Back-projection of COVID-19 diagnosis counts to assess infection incidence and control measures: analysis of Australian data.

Back-projection is an epidemiological analysis method that was developed to estimate HIV incidence using surveillance data on AIDS diagnoses. It was used extensively during the 1990s for this purpose as well as in other epidemiological contexts. Surveillance data on COVID-19 diagnoses can be analysed by the method of back-projection using information about the probability distribution of the time between infection and diagnosis, which is primarily determined by the incubation period. This paper demonstrates the value of such analyses using daily diagnoses from Australia. It is shown how back-projection can be used to assess the pattern of COVID-19 infection incidence over time and to assess the impact of control measures by investigating their temporal association with changes in incidence patterns. For Australia, these analyses reveal that peak infection incidence coincided with the introduction of border closures and social distancing restrictions, while the introduction of subsequent social distancing measures coincided with a continuing decline in incidence to very low levels. These associations were not directly discernible from the daily diagnosis counts, which continued to increase after the first stage of control measures. It is estimated that a one week delay in peak incidence would have led to a fivefold increase in total infections. Furthermore, at the height of the outbreak, half to three-quarters of all infections remained undiagnosed. Automated data analytics of routinely collected surveillance data are a valuable monitoring tool for the COVID-19 pandemic and may be useful for calibrating transmission dynamics models.

Long-term risk stratification for survivors of acute coronary syndromes. Results from the Long-term Intervention with Pravastatin in Ischemic Disease (LIPID) Study. LIPID Study Investigators.

OBJECTIVES: We developed a prognostic strategy for quantifying the long-term risk of coronary heart disease (CHD) events in survivors of acute coronary syndromes (ACS). BACKGROUND: Strategies for quantifying long-term risk of CHD events have generally been confined to primary prevention settings. The Long-term Intervention with Pravastatin in Ischemic Disease (LIPID) study, which demonstrated that pravastatin reduces CHD events in ACS survivors with a broad range of cholesterol levels, enabled assessment of long-term prognosis in a secondary prevention setting. METHODS: Based on outcomes in 8,557 patients in the LIPID study, a multivariate risk factor model was developed for prediction of CHD death or nonfatal myocardial infarction. Prognostic indexes were developed based on the model, and low-, medium-, high- and very high-risk groups were defined by categorizing the prognostic indexes. RESULTS: In addition to pravastatin treatment, the independently significant risk factors included: total and high density lipoprotein cholesterol, age, gender, smoking status, qualifying ACS, prior coronary revascularization, diabetes mellitus, hypertension and prior stroke. Pravastatin reduced coronary event rates in each risk level, and the relative risk reduction did not vary significantly between risk levels. The predicted five-year coronary event rates ranged from 5% to 19% for those assigned pravastatin and from 6.4% to 23.6% for those assigned placebo. CONCLUSIONS: Long-term prognosis of ACS survivors varied substantially according to conventional risk factor profile. Pravastatin reduced coronary risk within all risk levels; however, absolute risk remained high in treated patients with unfavorable profiles. Our risk stratification strategy enables identification of ACS survivors who remain at very high risk despite statin therapy.

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.

Interim monitoring of clinical trials based on long-term binary endpoints.

This paper discusses interim analysis of randomized clinical trials for which the primary endpoint is observed at a specific long-term follow-up time. For such trials subjects only yield direct information on the primary endpoint once they have been followed through to the long-term follow-up time, potentially eliminating a large proportion of the accrued sample from an interim analysis of the primary endpoint. We advocate more efficient interim analysis of long-term endpoints by augmenting long-term information with short-term information on subjects who have not yet been followed through to the long-term follow-up time. While retaining the long-term endpoint as the subject of the analysis, methods of jointly analysing short- and long-term data are discussed for reversible binary endpoints. It is shown theoretically and by simulation that the use of short-term information improves the efficiency with which long-term treatment differences are assessed based on interim data. Sequential analysis of treatment differences is discussed based on spending functions, and is illustrated with a numerical example from a cholesterol treatment trial.

Continued lamivudine versus delavirdine in combination with indinavir and zidovudine or stavudine in lamivudine-experienced patients: results of Adult AIDS Clinical Trials Group protocol 370.

