Quantitative literacy: Difference between revisions

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===Comparing benefits of competing interventions===
===Comparing benefits of competing interventions===
The hazard ratio is difficult to use<ref name="pmid30500891">{{cite journal| author=Stensrud MJ, Aalen JM, Aalen OO, Valberg M| title=Limitations of hazard ratios in clinical trials. | journal=Eur Heart J | year= 2019 | volume= 40 | issue= 17 | pages= 1378-1383 | pmid=30500891 | doi=10.1093/eurheartj/ehy770 | pmc= | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=30500891  }} </ref><ref name="Spiegelhalter2017">{{cite journal|last1=Spiegelhalter|first1=David|title=Risk and Uncertainty Communication|journal=Annual Review of Statistics and Its Application|volume=4|issue=1|year=2017|pages=31–60|issn=2326-8298|doi=10.1146/annurev-statistics-010814-020148}}</ref>.
Various formats including the [[number needed to treat]] have been tested to improve comprehension of quantitative comparisons of treatment benefit by patients<ref name="pmid14687273">{{cite journal |author=Sheridan SL, Pignone MP, Lewis CL |title=A randomized comparison of patients' understanding of number needed to treat and other common risk reduction formats |journal=J Gen Intern Med |volume=18 |issue=11 |pages=884–92 |year=2003 |month=November |pmid=14687273 |pmc=1494938 |doi= |url=http://www.blackwell-synergy.com/openurl?genre=article&sid=nlm:pubmed&issn=0884-8734&date=2003&volume=18&issue=11&spage=884 |issn=}}</ref><ref name="pmid17873258">{{cite journal |author=Schwartz LM, Woloshin S, Welch HG |title=The drug facts box: providing consumers with simple tabular data on drug benefit and harm |journal=Med Decis Making |volume=27 |issue=5 |pages=655–62 |year=2007 |pmid=17873258 |doi=10.1177/0272989X07306786 |url=http://mdm.sagepub.com/cgi/pmidlookup?view=long&pmid=17873258 |issn=}}</ref><ref name="pmid17310049">{{cite journal |author=Woloshin S, Schwartz LM, Welch HG |title=The effectiveness of a primer to help people understand risk: two randomized trials in distinct populations |journal=Ann. Intern. Med. |volume=146 |issue=4 |pages=256–65 |year=2007 |month=February |pmid=17310049 |doi= |url=http://www.annals.org/cgi/content/full/146/4/256 |issn=}}</ref><ref name="pmid18565218">{{cite journal |author=Stovring H, Gyrd-Hansen D, Kristiansen IS, Nexoe J, Nielsen JB |title=Communicating effectiveness of intervention for chronic diseases: what single format can replace comprehensive information? |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=25 |year=2008 |pmid=18565218 |pmc=2467410 |doi=10.1186/1472-6947-8-25 |url=http://www.biomedcentral.com/1472-6947/8/25 |issn=}}</ref><ref name="pmid18402680">{{cite journal |author=Dolan JG, Iadarola S |title=Risk communication formats for low probability events: an exploratory study of patient preferences |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=14 |year=2008 |pmid=18402680 |pmc=2330036 |doi=10.1186/1472-6947-8-14 |url=http://www.biomedcentral.com/1472-6947/8/14 |issn=}}</ref><ref name="pmid9412301">{{cite journal |author=Schwartz LM, Woloshin S, Black WC, Welch HG |title=The role of numeracy in understanding the benefit of screening mammography |journal=Ann. Intern. Med. |volume=127 |issue=11 |pages=966–72 |year=1997 |month=December |pmid=9412301 |doi= |url=http://www.annals.org/cgi/pmidlookup?view=long&pmid=9412301 |issn=}}</ref><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref> and by health care professionals<ref name="pmid11874195">{{cite journal |author=Sheridan SL, Pignone M |title=Numeracy and the medical student's ability to interpret data |journal=Eff Clin Pract |volume=5 |issue=1 |pages=35–40 |year=2002 |pmid=11874195 |doi= |url=http://www.acponline.org/journals/ecp/janfeb02/sheridan.htm |issn=}}</ref><ref name="pmid14512488">{{cite journal |author=Gigerenzer G, Edwards A |title=Simple tools for understanding risks: from innumeracy to insight |journal=BMJ |volume=327 |issue=7417 |pages=741–4 |year=2003 |month=September |pmid=14512488 |pmc=200816 |doi=10.1136/bmj.327.7417.741 |url=http://bmj.com/cgi/pmidlookup?view=long&pmid=14512488 |issn=}}</ref><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref>.
