Effective reproduction numbers are commonly overestimated early in a disease outbreak.

Reproduction numbers estimated from disease incidence data can give public health authorities valuable information about the progression and likely size of a disease outbreak. Here, we show that methods for estimating effective reproduction numbers commonly give overestimates early in an outbreak. This is due to many factors including the nature of outbreaks that are used for estimation, incorrectly accounting for imported cases and outbreaks arising in subpopulations with higher transmission rates. Awareness of this bias is necessary to correctly interpret estimates from early disease outbreak data.

Estimating reproduction numbers for adults and children from case data.

We present a method for estimating reproduction numbers for adults and children from daily onset data, using pandemic influenza A(H1N1) data as a case study. We investigate the impact of different underlying transmission assumptions on our estimates, and identify that asymmetric reproduction matrices are often appropriate. Under-reporting of cases can bias estimates of the reproduction numbers if reporting rates are not equal across the two age groups. However, we demonstrate that the estimate of the higher reproduction number is robust to disproportionate data-thinning. Applying the method to 2009 pandemic influenza H1N1 data from Japan, we demonstrate that the reproduction number for children was considerably higher than that of adults, and that our estimates are insensitive to our choice of reproduction matrix.

Type and quantity of data needed for an early estimate of transmissibility when an infectious disease emerges.

An early estimate of disease transmissibility is essential for a well-informed public health response to a newly emerged infectious disease. In this study, we ask what type and quantity of data are needed for useful estimation of the initial reproduction number (R). It is possible to estimate R from case incidence data alone when the growing incidence of cases displays a wave pattern, because the pattern provides information about the serial interval (the time elapsed between the onset of symptoms of a case and symptom onset in individuals infected by that case). When the mode of the serial interval distribution is small, 1.5 days or less, there is generally no informative wave pattern in the observed series of daily incidences. The precision of the estimate of R is then improved substantially by having some observations on the serial interval. For an infectious disease with characteristics such as those of influenza, an estimate of R able to inform plans to mitigate transmission is obtained when the cumulative incidence of cases reaches about 300 and about 10 observations on the serial interval are available.

Risk factors for infection with Campylobacter jejuni flaA genotypes.

We aimed to explore Campylobacter genotype-specific risk factors in Australia. Isolates collected prospectively from cases recruited into a case-control study were genotyped using flaA restriction fragment-length polymorphism typing (flaA genotyping). Exposure information for cases and controls was collected by telephone interview. Risk factors were examined for major flaA genotypes using logistic and multinomial regression. Five flaA genotypes accounted for 325 of 590 (55%) cases - flaA-6b (n=129), flaA-6 (n=70), flaA-10 (n=48), flaA-2 (n=43), flaA-131 (n=35). In Australia, infections due to flaA-10 and flaA-2 were found to be significantly associated with eating non-poultry meat (beef and ham, respectively) in both case-control and inter-genotype comparisons. All major genotypes apart from flaA-10 were associated with chicken consumption in the case-control comparisons. Based on several clinical criteria, infections due to flaA-2 were more severe than those due to other genotypes. Thus genotype analysis may reveal genotype-specific niches and differences in virulence and transmission routes.

Climatic factors associated with hospitalizations for rotavirus diarrhoea in children under 5 years of age.

This study compares the seasonality of rotavirus diarrhoeal hospital admissions and its relationship to climatic factors across three Australian cities. Weekly admission of rotavirus diarrhoea (1993-2003) in children aged <5 years and weekly average temperature and relative humidity for each city were modelled using a log-linear model with a cubic trend and season. Interactions were included to test for differences in the effect of temperature and humidity between seasons and between cities. Admissions of rotavirus diarrhoea peaked in winter and spring and were lowest in summer. Higher temperature and humidity in the previous week were associated with a decrease in rotavirus diarrhoeal admissions in three cities. The effects of both temperature and humidity on rotavirus admissions in Brisbane differed across seasons. Strategies to combat outbreaks of rotavirus diarrhoea should take climatic factors and seasonal effects into consideration to plan for the excess seasonal hospital admissions.

Evaluation of measures to reduce international spread of SARS.

