Quantitative literacy: Difference between revisions

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* 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.
* 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]]<ref name="isbn0-520-21978-3">{{cite book |author=Best, Joel |authorlink= |editor= |others= |title=Damned lies and statistics: untangling numbers from the media, politicians, and activists |edition= |language= |publisher=University of California Press |location=Berkeley |year=2001 |origyear= |pages= |quote= |isbn=0-520-21978-3 |oclc= |doi= |url= |accessdate=}}</ref><ref name="isbn0-520-23830-3">{{cite book |author=Best, Joel |authorlink= |editor= |others= |title=More damned lies and statistics: how numbers confuse public issues |edition= |language= |publisher=University of California Press |location=Berkeley |year=2004 |origyear= |pages= |quote= |isbn=0-520-23830-3 |oclc= |doi= |url= |accessdate=}}</ref> and [[health care]]<ref>Mark Kutner, Elizabeth Greenberg, Ying Jin, Christine Paulsen. (2006) [http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2006483 The Health Literacy of America’s Adults: Results From the 2003 National Assessment of Adult Literacy]. U.S. Department of Education.</ref><ref name="isbn0-520-25222-5">{{cite book |author=Schwartz, Lisa A.; Steven Woloshin |authorlink= |editor= |others= |title=Know Your Chances: Understanding Health Statistics |edition= |language= |publisher=University of California Press |location=Berkeley |year=2008 |origyear= |pages= |quote= |isbn=0-520-25222-5 |oclc= |doi= |url= |accessdate=}}</ref>.
Quantitative literacy is important in [[politics]]<ref>{{Cite journal| doi = 10.1093/poq/nfv051| last1 = Mérola| first1 = Vittorio| last2 = Hitt| first2 = Matthew P.| title = Numeracy and the Persuasive Effect of Policy Information and Party Cues| journal = Public Opinion Quarterly| date = 2015-12-31}}</ref><ref name="isbn0-520-21978-3">{{cite book |author=Best, Joel |authorlink= |editor= |others= |title=Damned lies and statistics: untangling numbers from the media, politicians, and activists |edition= |language= |publisher=University of California Press |location=Berkeley |year=2001 |origyear= |pages= |quote= |isbn=0-520-21978-3 |oclc= |doi= |url= |accessdate=}}</ref><ref name="isbn0-520-23830-3">{{cite book |author=Best, Joel |authorlink= |editor= |others= |title=More damned lies and statistics: how numbers confuse public issues |edition= |language= |publisher=University of California Press |location=Berkeley |year=2004 |origyear= |pages= |quote= |isbn=0-520-23830-3 |oclc= |doi= |url= |accessdate=}}</ref> and [[health care]]<ref name="pmid21768583">{{cite journal| author=Berkman ND, Sheridan SL, Donahue KE, Halpern DJ, Crotty K| title=Low health literacy and health outcomes: an updated systematic review. | journal=Ann Intern Med | year= 2011 | volume= 155 | issue= 2 | pages= 97-107 | pmid=21768583 | doi=10.7326/0003-4819-155-2-201107190-00005 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=21768583  }} </ref><ref>Mark Kutner, Elizabeth Greenberg, Ying Jin, Christine Paulsen. (2006) [http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2006483 The Health Literacy of America’s Adults: Results From the 2003 National Assessment of Adult Literacy]. U.S. Department of Education.</ref><ref name="isbn0-520-25222-5">{{cite book |author=Schwartz, Lisa A.; Steven Woloshin |authorlink= |editor= |others= |title=Know Your Chances: Understanding Health Statistics |edition= |language= |publisher=University of California Press |location=Berkeley |year=2008 |origyear= |pages= |quote= |isbn=0-520-25222-5 |oclc= |doi= |url= |accessdate=}}</ref>.


