Study of changes in the effect of marital status on cancer outcomes overlooks the way standard measures of association tend to be affected by the overall prevalence of an outcome
James Scanlan, James P. Scanlan, Attorney at Law
5 March 2012
There is a common tendency, particularly in discussion of inequalities in cancer outcomes, and even with respect to whether those inequalities are changing over time, to talk interchangeably in terms of differences in survival and differences in mortality. The distinction between the two, however, can be a crucial one. For reasons related to the shapes of normal distributions of factors associated with experiencing an outcome, as an outcome generally increases, relative difference in rates of experiencing the outcome tend to decrease, while relative differences in rates of failing to experience the outcome tend to increase.[2-6] Thus, solely for statistical reasons, improvements in cancer diagnosis and care, with attendant general increases in cancer survival rates, will tend to reduce relative differences in survival of advantaged and disadvantaged groups while increasing relative differences in the mortality of those groups. The patterns whereby relative differences in mortality and relative differences in survival tend to change in opposite directions are most evident when examined across age ranges, as shown, for example, in Tables 1 and 2 of reference 6 and throughout reference 7. In fact, it is the perception that the association between a factor and mortality varies across age ranges – arising from the observed greater relative differences in mortality among the young than the old, but without recognition that such a pattern is to be expected among the young because mortality is rarer among the young or that relative differences in survival tend to be greater among the old – that caused the authors to conduct separate analyses for those below age 70 and those aged 70 and above. But whether the association between a factor and an outcome in fact varies across age ranges is not established simply by different relative differences in mortality at different ages. In the title and several statements in the body of their article, Kravdal and Syse [1] suggest that they have studied changes over time in the effect of marital status on cancer survival in Norway between 1970 and 2007. But they then describe their results in terms of changes in excess mortality, finding that the excess mortality of never-married men compared with married men increased steadily during the period studied, particularly among the elderly. The authors studied differences in mortality in terms of odds ratios. Differences measured by odds ratios are the same whether one examines mortality or survival. But odds ratios tend also to be affected by changes in the overall prevalence of an outcome. Roughly, assuming the underlying distributions are normal, where survival is uncommon (less than 50% for both groups being compared), improvements in survival tend to reduce differences measured by odds ratios; where survival is already common (greater than 50% for both groups being compared) improvements in survival tend to increase differences measured by odds ratios; between these points, the distributionally-drive forces are more difficult to determine. See the introductory material in reference 8 (keeping in mind that patterns of change in absolute differences described there in detail are the opposite of the patterns of changes in differences measured by odds ratios.) Thus, the authors are mistaken in believing that it is unnecessary to analyze issues concerning the association of a factor with cancer mortality (or survival) separately by site. For survival rates can vary dramatically for different types of cancers. For some cancers survival rates are likely in ranges where in the case of further improvements, the above-described distributionally-driven forces will tend to increase differences measured by odds ratios; for other cancers the survival rates are in ranges where further increases will tend to decrease differences measured by odds ratios. So it is necessary to know the actual rates for each type of cancer to attempt to study the matter. None of this is to say that there was no change in the excess mortality (decreased survival) of the never married or even that in fact relative differences in mortality and relative differences in survival usually changed in opposite directions. The distributionally-driven patterns are only part of the story. The other part of the story, and that which is society’s actual concern, is whether the occurred a change in the relationships of the risk distributions of the two groups. It is possible that as a result of changes in the relationships of the risk distributions, both relative differences commonly changed in the same direction or the odds ratio commonly changed in a way contrary to that described above. In such cases we could cautiously infer that a meaningful change had occurred. And even when all measures change in accordance with the distributionally-driven forces, we can attempt to determine whether a change occurred by deriving from each relevant pair of rates the difference between the means of the underlying risk distributions.[9,10] Such approach, while imperfect in varied respects, can not only determine whether a change occurred but quantify the differences before and after the change in a way unaffected by changes in the general prevalence of an outcome. And it can be employed either to compare the size of the difference between the mortality/survival rates of the comparison groups at different points in time or to compare the size of the change each group experienced in its mortality/survival rate over time.[11,12] But to do any of these things one must have the actual rates of the groups being compared during each time period. Unfortunately, the authors did not provide those rates with the study. Further exploration of the issue must examine the actual rates with recognition of the distributionally-driven patterns described above. The authors provide a number of possible explanations for the perceived worsening of the comparative situation of the never married. None of these explanations is implausible. But it remains unknown whether such worsening in fact occurred. See reference 13 regarding similar issues raised in reference 13 to the Kravdal study. References: 1. Kravdal H, Syse A. Changes over time in the effect of marital status on cancer survival. BMC Public Health 2011;11:804 (doi:10.1186/1471-2458-804) 2. Scanlan JP. Can we actually measure health disparities? Chance 2006:19(2):47-51: http://www.jpscanlan.com/images/Can_We_Actually_Measure_Health_Disparities.pdf