Mathematical models are used to quantify the effect of border control measures in reducing the international spread of SARS. Border screening is shown to play a relatively minor role in reducing disease spread. Assuming detection rates similar to those reported for arrival screening in Australia, screening can detect up to 10% (95% CI 3-23) of infected travellers, and reduce the probability of a large outbreak by up to 7% (95% CI 2-17). Rapid reductions in the time to diagnosis and effective facilities for the isolation of cases are essential to ensure that there will not be a large outbreak, and each week of delay in responding to imported infection approximately doubles the total number of cases. While the control response is being developed in a currently uninfected region, border screening can provide up to one week's additional time in which to improve methods for early isolation of cases.

Characteristics of left ventricular diastolic dysfunction in the community: an echocardiographic survey.

OBJECTIVE: To determine the prevalence and predictors of left ventricular (LV) diastolic dysfunction in older adults. DESIGN, SETTING AND PARTICIPANTS: A cross-sectional survey of 1275 randomly selected residents of Canberra, aged 60 to 86 years (mean age 69.4; 50% men), conducted between February 2002 and June 2003. MAIN OUTCOME MEASURES: Prevalence of LV diastolic dysfunction as characterised by comprehensive Doppler echocardiography. RESULTS: The prevalence of any diastolic dysfunction was 34.7% (95% CI 32.1% to 37.4%) and that of moderate to severe diastolic dysfunction was 7.3% (95% CI 5.9% to 8.9%). Of subjects with moderate to severe diastolic dysfunction, 77.4% had an LV ejection fraction (EF) > 50% and 76.3% were in a preclinical stage of disease. Predictors of diastolic dysfunction were higher age (p < 0.0001), reduced EF (p < 0.0001), obesity (p < 0.0001) and a history of hypertension (p < 0.0001), diabetes (p = 0.02) and myocardial infarction (p = 0.003). Moderate to severe diastolic dysfunction with normal EF, although predominantly preclinical, was independently associated with increased LV mass (p < 0.0001), left atrial volume (p < 0.0001), and circulating amino-terminal pro-B-type natriuretic peptide concentrations (p < 0.0001), and with decreased quality of life (p < 0.005). CONCLUSION: Diastolic dysfunction is common in the community and often unaccompanied by overt congestive heart failure. Despite the lack of symptoms, advanced diastolic dysfunction with normal EF is associated with reduced quality of life and structural abnormalities that reflect increased cardiovascular risk.

Health inequalities across socio-economic groups: comparing geographic-area-based and individual-based indicators.

OBJECTIVES: To compare health inequality estimates obtained with different types of indicators of socio-economic status (SES), and study whether some of these are better predictors of health status, as indicated by observed disability data, than others. METHODS: Australian data were used to compare the use of the geographically based Socio-economic Index for Areas (SEIFA) in health inequality studies with two individual-based SES indicators able to account for family income and size. Inequalities in disability prevalences by SES were measured using age-standardized rate ratios. Logistic regression was used to determine which type of SES measure is a better predictor of the observed disability prevalences. RESULTS: Estimates of health inequalities obtained with the SEIFA were considerably lower than those obtained with the individual-based SES indicators. With the SEIFA, the proportion of disabled people amongst the most disadvantaged 20% of Australians was estimated to be 82% higher than amongst the most advantaged 20%, compared with over 150% with the individual-based SES measures. Also, the individual-based indicators were considerably better predictors of observed disability status than the SEIFA. CONCLUSION: An individual-level SES indicator, such as one based on family income, is a better predictor of people with a disability than a geographic-area-based index. Also, the main reason for the considerably lower inequality estimates obtained with the SEIFA is that, unlike the individual-based indicators, such location-based indices cannot account for the significant, often age-related variations in SES that exist amongst people living in a particular area.

Deep vein thrombosis and air travel: record linkage study.