OBJECTIVE: To compare the virologic activity of continued lamivudine (3TC) versus a switch to delavirdine (DLV) when initiating protease inhibitor therapy in nucleoside-experienced patients. DESIGN: Randomized, open-label, multi-center study. SETTING: Adult AIDS clinical trials units. PATIENTS: Protease and non-nucleoside reverse transcriptase inhibitor-naive patients who had received 3TC plus zidovudine (ZDV), stavudine (d4T), or didanosine (ddl) for at least 24 weeks. INTERVENTIONS: Patients with plasma HIV-1 RNA levels > 500 copies/ml who previously received d4T + 3TC or ddI + 3TC were randomized to ZDV + 3TC + indinavir (IDV) or ZDV + DLV + IDV. MAIN OUTCOME MEASURES: Primary endpoints were the proportion of patients with plasma HIV-1 RNA levels < or = 200 copies/ml at 24 weeks, and occurrence of serious adverse events. The proportion of patients with plasma HIV-1 RNA levels < or = 200 copies/ml at week 48 was a secondary endpoint. RESULTS: At week 24, 58% of subjects in the ZDV + 3TC + IDV arm and 73% in the ZDV + DLV + IDV arm had plasma HIV-1 RNA levels < or = 200 copies/ml (P = 0.29). At week 48, plasma HIV-1 RNA levels were < or = 200 copies/ml in 48% and 83%, respectively (P = 0.007). Rash and hyperbilirubinemia occurred more frequently in the DLV arm than in the 3TC arm. Steady-state plasma IDV levels were higher among patients in the DLV arm as compared with the 3TC arm. CONCLUSIONS: Substituting DLV for 3TC when adding IDV improved virologic outcome in nucleoside-experienced patients. This result might be explained, in part, by the positive effect of DLV on IDV pharmacokinetics.

Joint analysis of HIV and AIDS surveillance data in back-calculation.

AIDS surveillance data are the main source of information to perform back-calculation of HIV incidence. We propose a method to incorporate additional information gained by linkage with an HIV surveillance system, containing data on the time of first positive HIV test. In this paper we generalize an earlier method that was developed to use HIV testing data available only for AIDS cases. The new method also makes use of cases with an HIV positive test who have not yet developed AIDS, typically a substantial proportion of the HIV-infected population. Furthermore, we use a more realistic model for the HIV testing rate, incorporating dependence on both time since infection and calendar time. The method makes use of an EM algorithm with generalized additive model smoothing, and is applied to data from Veneto, a region of northern Italy. Our results show that HIV incidence in Veneto peaked in the late 1980s, and decreased thereafter. Importantly, the HIV incidence estimates based on joint analysis of HIV and AIDS surveillance data are more efficient than estimates based on AIDS surveillance data alone. Our estimates also show a decreasing trend in the HIV testing rate over time, which leads to the conclusion that the interval between HIV infection and first positive test has lengthened over time. Furthermore, it is found that for infected individuals, the probability of seeking on HIV test is highest soon after infection.

Clinical trials using HIV-1 RNA-based primary endpoints: statistical analysis and potential biases.

Clinical trial endpoints based on magnitude of reduction in HIV-1 RNA levels provide an important complement to endpoints based on percentage of patients achieving complete virologic suppression. However, interpretation of magnitude of reduction can be biased by measurement limitations of virologic assays, particularly lower and upper limits of quantification. Using data from two AIDS Clinical Trials Group (ACTG) studies, widely used crude methods of analyzing HIV-1 RNA reductions were compared with methods that take into account censoring of HIV-1 RNA measurements. Such methods include Kaplan-Meier and censored regression analyses. It was found that standard crude methods of analysis consistently underestimated treatment effects. In some cases, the bias induced by crude methods masked statistically significant differences between treatment arms. Although statistically significant, adjustment for baseline HIV-1 RNA levels had little effect on estimated treatment differences. Furthermore, convenient parametric analyses performed as well as more complex nonparametric analyses. It is concluded that conveniently implemented censored data analyses should be conducted in preference to widely used crude analyses of magnitude of HIV-1 RNA reduction. To obtain complete information about virologic response to antiretroviral therapy, such analyses of magnitude of virologic response should be used to complement analyses of the percentage of patients having complete virologic suppression.