3. Scanlan JP. Race and mortality. Society 2000;37(2):19-35: http://www.jpscanlan.com/images/Race_and_Mortality.pdf
5. Scanlan JP. The Misunderstood Relationship Between Declining Mortality and Increasing Racial and Socioeconomic Disparities in Mortality Rates, presented at the conference "Making a Difference: Is the Health Gap Widening?" sponsored by the Norwegian National Institute of Public Health, Oslo Norway, May 14, 2001: http://www.jpscanlan.com/images/Oslo_presentation.ppt 6. Morality and Survival page of jpscanlan.com: http://jpscanlan.com/mortalityandsurvival2.html 7. Life Tables Illustrations sub-page of Scanlan’s Rule page of jpscanlan.com: http://jpscanlan.com/scanlansrule/lifetableillustrations.html 8. Scanlan’s Rule page of jpscanlan.com: http://jpscanlan.com/scanlansrule.html 9. Scanlan JP. Measures of Health Inequalities that are Unaffected by the Prevalence of an Outcome, presented at the 16th Nordic Demographic Symposium, Helsinki, Finland, June 5-7, 2008:http://jpscanlan.com/images/Scanlan_JP_NDS_Presentation_2R.ppt 10. Solutions sub-page of Measuring Health Disparities page of jpscanlan.com: http://www.jpscanlan.com/measuringhealthdisp/solutions.html 11. Scanlan JP. Interpreting Differential Effects in Light of Fundamental Statistical Tendencies, presented at 2009 Joint Statistical Meetings of the American Statistical Association, International Biometric Society, Institute for Mathematical Statistics, and Canadian Statistical Society, Washington, DC, Aug. 1-6, 2009: http://www.jpscanlan.com/images/JSM_2009_ORAL.pdf 12. Subgroup Effects sub-page of Scanlan’s Rule page of jpscanlan.com: http://www.jpscanlan.com/scanlansrule/subgroupeffects.html 13. Scanlan JP. Studies of trends in the relationship of marital status to mortality must consider the implications of general changes in mortality. BMC Public Health Nov. 7, 2011 (responding to Berntsen KN. Trends in total and cause-specific mortality by marital status among elderly Norwegian men and women. BMC Public Health 2011; 11:537): http://www.biomedcentral.com/1471-2458/11/537/comments#608693
Study of changes in the effect of marital status on cancer outcomes overlooks the way standard measures of association tend to be affected by the overall prevalence of an outcome
5 March 2012
There is a common tendency, particularly in discussion of inequalities in cancer outcomes, and even with respect to whether those inequalities are changing over time, to talk interchangeably in terms of differences in survival and differences in mortality. The distinction between the two, however, can be a crucial one. For reasons related to the shapes of normal distributions of factors associated with experiencing an outcome, as an outcome generally increases, relative difference in rates of experiencing the outcome tend to decrease, while relative differences in rates of failing to experience the outcome tend to increase.[2-6] Thus, solely for statistical reasons, improvements in cancer diagnosis and care, with attendant general increases in cancer survival rates, will tend to reduce relative differences in survival of advantaged and disadvantaged groups while increasing relative differences in the mortality of those groups.
The patterns whereby relative differences in mortality and relative differences in survival tend to change in opposite directions are most evident when examined across age ranges, as shown, for example, in Tables 1 and 2 of reference 6 and throughout reference 7. In fact, it is the perception that the association between a factor and mortality varies across age ranges – arising from the observed greater relative differences in mortality among the young than the old, but without recognition that such a pattern is to be expected among the young because mortality is rarer among the young or that relative differences in survival tend to be greater among the old – that caused the authors to conduct separate analyses for those below age 70 and those aged 70 and above. But whether the association between a factor and an outcome in fact varies across age ranges is not established simply by different relative differences in mortality at different ages.
In the title and several statements in the body of their article, Kravdal and Syse [1] suggest that they have studied changes over time in the effect of marital status on cancer survival in Norway between 1970 and 2007. But they then describe their results in terms of changes in excess mortality, finding that the excess mortality of never-married men compared with married men increased steadily during the period studied, particularly among the elderly.
The authors studied differences in mortality in terms of odds ratios. Differences measured by odds ratios are the same whether one examines mortality or survival. But odds ratios tend also to be affected by changes in the overall prevalence of an outcome. Roughly, assuming the underlying distributions are normal, where survival is uncommon (less than 50% for both groups being compared), improvements in survival tend to reduce differences measured by odds ratios; where survival is already common (greater than 50% for both groups being compared) improvements in survival tend to increase differences measured by odds ratios; between these points, the distributionally-drive forces are more difficult to determine. See the introductory material in reference 8 (keeping in mind that patterns of change in absolute differences described there in detail are the opposite of the patterns of changes in differences measured by odds ratios.)