Various formats including the [[number needed to treat]] have been tested to improve comprehension of quantitative comparisons of treatment benefit by patients<ref name="pmid14687273">{{cite journal |author=Sheridan SL, Pignone MP, Lewis CL |title=A randomized comparison of patients' understanding of number needed to treat and other common risk reduction formats |journal=J Gen Intern Med |volume=18 |issue=11 |pages=884–92 |year=2003 |month=November |pmid=14687273 |pmc=1494938 |doi= |url=http://www.blackwell-synergy.com/openurl?genre=article&sid=nlm:pubmed&issn=0884-8734&date=2003&volume=18&issue=11&spage=884 |issn=}}</ref><ref name="pmid17873258">{{cite journal |author=Schwartz LM, Woloshin S, Welch HG |title=The drug facts box: providing consumers with simple tabular data on drug benefit and harm |journal=Med Decis Making |volume=27 |issue=5 |pages=655–62 |year=2007 |pmid=17873258 |doi=10.1177/0272989X07306786 |url=http://mdm.sagepub.com/cgi/pmidlookup?view=long&pmid=17873258 |issn=}}</ref><ref name="pmid17310049">{{cite journal |author=Woloshin S, Schwartz LM, Welch HG |title=The effectiveness of a primer to help people understand risk: two randomized trials in distinct populations |journal=Ann. Intern. Med. |volume=146 |issue=4 |pages=256–65 |year=2007 |month=February |pmid=17310049 |doi= |url=http://www.annals.org/cgi/content/full/146/4/256 |issn=}}</ref><ref name="pmid18565218">{{cite journal |author=Stovring H, Gyrd-Hansen D, Kristiansen IS, Nexoe J, Nielsen JB |title=Communicating effectiveness of intervention for chronic diseases: what single format can replace comprehensive information? |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=25 |year=2008 |pmid=18565218 |pmc=2467410 |doi=10.1186/1472-6947-8-25 |url=http://www.biomedcentral.com/1472-6947/8/25 |issn=}}</ref><ref name="pmid18402680">{{cite journal |author=Dolan JG, Iadarola S |title=Risk communication formats for low probability events: an exploratory study of patient preferences |journal=BMC Med Inform Decis Mak |volume=8 |issue= |pages=14 |year=2008 |pmid=18402680 |pmc=2330036 |doi=10.1186/1472-6947-8-14 |url=http://www.biomedcentral.com/1472-6947/8/14 |issn=}}</ref><ref name="pmid9412301">{{cite journal |author=Schwartz LM, Woloshin S, Black WC, Welch HG |title=The role of numeracy in understanding the benefit of screening mammography |journal=Ann. Intern. Med. |volume=127 |issue=11 |pages=966–72 |year=1997 |month=December |pmid=9412301 |doi= |url=http://www.annals.org/cgi/pmidlookup?view=long&pmid=9412301 |issn=}}</ref><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref> and by health care professionals<ref name="pmid11874195">{{cite journal |author=Sheridan SL, Pignone M |title=Numeracy and the medical student's ability to interpret data |journal=Eff Clin Pract |volume=5 |issue=1 |pages=35–40 |year=2002 |pmid=11874195 |doi= |url=http://www.acponline.org/journals/ecp/janfeb02/sheridan.htm |issn=}}</ref><ref name="pmid14512488">{{cite journal |author=Gigerenzer G, Edwards A |title=Simple tools for understanding risks: from innumeracy to insight |journal=BMJ |volume=327 |issue=7417 |pages=741–4 |year=2003 |month=September |pmid=14512488 |pmc=200816 |doi=10.1136/bmj.327.7417.741 |url=http://bmj.com/cgi/pmidlookup?view=long&pmid=14512488 |issn=}}</ref><ref name="pmid16174840">{{cite journal |author=Wen L, Badgett R, Cornell J |title=Number needed to treat: a descriptor for weighing therapeutic options |journal=Am J Health Syst Pharm |volume=62 |issue=19 |pages=2031–6 |year=2005 |month=October |pmid=16174840 |doi=10.2146/ajhp040558 |url=http://www.ajhp.org/cgi/pmidlookup?view=long&pmid=16174840 |issn=}}</ref>.
Originally in oncology<ref name="pmid28975263">{{cite journal| author=Pak K, Uno H, Kim DH, Tian L, Kane RC, Takeuchi M | display-authors=etal| title=Interpretability of Cancer Clinical Trial Results Using Restricted Mean Survival Time as an Alternative to the Hazard Ratio. | journal=JAMA Oncol | year= 2017 | volume= 3 | issue= 12 | pages= 1692-1696 | pmid=28975263 | doi=10.1001/jamaoncol.2017.2797 | pmc=5824272 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=28975263  }} </ref><ref name="pmid31050784">{{cite journal| author=Wang ZX, Wu HX, Xie L, Wang YN, Yang LP, He MM | display-authors=etal| title=Correlation of Milestone Restricted Mean Survival Time Ratio With Overall Survival Hazard Ratio in Randomized Clinical Trials of Immune Checkpoint Inhibitors: A Systematic Review and Meta-analysis. | journal=JAMA Netw Open | year= 2019 | volume= 2 | issue= 5 | pages= e193433 | pmid=31050784 | doi=10.1001/jamanetworkopen.2019.3433 | pmc=6503508 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=31050784  }} </ref><ref name="pmid29788167">{{cite journal| author=Liang F, Zhang S, Wang Q, Li W| title=Treatment effects measured by restricted mean survival time in trials of immune checkpoint inhibitors for cancer. | journal=Ann Oncol | year= 2018 | volume= 29 | issue= 5 | pages= 1320-1324 | pmid=29788167 | doi=10.1093/annonc/mdy075 | pmc= | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=29788167  }} </ref> but now in other clinical areas<ref name="pmid32203984">{{cite journal| author=Kloecker DE, Davies MJ, Khunti K, Zaccardi F| title=Uses and Limitations of the Restricted Mean Survival Time: Illustrative Examples From Cardiovascular Outcomes and Mortality Trials in Type 2 Diabetes. | journal=Ann Intern Med | year= 2020 | volume= 172 | issue= 8 | pages= 541-552 | pmid=32203984 | doi=10.7326/M19-3286 | pmc= | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=32203984  }} </ref>, the restricted mean survival time ratio (RMST).


