D
Calculation of Expected Number of Deaths in the U.S. Air Force Ranch Hand Morbidity Study Cohort over the Next 10 Years

As noted in Chapters 2 and 5, the latest Air Force Health Study (AFHS) mortality update (Ketchum and Michalek, 2005) reported an elevated relative risk for all-cause mortality among all Ranch Hand veterans and a statistically significant increase in the risk of death from circulatory system diseases among veterans with the highest serum dioxin levels. If confirmed by further follow-up, these trends could have implications for the cohort and possibly for Vietnam veterans in general. This appendix presents a calculation of the expected number of deaths over the next 10 years among the participants of the morbidity study and the statistical power to detect excess relative risks.

CALCULATION OF THE EXPECTED NUMBER OF DEATHS

One possible future application of the AFHS data assets is to further investigate associations between cause-specific mortality, herbicide exposure, and information on the various risk factors and characteristics of participants obtained during the course of the study. To determine the usefulness of continuing a mortality follow-up—through, for example, the U.S. National Death Index (NDI)—it is useful to estimate the estimated number of deaths that would occur for a fixed follow-up period and the resulting statistical power to identify excess relative risks.

Brookmeyer and colleagues (1985) provide one statistical framework for this calculation based on standard survival methods, in which rates of the cause of death of interest as well as other censoring mechanisms are included (i.e., deaths from other causes, losses to follow-up). This calculation requires knowledge of age-specific rates as well as censoring mechanisms.



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Disposition of the Air Force Health Study D Calculation of Expected Number of Deaths in the U.S. Air Force Ranch Hand Morbidity Study Cohort over the Next 10 Years As noted in Chapters 2 and 5, the latest Air Force Health Study (AFHS) mortality update (Ketchum and Michalek, 2005) reported an elevated relative risk for all-cause mortality among all Ranch Hand veterans and a statistically significant increase in the risk of death from circulatory system diseases among veterans with the highest serum dioxin levels. If confirmed by further follow-up, these trends could have implications for the cohort and possibly for Vietnam veterans in general. This appendix presents a calculation of the expected number of deaths over the next 10 years among the participants of the morbidity study and the statistical power to detect excess relative risks. CALCULATION OF THE EXPECTED NUMBER OF DEATHS One possible future application of the AFHS data assets is to further investigate associations between cause-specific mortality, herbicide exposure, and information on the various risk factors and characteristics of participants obtained during the course of the study. To determine the usefulness of continuing a mortality follow-up—through, for example, the U.S. National Death Index (NDI)—it is useful to estimate the estimated number of deaths that would occur for a fixed follow-up period and the resulting statistical power to identify excess relative risks. Brookmeyer and colleagues (1985) provide one statistical framework for this calculation based on standard survival methods, in which rates of the cause of death of interest as well as other censoring mechanisms are included (i.e., deaths from other causes, losses to follow-up). This calculation requires knowledge of age-specific rates as well as censoring mechanisms.

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Disposition of the Air Force Health Study An alternative approach—which has sufficient accuracy to make a rough estimate of statistical power1—is to calculate the expected number of deaths in the cohort over a given period of follow-up. For the purpose of this exercise, the committee chose a 10-year follow-up beginning in 2005 and ending in 2015. Calculations were made for each AFHS subject who was alive on January 1, 2005, by making use of the U.S. life table (NCHS, 2004c) for men. Specifically, for each subject we multiplied the age-specific probabilities of surviving in each age interval across the length of follow-up, subtracting this probability from unity to obtain the cumulative probability of dying, and then summing over all subjects. In equation form—for each AFHS subject alive on January 1, 2005—if one designates pa as the probability of surviving through each 1-year age interval a, then the estimated probability of dying over a specified period of follow-up is: and e, the estimated number of deaths in the cohort, is the sum of each subject’s contribution where agealive was the age of the subject on January 1, 2005, and agefollowup is the age of each subject in 2015. Calculations were truncated at age 99. AFHS staff provided the committee with a denominalized file containing the relevant information to carry out this calculation (AFHS, 2005). The data comprised a randomly assigned ID number; an indicator for whether the subject was a Ranch Hand or comparison veteran; the year the subject was last known to be alive; age at that year; and an indicator of whether the subject participated in one or more cycle exams (compliant in the study’s terminology) or not (noncompliant). The calculations, which were performed on data for compliant subjects only, yield estimates for deaths from all causes combined. To partition these estimated deaths according to specific causes, the percentages of deaths from selected causes for ages 60–89 years (in 5-year intervals) were extracted from National Center for Health Statistics data (NCHS, 2004a) and averaged across the intervals. This exercise yielded the following estimates for the proportion of deaths for some of the most common causes of death: Malignant neoplasms: 33.9 percent of all deaths Diseases of the heart: 23.6 percent of all deaths Chronic lower respiratory diseases: 7.5 percent of all deaths 1   Statistical power is the probability that a statistical test will produce a significant difference at a given significance level.

