Appendix D
Technical Explanation of Statistical Method for Community Comparisons
As the number of female veterans responding to the survey (223) is small and represents only part of the total cohort of women on the nominal roll (484), ranges were calculated for the prevalence of conditions reported. The range can be interpreted as an approximate 95% confidence interval, assuming the respondents represent a random sample drawn from a total population of size 484. The range was calculated as the observed prevalence ±2 times the estimate of the standard error using a standard formula for the estimate of variance for a sample proportion p with n=223, N=484: variance (p) = (1-n/N) p (1-p) / (n-1), derived from the normal approximation to the binomial distribution and standard sampling theory. When the number of veterans reporting conditions was small (<5), 95% confidence intervals were calculated using standard exact methods implemented in the package StatXact_3, Version 3.1, 199740, with exact probabilities derived from the binomial distribution.
A different formula was used for calculating the ranges for conditions related to children and pregnancy since the population size was unknown. It would be difficult to accurately estimate the total number of pregnancies for the female veterans who did not respond to the survey or whose locations were not found. The standard formula for estimating the variance of a sample proportion from an infinite population p(1-p)/n for these conditions was used in this case. This probably leads to a slight overestimation of the range.
The range is provided to indicate that the observed prevalence is only an estimate of the true prevalence for the veteran cohort*. It should be stressed that the range only reflects the possible variation in the estimate due to the size of the sample. It does not reflect the sampling error which may be present due to the non-representativeness of the women who were contacted and responded relative to the total cohort of female veterans.
Ranges were also calculated for the expected numbers of cases of each condition since they are based on estimates of the community prevalence. Each range was calculated as ±2 times the estimate of the standard error and so corresponds to an approximate 95% confidence interval. The expected range is relatively small when the rate is estimated from national prevalence rates, but can be substantial if the estimate of the rate is based on a relatively small community sample.
Comparisons of the veterans with the general community are based on comparing the ranges rather than the reported and expected numbers. Overlapping intervals were interpreted as indicating that the difference in the point estimates may be due to variation by chance and nonoverlapping intervals as indicating differences that may be due to factors other than chance. It should be stressed that Vietnam service is only one of a number of possible factors contributing to the observed difference. Others include:
- the higher than expected number of single rather than married/de facto female Vietnam veterans in the sample;
- a healthy worker effect1 that is possibly still in evidence despite the elapsed time since entry into the services; or
- other relevant exposure since leaving Vietnam.
* Ranges were not provided for the responses in the male veterans report since the substantially larger size of the male veteran cohort and the much larger sampling fraction lead to more precise estimates of the prevalence.
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