==Health care==
==Health care==
Health care numeracy is problematic. Health care providers<ref name="pmid3701813">{{cite journal| author=Bergman DA, Pantell RH| title=The impact of reading a clinical study on treatment decisions of physicians and residents. | journal=J Med Educ | year= 1986 | volume= 61 | issue= 5 | pages= 380-6 | pmid=3701813 | doi= | pmc= | url= }} </ref><ref name="pmid7315859">{{cite journal| author=Berwick DM, Fineberg HV, Weinstein MC| title=When doctors meet numbers. | journal=Am J Med | year= 1981 | volume= 71 | issue= 6 | pages= 991-8 | pmid=7315859 | doi= | pmc= | url= }} </ref><ref name="pmid15175211">{{cite journal| author=Phelps MA, Levitt MA| title=Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine? | journal=Acad Emerg Med | year= 2004 | volume= 11 | issue= 6 | pages= 692-4 | pmid=15175211 | doi= | pmc= | url= }} </ref><ref name="pmid9576412">{{cite journal| author=Reid MC, Lane DA, Feinstein AR| title=Academic calculations versus clinical judgments: practicing physicians' use of quantitative measures of test accuracy. | journal=Am J Med | year= 1998 | volume= 104 | issue= 4 | pages= 374-80 | pmid=9576412 | doi= | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=9576412  }} </ref><ref name="pmid11934776">{{cite journal| author=Steurer J, Fischer JE, Bachmann LM, Koller M, ter Riet G| title=Communicating accuracy of tests to general practitioners: a controlled study. | journal=BMJ | year= 2002 | volume= 324 | issue= 7341 | pages= 824-6 | pmid=11934776 | doi= | pmc=PMC100792 | url= }} </ref> and patients<ref name="pmid15150208">{{cite journal| author=Epstein RM, Alper BS, Quill TE| title=Communicating evidence for participatory decision making. | journal=JAMA | year= 2004 | volume= 291 | issue= 19 | pages= 2359-66 | pmid=15150208 | doi=10.1001/jama.291.19.2359 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=15150208 }} </ref><ref name="pmid8554250">{{cite journal| author=Friedmann PD, Brett AS, Mayo-Smith MF| title=Differences in generalists' and cardiologists' perceptions of cardiovascular risk and the outcomes of preventive therapy in cardiovascular disease. | journal=Ann Intern Med | year= 1996 | volume= 124 | issue= 4 | pages= 414-21 | pmid=8554250 | doi= | pmc= | url= }} </ref><ref name="pmid9673608">{{cite journal| author=Hamm RM, Smith SL| title=The accuracy of patients' judgments of disease probability and test sensitivity and specificity. | journal=J Fam Pract | year= 1998 | volume= 47 | issue= 1 | pages= 44-52 | pmid=9673608 | doi= | pmc= | url= }} </ref><ref name="pmid8271086">{{cite journal| author=Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM| title=The framing effect of relative and absolute risk. | journal=J Gen Intern Med | year= 1993 | volume= 8 | issue= 10 | pages= 543-8 | pmid=8271086 | doi= | pmc= | url= }} </ref><ref name="pmid1443954">{{cite journal| author=Naylor CD, Chen E, Strauss B| title=Measured enthusiasm: does the method of reporting trial results alter perceptions of therapeutic effectiveness? | journal=Ann Intern Med | year= 1992 | volume= 117 | issue= 11 | pages= 916-21 | pmid=1443954 | doi= | pmc= | url= }} </ref><ref name="pmid8271086">{{cite journal| author=Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM| title=The framing effect of relative and absolute risk. | journal=J Gen Intern Med | year= 1993 | volume= 8 | issue= 10 | pages= 543-8 | pmid=8271086 | doi= | pmc= | url= }} </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 | year= 1997 | volume= 127 | issue= 11 | pages= 966-72 | pmid=9412301 | doi= | pmc= | url= }} </ref> both have problems with quantitative reasoning. Some of the difficulty is doe to interpreting relative versus absolute measures of efficacy.<ref name="pmid7950558">{{cite journal| author=Bucher HC, Weinbacher M, Gyr K| title=Influence of method of reporting study results on decision of physicians to prescribe drugs to lower cholesterol concentration. | journal=BMJ | year= 1994 | volume= 309 | issue= 6957 | pages= 761-4 | pmid=7950558 | doi= | pmc=PMC2541000 | url= }} </ref><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 | year= 2003 | volume= 18 | issue= 11 | pages= 884-92 | pmid=14687273 | doi= | pmc=PMC1494938 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=14687273  }} </ref> The problem is confounded by scientific journals not well presenting quantitative results.<ref name="pmid12038920">{{cite journal |author=Nuovo J, Melnikow J, Chang D |title=Reporting number needed to treat and absolute risk reduction in randomized controlled trials |journal=JAMA |volume=287 |issue=21 |pages=2813–4 |year=2002 |month=June |pmid=12038920 |doi= |url=http://jama.ama-assn.org/cgi/pmidlookup?view=long&pmid=12038920 |issn=}}</ref>