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Disposition of the Air Force Health Study To estimate the statistical power for rarer health outcomes, the committee also carried out calculations for hypothetical endpoints that have proportions of 5 percent (for example, influenza) and 3 percent (diabetes mellitus) of total deaths. Standard formulas were used to calculate the power of observing specific relative risks (= observed number of events/expected number of events) with these estimated values. RESULTS Table D-1 shows the number of compliant subjects presently in the Ranch Hand and comparison cohorts and how those numbers would change over a 10-year (2005–2015) follow-up period if mortality followed the same pattern as the general U.S. population for the corresponding age range. Estimates of mortality were made using data from the U.S. 2002 life tables (NCHS, 2004c). The figures shown in Table D-2 indicate that there is at present (2005) sufficient statistical power to detect a relatively modest excess risk for all-cause mortality. Table D-3 extends this analysis to other causes of death, using the power to detect a relative risk of 1.5 as the benchmark and the expected percentage of cause-specific mortality listed above. The table shows that although there is sufficient power to detect a relative risk of 1.5 for malignant neoplasms and diseases of the heart, there is insufficient power to detect this excess risk for less common ailments, and that it is not possible to detect lower relative risks. Tables D-4 through D-9 present rough estimates of the estimated numbers of deaths and statistical power to detect relative risks of 1.2, 1.5, and 2.0 for the hypothetical 10-year (2005–2015) mortality follow-up of the compliant members of the AFHS cohorts. All-cause mortality and selected causes of death are considered. The estimates suggest that a 10-year follow-up makes it possible to confidently detect small increases in the relative risk of health outcomes common to aging males and markedly increases the power of the study to detect larger risk increases for relatively rare outcomes. A follow-up that included the much larger pool of noncompliant potential comparison subjects (9,500 persons in total2) would greatly increase the power of the calculations to detect differences in mortality rates between AFHS cohort veterans and the general population for less common health outcomes. However, it would do so at the expense of the detailed information on individuals that would allow in-depth empirical examination of the possible determinants of the differences. It is relatively inexpensive to perform a periodic mortality update. Assuming that a National Death Index search is performed on the entire compliant cohort known to be alive at the time of the last update and that cause of death codes are 2   This figure is the approximate number of compliant and noncompliant subjects alive on January 1, 2005, according to data provided by AFHS.

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Disposition of the Air Force Health Study TABLE D-1 Summary Statistics for the Compliant Cohorts and Estimated Numbers of Deaths from 2005 until 2015   Ranch Hand Cohort Comparison Cohort Number of subjects who died before 2005 199 258 Number of subjects alive in 2005 998 1,597 Mean age (std. dev.) of subject alive in 2005 64.8 (7.2) 64.4 (7.1) Estimated number of deaths 2005–2015 281 436 Estimated percent of deaths 2005–2015 28% 27% Estimated number of subjects alive in 2015 717 1,161 NOTE: Numbers may not add up because of independent rounding. TABLE D-2 Power to Detect Various Relative Risks for All-Cause Mortality, if There Is No Further Follow-Up* Relative Risk Ranch Hand Cohort Comparison Cohort 1.2 85.4 100 1.5 100 100 2.0 100 100 *Based on the number of subjects who died before 2005. requested for subjects found to be deceased, it would cost ~$650 to obtain the data from NCHS exclusive of the labor to generate the request.3 A survey of the entire compliant and non-compliant cohort would cost ~$2,100. To make meaningful use of these data, they would need to be reviewed and coded by a nosologist as part of whatever study was planned. In sum, rough estimates suggest that the AFHS cohort is big enough to detect moderate to large associations in future mortality analyses of health outcomes of potential interest to Vietnam veterans, using a well-established and relatively inexpensive research approach. 3   This estimate is based on a charge of $.21 per subject per year searched × 2,600 subjects, plus a service charge of $100 for a repeat user of the NDI (NCHS, 2004b).

