATE OF COMPLETE SPECTACLE INDEPENDENCE WITH A TRIFOCAL IOL: A SYSTEMATIC LITERATURE REVIEW AND META-ANALYSIS. VALUE IN HEALTH, Vol. 25(12) (pp S378-S378) RIS download Bibtex download
  • Ren S, Strong M & Welton N (2022) AN EXTENDED SIMULATED TREATMENT COMPARISON APPROACH ACCOUNTING FOR UNOBSERVED CONFOUNDING IN INDIRECT COMPARISONS FOR SINGLE-ARM TRIALS. VALUE IN HEALTH, Vol. 25(12) (pp S358-S358) RIS download Bibtex download
  • Thokala P, Stevenson M, Kumar VM, Ren S, Chapman R, Ellis A & Rind D (2019) . Value in Health, Vol. 22 (pp S337-S338) RIS download Bibtex download
  • Ren S, Oakley JE & Stevens JW (2017) EVIDENCE SYNTHESIS FOR HEALTH TECHNOLOGY ASSESSMENT WITH LIMITED STUDIES. VALUE IN HEALTH, Vol. 20(9) (pp A770-A770) RIS download Bibtex download
  • Harnan S, Ren S, Gomersall T, Everson-Hock E, Sutton A, Dhanasiri S & Kulasekararaj A (2014) . Blood, Vol. 124(21) (pp 1934-1934) RIS download Bibtex download
  • Almond C, Stevens JW, Ren K & Batty A (2013) . Value in Health, Vol. 16(7) (pp A397-A397) RIS download Bibtex download

Posters

  • Zhu D, Ren S, Mills K, Lemp-Hull J, Dhariwal M & Srivastava T (2022) MT2 Rate of Complete Spectacle Independence With a Trifocal IOL: A Systematic Literature Review and Meta-Analysis. RIS download Bibtex download
  • Ghabri S, Simpson EL, Ren S, Hock E, Archer R, Binard A, Pers Y, Stevens JW, Herpin C & Stevenson M (2018) PMS4 - RHEUMATOID ARTHRITIS TREATED WITH SIX-MONTHS OF FIRST-LINE BIOLOGIC OR BIOSIMILAR THERAPY: A SYSTEMATIC REVIEW AND NETWORK META-ANALYSIS. RIS download Bibtex download
  • Ren S, Oakley J & Stevens JW (2018) Evidence synthesis with limited studies. HTAi 2018, Vancouver, Canada. RIS download Bibtex download
  • Ren S, Oakley J & Stevens JW (2017) Evidence synthesis for health technology assessment with limited studies.. . ISPOR Glasgow 2017. RIS download Bibtex download
  • Goodacre S (2014) PRE-HOSPITAL NON-INVASIVE VENTILATION FOR ACUTE RESPIRATORY FAILURE: A SYSTEMATIC REVIEW AND NETWORK META ANALYSIS. RIS download Bibtex download
  • Ren S, Cooper K, Cooper J, Smith H & Shaikh S A systematic review and network meta - analysis of pharmacological therapies used for patients with advanced Parkinson's disease (2014). RIS download Bibtex download
  • Goodacre S, Pandor A, Poku E, Stevens JW, Ren S & Cantrell A Pre-hospital non-invasive ventilation for acute respiratory failure: a systematic review and network meta-analysis. 999 EMS Research Forum Conference. RIS download Bibtex download

Preprints

  • Thokala P, Fuller GW, Goodacre S, Keating S, Herbert E, Perkins G, Rosser A, Gunson I, Miller J, Ward M , Bradburn M et al (2021) , Research Square Platform LLC. RIS download Bibtex download
  • Thokala P, Fuller GW, Goodacre S, Keating S, Herbert E, Perkins G, Rosser A, Gunson I, Miller J, Ward M , Bradburn M et al (2020) , Research Square Platform LLC. RIS download Bibtex download
  • Thokala P, Fuller GW, Keating S, Herbert E, Rosser A, Gunson I, Miller J, Ward M, Bradburn M, Marsh M & Ren K (2020) , Research Square Platform LLC. RIS download Bibtex download
  • Duro E, Julious PS & Ren S () , Research Square Platform LLC. RIS download Bibtex download
Grants
  • NIHR Evidence Synthesis Group (2023-2028, £4,507,538) Co-investigator.
  • NIHR Technology Assessment Reviews (2022-2027, £6,999,908) Co-investigator.
  • NIHR Advanced Fellowship (2021-2025, £368,269) Principal investigator.
  • NIHR HTA Programme: Effectiveness of interventions for fatigue in long-term conditions (2023-2025, £332,575) Co-investigator.
  • NIHR HTA Programme: Diagnostic strategies for suspected acute aortic syndrome (2023-2024, £184,095) Co-investigator.
  • NIHR HTA Programme: Medically unexplained symptoms: primary care intervention (2015-2017, £171,405) Co-investigator.
Teaching interests

Evidence synthesis, survival analysis