Health care numeracy by patients is associated with improved health<ref name="pmid21768583">{{cite journal| author=Berkman ND, Sheridan SL, Donahue KE, Halpern DJ, Crotty K| title=Low health literacy and health outcomes: an updated systematic review. | journal=Ann Intern Med | year= 2011 | volume= 155 | issue= 2 | pages= 97-107 | pmid=21768583 | doi=10.7326/0003-4819-155-2-201107190-00005 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=21768583  }} </ref><ref name="pmid25943579">{{cite journal| author=Garcia-Retamero R, Andrade A, Sharit J, Ruiz JG| title=Is patients' numeracy related to physical and mental health? | journal=Med Decis Making | year= 2015 | volume= 35 | issue= 4 | pages= 501-11 | pmid=25943579 | doi=10.1177/0272989X15578126 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=25943579  }} </ref>. However, health care numeracy is problematic as health care providers<ref name="pmid3701813">{{cite journal| author=Bergman DA, Pantell RH| title=The impact of reading a clinical study on treatment decisions of physicians and residents. | journal=J Med Educ | year= 1986 | volume= 61 | issue= 5 | pages= 380-6 | pmid=3701813 | doi= | pmc= | url= }} </ref><ref name="pmid7315859">{{cite journal| author=Berwick DM, Fineberg HV, Weinstein MC| title=When doctors meet numbers. | journal=Am J Med | year= 1981 | volume= 71 | issue= 6 | pages= 991-8 | pmid=7315859 | doi= | pmc= | url= }} </ref><ref name="pmid15175211">{{cite journal| author=Phelps MA, Levitt MA| title=Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine? | journal=Acad Emerg Med | year= 2004 | volume= 11 | issue= 6 | pages= 692-4 | pmid=15175211 | doi= | pmc= | url= }} </ref><ref name="pmid9576412">{{cite journal| author=Reid MC, Lane DA, Feinstein AR| title=Academic calculations versus clinical judgments: practicing physicians' use of quantitative measures of test accuracy. | journal=Am J Med | year= 1998 | volume= 104 | issue= 4 | pages= 374-80 | pmid=9576412 | doi= | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=9576412 }} </ref><ref name="pmid11934776">{{cite journal| author=Steurer J, Fischer JE, Bachmann LM, Koller M, ter Riet G| title=Communicating accuracy of tests to general practitioners: a controlled study. | journal=BMJ | year= 2002 | volume= 324 | issue= 7341 | pages= 824-6 | pmid=11934776 | doi= | pmc=PMC100792 | url= }} </ref> and patients<ref name="pmid15150208">{{cite journal| author=Epstein RM, Alper BS, Quill TE| title=Communicating evidence for participatory decision making. | journal=JAMA | year= 2004 | volume= 291 | issue= 19 | pages= 2359-66 | pmid=15150208 | doi=10.1001/jama.291.19.2359 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=15150208  }} </ref><ref name="pmid8554250">{{cite journal| author=Friedmann PD, Brett AS, Mayo-Smith MF| title=Differences in generalists' and cardiologists' perceptions of cardiovascular risk and the outcomes of preventive therapy in cardiovascular disease. | journal=Ann Intern Med | year= 1996 | volume= 124 | issue= 4 | pages= 414-21 | pmid=8554250 | doi= | pmc= | url= }} </ref><ref name="pmid9673608">{{cite journal| author=Hamm RM, Smith SL| title=The accuracy of patients' judgments of disease probability and test sensitivity and specificity. | journal=J Fam Pract | year= 1998 | volume= 47 | issue= 1 | pages= 44-52 | pmid=9673608 | doi= | pmc= | url= }} </ref><ref name="pmid8271086">{{cite journal| author=Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM| title=The framing effect of relative and absolute risk. | journal=J Gen Intern Med | year= 1993 | volume= 8 | issue= 10 | pages= 543-8 | pmid=8271086 | doi= | pmc= | url= }} </ref><ref name="pmid1443954">{{cite journal| author=Naylor CD, Chen E, Strauss B| title=Measured enthusiasm: does the method of reporting trial results alter perceptions of therapeutic effectiveness? | journal=Ann Intern Med | year= 1992 | volume= 117 | issue= 11 | pages= 916-21 | pmid=1443954 | doi= | pmc= | url= }} </ref><ref name="pmid8271086">{{cite journal| author=Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM| title=The framing effect of relative and absolute risk. | journal=J Gen Intern Med | year= 1993 | volume= 8 | issue= 10 | pages= 543-8 | pmid=8271086 | doi= | pmc= | url= }} </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 | year= 1997 | volume= 127 | issue= 11 | pages= 966-72 | pmid=9412301 | doi= | pmc= | url= }} </ref> both have problems with quantitative reasoning. Some of the difficulty is doe to interpreting relative versus absolute measures of efficacy.<ref name="pmid7950558">{{cite journal| author=Bucher HC, Weinbacher M, Gyr K| title=Influence of method of reporting study results on decision of physicians to prescribe drugs to lower cholesterol concentration. | journal=BMJ | year= 1994 | volume= 309 | issue= 6957 | pages= 761-4 | pmid=7950558 | doi= | pmc=PMC2541000 | url= }} </ref><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 | year= 2003 | volume= 18 | issue= 11 | pages= 884-92 | pmid=14687273 | doi= | pmc=PMC1494938 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=14687273  }} </ref> The problem is confounded by scientific journals not well presenting quantitative results.<ref name="pmid12038920">{{cite journal |author=Nuovo J, Melnikow J, Chang D |title=Reporting number needed to treat and absolute risk reduction in randomized controlled trials |journal=JAMA |volume=287 |issue=21 |pages=2813–4 |year=2002 |month=June |pmid=12038920 |doi= |url=http://jama.ama-assn.org/cgi/pmidlookup?view=long&pmid=12038920 |issn=}}</ref>
 