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Disposition of the Air Force Health Study TABLE D-3 Power to Detect Relative Risks of 1.5 by Cause of Death, if There Is No Further Follow-Up*   Ranch Hand Cohort Comparison Cohort Malignant neoplasms 98.0 99.5 Diseases of the heart 92.5 96.9 Chronic lower respiratory diseases 54.0 63.3 A disease that contributes 5% to the total number of deaths 41.4 49.0 A disease that contributes 3% to the total number of deaths 29.5 34.7 *Based on the number of subjects who died before 2005. TABLE D-4 All-Cause Mortality: Estimated Number of Deaths and Power to Detect Various Relative Risks with an Additional 10 Years of Follow-Up   Ranch Hand Cohort Comparison Cohort Estimated* number of deaths in cohort by 2015 480 694 Power to detect relative risks of:     1.2 99.5 100 1.5 100 100 2.0 100 100 *The number of deaths observed before 2005 plus estimated number of deaths between 2005–2015. TABLE D-5 Malignant Neoplasms: Estimated Number of Deaths and Power to Detect Various Relative Risks with an Additional 10 Years of Follow-Up   Ranch Hand Cohort Comparison Cohort Estimated* number of deaths in cohort by 2015 163 271 Power to detect relative risks of:     1.2 78.7 93.4 1.5 100 100 2.0 100 100 *The estimated number of deaths from ailment before 2005 plus estimated number of deaths between 2005–2015.

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Disposition of the Air Force Health Study TABLE D-6 Diseases of the Heart: Estimated Number of Deaths and Power to Detect Various Relative Risks with an Additional 10 Years of Follow-Up   Ranch Hand Cohort Comparison Cohort Estimated* number of deaths in cohort by 2015 113 164 Power to detect relative risks of:     1.2 65.1 79.0 1.5 99.1 100 2.0 100 100 *The estimated number of deaths from ailment before 2005 plus estimated number of deaths between 2005–2015. TABLE D-7 Chronic Lower Respiratory Diseases: Estimated Number of Deaths and Power to Detect Various Relative Risks with an Additional 10 Years of Follow-Up   Ranch Hand Cohort Comparison Cohort Estimated* number of deaths in cohort by 2015 36 52 Power to detect relative risks of:     1.2 31.0 39.6 1.5 85.5 94.5 2.0 100 100 *The estimated number of deaths from ailment before 2005 plus estimated number of deaths between 2005–2015. TABLE D-8 A Disease That Contributes 5 Percent to the Total Number of Deaths: Estimated Number of Deaths and Power to Detect Various Relative Risks with an Additional 10 Years of Follow-Up   Ranch Hand Cohort Comparison Cohort Estimated* number of deaths in cohort by 2015 24 35 Power to detect relative risks of:     1.2 24.1 30.5 1.5 71.3 83.6 2.0 99.2 99.9 *The estimated number of deaths from ailment before 2005 plus estimated number of deaths between 2005–2015.

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Disposition of the Air Force Health Study TABLE D-9 A Disease That Contributes 3 Percent to the Total Number of Deaths: Estimated Number of Deaths and Power to Detect Various Relative Risks with an Additional 10 Years of Follow-Up   Ranch Hand Cohort Comparison Cohort Estimated* number of deaths in cohort by 2015 15 21 Power to detect relative risks of:     1.2 18.4 22.2 1.5 54.0 66.3 2.0 94.2 98.5 *The estimated number of deaths from ailment before 2005 plus estimated number of deaths between 2005–2015. REFERENCES AFHS (Air Force Health Study). 2005. Microsoft Excel file (04-12-05—IOM—Part 1—Q1.xls) provided in response to committee request. Brooks AFB, TX. Brookmeyer R, Day N, Pompe-Kirn V. 1985. Assessing the impact of additional follow-up in cohort studies. American Journal of Epidemiology 121(4):611–619. Ketchum NS, Michalek JE. 2005. Postservice mortality of Air Force veterans occupationally exposed to herbicides during the Vietnam War: 20-year follow-up results. Military Medicine 170(5): 406–413. NCHS (National Center for Health Statistics). 2004a. Deaths, Percent of Total Deaths, and Death Rates for the 15 Leading Causes of Death in 5-Year Age Groups, by Race and Sex: United States, 2001. [Online]. Available: http://www.cdc.gov/nchs/data/dvs/LCWK1_2001.pdf [accessed October 11, 2005]. NCHS. 2004b. National Death Index User Fees. Effective October 1, 2004. [Online]. Available: www.cdc.gov/nchs/r&d/ndi/Users_Fees_Worksheet.pdf [accessed October 11, 2005]. NCHS. 2004c. United States Life Tables, 2002. [Online]. Available: http://www.cdc.gov/nchs/data/dvs/life2002.pdf [accessed October 11, 2005].