A model-based estimate of the mean incubation period for AIDS in homosexual men.

Because of the difficulty in identifying the date of exposure to type 1 of the human immunodeficiency virus (HIV-1) infection in persons other than transfusion recipients, studies of the incubation periods for acquired immunodeficiency syndrome (AIDS) have been limited. When data from a cohort of 84 homosexual and bisexual men that provided the information to determine the years of conversion of sera infected with HIV-1 were analyzed, a model for the proportion likely to develop AIDS and the incubation period for AIDS in homosexual men could be derived. The maximum likelihood estimate for the proportion of infected homosexual men developing AIDS is 0.99 (90% confidence interval ranging from 0.38 to 1). Furthermore, the maximum likelihood estimate for the mean incubation period for AIDS in homosexual men is 7.8 years (90% confidence interval ranging from 4.2 years to 15.0 years), which is close to the estimate of 8.2 years for adults developing transfusion-associated AIDS.

Amantadine prophylaxis during an institutional outbreak of type A (H1N1) influenza.

In January 1984, an outbreak of influenza caused by A/Victoria/7/83-like virus, a new H1N1 variant, occurred in an institution for mentally handicapped children and adults. During the first 18 days of the outbreak, 35 (81%) of 43 residents in two housing modules became ill, nearly all of whom had received influenza vaccine the previous autumn. Amantadine hydrochloride prophylaxis was initiated in two other housing modules and was continued for 28 days. While factors influencing the risk of introduction and secondary spread of influenza virus were comparable in all four modules, only ten (16%) of 63 residents who received amantadine were infected, only one of whom became symptomatic. Most side effects associated with amantadine were mild, but residents with active, preexisting major-motor seizure disorders demonstrated an increase in seizure activity compared with the previous eight-month period; those who took the maximum daily dose of amantadine hydrochloride (200 mg) and those who were also taking anticonvulsants other than phenobarbital were at highest risk.

The roles of vaccination and amantadine prophylaxis in controlling an outbreak of influenza A (H3N2) in a nursing home.

An outbreak caused by influenza A/Philippines/2/82 (H3N2)-like viruses occurred in a partially vaccinated nursing home population in January 1985. During the first six days of the outbreak, 14 (25%) of 55 residents developed influenzalike illness. The risk of illness was most strongly associated with undetectable levels of antibody against the epidemic strain, with unvaccinated case-patients having more severe illnesses and a higher rate of hospitalization than vaccinated case-patients (5/8 vs 0/6). During the period of amantadine hydrochloride prophylaxis (100 mg/d) from days 7 to 35, only two (5%) of the remaining 41 residents became ill, even though 11 (27%) had no detectable antibody. Serum amantadine levels obtained on day 35 ranged from 117 to 737 ng/mL (mean 309 ng/mL), similar to therapeutic levels documented in younger adults who have taken the standard regimen of 200 mg/d; there were few clinically significant side effects. These findings illustrate the benefits of influenza vaccination and support the use of amantadine hydrochloride at a dosage of 100 mg daily for outbreak control among elderly persons.

Interval estimation of the attributable risk in case-control studies with matched pairs.

OBJECTIVE: The attributable risk (AR), which represents the proportion of cases who can be preventable when we completely eliminate a risk factor in a population, is the most commonly used epidemiological index to assess the impact of controlling a selected risk factor on community health. The goal of this paper is to develop and search for good interval estimators of the AR for case-control studies with matched pairs. METHODS: This paper considers five asymptotic interval estimators of the AR, including the interval estimator using Wald's statistic suggested elsewhere, the two interval estimators using the logarithmic transformations: log(x) and log(1-x), the interval estimator using the logit transformation log(x/(1-x)), and the interval estimator derived from a simple quadratic equation developed in this paper. This paper compares the finite sample performance of these five interval estimators by calculation of their coverage probability and average length in a variety of situations. RESULTS: This paper demonstrates that the interval estimator derived from the quadratic equation proposed here can not only consistently perform well with respect to the coverage probability, but also be more efficient than the interval estimator using Wald's statistic in almost all the situations considered here. This paper notes that although the interval estimator using the logarithmic transformation log(1-x) may also perform well with respect to the coverage probability, using this estimator is likely to be less efficient than the interval estimator using Wald's statistic. Finally, this paper notes that when both the underlying odds ratio (OR) and the prevalence of exposure (PE) in the case group are not large (OR < or =2 and PE < or =0.10), the application of the two interval estimators using the transformations log(x) and log(x/(1-x)) can be misleading. However, when both the underlying OR and PE in the case group are large (OR > or =4 and PE > or =0.50), the interval estimator using the logit transformation can actually outperform all the other estimators considered here in terms of efficiency. CONCLUSIONS: When there is no prior knowledge of the possible range for the underlying OR and PE, the interval estimator derived from the quadratic equation developed here for general use is recommended. When it is known that both the OR and PE in the case group are large (OR > or =4 and PE > or =0.50), it is recommended that the interval estimator using the logit transformation is used.

