Popham, Fran

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Letter to the Editor Re: Lies, Damned Lies, and Health Inequality Measurements. Understanding the Value Judgments. Frank Popham MRC/CSO Social and Public Health Sciences Unit, University of Glasgow, 200 Renfield Street, Glasgow, UK, G2 3QB.  frank.popham@glasgow.ac.uk +44(0)141 353 7500 Conflict of interest None Funding FP’s post is funded by the Medical Research Council, UK and Chief Scientist Office, Scotland  (MC_UU_12017/7). These are the author’s views only and not those of any funder.    To the editor:  In their interesting paper Kjellsson and colleagues suggest that relative measures of health inequality for bounded variables may depend on whether the probability of success (attainment) or failure (shortfall) is studied. Thus they argue there is a temptation for researchers studying health inequality trends to select either relative success or relative failure as their relative measure; whichever is more favourable to their position [1].   However, it is worth emphasising that a frequently used relative measure, the odds ratio, like measures of absolute difference, is symmetrical [2, 3]. It does not matter if attainment or shortfall is studied; the odds ratio for one will be the reciprocal of the other, so the trend will be the same whether attainment or shortfall is studied. To illustrate let us take their example of life expectancy, where attainment was life expectancy and shortfall was lost life expectancy (100 years -life expectancy). The table compares their group B to A under their various scenarios: an initial situation and various levels of change in attainment and shortfall to achieve an average life expectancy increase of 25 years.  As the authors show, the risk ratios for attainment and shortfall under the various scenarios show a different change in inequality from the initial position.  Because life expectancy and short fall life expectancy in group A and B in the change scenarios are mirror opposites these risk ratios are reciprocal, this is not always the case as shown by the initial scenario. The odds ratio on the other hand gives the same result whether attainment or shortfall is studied.  Comparing relative trends using odds ratios may be problematic for many other reasons such as the odds ratio only equating to the relative risk when studying a rare event and the non-collapsibility of odds ratios [2, 3] but the trend will be the same whether the outcome is studied as a failure or success. Frank Popham   1 Kjellsson G, Gerdtham U-G, Petrie D. Lies, Damned Lies, and Health Inequality Measurements: Understanding the Value Judgments. Epidemiology 2015; 015;26:673-80 2 Pang M, Kaufman JS, Platt RW. Studying noncollapsibility of the odds ratio with marginal structural and logistic regression models. Stat Methods Med Res 2013; doi:10.1177/0962280213505804 3 Cummings P. The relative merits of risk ratios and odds ratios. Arch Pediatr Adolesc Med 2009;163:438-45.    Table. Odds ratios and risk ratios for Kjellsson and colleagues’ four life expectancy scenarios studied as attainment and shortfall. Shortfall is presented as the inverse for ease of comparison.  Authors’ Scenarios OR attainment 1 / OR shortfall RR attainment 1/ RR shortfall Initial 1.71 1.71 1.5 1.14 Red / Yellow (same absolute increase) 1.49 1.49 1.22 1.22 Blue (same proportional increase in attainment) 2.25 2.25 1.5 1.5 Green (same proportional increase in shortfall) 1.31 1.31 1.14 1.14    

Re: Lies, damned lies, and health inequality measurements: understanding the value judgments

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Letter to the Editor 
Re: Lies, Damned Lies, and Health Inequality Measurements. Understanding the Value Judgments. 
Frank Popham 
MRC/CSO Social and Public Health Sciences Unit, University of Glasgow, 200 Renfield Street, 
Glasgow, UK, G2 3QB.  
frank.popham@glasgow.ac.uk 
+44(0)141 353 7500 
Conflict of interest 
None 
Funding 
FP’s post is funded by the Medical Research Council, UK and Chief Scientist Office, Scotland  
(MC_UU_12017/7). These are the author’s views only and not those of any funder. 
  
 To the editor:  
In their interesting paper Kjellsson and colleagues suggest that relative measures of health inequality 
for bounded variables may depend on whether the probability of success (attainment) or failure 
(shortfall) is studied. Thus they argue there is a temptation for researchers studying health inequality 
trends to select either relative success or relative failure as their relative measure; whichever is 
more favourable to their position [1].   However, it is worth emphasising that a frequently used 
relative measure, the odds ratio, like measures of absolute difference, is symmetrical [2, 3]. It does 
not matter if attainment or shortfall is studied; the odds ratio for one will be the reciprocal of the 
other, so the trend will be the same whether attainment or shortfall is studied. To illustrate let us 
take their example of life expectancy, where attainment was life expectancy and shortfall was lost 
life expectancy (100 years -life expectancy). The table compares their group B to A under their 
various scenarios: an initial situation and various levels of change in attainment and shortfall to 
achieve an average life expectancy increase of 25 years.  As the authors show, the risk ratios for 
attainment and shortfall under the various scenarios show a different change in inequality from the 
initial position.  Because life expectancy and short fall life expectancy in group A and B in the change 
scenarios are mirror opposites these risk ratios are reciprocal, this is not always the case as shown 
by the initial scenario. The odds ratio on the other hand gives the same result whether attainment or 
shortfall is studied.  Comparing relative trends using odds ratios may be problematic for many other 
reasons such as the odds ratio only equating to the relative risk when studying a rare event and the 
non-collapsibility of odds ratios [2, 3] but the trend will be the same whether the outcome is studied 
as a failure or success. 
Frank Popham  
 
1 Kjellsson G, Gerdtham U-G, Petrie D. Lies, Damned Lies, and Health Inequality 
Measurements: Understanding the Value Judgments. Epidemiology 2015; 015;26:673-80 
2 Pang M, Kaufman JS, Platt RW. Studying noncollapsibility of the odds ratio with marginal 
structural and logistic regression models. Stat Methods Med Res 2013; 
doi:10.1177/0962280213505804 
3 Cummings P. The relative merits of risk ratios and odds ratios. Arch Pediatr Adolesc Med 
2009;163:438-45. 
  
 Table. Odds ratios and risk ratios for Kjellsson and colleagues’ four life expectancy scenarios studied 
as attainment and shortfall. Shortfall is presented as the inverse for ease of comparison.  
Authors’ 
Scenarios 
OR attainment 1 / OR shortfall RR attainment 1/ RR shortfall 
Initial 1.71 1.71 1.5 1.14 
Red / Yellow 
(same absolute 
increase) 
1.49 1.49 1.22 1.22 
Blue (same 
proportional 
increase in 
attainment) 
2.25 2.25 1.5 1.5 
Green (same 
proportional 
increase in 
shortfall) 
1.31 1.31 1.14 1.14 
 
 
 


Frank Popham

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http://dx.doi.org/10.1097/EDE.0000000000000440

Re: Lies, damned lies, and health inequality measurements: understanding the value judgments

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