Design of HIV viral dynamics studies.

HIV viral dynamics studies involve repeated measurement of viral load in HIV-infected individuals, to assess short-term rates of viral load change in response to interventions such as initiation or withdrawal of antiviral therapy. Such studies are an important source of information on HIV pathogenesis. This paper concerns some statistical issues arising in their design. Using a linear random-effects model to incorporate between-patient differences in rates of viral load change, I discuss the choice of number of individuals and frequency of observation per individual. I suggest an approach for calculating the optimal sample size and observation frequency, based on minimizing the total number of viral load measurements that one needs to undertake. The conclusion, using this approach, is that over a period of linear change in viral load, three to five measurements per individual is generally appropriate. I also examine the observation frequency when the number of available individuals is limited, in which case it is shown that one can use a higher frequency of measurement per individual to achieve adequate power or precision. Finally, I consider sources of data for prior specification of variance components, together with conservative designs that are insensitive to a lack of prior information about between-patient differences.

Statistical issues for HIV surrogate endpoints: point/counterpoint. An NIAID workshop.

This paper summarizes the proceedings of an NIAID-sponsored workshop on statistical issues for HIV surrogate endpoints. The workshop brought together statisticians and clinicians in an attempt to shed light on some unresolved issues in the use of HIV laboratory markers (such as HIV RNA and CD4+ cell counts) in the design and analysis of clinical studies and in patient management. Utilizing a debate format, the workshop explored a series of specific questions dealing with the relationship between markers and clinical endpoints, and the choice of endpoints and methods of analysis in clinical studies. This paper provides the position statements from the two debaters on each issue. Consensus conclusions, based on the presentations and discussion, are outlined. While not providing final answers, we hope that these discussions have helped clarify a number of issues, and will stimulate further consideration of some of the highlighted problems. These issues will be critical in the proper assessment and use of future therapies for HIV disease.

Maintenance antiretroviral therapies in HIV-infected subjects with undetectable plasma HIV RNA after triple-drug therapy. AIDS Clinical Trials Group Study 343 Team.

BACKGROUND: Combination antiretroviral therapy with indinavir, zidovudine, and lamivudine can suppress the level of human immunodeficiency virus (HIV) RNA in plasma below the threshold of detection for two years or more. We investigated whether a less intensive maintenance regimen could sustain viral suppression after an initial response to combination therapy. METHODS: HIV-infected subjects who had CD4 cell counts greater than 200 per cubic millimeter, who had been treated with indinavir, lamivudine, and zidovudine, and who had less than 200 copies of HIV RNA per milliliter of plasma after 16, 20, and 24 weeks of induction therapy were randomly assigned to receive either continued triple-drug therapy (106 subjects), indinavir alone (103 subjects), or a combination of zidovudine and lamivudine (107 subjects). The primary end point was loss of viral suppression, which was defined as a plasma level of at least 200 copies of HIV RNA per milliliter on two consecutive measurements during maintenance therapy. RESULTS: During maintenance treatment, 23 percent of the subjects receiving indinavir and 23 percent of those receiving zidovudine and lamivudine, but only 4 percent of those receiving all three drugs, had loss of viral suppression (P<0.001 for the comparison between triple-drug therapy and the other two maintenance regimens). Subjects with greater increases in CD4 cell counts during induction therapy, higher viral loads at base line (i.e., at the beginning of induction therapy), and slower rates of viral clearance were at greater risk for loss of viral suppression. The presence of zidovudine-resistance mutations in HIV RNA at base line was strongly predictive of the loss of viral suppression in subjects treated with zidovudine and lamivudine. CONCLUSIONS: The suppression of plasma HIV RNA after six months of treatment with indinavir, zidovudine, and lamivudine is better sustained by the continuation of these three drugs than by maintenance therapy with either indinavir alone or zidovudine and lamivudine.

Flexible assessment of trends in age-specific HIV incidence using two-dimensional penalized likelihood.