An application of the empirical Bayes approach to directly adjusted rates: a note on suicide mapping in California.

A simple, reliable, and comparable measure for suicide mapping and other health problems is needed. Because standardized mortality ratios (SMRs) may not indicate the relative meaning of their magnitudes when compared with one another, and statistical significance levels of tests for SMRs overlook the areas that have small populations, neither of these approaches provides a satisfactory index. The results using directly adjusted rates can be ordered directly according to their magnitudes. However, because of the lack of reliable estimates of local age-specific rates, the usefulness of directly adjusted rates in mapping suicide is also limited. To extend the usefulness of directly adjusted rates, an empirical Bayes approach whereby information from other areas is borrowed to improve the precision of the estimates of local age-specific rates in calculating directly adjusted rates--especially in the areas with small population sizes--is proposed. When an empirical Bayes approach was applied to the 1983 suicide data for California counties, a more reasonable conclusion than could be obtained by using directly adjusted rates was reached.

Estimation of sample sizes in case-control studies with multiple controls per case: dichotomous data.

In planning case-control studies with matched sets, the calculation of exact sample sizes is difficult, because this calculation depends on some nuisance parameters that are usually unknown in practice. Using the Pitman efficiency of Miettinen's test relative to McNemar's test, Schlesselman and Stolley (Case-control studies: design, conduct, analysis. Oxford: Oxford University Press, 1982:144-70) derived an approximate sample size formula which requires the assumption that the difference in exposure rates between cases and controls is small. Furthermore, on the basis of an assumption similar to that used in Schlesselman and Stolley's approach, Taylor (Stat Med 1986;5:29-36) proposed another approximation formula. In this paper, an alternative and explicit formula that does not require the exposure difference to be small between case and control groups has been derived. Monte Carlo studies are given for comparing the accuracy of these three procedures. The results indicate that when odds ratios of exposure between cases and controls are small (less than or equal to 4) and there is more than one matched control per case, the formula derived in this paper seems to be the best. When odds ratios are large (greater than or equal to 5), however, Taylor's more conservative estimate is recommended, unless the exposure prevalence in the general population is large (0.9).

A note on the effect of the intraclass correlation in the multiple reading procedure with a unanimity rule.

The use of multiple reading procedures to improve the performance of a diagnostic test occurs often in practice. Evaluation of the utility of multiple reading procedures, however, usually ignores the effect of the intraclass correlation. This paper provides a quantitative assessment of this effect in the multiple reading procedure with a unanimity rule with respect to sensitivity, specificity, positive and negative predictive values. We have found that when the disease prevalence is rare or moderate (less than or equal to 0.20), use of the multiple reading procedure with a unanimity rule is effective in increasing the positive predictive value of a single reading procedure for the situation in which the variation of responses among different subjects and the intraclass correlation among repeated tests are small. This is, however, not true for the situation in which the disease is rare and the variation of responses among different subjects is large, even when the intraclass correlation is small or 0. Furthermore, when the disease is rare and the variation of responses among subjects is small, a small or moderate intraclass correlation can substantially decrease the positive predictive value that one calculates under the assumption that the intraclass correlation is equal to 0. In general, when the disease is rare or moderate (less than or equal to 0.20), the intraclass correlation between repeated tests and the variation of responses among subjects have little effect on the negative predictive value.