When weighing the impact of benefits versus harms, various methods have been studied to help patients prioritize values.<ref name="pmid23400279">{{cite journal| author=Pignone MP, Howard K, Brenner AT, Crutchfield TM, Hawley ST, Lewis CL et al.| title=Comparing 3 techniques for eliciting patient values for decision making about prostate-specific antigen screening: a randomized controlled trial. | journal=JAMA Intern Med | year= 2013 | volume= 173 | issue= 5 | pages= 362-8 | pmid=23400279 | doi=10.1001/jamainternmed.2013.2651 | pmc=3974265 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=23400279  }} </ref>
When weighing the impact of benefits versus harms, various methods have been studied to help patients prioritize values.<ref name="pmid23400279">{{cite journal| author=Pignone MP, Howard K, Brenner AT, Crutchfield TM, Hawley ST, Lewis CL et al.| title=Comparing 3 techniques for eliciting patient values for decision making about prostate-specific antigen screening: a randomized controlled trial. | journal=JAMA Intern Med | year= 2013 | volume= 173 | issue= 5 | pages= 362-8 | pmid=23400279 | doi=10.1001/jamainternmed.2013.2651 | pmc=3974265 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=23400279  }} </ref>

Revision as of 01:11, 12 October 2020

In education and literacy, Quantitative literacy (also called numeracy) is "the knowledge and skills required to apply arithmetic operations, either alone or sequentially, using numbers embedded in printed materials; for example, balancing a checkbook, figuring out a tip, completing an order form, or determining the amount of interest from a loan advertisement."[1]

Comprehension of numbers can be divided into:[2][3]

  • Verbatim comprehension: "the ability to correctly read numbers from graphs"
  • Gist comprehension: "the ability to identify the essential point of the information presented", or more specifically, correctly rank the magnitude of two or more options.

Quantitative literacy is important in politics[4][5][6] and health care[7][8][9].

Health care

Health care numeracy by patients is associated with improved health[7][10]. However, health care numeracy is problematic as health care providers[11][12][13][14][15] and patients[16][17][18][19][20][19][21] both have problems with quantitative reasoning. Some of the difficulty is doe to interpreting relative versus absolute measures of efficacy.[22][23] The problem is confounded by scientific journals not well presenting quantitative results.[24]

Many methods exist to measure health literacy.[25]

Describing the impact of a single choice

Presenting lifetime risk increases patients' accepting treatment as compared to presenting risk of a shorter time frame[26].

