Bias due to secondary transmission in estimation of attributable risk from intervention trials

BACKGROUND: An important concept in epidemiology is attributable risk, defined as the difference in risk between an exposed and an unexposed group. For example, in an intervention trial, the attributable risk is the difference in risk between a group that receives an intervention and another that does not. A fundamental assumption in estimating the attributable risk associated with the intervention is that disease outcomes are independent. When estimating population risks associated with treatment regimens designed to affect exposure to infectious pathogens, however, there may be bias due to the fact that infectious pathogens can be transmitted from host to host causing a potential statistical dependency in disease status among participants. METHODS: To estimate this bias, we used a mathematical model of community- and household-level disease transmission to explicitly incorporate the dependency among participants. We illustrate the method using a plausible model of infectious diarrheal disease. RESULTS: Analysis of the model suggests that this bias in attributable risk estimates is a function of transmission from person to person, either directly or indirectly via the environment. CONCLUSIONS: By incorporating these dependencies among individuals in a transmission model, we show how the bias of attributable risk estimates could be quantified to adjust effect estimates reported from intervention trials.     

The effects of joint misclassification of exposure and disease on the attributable risk

While there is extensive methodological literature analysing the effects of misclassification on the relative risk under various misclassification scenarios, for the attributable risk only the effects of non-differential misclassification either of exposure or disease, and the effects of non-differential independent misclassification of exposure and disease have been discussed for the 2 x 2-situation. The paper investigates the effects of non-differential correlated misclassification of exposure and disease on the attributable risk taking possible correlations of both types of misclassification into account. Furthermore, a comparison with the corresponding effects on the relative risk is drawn. We propose a matrix-based approach to describe the underlying structure of non-differential misclassification. The bias arising from non-differential misclassification in the attributable risk and relative risk is evaluated in four examples assuming under- or overreporting of exposure and disease. In each of the four examples we found scenarios where pronounced differences in degree and, more importantly, in direction of bias occurred. Our results clearly demonstrate the danger lying in the stereotype transfer of findings regarding misclassification effects on the relative risk to other epidemiologic risk measures and underline the necessity of specific analyses of the effects of misclassification on the attributable risk.     

A causal model for longitudinal randomised trials with time‐dependent non‐compliance

In the presence of non‐compliance, conventional analysis by intention‐to‐treat provides an unbiased comparison of treatment policies but typically under‐estimates treatment efficacy. With all‐or‐nothing compliance, efficacy may be specified as the complier‐average causal effect (CACE), where compliers are those who receive intervention if and only if randomised to it. We extend the CACE approach to model longitudinal data with time‐dependent non‐compliance, focusing on the situation in which those randomised to control may receive treatment and allowing treatment effects to vary arbitrarily over time. Defining compliance type to be the time of surgical intervention if randomised to control, so that compliers are patients who would not have received treatment at all if they had been randomised to control, we construct a causal model for the multivariate outcome conditional on compliance type and randomised arm. This model is applied to the trial of alternative regimens for glue ear treatment evaluating surgical interventions in childhood ear disease, where outcomes are measured over five time points, and receipt of surgical intervention in the control arm may occur at any time. We fit the models using Markov chain Monte Carlo methods to obtain estimates of the CACE at successive times after receiving the intervention. In this trial, over a half of those randomised to control eventually receive intervention. We find that surgery is more beneficial than control at 6months, with a small but non‐significant beneficial effect at 12months. © 2015 The Authors. Statistics in Medicine Published by JohnWiley & Sons Ltd.     

Using multiple timescale models for the evaluation of a time‐dependent treatment

In survival analysis, the absolute measure of cumulative risk provided by the Kaplan‐Meier estimator is still the most used quantity for its easy calculation and direct interpretability. However, for describing the survival after an intervention that may occur at different times from baseline observation, the Kaplan‐Meier estimator generally yields to biased results if intervention is considered as fixed at baseline. The main focus of the present paper is to extend the use of a multiple timescale model in the presence of a time dependent intervention. The aim is to obtain 1) an estimate of treatment effect in terms of hazard ratios by flexible modeling, 2) a valid prediction tool, i.e. estimate of prognosis for a patient who changes treatment later in time, and 3) an appropriate graphical representation of survival in the presence of a time dependent treatment change, accounting for different timescales. We will show the advantages of this approach on the comparison of chemotherapy versus transplant in children with high‐risk acute lymphoblastic leukemia in first remission. We considered a model with two timescales that accounts for the change in treatment at different times in the disease course. An alternative approach to survival estimates is also proposed which has some advantages over the traditional landmark approach: it uses all the data available to plot survival from the date of remission, it avoids the arbitrary choice of a landmark time and explicitly models the change in hazard due to transplant. Copyright © 2015 John Wiley & Sons, Ltd.     

Sample size and power based on the population attributable fraction.

Most methods for calculating sample size use the relative risk (RR) to indicate the strength of the association between exposure and disease. For measuring the public health importance of a possible association, the population attributable fraction (PAF)--the proportion of disease incidence in a population that is attributable to an exposure--is more appropriate. We determined sample size and power for detecting a specified PAF in both cohort and case-control studies and compared the results with those obtained using conventional estimates based on the relative risk. When an exposure is rare, a study that has little power to detect a small RR often has adequate power to detect a small PAF. On the other hand, for common exposures, even a relatively large study may have inadequate power to detect a small PAF. These comparisons emphasize the importance of selecting the most pertinent measure of association, either relative risk or population attributable fraction, when calculating power and sample size.     