Sample size for the exact conditional test under inverse sampling.

Inverse sampling is a sampling design in which one continues sampling subjects until one obtains a predetermined number of index subjects. This paper derives a procedure for calculation of the minimum required number of index subjects on the basis of the exact conditional test under inverse sampling. This paper studies quantitatively the effect on power calculations of the number of index subjects. To facilitate use of inverse sampling in study designs, this paper further provides a table that summarizes, in a variety of situations, the minimum required number of index subjects for powers equal to 0.90 and 0.80 at 0.05-level. It also includes a discussion on use of the approximation sample size formula derived on the basis of a variance-stabilizing transformation and large sample theory.

Sample size determination for repeated measurements in bioequivalence test.

When the measurement of outcome is unreliable or the cost of obtaining an additional subject is relatively high compared to the cost of obtaining an additional measurement from the same subject, it may be desirable to consider taking more than one measurement per subject to increase power or to minimize the cost in a clinical trial. When each subject in two comparison groups has a fixed number of repeated measurements, this paper develops an asymptotic procedure to calculate the number of subjects per group required to achieve a given power for an a-level bioequivalence test. Furthermore, Monte Carlo simulation is used to evaluate the accuracy of the approximate sample size calculation procedure and a brief discussion on how to determine the optimal number of repeated measurements is included.

Interval estimation of the risk ratio between a secondary infection, given a primary infection, and the primary infection.

This paper discusses interval estimation of the risk ratio (RR) between a secondary infection, given a primary infection, and the primary infection. Three asymptotic closed-form interval estimators are developed using Wald's test statistic, the logarithmic transformation, and Fieller's theorem. The performance of these interval estimators is compared with respect to the coverage probability and the expected length of the resulting confidence intervals. When the underlying probability of a primary infection is high (say, 0.80), all three estimators perform reasonably well. In fact, in this case, they are all essentially equivalent when the number of subjects n > or = 100. When the probability of a primary infection is small (say, 0.20) or moderate (say, 0.30 to 0.50), the interval estimator using the logarithmic transformation outperforms the other two estimators when n < or = 100. In fact, the coverage probability of the former estimator is consistently greater than or equal to the desired confidence level in all the situations considered in this paper and hence is recommended for general use.

The performance of the O'Brien-Fleming multiple testing procedure in the presence of intraclass correlation.

Assuming that all subject responses were independent, O'Brien and Fleming (1979, Biometrics 35, 549-556) proposed a simple and useful multiple testing procedure for clinical trials for comparing two treatments with dichotomous data. Differences in the methods of evaluating subject responses at each evaluation time, however, may induce an intraclass correlation among these responses used in calculating the O'Brien-Fleming multiple testing procedure. On the basis of Monte Carlo simulations, we note that even a small intraclass correlation among subject responses in the same analysis can substantially inflate the Type I error of the O'Brien-Fleming multiple testing procedure. Furthermore, this inflation generally increases as either the number of analyses or the underlying response probability increases. We also have demonstrated that if we were able to maintain a uniform medical test procedure between the two treatments for each analysis, the actual Type I error of the O'Brien-Fleming multiple testing procedure may conversely become conservative.

Confidence limits for the population prevalence rate based on the negative binomial distribution.

This paper shows that the extension of the simple procedure of George and Elston in calculation of confidence limits for the underlying prevalence rate to accommodate any finite number of cases in inverse sampling is straightforward. To appreciate the fact that the length of the confidence interval calculated on the basis of the first single case may be too wide for general utility, I include a quantiative discussion on the effect due to an increase in the number of cases requested in the sample on the expected length of confidence intervals. To facilitate further the application of the results presented in this paper, I present a table that summarizes in a variety of situations the minimum required number of cases for the ratio of the expected length of a confidence interval relative to the underlying prevalence rate to be less than or equal to a given value. I also include a discussion on the relation between Clemans's confidence limits on the expected number of trials before the failure of a given device and those presented here.

Sample size determination for case-control studies: the influence of the joint distribution of exposure and confounder.