Many methods exist to measure health literacy.<ref name="pmid26162954">{{cite journal| author=Duell P, Wright D, Renzaho AM, Bhattacharya D| title=Optimal health literacy measurement for the clinical setting: A systematic review. | journal=Patient Educ Couns | year= 2015 | volume= 98 | issue= 11 | pages= 1295-307 | pmid=26162954 | doi=10.1016/j.pec.2015.04.003 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=26162954  }} </ref>
 
===Describing the impact of a single choice===
Presenting lifetime risk increases patients' accepting treatment as compared to presenting risk of a shorter time frame<ref>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</ref>.
 
In oncology, the value of [[progression-free survival]] as an outcome measure is debated<ref name="pmid31556921">{{cite journal| author=Raphael MJ, Robinson A, Booth CM, O'Donnell J, Palmer M, Eisenhauer E | display-authors=etal| title=The Value of Progression-Free Survival as a Treatment End Point Among Patients With Advanced Cancer: A Systematic Review and Qualitative Assessment of the Literature. | journal=JAMA Oncol | year= 2019 | volume=  | issue=  | pages=  | pmid=31556921 | doi=10.1001/jamaoncol.2019.3338 | pmc= | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=31556921  }} </ref><ref name="pmid31922558">{{cite journal| author=Paoletti X, Lewsley LA, Daniele G, Cook A, Yanaihara N, Tinker A | display-authors=etal| title=Assessment of Progression-Free Survival as a Surrogate End Point of Overall Survival in First-Line Treatment of Ovarian Cancer: A Systematic Review and Meta-analysis. | journal=JAMA Netw Open | year= 2020 | volume= 3 | issue= 1 | pages= e1918939 | pmid=31922558 | doi=10.1001/jamanetworkopen.2019.18939 | pmc=6991254 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=31922558  }} </ref><ref name="pmid32702645">{{cite journal| author=Pasalic D, McGinnis GJ, Fuller CD, Grossberg AJ, Verma V, Mainwaring W | display-authors=etal| title=Progression-free survival is a suboptimal predictor for overall survival among metastatic solid tumour clinical trials. | journal=Eur J Cancer | year= 2020 | volume= 136 | issue=  | pages= 176-185 | pmid=32702645 | doi=10.1016/j.ejca.2020.06.015 | pmc= | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=32702645  }} </ref><ref name="pmid32897371">{{cite journal| author=Kok PS, Cho D, Yoon WH, Ritchie G, Marschner I, Lord S | display-authors=etal| title=Validation of Progression-Free Survival Rate at 6 Months and Objective Response for Estimating Overall Survival in Immune Checkpoint Inhibitor Trials: A Systematic Review and Meta-analysis. | journal=JAMA Netw Open | year= 2020 | volume= 3 | issue= 9 | pages= e2011809 | pmid=32897371 | doi=10.1001/jamanetworkopen.2020.11809 | pmc=7489825 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=32897371  }} </ref><ref name="pmid30285081">{{cite journal| author=Kovic B, Jin X, Kennedy SA, Hylands M, Pedziwiatr M, Kuriyama A | display-authors=etal| title=Evaluating Progression-Free Survival as a Surrogate Outcome for Health-Related Quality of Life in Oncology: A Systematic Review and Quantitative Analysis. | journal=JAMA Intern Med | year= 2018 | volume= 178 | issue= 12 | pages= 1586-1596 | pmid=30285081 | doi=10.1001/jamainternmed.2018.4710 | pmc=6583599 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=30285081  }} </ref><ref name="pmid30646078">{{cite journal| author=Gyawali B, Hey SP, Kesselheim AS| title=A Comparison of Response Patterns for Progression-Free Survival and Overall Survival Following Treatment for Cancer With PD-1 Inhibitors: A Meta-analysis of Correlation and Differences in Effect Sizes. | journal=JAMA Netw Open | year= 2018 | volume= 1 | issue= 2 | pages= e180416 | pmid=30646078 | doi=10.1001/jamanetworkopen.2018.0416 | pmc=6324401 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=30646078  }} </ref><ref name="pmid26181024">{{cite journal| author=Shyr Y, Horn L, Berry L| title=Are We Making Progress in Lung Cancer Using Progression-Free Survival as a Surrogate End Point? | journal=JAMA Oncol | year= 2015 | volume= 1 | issue= 2 | pages= 202-3 | pmid=26181024 | doi=10.1001/jamaoncol.2015.0407 | pmc= | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=26181024  }} </ref>.
 
===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>.


===Comparing benefits of two treatments===
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) has been used. A [[randomized controlled trial]] found favorable impact from the RMST<ref name="pmid33901300">{{cite journal| author=Kim DH, Shi SM, Carroll D, Najafzadeh M, Wei LJ| title=Restricted mean survival time versus conventional measures for treatment decision-making. | journal=J Am Geriatr Soc | year= 2021 | volume= 69 | issue= 8 | pages= 2282-2289 | pmid=33901300 | doi=10.1111/jgs.17195 | pmc=8373742 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=33901300  }} </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>