OBJECTIVE: To investigate the time relations between long haul air travel and venous thromboembolism. DESIGN: Record linkage study using the case crossover approach. SETTING: Western Australia. PARTICIPANTS: 5408 patients admitted to hospital with venous thromboembolism and matched with data for arrivals of international flights during 1981-99. RESULTS: The risk of venous thromboembolism is increased for only two weeks after a long haul flight; 46 Australian citizens and 200 non-Australian citizens had an episode of venous thromboembolism during this so called hazard period. The relative risk during this period for Australian citizens was 4.17 (95% confidence interval, 2.94 to 5.40), with 76% of cases (n = 35) attributable to the preceding flight. A "healthy traveller" effect was observed, particularly for Australian citizens. CONCLUSIONS: The annual risk of venous thromboembolism is increased by 12% if one long haul flight is taken yearly. The average risk of death from flight related venous thromboembolism is small compared with that from motor vehicle crashes and injuries at work. The individual risk of death from flight related venous thromboembolism for people with certain pre-existing medical conditions is, however, likely to be greater than the average risk of 1 per 2 million for passengers arriving from a flight. Airlines and health authorities should continue to advise passengers on how to minimise risk.

Advances in medical statistics arising from the AIDS epidemic.

Many statisticians have contributed to studies of the HIV epidemic and progression to AIDS. They have developed new statistical methodology, where needed, to address HIV-related issues. The transfer of methods from one area to another often involves a substantial delay. This paper points to methods that were developed in the HIV context and have either already found applications in other areas of medical research or have the potential for such applications, with the hope that this will promote a speedier transfer of the research methods. Among the new tools that HIV studies have placed firmly into the pool of statistical methods for medical research are the methods of back-calculation, methods for the analysis of retrospective ascertainment data and methods of analysis for the combined data from clinical trials and associated longitudinal studies. Notions that have been stimulated substantially are use of surrogate endpoints in clinical trials and screening blood products by the use of pooled serum samples. Research activity in many other areas has been boosted substantially through contributions motivated by HIV/AIDS studies. Noteworthy examples are analyses for doubly-censored lifetime data and methods for assessing vaccines for transmissible diseases.

Inference for an epidemic when susceptibility varies.

A stochastic epidemic model featuring fixed-length latent periods, gamma-distributed infectious periods and randomly varying heterogeneity among susceptibles is considered. A Markov chain Monte Carlo algorithm is developed for performing Bayesian inference for the parameters governing the infectious-period length and the hyper-parameters governing the heterogeneity of susceptibility. This method of analysis applies to a wider class of diseases than methods proposed previously. An application to smallpox data confirms results about heterogeneity suggested by an earlier analysis that relied on less realistic assumptions.

Estimating HIV incidence using dates of both HIV and AIDS diagnoses.

Knowledge of HIV incidence is important to formulate sensible strategies aimed at controlling the HIV/AIDS epidemic. Back-projection is one of the methods for reconstructing the HIV incidence curve from AIDS incidence data. However, because of the low risk of developing AIDS during the first few years after infection, precise estimates of HIV incidence for the recent past are unlikely if we use AIDS incidence data only. As a result there have been recent attempts to use, not only the date of AIDS diagnosis, but also to use the date of their first positive HIV test. The objective of this paper is to incorporate into back-projection the additional information provided by those individuals who have tested HIV positive but have not yet developed AIDS. This adds information on a very large number of other individuals, and provides the hope that the precision of back-projection is improved considerably. The date of a positive HIV test or an AIDS diagnosis of an individual, whichever comes first, is used in a generalized convolution equation for the purpose of back-projection. The method is illustrated by an application to Australian HIV and AIDS data. Study results show that dramatic improvement in precision is gained for estimates of HIV incidence in recent years when both HIV and AIDS diagnosis dates are used on all individuals.

Estimating the immunity coverage required to prevent epidemics in a community of households.

An estimation of the immunity coverage needed to prevent future outbreaks of an infectious disease is considered for a community of households. Data on outbreak size in a sample of households from one epidemic are used to derive maximum likelihood estimates and confidence bounds for parameters of a stochastic model for disease transmission in a community of households. These parameter estimates induce estimates and confidence bounds for the basic reproduction number and the critical immunity coverage, which are the parameters of main interest when aiming at preventing major outbreaks in the future. The case when individuals are homogeneous, apart from the size of their household, is considered in detail. The generalization to the case with variable infectivity, susceptibility and/or mixing behaviour is discussed more briefly. The methods are illustrated with an application to data on influenza in Tecumseh, Michigan.

Estimating the transmission rate for a highly infectious disease.