Comparing benefits of competing interventions

The hazard ratio is difficult to use[27][28].

Various formats including the number needed to treat have been tested to improve comprehension of quantitative comparisons of treatment benefit by patients[23][29][30][31][32][21][33] and by health care professionals[34][35][33].

Originally in oncology[36][37][38] but now in other clinical areas[39], the restricted mean survival time ratio (RMST).

When weighing the impact of benefits versus harms, various methods have been studied to help patients prioritize values.[40]

In practicing evidence-based medicine, framing bias is best avoided by using numeracy with absolute measures of efficacy.[41][42]

Pictographs (Pictograms)

Pictographs, compared to usual care or no decision aids, improved clinical processes.[43] Pictographs add to simple text statements that quantify risk.[44] Patients may prefer bar graphs.[45] However, pictographs may be better than bargraphs when event rates are small.[46]

When designing pictographs:

  • Anthropomorphic icons (restroom icons, head outlines, and photos), especially restroom icons, may be best.[47][48]
  • Patients may have more trust when the characters are randomly highlighted vs highlighted in groups.[45][49]
  • Pictographs best depict only one outcome.[50]

Tables

Types of tables include 'fact boxes'[51] and 'balance sheets'[40].

Comparing accuracy of competing diagnostic strategies

Various formats have been tested to improve comprehension of quantitative comparisons of diagnostic accuracy.[34][52][53] However, improved understanding of probabilities may not affect decision making by physicians.[53]