In practicing [[evidence-based medicine]], framing bias is best avoided by using numeracy with absolute measures of efficacy.<ref name="pmid21792695">{{cite journal| author=Perneger TV, Agoritsas T| title=Doctors and Patients' Susceptibility to Framing Bias: A Randomized Trial. | journal=J Gen Intern Med | year= 2011 | volume=  | issue=  | pages=  | pmid=21792695 | doi=10.1007/s11606-011-1810-x | pmc= | url= }} </ref><ref name="pmid21768582">{{cite journal| author=Woloshin S, Schwartz LM| title=Communicating data about the benefits and harms of treatment: a randomized trial. | journal=Ann Intern Med | year= 2011 | volume= 155 | issue= 2 | pages= 87-96 | pmid=21768582 | doi=10.1059/0003-4819-155-2-201107190-00004 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=21768582  }} </ref>
In practicing [[evidence-based medicine]], framing bias is best avoided by using numeracy with absolute measures of efficacy.<ref name="pmid21792695">{{cite journal| author=Perneger TV, Agoritsas T| title=Doctors and Patients' Susceptibility to Framing Bias: A Randomized Trial. | journal=J Gen Intern Med | year= 2011 | volume=  | issue=  | pages=  | pmid=21792695 | doi=10.1007/s11606-011-1810-x | pmc= | url= }} </ref><ref name="pmid21768582">{{cite journal| author=Woloshin S, Schwartz LM| title=Communicating data about the benefits and harms of treatment: a randomized trial. | journal=Ann Intern Med | year= 2011 | volume= 155 | issue= 2 | pages= 87-96 | pmid=21768582 | doi=10.1059/0003-4819-155-2-201107190-00004 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=21768582  }} </ref>


====Pictographs (Pictograms)====
====Pictographs (Pictograms)====
Pictographs may been studied, but patients may prefer bar graphs.<ref name="pmid16950729">{{cite journal| author=Schapira MM, Nattinger AB, McAuliffe TL| title=The influence of graphic format on breast cancer risk communication. | journal=J Health Commun | year= 2006 | volume= 11 | issue= 6 | pages= 569-82 | pmid=16950729 | doi=10.1080/10810730600829916 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=16950729  }} </ref> However, pictographs may be better when event rates are small.<ref name="pmid22074912">{{cite journal| author=McCaffery KJ, Dixon A, Hayen A, Jansen J, Smith S, Simpson JM| title=The influence of graphic display format on the interpretations of quantitative risk information among adults with lower education and literacy: a randomized experimental study. | journal=Med Decis Making | year= 2012 | volume= 32 | issue= 4 | pages= 532-44 | pmid=22074912 | doi=10.1177/0272989X11424926 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=22074912  }} </ref>
Pictographs, compared to usual care or no decision aids, improved clinical processes.<ref name="pmid22496116">{{cite journal| author=Hess EP, Knoedler MA, Shah ND, Kline JA, Breslin M, Branda ME et al.| title=The chest pain choice decision aid: a randomized trial. | journal=Circ Cardiovasc Qual Outcomes | year= 2012 | volume= 5 | issue= 3 | pages= 251-9 | pmid=22496116 | doi=10.1161/CIRCOUTCOMES.111.964791 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=22496116  }} </ref> Pictographs add to simple text statements that quantify risk.<ref name="pmid18602242">{{cite journal| author=Zikmund-Fisher BJ, Ubel PA, Smith DM, Derry HA, McClure JB, Stark A et al.| title=Communicating side effect risks in a tamoxifen prophylaxis decision aid: the debiasing influence of pictographs. | journal=Patient Educ Couns | year= 2008 | volume= 73 | issue= 2 | pages= 209-14 | pmid=18602242 | doi=10.1016/j.pec.2008.05.010 | pmc=2649664 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=18602242  }} </ref> Patients may prefer bar graphs<ref name="pmid34297713">{{cite journal| author=Scalia P, Schubbe DC, Lu ES, Durand MA, Frascara J, Noel G | display-authors=etal| title=Comparing the impact of an icon array versus a bar graph on preference and understanding of risk information: Results from an online, randomized study. | journal=PLoS One | year= 2021 | volume= 16 | issue= 7 | pages= e0253644 | pmid=34297713 | doi=10.1371/journal.pone.0253644 | pmc=8301663 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=34297713  }} </ref><ref name="pmid16950729">{{cite journal| author=Schapira MM, Nattinger AB, McAuliffe TL| title=The influence of graphic format on breast cancer risk communication. | journal=J Health Commun | year= 2006 | volume= 11 | issue= 6 | pages= 569-82 | pmid=16950729 | doi=10.1080/10810730600829916 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=16950729  }} </ref>. However, pictographs may be better than bargraphs when event rates are small.<ref name="pmid22074912">{{cite journal| author=McCaffery KJ, Dixon A, Hayen A, Jansen J, Smith S, Simpson JM| title=The influence of graphic display format on the interpretations of quantitative risk information among adults with lower education and literacy: a randomized experimental study. | journal=Med Decis Making | year= 2012 | volume= 32 | issue= 4 | pages= 532-44 | pmid=22074912 | doi=10.1177/0272989X11424926 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=22074912 }} </ref> THe type of icon in a pictograph may be important - patients may prefer images of people such as sed for restroom pictograms<ref name="pmid24246564">{{cite journal| author=Zikmund-Fisher BJ, Witteman HO, Dickson M, Fuhrel-Forbis A, Kahn VC, Exe NL | display-authors=etal| title=Blocks, ovals, or people? Icon type affects risk perceptions and recall of pictographs. | journal=Med Decis Making | year= 2014 | volume= 34 | issue= 4 | pages= 443-53 | pmid=24246564 | doi=10.1177/0272989X13511706 | pmc=3991751 | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=24246564 }} </ref>