We present a method for estimating age- and time-specific HIV incidence using back-calculations of AIDS incidence data. Two-dimensional penalized likelihood is employed, using a flexible bivariate step function model of HIV incidence, together with a quadratic roughness penalty which leads to thin-plate spline smoothing. This allows incidence estimates to vary flexibly and smoothly in both age and time. We propose generalized cross-validation as a guide for choice of an appropriate level of smoothing and describe an EM algorithm for computing the estimates. We propose the method primarily for qualitative assessment of trends in age-specific incidence over time and apply it to a small Italian data set on men who have sex with men. The analysis suggests a trend over time of increasing relative incidence among younger individuals, consistent with incidence patterns observed in other countries.

Use of changes in plasma levels of human immunodeficiency virus type 1 RNA to assess the clinical benefit of antiretroviral therapy.

Data from 1330 human immunodeficiency virus type 1 (HIV-1)-infected patients enrolled in seven antiretroviral treatment trials were analyzed to characterize the clinical benefit of treatment-mediated reductions in plasma HIV-1 RNA levels. The risk of a new AIDS-defining event or death was reduced proportionally to the magnitude of the reduction of the HIV-1 RNA level during the first 6 months of therapy. Pretherapy HIV-1 RNA levels were prognostic independently of on-therapy levels. In addition, the reduction in risk associated with any given reduction of the level of HIV-1 RNA did not vary by pretherapy level. Having either a reduction in HIV-1 RNA level or an increase in CD4+ lymphocyte count, or both, was associated with a delay in clinical disease progression. This indicates that patient prognosis should be assessed using both HIV-1 RNA and CD4+ lymphocyte responses to therapy.

Deterioration of detectable human immunodeficiency virus serum p24 antigen in samples stored for batch testing.

Virologic measurements are becoming important surrogate markers for therapeutic efficacy in clinical trials with human immunodeficiency virus (HIV)-infected subjects. One such marker which is inexpensive and easily evaluated is the HIV p-24 antigen. To determine the storage stability of p24 antigen assayed by enzyme-linked immunosorbent assay of serum collected during clinical trials, a retrospective analysis was performed. The p24 antigen results were available from four Adult or Pediatric AIDS Clinical Trials Group protocols: studies 047, 050, 128, and 213. Paired samples (n = 930) which were assayed by ELISA for p24 antigen both in real time and in batch were analyzed for agreement. Batch and real-time values were correlated; however, there was a lack of agreement which increased with prolonged storage time of batched samples and greater p24 antigen levels. The p24 antigen values were significantly lower in the batched samples, which had a maximum storage time of 1,548 days. The degradation rate of p24 antigen per year was 0.052 log10 for samples with less than 30 pg/ml, 0.197 log10 for those with 30 to 100 pg/ml, and 0.245 log10 for those with > 100 pg/ml. Due to degradation over time, use of p24 antigen values from batch assays with long-term storage could bias study results toward a lack of treatment effect. On the basis of these results we make the following recommendations. (i) Samples should be assayed either in real time by laboratories undergoing quality assurance or in batch with short-term storage (less than 1 year). (ii) When real-time assays are to be performed, the serum samples should not be stored at 4 degrees C, but should be frozen immediately after processing and stored frozen until tested.

Standardized peripheral blood mononuclear cell culture assay for zidovudine susceptibility testing of clinical human immunodeficiency virus type 1 isolates: effect of reducing the numbers of replicates and concentrations.

Zidovudine susceptibility was assessed for 525 clinical human immunodeficiency virus type 1 isolates, before and after reducing the number of replicates and zidovudine concentrations in the standardized consensus peripheral blood mononuclear cell culture assay. We conclude that omitting the 0.001 microM concentration and using duplicate rather than triplicate wells are valid and cost-effective modifications of this expensive assay.

A method for assessing age-time disease incidence using serial prevalence data.

This paper considers nonparametric estimation of age- and time-specific trends in disease incidence using serial prevalence data collected from multiple cross-sectional samples of a population over time. The methodology accounts for differential selection of diseased and undiseased individuals resulting, for example, from differences in mortality. It is shown that when a log-linear incidence odds model is adopted, an EM algorithm provides a convenient method for carrying out maximum likelihood estimation, primarily using existing generalized linear models software. The procedure is quite general, allowing a range of age-time incidence models to be fitted under the same framework. Furthermore, by making use of existing software for fitting generalized additive models, the procedure can be generalized with virtually no extra complexity to allow maximization of a penalized likelihood for smooth nonparametric estimation. Automatic choice of smoothing level for the penalized likelihood estimates is discussed, using generalized cross-validation. The method is applied to a data set on serial toxoplasmosis prevalence, which has previously been analyzed under the assumption of nondifferential selection. A variety of age-time incidence models are fitted, and the sensitivity to plausible differential selection patterns is considered. It is found that nonmultiplicative models are unnecessary and that qualitative incidence trends are fairly robust to differential selection.