It is pointed out that estimates of disease transmission parameters based on the final size of an epidemic are unsatisfactory when all susceptibles are infected and that this is an event with a substantial probability for communities of practical interest. We propose a method for estimating the transmission rate for such highly infectious diseases under the assumptions that the removal process of the disease is fully observed and that the mean duration of the infectious period is known. The method uses smoothed differentiation of the removal process. A simulation study shows that the method performs satisfactorily.

The effect of random vaccine response on the vaccination coverage required to prevent epidemics.

The response people have to vaccination varies because their immune systems differ and vaccine failures occur. Here we consider the effect that a random response, independent for each vaccinee, has on the vaccination coverage required to prevent epidemics in a large community. For a community of uniformly mixing individuals an explicit expression is found for the critical vaccination coverage (CVC) and the effect of the vaccine response is determined entirely by the mean E(AB), where A and B, respectively, reflect the infectivity and susceptibility of a vaccinated individual. This result shows that the usual concept of vaccine efficacy, which focuses on the amount of protection the vaccine provides the vaccinee against infection, is not adequate to describe the requirements for preventing epidemics when vaccination affect infectivity. The estimation of E(AB) poses a problem because A and B refer to the vaccine response of the same individual. Similar results are found when there are different types of individual, but now the mean E(AB) may differ between types. However, for a community made up of households it is shown that the CVC also depends on other characteristics of the vaccine response distribution. In practice this means that estimating a single measure of vaccine effectiveness is generally not enough to determine the CVC. For a specific community of households it is found that the vaccination coverage required to prevent epidemics decreases as the variation in the vaccine response increases.

The effect of community structure on the immunity coverage required to prevent epidemics.

Estimation of the immunity coverage required to effectively control disease transmission is an important public health problem. Using data on the eventual size of a major epidemic, we compare estimates based on the simplifying assumption that the community consists of uniformly mixing individuals with estimates obtained when the more complex community structure is acknowledged. The alternative community structures considered include households and localities that are quite separate. Several inequalities are established for estimates of the critical immunity coverage. For several settings, the coverage estimated by assuming an oversimplified community structure is found to actually be an underestimate. A serious consequence of this finding is that we may be misled into believing that we have estimated an immunity coverage that can prevent epidemics when it in fact cannot. The conclusion is that the heterogeneity in the community must be taken into account when estimating the critical immunity coverage.

Estimating a delay distribution from incomplete data, with application to reporting lags for AIDS cases.

Statistical inference for the probability distribution of a reporting delay is considered when delays are recorded only after a certain point in time tau. A method is proposed which utilizes data on incidences arising prior to tau. By a suitable choice of parameters we find explicit expressions for maximum likelihood estimates and standard errors. An application to reporting delay data on Australian AIDS diagnoses demonstrates that inclusion of data on AIDS diagnoses made prior to tau results in significant gains in the precision of estimates. A simulation study indicates for this data set that there is minimal bias in the estimates and the large sample formulae for the standard errors give good estimates of the standard deviation of the estimators.

Preventing epidemics with age-specific vaccination schedules.

A method is proposed for computing the coverage required to prevent epidemics by age-specific vaccination schedules. The method applies in a very general setting and provides explicit expressions in many cases. It can accommodate vaccination doses administered at different ages, heterogeneity among individuals of different ages, a community structured into households, and waning of vaccine-induced immunity. A comparison of results for two specific community settings, with analogous parameter values, indicates that the immunity coverage required to prevent epidemics in a community of households is less than that required for a community of uniformly mixing individuals.

Uses of the EM algorithm in the analysis of data on HIV/AIDS and other infectious diseases.

The analysis of data on infectious diseases is a natural setting for applications of the EM algorithm, because the infection process is only partially observable. Difficulties in determining the expectation at the E step have been side-stepped by adopting pragmatic models which reflect only part of the mechanism that generates the data. In the HIV/AIDS context the EM algorithm has helped in the reconstruction of the unobserved HIV infection curve, the so-called backprojection problem, as well as in the estimation of the distribution for the incubation period until AIDS, in estimating the infectivity of HIV in partnerships and in estimating parameters describing the decline in the immune system. There is a need for smooth estimates of functions in these applications, suggesting the use of the EMS algorithm or use of the EM algorithm to maximize a penalized likelihood. For data on other infectious diseases the application of the EM algorithm has so far been restricted to analyses of data on the size of outbreaks in a sample of households.