Thus, the authors are mistaken in believing that it is unnecessary to analyze issues concerning the association of a factor with cancer mortality (or survival) separately by site. For survival rates can vary dramatically for different types of cancers. For some cancers survival rates are likely in ranges where in the case of further improvements, the above-described distributionally-driven forces will tend to increase differences measured by odds ratios; for other cancers the survival rates are in ranges where further increases will tend to decrease differences measured by odds ratios. So it is necessary to know the actual rates for each type of cancer to attempt to study the matter.
None of this is to say that there was no change in the excess mortality (decreased survival) of the never married or even that in fact relative differences in mortality and relative differences in survival usually changed in opposite directions. The distributionally-driven patterns are only part of the story. The other part of the story, and that which is society’s actual concern, is whether the occurred a change in the relationships of the risk distributions of the two groups. It is possible that as a result of changes in the relationships of the risk distributions, both relative differences commonly changed in the same direction or the odds ratio commonly changed in a way contrary to that described above. In such cases we could cautiously infer that a meaningful change had occurred. And even when all measures change in accordance with the distributionally-driven forces, we can attempt to determine whether a change occurred by deriving from each relevant pair of rates the difference between the means of the underlying risk distributions.[9,10] Such approach, while imperfect in varied respects, can not only determine whether a change occurred but quantify the differences before and after the change in a way unaffected by changes in the general prevalence of an outcome. And it can be employed either to compare the size of the difference between the mortality/survival rates of the comparison groups at different points in time or to compare the size of the change each group experienced in its mortality/survival rate over time.[11,12] But to do any of these things one must have the actual rates of the groups being compared during each time period. Unfortunately, the authors did not provide those rates with the study. Further exploration of the issue must examine the actual rates with recognition of the distributionally-driven patterns described above.
The authors provide a number of possible explanations for the perceived worsening of the comparative situation of the never married. None of these explanations is implausible. But it remains unknown whether such worsening in fact occurred.
See reference 13 regarding similar issues raised in reference 13 to the Kravdal study.
References:
1. Kravdal H, Syse A. Changes over time in the effect of marital status on cancer survival. BMC Public Health 2011;11:804 (doi:10.1186/1471-2458-804)
2. Scanlan JP. Can we actually measure health disparities? Chance 2006:19(2):47-51:
http://www.jpscanlan.com/images/Can_We_Actually_Measure_Health_Disparities.pdf
3. Scanlan JP. Race and mortality. Society 2000;37(2):19-35: http://www.jpscanlan.com/images/Race_and_Mortality.pdf
4. Scanlan JP. Divining difference. Chance 1994;7(4):38-9,48: http://jpscanlan.com/images/Divining_Difference.pdf
5. Scanlan JP. The Misunderstood Relationship Between Declining Mortality and Increasing Racial and Socioeconomic Disparities in Mortality Rates, presented at the conference "Making a Difference: Is the Health Gap Widening?" sponsored by the Norwegian National Institute of Public Health, Oslo Norway, May 14, 2001: http://www.jpscanlan.com/images/Oslo_presentation.ppt
6. Morality and Survival page of jpscanlan.com: http://jpscanlan.com/mortalityandsurvival2.html
7. Life Tables Illustrations sub-page of Scanlan’s Rule page of jpscanlan.com: http://jpscanlan.com/scanlansrule/lifetableillustrations.html
8. Scanlan’s Rule page of jpscanlan.com: http://jpscanlan.com/scanlansrule.html
9. Scanlan JP. Measures of Health Inequalities that are Unaffected by the Prevalence of an Outcome, presented at the 16th Nordic Demographic Symposium, Helsinki, Finland, June 5-7, 2008:http://jpscanlan.com/images/Scanlan_JP_NDS_Presentation_2R.ppt
10. Solutions sub-page of Measuring Health Disparities page of jpscanlan.com: http://www.jpscanlan.com/measuringhealthdisp/solutions.html
11. Scanlan JP. Interpreting Differential Effects in Light of Fundamental Statistical Tendencies, presented at 2009 Joint Statistical Meetings of the American Statistical Association, International Biometric Society, Institute for Mathematical Statistics, and Canadian Statistical Society, Washington, DC, Aug. 1-6, 2009: http://www.jpscanlan.com/images/JSM_2009_ORAL.pdf
12. Subgroup Effects sub-page of Scanlan’s Rule page of jpscanlan.com: http://www.jpscanlan.com/scanlansrule/subgroupeffects.html
13. Scanlan JP. Studies of trends in the relationship of marital status to mortality must consider the implications of general changes in mortality. BMC Public Health Nov. 7, 2011 (responding to Berntsen KN. Trends in total and cause-specific mortality by marital status among elderly Norwegian men and women. BMC Public Health 2011; 11:537): http://www.biomedcentral.com/1471-2458/11/537/comments#608693
Competing interests
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