In case-control studies, the results about how the exposure distribution affects sample size are well known. This paper extends previous results by incorporating the effect of a confounder into the calculation of sample size for a desired size and power of a statistical test. The paper also includes a quantitative discussion on the influence of the joint distribution for exposure to a putative cause and a a confounder on required sample sizes. The results show that, to detect a specified alternative for a given size and power, the required sample size decreases as either the variance of exposure or the effect of exposure on disease increases. The required sample size, however, increases as either the variance of the confounder or the effect of the confounder on disease increases. Generally, the higher is the absolute value of the simple correlation between the exposure and the confounder, the larger is the required sample size.

Sample sizes for repeated measurements in dichotomous data.

When the measurement of outcome varies within studied subjects and the cost of additional subjects is high, taking more than one measurement for each subject constitutes a useful alternative to increase the power or to reduce the total cost of the study. In this paper, I present sample size formulae for repeated measurements in dichotomous data under different situations. I also discuss optimal sample allocation for repeated measurements.

Exact equivalence test for risk ratio and its sample size determination under inverse sampling.

When data are dichotomous, this paper notes the utility of inverse sampling in establishing equivalence with respect to the risk ratio. This paper develops an exact equivalence test that accounts for the risk ratio under inverse sampling and further discusses the relationship between the exact equivalence test and the exact conditional confidence limits. Also included are an exact and two asymptotic procedures for calculation of the minimum required number of index subjects for a desired power 1--beta at a given alpha-level. Finally, this paper provides a table that summarizes the minimum required number of index subjects for powers equal to 0.90 and 0.80 in application of the proposed exact equivalence test at 0.05-level in a variety of situations.

A discussion on the conventional estimator of sensitivity and specificity in multiple tests.

Both the variation of positive responses (negative responses) among individuals and the internal correlation among responses for the same individual affect the precision of the estimate of sensitivity (specificity). To estimate the sensitivity (specificity) of a medical diagnostic test, this paper proposes a Bayesian approach with a simple Markov model to evaluate the performance of the conventional estimator under different situations. On the basis of the assumed model, we derive a general formula for the variance of the conventional estimator regarding multiple tests and present a quantitative discussion on the limitations of this estimator.

A note on interval estimation of the relative difference in data with matched pairs.

For controlled comparative trials with matched pairs, in an attempt to improve the asymptotic interval estimator of the relative difference proposed elsewhere, I develop two asymptotic closed-form interval estimators with use of the logarithmic transformation and an idea used for deriving Fieller's theorem, respectively. I use Monte Carlo simulation to compare the performance of these three interval estimators. Findings reveal that when the number of pairs is as small as 20, the asymptotic interval estimator with use of the logarithmic transformation can actually perform quite well and is generally preferable to the other two asymptotic interval estimators with respect to both the coverage probability and the average length of the resulting confidence intervals. When the number of pairs is large (n > or = 100), results show that the three interval estimators considered here are all appropriate for use; they are essentially equivalent in a variety of situations.

Notes on interval estimation of the attributable risk in cross-sectional sampling.

The attributable risk (AR) is probably the most useful and commonly used epidemiologic index to measure the importance of a risk factor in public health issues. This paper focuses the discussion on interval estimation of the AR in cross-sectional studies and compares the finite-sample performance of five asymptotic interval estimators of the AR by calculating the coverage probability and the average length in a variety of situations. This paper notes that the coverage probability of the two interval estimators proposed by Leung and Kupper, including the one that combines the interval estimator on the basis of Wald's test statistic, can be substantially less than the desired confidence level when the underlying risk ratio equals 1. As long as the sample size is reasonably large (> or =100) and the probability of exposure is moderate (> or =0.20), the interval estimator suggested by Fleiss can consistently perform well with respect to the coverage probability in a variety of situations considered here. However, using this interval estimator tends to generally lose efficiency. This paper also finds that with respect to the coverage probability, the interval estimator using Fieller's theorem is generally preferable to the interval estimator on the basis of Wald's test statistic when the prevalence rate ratio (RR) between the exposure and the non-exposure groups is > or =2. Finally, this paper notes that if we know that the underlying parameter RR is large (> or =4) and the probability of exposure is not small (> or =0.05), the interval estimator suggested by Leung and Kupper will probably be preferable to all the other estimators considered here.