1122
Letters to the
Editors
MODELS, DATA AND ANALYSES The “Variance and Dissent” section on obesity and mortality in the Journal of Clinical Epidemiology 1990: 43; 743-756, provoked me to the following comment. Dr Rimm in his Dissent [l] is right to request original data, whether stratified or not. A model cannot substitute for irregular data (as Wilcosky in his Response [2] admits the data are). A model just adds a measure of (un)certainty (CIs for estimates or p-values for tests) to what regularity already can be seen in the data at face value. If only irregularities are seen, a model is most likely to add random information. In his response, Dr Wilcosky does not give an adequate explanation of why he used the Cox model, and why he prefers it to mortality rates. In fact, I suspect he and his co-authors think it is about mortality rates, as they write in the Presentation [3]: “Cox regression (survivorship) models [J were used to estimate the associations between the obesity indices and the three mortality endpoints.” The Cox model is based on an entity different from mortality rate: it is based on survival time. This implies that even those who have dropped out, in other words are “censored”, before mortality follow-up (Dr Wilcosky does not tell us how many) contribute some information on survival time, and so do those “censored” at follow-up because they were not deceased (again, we do not know how many). Thus, the Cox model is based on more information than mortality rates alone. However, this means that to evaluate the data, insight is needed not only in crude age-specific mortality rates, but also in the age-specific rates of censoring before and at follow-up. It is a serious *Present address: Longitudinal Aging Study Amsterdam, Department of Psychiatry, Free University Faculty of Medicine, Valeriusplein 9, 1075 BG Amsterdam, The Netherlands.
omission of the authors that they do not state drop-out rates. There is another issue related to age-specific rates in this context which is best illustrated for those surviving the 8.4 years of follow-up in the present study (which we assume to be the majority of the 3563 + 1889 - 163 - 66 = 5223 or 96% non-deceased). The amount of information contributed by those censored differs for a person aged 30 and one aged 69. In 8.4 years, a male survivor aged 69 has outlived 35% of his contemporaries and thus shows some capacity for survival, whereas a male survivor aged 30 has outlived only 2% of his contemporaries [4], which does not give much information about his capacity for survival. Now does adjustment for age solve this problem? Not exactly, but perhaps in this case there is no better alternative. Or perhaps there is: wait until more subjects have contributed more information on survival time. Perhaps the data will then show more regularity. In this as well as in other respects, the Wilcosky et al. presentation is a premature one. DORLY J. H. DEEG* Tokyo Metropolitan Institute of Gerontology Department of Community Health Sakae -cho 35-2 Itabashi-ku Tokyo - 173 Japan
REFERENCES Rimm AA. A reveal-conceal test for manuscript review: its application in the obesity mortality study. J Clin Epidemiol 1990; 43: 753-754. Wilcosky T. Analysis of sparse data. J Clin Epidemiol 1990; 43: 755-756. Wilcosky T, Hyde J, Anderson JJB et al. Obesity and mortality in the Lipid Research Clinics Program Follow-up Study. J Clin Epidemiol 1990; 43: 743-752. U. S. Department of Commerce. Statistical Abstract of the United States 1989.
Responses RESPONSE TO DR DEEG Dr to Dr the
Deeg’s letter presents the opportunity correct two errors in our paper [l]. As Deeg indicated, we inadvertently omitted percentage for follow-up loss, which was
less than 0.5%. Therefore, censored observations in the Cox regression analysis essentially comprise only persons who were alive at the end of follow-up. The second error was
Letters to the
Editors
MODELS, DATA AND ANALYSES The “Variance and Dissent” section on obesity and mortality in the Journal of Clinical Epidemiology 1990: 43; 743-756, provoked me to the following comment. Dr Rimm in his Dissent [l] is right to request original data, whether stratified or not. A model cannot substitute for irregular data (as Wilcosky in his Response [2] admits the data are). A model just adds a measure of (un)certainty (CIs for estimates or p-values for tests) to what regularity already can be seen in the data at face value. If only irregularities are seen, a model is most likely to add random information. In his response, Dr Wilcosky does not give an adequate explanation of why he used the Cox model, and why he prefers it to mortality rates. In fact, I suspect he and his co-authors think it is about mortality rates, as they write in the Presentation [3]: “Cox regression (survivorship) models [J were used to estimate the associations between the obesity indices and the three mortality endpoints.” The Cox model is based on an entity different from mortality rate: it is based on survival time. This implies that even those who have dropped out, in other words are “censored”, before mortality follow-up (Dr Wilcosky does not tell us how many) contribute some information on survival time, and so do those “censored” at follow-up because they were not deceased (again, we do not know how many). Thus, the Cox model is based on more information than mortality rates alone. However, this means that to evaluate the data, insight is needed not only in crude age-specific mortality rates, but also in the age-specific rates of censoring before and at follow-up. It is a serious *Present address: Longitudinal Aging Study Amsterdam, Department of Psychiatry, Free University Faculty of Medicine, Valeriusplein 9, 1075 BG Amsterdam, The Netherlands.
omission of the authors that they do not state drop-out rates. There is another issue related to age-specific rates in this context which is best illustrated for those surviving the 8.4 years of follow-up in the present study (which we assume to be the majority of the 3563 + 1889 - 163 - 66 = 5223 or 96% non-deceased). The amount of information contributed by those censored differs for a person aged 30 and one aged 69. In 8.4 years, a male survivor aged 69 has outlived 35% of his contemporaries and thus shows some capacity for survival, whereas a male survivor aged 30 has outlived only 2% of his contemporaries [4], which does not give much information about his capacity for survival. Now does adjustment for age solve this problem? Not exactly, but perhaps in this case there is no better alternative. Or perhaps there is: wait until more subjects have contributed more information on survival time. Perhaps the data will then show more regularity. In this as well as in other respects, the Wilcosky et al. presentation is a premature one. DORLY J. H. DEEG* Tokyo Metropolitan Institute of Gerontology Department of Community Health Sakae -cho 35-2 Itabashi-ku Tokyo - 173 Japan
REFERENCES Rimm AA. A reveal-conceal test for manuscript review: its application in the obesity mortality study. J Clin Epidemiol 1990; 43: 753-754. Wilcosky T. Analysis of sparse data. J Clin Epidemiol 1990; 43: 755-756. Wilcosky T, Hyde J, Anderson JJB et al. Obesity and mortality in the Lipid Research Clinics Program Follow-up Study. J Clin Epidemiol 1990; 43: 743-752. U. S. Department of Commerce. Statistical Abstract of the United States 1989.
Responses RESPONSE TO DR DEEG Dr to Dr the
Deeg’s letter presents the opportunity correct two errors in our paper [l]. As Deeg indicated, we inadvertently omitted percentage for follow-up loss, which was
less than 0.5%. Therefore, censored observations in the Cox regression analysis essentially comprise only persons who were alive at the end of follow-up. The second error was