References

  1. Irwin S. Kirsch, Ann Jungeblut, Lynn Jenkins, and Andrew Kolstad. (1993). Adult Literacy in America: a first look at the findings of the National Adult Literacy Survey, (NCES 93275). U.S. Department of Education.
  2. Nelson W, Reyna VF, Fagerlin A, Lipkus I, Peters E (2008). "Clinical implications of numeracy: theory and practice". Ann Behav Med. 35 (3): 261–74. doi:10.1007/s12160-008-9037-8. PMC 3694344. PMID 18677452.
  3. Hawley ST, Zikmund-Fisher B, Ubel P, Jancovic A, Lucas T, Fagerlin A (2008). "The impact of the format of graphical presentation on health-related knowledge and treatment choices". Patient Educ Couns. 73 (3): 448–55. doi:10.1016/j.pec.2008.07.023. PMID 18755566.
  4. Mérola, Vittorio; Hitt, Matthew P. (2015-12-31). "Numeracy and the Persuasive Effect of Policy Information and Party Cues". Public Opinion Quarterly. doi:10.1093/poq/nfv051.
  5. Best, Joel (2001). Damned lies and statistics: untangling numbers from the media, politicians, and activists. Berkeley: University of California Press. ISBN 0-520-21978-3.
  6. Best, Joel (2004). More damned lies and statistics: how numbers confuse public issues. Berkeley: University of California Press. ISBN 0-520-23830-3.
  7. 7.0 7.1 Berkman ND, Sheridan SL, Donahue KE, Halpern DJ, Crotty K (2011). "Low health literacy and health outcomes: an updated systematic review". Ann Intern Med. 155 (2): 97–107. doi:10.7326/0003-4819-155-2-201107190-00005. PMID 21768583.
  8. Mark Kutner, Elizabeth Greenberg, Ying Jin, Christine Paulsen. (2006) The Health Literacy of America’s Adults: Results From the 2003 National Assessment of Adult Literacy. U.S. Department of Education.
  9. Schwartz, Lisa A.; Steven Woloshin (2008). Know Your Chances: Understanding Health Statistics. Berkeley: University of California Press. ISBN 0-520-25222-5.
  10. Garcia-Retamero R, Andrade A, Sharit J, Ruiz JG (2015). "Is patients' numeracy related to physical and mental health?". Med Decis Making. 35 (4): 501–11. doi:10.1177/0272989X15578126. PMID 25943579.
  11. Bergman DA, Pantell RH (1986). "The impact of reading a clinical study on treatment decisions of physicians and residents". J Med Educ. 61 (5): 380–6. PMID 3701813.
  12. Berwick DM, Fineberg HV, Weinstein MC (1981). "When doctors meet numbers". Am J Med. 71 (6): 991–8. PMID 7315859.
  13. Phelps MA, Levitt MA (2004). "Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine?". Acad Emerg Med. 11 (6): 692–4. PMID 15175211.
  14. Reid MC, Lane DA, Feinstein AR (1998). "Academic calculations versus clinical judgments: practicing physicians' use of quantitative measures of test accuracy". Am J Med. 104 (4): 374–80. PMID 9576412.
  15. Steurer J, Fischer JE, Bachmann LM, Koller M, ter Riet G (2002). "Communicating accuracy of tests to general practitioners: a controlled study". BMJ. 324 (7341): 824–6. PMC 100792. PMID 11934776.
  16. Epstein RM, Alper BS, Quill TE (2004). "Communicating evidence for participatory decision making". JAMA. 291 (19): 2359–66. doi:10.1001/jama.291.19.2359. PMID 15150208.
  17. Friedmann PD, Brett AS, Mayo-Smith MF (1996). "Differences in generalists' and cardiologists' perceptions of cardiovascular risk and the outcomes of preventive therapy in cardiovascular disease". Ann Intern Med. 124 (4): 414–21. PMID 8554250.
  18. Hamm RM, Smith SL (1998). "The accuracy of patients' judgments of disease probability and test sensitivity and specificity". J Fam Pract. 47 (1): 44–52. PMID 9673608.
  19. 19.0 19.1 Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM (1993). "The framing effect of relative and absolute risk". J Gen Intern Med. 8 (10): 543–8. PMID 8271086.
  20. Naylor CD, Chen E, Strauss B (1992). "Measured enthusiasm: does the method of reporting trial results alter perceptions of therapeutic effectiveness?". Ann Intern Med. 117 (11): 916–21. PMID 1443954.
  21. 21.0 21.1 Schwartz LM, Woloshin S, Black WC, Welch HG (1997). "The role of numeracy in understanding the benefit of screening mammography". Ann Intern Med. 127 (11): 966–72. PMID 9412301.
  22. Bucher HC, Weinbacher M, Gyr K (1994). "Influence of method of reporting study results on decision of physicians to prescribe drugs to lower cholesterol concentration". BMJ. 309 (6957): 761–4. PMC 2541000. PMID 7950558.
  23. 23.0 23.1 Sheridan SL, Pignone MP, Lewis CL (2003). "A randomized comparison of patients' understanding of number needed to treat and other common risk reduction formats". J Gen Intern Med. 18 (11): 884–92. PMC 1494938. PMID 14687273.
  24. Nuovo J, Melnikow J, Chang D (2002). "Reporting number needed to treat and absolute risk reduction in randomized controlled trials". JAMA. 287 (21): 2813–4. PMID 12038920. Unknown parameter |month= ignored (help)