Decreasing age at infection for homosexually acquired HIV in Italy: results of a back-calculation analysis.

The age-specific incidence of homosexually acquired HIV in Italy was examined, based on 3918 AIDS cases diagnosed by the end of 1994 and reported by the end of 1995 through the national surveillance system. Using a smoothed back-calculation analysis, the estimated median age at infection decreased over time, and HIV incidence among younger age groups peaked much later than among older age groups. These results support recent findings from other developed countries, and suggest that measures for preventing homosexual transmission of HIV are best targeted at younger age groups.

Fitting a multiplicative incidence model to age- and time-specific prevalence data.

We discuss the assessment of age- and time-specific disease incidence using prevalence data. A method is described for conveniently fitting a discrete-time multiplicative model, subject to positivity constraints, using the EM-algorithm. Together with smoothing, it allows essentially nonparametric assessment of incidence trends. The method is illustrated using previously analyzed data on toxoplasmosis.

Assessment of HIV testing rates among HIV infected individuals using incidence data on HIV and AIDS diagnoses.

This paper considers estimation of the rate HIV diagnosis in a population of HIV positive individuals. A number of previous papers have studied the situation where time of first positive HIV test is available for AIDS cases, and possibly for individuals who have not yet developed AIDS. In this context, AIDS diagnoses are linked to prior HIV diagnoses. The present paper focuses on the case where AIDS incidence data, and data on new HIV diagnoses, are unlinked. Although there is less information available when there is no linking AIDS diagnosis and HIV tests, it is shown that a useful assessment can be made of the pattern of HIV testing over time. The methodology makes use of back-projection estimates of HIV incidence and involves fitting a model for HIV diagnosis to the observed pattern of new positive HIV tests. Smooth non-parametric estimates are obtained by minimizing a penalized residual sum of squares. In analysis of data on HIV diagnoses among the homosexual/bisexual population in the state of Victoria, Australia, we find strong evidence of a significant decrease in testing rates during the latter part of the 1980s. Subsequent testing rate estimates are subject to greater uncertainty, but are of a comparable magnitude to estimates based on linked data in other countries.

The association between El Niño/Southern Oscillation events and typhoons in the Marshall Islands.

An analysis of the historic record of typhoons in the Marshall Islands has identified a significant association between the occurrence of the El Niño/Southern Oscillation phenomenon (ENSO) and the occurrence of typhoons in the Marshall Islands. Whilst typhoons normally occur further to the east, the warming of the ocean waters around the Marshall Islands, as part of the ENSO phenomenon, generates typhoons further to the west. The results suggest that typhoons are 2.6 times more likely to occur during ENSO years, with a 71 per cent chance of a typhoon striking during an ENSO year, and only a 26 per cent chance of one happening during a non-ENSO year. This has implications for planning and public safety, which the relevant authorities may wish to take note of.

Lombok Hepatitis B Model Immunization Project: toward universal infant hepatitis B immunization in Indonesia.

The Lombok Hepatitis B (HB) Model Immunization Project was the first mass infant HB immunization project in Indonesia. Key aspects were the procurement of low-cost HB vaccine, integration into routine infant immunization services, and delivery of the first dose in the home within 1 week of birth. The project achieved > 90% coverage with 3 doses of vaccine. The prevalence of HB surface antigen was 1.4% in infants who received 3 doses (with the first dose within 7 days of birth) and 3.0% in those who received the first dose > 7 days after birth, compared with a baseline prevalence of 6.2% (P < .001 in each case). Most vaccine failures occurred in children born to HBe antigen-positive mothers. Antibody prevalence and titers did not correlate with protection. HB vaccine can be successfully integrated into the Expanded Programme on Immunization (EPI), strengthening the EPI and significantly reducing chronic HB infection.