When designing pictographs:
When designing pictographs:
* "Risk recall was significantly higher with more anthropomorphic icons (restroom icons, head outlines, and photos) than with other icon types, and participants rated restroom icons as most preferred."<ref name="pmid24246564">{{cite journal| author=Zikmund-Fisher BJ, Witteman HO, Dickson M, Fuhrel-Forbis A, Kahn VC, Exe NL et al.| title=Blocks, ovals, or people? Icon type affects risk perceptions and recall of pictographs. | journal=Med Decis Making | year= 2014 | volume= 34 | issue= 4 | pages= 443-53 | pmid=24246564 | doi=10.1177/0272989X13511706 | pmc=3991751 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=24246564  }} </ref>
* Anthropomorphic icons (restroom icons, head outlines, and photos), especially restroom icons, may be best.<ref name="pmid27089046">{{cite journal| author=Kreuzmair C, Siegrist M, Keller C| title=Does Iconicity in Pictographs Matter? The Influence of Iconicity and Numeracy on Information Processing, Decision Making, and Liking in an Eye-Tracking Study. | journal=Risk Anal | year= 2016 | volume=  | issue=  | pages=  | pmid=27089046 | doi=10.1111/risa.12623 | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=27089046  }} </ref><ref name="pmid24246564">{{cite journal| author=Zikmund-Fisher BJ, Witteman HO, Dickson M, Fuhrel-Forbis A, Kahn VC, Exe NL et al.| title=Blocks, ovals, or people? Icon type affects risk perceptions and recall of pictographs. | journal=Med Decis Making | year= 2014 | volume= 34 | issue= 4 | pages= 443-53 | pmid=24246564 | doi=10.1177/0272989X13511706 | pmc=3991751 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=24246564  }} </ref>
* Patients may have more trust when the characters are randomly highlighted vs highlighted in groups.<ref name="pmid16950729"/>
* Patients may have more trust when the characters are randomly highlighted vs highlighted in groups.<ref name="pmid16950729"/><ref name="pmid22832208">{{cite journal| author=Zikmund-Fisher BJ, Witteman HO, Fuhrel-Forbis A, Exe NL, Kahn VC, Dickson M| title=Animated graphics for comparing two risks: a cautionary tale. | journal=J Med Internet Res | year= 2012 | volume= 14 | issue= 4 | pages= e106 | pmid=22832208 | doi=10.2196/jmir.2030 | pmc=3409597 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=22832208  }} </ref>
* Pictographs best depict only one outcome.<ref name="pmid20375419">{{cite journal| author=Zikmund-Fisher BJ, Fagerlin A, Ubel PA| title=A demonstration of ''less can be more'' in risk graphics. | journal=Med Decis Making | year= 2010 | volume= 30 | issue= 6 | pages= 661-71 | pmid=20375419 | doi=10.1177/0272989X10364244 | pmc=3576697 | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=20375419  }} </ref>


===Comparing accuracy of diagnostic methods===
====Tables====
Various formats have been tested to improve comprehension of quantitative comparisons of diagnostic accuracy.<ref name="pmid16061916">{{cite journal |author=Puhan MA, Steurer J, Bachmann LM, ter Riet G |title=A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates |journal=Ann. Intern. Med. |volume=143 |issue=3 |pages=184–9 |url=http://www.annals.org/cgi/content/full/143/3/184|year=2005 |pmid=16061916 |doi= |issn=}}</ref><ref name="pmid7898300">{{cite journal |author=Poses RM ''et al.''|title=You can lead a horse to water--improving physicians' knowledge of probabilities may not affect their decisions |journal=Medical Decision Making |volume=15  |pages=65–75 |year=1995 |pmid=7898300 |doi=}}</ref>
Types of tables include 'fact boxes'<ref name="pmid19221371">{{cite journal| author=Schwartz LM, Woloshin S, Welch HG| title=Using a drug facts box to communicate drug benefits and harms: two randomized trials. | journal=Ann Intern Med | year= 2009 | volume= 150 | issue= 8 | pages= 516-27 | pmid=19221371 | doi= | pmc= | url=http://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=19221371  }} </ref> and 'balance sheets'<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>.
<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 | year= 2002 | volume= 5 | issue= 1 | pages= 35-40 | pmid=11874195 | doi= | pmc= | url= }} </ref>
 