  25. Duell P, Wright D, Renzaho AM, Bhattacharya D (2015). "Optimal health literacy measurement for the clinical setting: A systematic review". Patient Educ Couns. 98 (11): 1295–307. doi:10.1016/j.pec.2015.04.003. PMID 26162954.
  26. Navar AM, Wang TY, Mi X, Robinson JG, Virani SS, Roger VL, Wilson PWF, Goldberg AC, Peterson ED. Influence of Cardiovascular Risk Communication Tools and Presentation Formats on Patient Perceptions and Preferences. JAMA Cardiol. 2018 Nov 7. doi: 10.1001/jamacardio.2018.3680. [Epub ahead of print] PubMed PMID: 30419113
  27. Stensrud MJ, Aalen JM, Aalen OO, Valberg M (2019). "Limitations of hazard ratios in clinical trials". Eur Heart J. 40 (17): 1378–1383. doi:10.1093/eurheartj/ehy770. PMID 30500891.
  28. Spiegelhalter, David (2017). "Risk and Uncertainty Communication". Annual Review of Statistics and Its Application. 4 (1): 31–60. doi:10.1146/annurev-statistics-010814-020148. ISSN 2326-8298.
  29. Schwartz LM, Woloshin S, Welch HG (2007). "The drug facts box: providing consumers with simple tabular data on drug benefit and harm". Med Decis Making. 27 (5): 655–62. doi:10.1177/0272989X07306786. PMID 17873258.
  30. Woloshin S, Schwartz LM, Welch HG (2007). "The effectiveness of a primer to help people understand risk: two randomized trials in distinct populations". Ann. Intern. Med. 146 (4): 256–65. PMID 17310049. Unknown parameter |month= ignored (help)
  31. Stovring H, Gyrd-Hansen D, Kristiansen IS, Nexoe J, Nielsen JB (2008). "Communicating effectiveness of intervention for chronic diseases: what single format can replace comprehensive information?". BMC Med Inform Decis Mak. 8: 25. doi:10.1186/1472-6947-8-25. PMC 2467410. PMID 18565218.
  32. Dolan JG, Iadarola S (2008). "Risk communication formats for low probability events: an exploratory study of patient preferences". BMC Med Inform Decis Mak. 8: 14. doi:10.1186/1472-6947-8-14. PMC 2330036. PMID 18402680.
  33. 33.0 33.1 Wen L, Badgett R, Cornell J (2005). "Number needed to treat: a descriptor for weighing therapeutic options". Am J Health Syst Pharm. 62 (19): 2031–6. doi:10.2146/ajhp040558. PMID 16174840. Unknown parameter |month= ignored (help)
  34. 34.0 34.1 Sheridan SL, Pignone M (2002). "Numeracy and the medical student's ability to interpret data". Eff Clin Pract. 5 (1): 35–40. PMID 11874195.
  35. Gigerenzer G, Edwards A (2003). "Simple tools for understanding risks: from innumeracy to insight". BMJ. 327 (7417): 741–4. doi:10.1136/bmj.327.7417.741. PMC 200816. PMID 14512488. Unknown parameter |month= ignored (help)
  36. Pak K, Uno H, Kim DH, Tian L, Kane RC, Takeuchi M; et al. (2017). "Interpretability of Cancer Clinical Trial Results Using Restricted Mean Survival Time as an Alternative to the Hazard Ratio". JAMA Oncol. 3 (12): 1692–1696. doi:10.1001/jamaoncol.2017.2797. PMC 5824272. PMID 28975263.
  37. Wang ZX, Wu HX, Xie L, Wang YN, Yang LP, He MM; et al. (2019). "Correlation of Milestone Restricted Mean Survival Time Ratio With Overall Survival Hazard Ratio in Randomized Clinical Trials of Immune Checkpoint Inhibitors: A Systematic Review and Meta-analysis". JAMA Netw Open. 2 (5): e193433. doi:10.1001/jamanetworkopen.2019.3433. PMC 6503508 Check |pmc= value (help). PMID 31050784.
  38. Liang F, Zhang S, Wang Q, Li W (2018). "Treatment effects measured by restricted mean survival time in trials of immune checkpoint inhibitors for cancer". Ann Oncol. 29 (5): 1320–1324. doi:10.1093/annonc/mdy075. PMID 29788167.
  39. Kloecker DE, Davies MJ, Khunti K, Zaccardi F (2020). "Uses and Limitations of the Restricted Mean Survival Time: Illustrative Examples From Cardiovascular Outcomes and Mortality Trials in Type 2 Diabetes". Ann Intern Med. 172 (8): 541–552. doi:10.7326/M19-3286. PMID 32203984 Check |pmid= value (help).
  40. 40.0 40.1 Pignone MP, Howard K, Brenner AT, Crutchfield TM, Hawley ST, Lewis CL; et al. (2013). "Comparing 3 techniques for eliciting patient values for decision making about prostate-specific antigen screening: a randomized controlled trial". JAMA Intern Med. 173 (5): 362–8. doi:10.1001/jamainternmed.2013.2651. PMC 3974265. PMID 23400279.
  41. Perneger TV, Agoritsas T (2011). "Doctors and Patients' Susceptibility to Framing Bias: A Randomized Trial". J Gen Intern Med. doi:10.1007/s11606-011-1810-x. PMID 21792695.
  42. Woloshin S, Schwartz LM (2011). "Communicating data about the benefits and harms of treatment: a randomized trial". Ann Intern Med. 155 (2): 87–96. doi:10.1059/0003-4819-155-2-201107190-00004. PMID 21768582.
  43. Hess EP, Knoedler MA, Shah ND, Kline JA, Breslin M, Branda ME; et al. (2012). "The chest pain choice decision aid: a randomized trial". Circ Cardiovasc Qual Outcomes. 5 (3): 251–9. doi:10.1161/CIRCOUTCOMES.111.964791. PMID 22496116.
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