===Comparing accuracy of competing diagnostic strategies===
Various formats have been tested to improve comprehension of quantitative comparisons of diagnostic accuracy.<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 | year= 2002 | volume= 5 | issue= 1 | pages= 35-40 | pmid=11874195 | doi= | pmc= | url= }} </ref><ref name="pmid16061916">{{cite journal |author=Puhan MA, Steurer J, Bachmann LM, ter Riet G |title=A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates |journal=Ann. Intern. Med. |volume=143 |issue=3 |pages=184–9 |url=http://www.annals.org/cgi/content/full/143/3/184|year=2005 |pmid=16061916 |doi= |issn=}}</ref><ref name="pmid7898300">{{cite journal |author=Poses RM ''et al.''|title=You can lead a horse to water--improving physicians' knowledge of probabilities may not affect their decisions |journal=Medical Decision Making |volume=15  |pages=65–75 |year=1995 |pmid=7898300 |doi=}}</ref> However, improved understanding of probabilities may not affect decision making by physicians.<ref name="pmid7898300"/>
 
==See also==
* [[Shared decision making]]
 
==External links==


== References ==
== References ==
{{Reflist|2}}
{{Reflist|2}}
== External links ==


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Latest revision as of 01:06, 29 October 2022

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].

In oncology, the value of progression-free survival as an outcome measure is debated[27][28][29][30][31][32][33].

Comparing benefits of competing interventions

The hazard ratio is difficult to use[34][35].

Various formats including the number needed to treat have been tested to improve comprehension of quantitative comparisons of treatment benefit by patients[23][36][37][38][39][21][40] and by health care professionals[41][42][40].

Originally in oncology[43][44][45] but now in other clinical areas[46], the restricted mean survival time ratio (RMST) has been used. A randomized controlled trial found favorable impact from the RMST[47].

When weighing the impact of benefits versus harms, various methods have been studied to help patients prioritize values.[48]

In practicing evidence-based medicine, framing bias is best avoided by using numeracy with absolute measures of efficacy.[49][50]

Pictographs (Pictograms)

Pictographs, compared to usual care or no decision aids, improved clinical processes.[51] Pictographs add to simple text statements that quantify risk.[52] Patients may prefer bar graphs[53][54]. However, pictographs may be better than bargraphs when event rates are small.[55] THe type of icon in a pictograph may be important - patients may prefer images of people such as sed for restroom pictograms[56]

When designing pictographs:

  • Anthropomorphic icons (restroom icons, head outlines, and photos), especially restroom icons, may be best.[57][56]
  • Patients may have more trust when the characters are randomly highlighted vs highlighted in groups.[54][58]
  • Pictographs best depict only one outcome.[59]

Tables

Types of tables include 'fact boxes'[60] and 'balance sheets'[48].

Comparing accuracy of competing diagnostic strategies

Various formats have been tested to improve comprehension of quantitative comparisons of diagnostic accuracy.[41][61][62] However, improved understanding of probabilities may not affect decision making by physicians.[62]

See also

External links

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. ↑ Raphael MJ, Robinson A, Booth CM, O'Donnell J, Palmer M, Eisenhauer E; et al. (2019). "The Value of Progression-Free Survival as a Treatment End Point Among Patients With Advanced Cancer: A Systematic Review and Qualitative Assessment of the Literature". JAMA Oncol. doi:10.1001/jamaoncol.2019.3338. PMID 31556921.
  28. ↑ Paoletti X, Lewsley LA, Daniele G, Cook A, Yanaihara N, Tinker A; et al. (2020). "Assessment of Progression-Free Survival as a Surrogate End Point of Overall Survival in First-Line Treatment of Ovarian Cancer: A Systematic Review and Meta-analysis". JAMA Netw Open. 3 (1): e1918939. doi:10.1001/jamanetworkopen.2019.18939. PMC 6991254 Check |pmc= value (help). PMID 31922558.
  29. ↑ Pasalic D, McGinnis GJ, Fuller CD, Grossberg AJ, Verma V, Mainwaring W; et al. (2020). "Progression-free survival is a suboptimal predictor for overall survival among metastatic solid tumour clinical trials". Eur J Cancer. 136: 176–185. doi:10.1016/j.ejca.2020.06.015. PMID 32702645 Check |pmid= value (help).
  30. ↑ Kok PS, Cho D, Yoon WH, Ritchie G, Marschner I, Lord S; et al. (2020). "Validation of Progression-Free Survival Rate at 6 Months and Objective Response for Estimating Overall Survival in Immune Checkpoint Inhibitor Trials: A Systematic Review and Meta-analysis". JAMA Netw Open. 3 (9): e2011809. doi:10.1001/jamanetworkopen.2020.11809. PMC 7489825 Check |pmc= value (help). PMID 32897371 Check |pmid= value (help).
  31. ↑ Kovic B, Jin X, Kennedy SA, Hylands M, Pedziwiatr M, Kuriyama A; et al. (2018). "Evaluating Progression-Free Survival as a Surrogate Outcome for Health-Related Quality of Life in Oncology: A Systematic Review and Quantitative Analysis". JAMA Intern Med. 178 (12): 1586–1596. doi:10.1001/jamainternmed.2018.4710. PMC 6583599 Check |pmc= value (help). PMID 30285081.
  32. ↑ Gyawali B, Hey SP, Kesselheim AS (2018). "A Comparison of Response Patterns for Progression-Free Survival and Overall Survival Following Treatment for Cancer With PD-1 Inhibitors: A Meta-analysis of Correlation and Differences in Effect Sizes". JAMA Netw Open. 1 (2): e180416. doi:10.1001/jamanetworkopen.2018.0416. PMC 6324401. PMID 30646078.
  33. ↑ Shyr Y, Horn L, Berry L (2015). "Are We Making Progress in Lung Cancer Using Progression-Free Survival as a Surrogate End Point?". JAMA Oncol. 1 (2): 202–3. doi:10.1001/jamaoncol.2015.0407. PMID 26181024.
  34. ↑ 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.
  35. ↑ 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.
  36. ↑ 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.
  37. ↑ 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)
  38. ↑ 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.
  39. ↑ 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.
  40. ↑ 40.0 40.1 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)
  41. ↑ 41.0 41.1 Sheridan SL, Pignone M (2002). "Numeracy and the medical student's ability to interpret data". Eff Clin Pract. 5 (1): 35–40. PMID 11874195.
  42. ↑ 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)
  43. ↑ 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.
  44. ↑ 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.
  45. ↑ 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.
  46. ↑ 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).
  47. ↑ Kim DH, Shi SM, Carroll D, Najafzadeh M, Wei LJ (2021). "Restricted mean survival time versus conventional measures for treatment decision-making". J Am Geriatr Soc. 69 (8): 2282–2289. doi:10.1111/jgs.17195. PMC 8373742 Check |pmc= value (help). PMID 33901300 Check |pmid= value (help).
  48. ↑ 48.0 48.1 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.
  49. ↑ 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.
  50. ↑ 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.
  51. ↑ 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.
  52. ↑ Zikmund-Fisher BJ, Ubel PA, Smith DM, Derry HA, McClure JB, Stark A; et al. (2008). "Communicating side effect risks in a tamoxifen prophylaxis decision aid: the debiasing influence of pictographs". Patient Educ Couns. 73 (2): 209–14. doi:10.1016/j.pec.2008.05.010. PMC 2649664. PMID 18602242.
  53. ↑ Scalia P, Schubbe DC, Lu ES, Durand MA, Frascara J, Noel G; et al. (2021). "Comparing the impact of an icon array versus a bar graph on preference and understanding of risk information: Results from an online, randomized study". PLoS One. 16 (7): e0253644. doi:10.1371/journal.pone.0253644. PMC 8301663 Check |pmc= value (help). PMID 34297713 Check |pmid= value (help).
  54. ↑ 54.0 54.1 Schapira MM, Nattinger AB, McAuliffe TL (2006). "The influence of graphic format on breast cancer risk communication". J Health Commun. 11 (6): 569–82. doi:10.1080/10810730600829916. PMID 16950729.
  55. ↑ McCaffery KJ, Dixon A, Hayen A, Jansen J, Smith S, Simpson JM (2012). "The influence of graphic display format on the interpretations of quantitative risk information among adults with lower education and literacy: a randomized experimental study". Med Decis Making. 32 (4): 532–44. doi:10.1177/0272989X11424926. PMID 22074912.
  56. ↑ 56.0 56.1 Zikmund-Fisher BJ, Witteman HO, Dickson M, Fuhrel-Forbis A, Kahn VC, Exe NL; et al. (2014). "Blocks, ovals, or people? Icon type affects risk perceptions and recall of pictographs". Med Decis Making. 34 (4): 443–53. doi:10.1177/0272989X13511706. PMC 3991751. PMID 24246564.
  57. ↑ Kreuzmair C, Siegrist M, Keller C (2016). "Does Iconicity in Pictographs Matter? The Influence of Iconicity and Numeracy on Information Processing, Decision Making, and Liking in an Eye-Tracking Study". Risk Anal. doi:10.1111/risa.12623. PMID 27089046.
  58. ↑ Zikmund-Fisher BJ, Witteman HO, Fuhrel-Forbis A, Exe NL, Kahn VC, Dickson M (2012). "Animated graphics for comparing two risks: a cautionary tale". J Med Internet Res. 14 (4): e106. doi:10.2196/jmir.2030. PMC 3409597. PMID 22832208.
  59. ↑ Zikmund-Fisher BJ, Fagerlin A, Ubel PA (2010). "A demonstration of less can be more in risk graphics". Med Decis Making. 30 (6): 661–71. doi:10.1177/0272989X10364244. PMC 3576697. PMID 20375419.
  60. ↑ Schwartz LM, Woloshin S, Welch HG (2009). "Using a drug facts box to communicate drug benefits and harms: two randomized trials". Ann Intern Med. 150 (8): 516–27. PMID 19221371.
  61. ↑ Puhan MA, Steurer J, Bachmann LM, ter Riet G (2005). "A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates". Ann. Intern. Med. 143 (3): 184–9. PMID 16061916.
  62. ↑ 62.0 62.1 Poses RM; et al. (1995). "You can lead a horse to water--improving physicians' knowledge of probabilities may not affect their decisions". Medical Decision Making. 15: 65–75. PMID 7898300.


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