Modelling infectious disease transmission with complex exposure pattern and sparse outcome data

We present a regression modelling framework to analyse infectious disease transmission during a time period where extensive exposure data are available, but where the outcome data are sparse. A latent variable model is used for each exposure time, allowing a straight-forward accumulation of risk for a collection of exposures for which outcome data are available. We describe an analysis of HIV infection from blood products among a cohort of haemophiliacs in Ireland between 1980 and 1985. The analysis provides estimates of the time pattern and batch effects; we show how analytical complexity such as smoothly varying coefficients or random coefficient models can be accommodated by the model. Finally, we discuss other problems where the model is applicable.     

Epidemiology in risk management for chemicals

Risk management is the process by which choices are made between alternative actions or policies according to the likelihood of beneficial or adverse outcomes. It entails an assessment of the potential risks and benefits associated with each possible option, and the application of value judgements to decide which option should be chosen. Informal risk management for chemicals, a distinction is made between hazard (a potential adverse effect of the substance) and risk (the probability that that a hazard will be realised given the circumstances and extent of exposure to the substance). Where there is uncertainty about the existence of a hazard or about the level of risk associated with an exposure, this must also be taken into account. Of the various measures of risk, the two that are most relevant to risk management are the individual attributable risk and the population attributable risk. Assessment of risk entails the identification and characterisation of hazards, and estimation of the risks associated with the exposure circumstances that will follow from different policy options. Examples are given of the way in which epidemiology can contribute to this process, and also to checking that the outcomes of decisions in risk management accord with what was predicted by underpinning risk assessments. The strengths and limitations of epidemiology as a tool in risk management are discussed.     

Mediation analysis with causally ordered mediators using Cox proportional hazards model

Causal mediation analysis aims to investigate the mechanism linking an exposure and an outcome. However, studies regarding mediation effects on survival outcomes are limited, particularly in multi-mediator settings. The existing multi-mediator analyses for survival outcomes are either performed under special model specifications such as probit models or additive hazard models, or they assume a rare outcome. Here, we propose a novel multi-mediation analysis based on the widely used Cox proportional hazards model without the rare outcome assumption. We develop a methodology under a counterfactual framework to identify path-specific effects (PSEs) of the exposure on the outcome through the mediator(s) and derive the closed-form formula for PSEs on a transformed survival time. Moreover, we show that the convolution of an extreme value and Gaussian random variables converges to another Gaussian, provided that the variance of the original Gaussian gets large. Based on that, we further derive closed-form expressions for PSEs on survival probabilities. Asymptotic properties are established for both estimators. Extensive simulation is conducted to evaluate the finite sample performance of our proposed estimators and to compare with existing methods. The utility of the proposed method is illustrated in a hepatitis study of liver cancer risk.     

Efficacy of a randomized cell phone-based counseling intervention in postponing subsequent pregnancy among teen mothers

Adolescent mothers in Washington, DC have a high rate of subsequent teen pregnancies, often within 24 months. Children of teen mothers are at risk for adverse psychosocial outcomes. When adolescents are strongly attached to parents, schools, and positive peers, they may be less likely to repeat a pregnancy. This study tested the efficacy of a counseling intervention delivered by cell phone and focused on postponing subsequent teen pregnancies by strengthening healthy relationships, reproductive practices, and positive youth assets. The objective of this study was to compare time to a repeat pregnancy between the intervention and usual care groups, and, secondarily, to determine whether treatment intensity influenced time to subsequent conception. Primiparous pregnant teens ages 15-19, were recruited in Washington, DC. Of 849 teens screened, 29.3% (n = 249) met inclusion criteria, consented to participate, and completed baseline measures. They were then randomized to the intervention (N = 124) or to usual care (N = 125). Intervention group teens received cell phones for 18 months of counseling sessions, and quarterly group sessions. Follow-up measures assessed subsequent pregnancy through 24 months post-delivery. A survival analysis compared time to subsequent conception in the two treatment groups. Additional models examined the effect of treatment intensity. By 24 months, 31% of the intervention and 36% of usual care group teens had a subsequent pregnancy. Group differences were not statistically significant in intent-to-treat analysis. Because there was variability in the degree of exposure of teens to the curriculum, a survival analysis accounting for treatment intensity was performed and a significant interaction with age was detected. Participants who were aged 15-17 years at delivery showed a significant reduction in subsequent pregnancy with increased levels of intervention exposure (P < 0.01), but not those ≥ 18 years. Adolescents ≥ 18 years faced considerable challenges to treatment success. Individual, social, and contextual factors are all important to consider in the prevention of repeat teen pregnancy. Cell phone-based approaches to counseling may not be the most ideal for addressing complex, socially-mediated behaviors such as this, except for selective subgroups. A lack of resources within the community for older teens may interfere with program success.     

On the comparable quantification of health risks: lessons from the Global Burden of Disease Study.

Extensive discussion and comments on the Global Burden of Disease Study findings have suggested the need to examine more carefully the basis for comparing the magnitude of different health risks. Attributable burden can be defined as the difference between burden currently observed and burden that would have been observed under an alternative population distribution of exposure. Population distributions of exposure may be defined over many different levels and intensities of exposure (such as systolic or diastolic blood pressure on a continuous scale), and the comparison distribution of exposure need not be zero. Avoidable burden is defined as the reduction in the future burden of disease if the current levels of exposure to a risk factor were reduced to those specified by the counterfactual distribution of exposure. Choosing the alternative population distribution for a variable, the counterfactual distribution of exposure, is the critical step in developing a more general and standardized concept of comparable, attributable, or avoidable burden. We have identified four types of distributions of exposure that could be used as the counterfactual distributions: theoretical minimum risk, plausible minimum risk, feasible minimum risk, and cost-effective minimum risk. Using tobacco and alcohol as examples, we explore the implications of using these different types of counterfactual distributions to define attributable and avoidable burden. The ten risk factor assessments included in the Global Burden of Disease Study reflect a range of methods and counterfactual distributions. We recommend that future assessments should focus on avoidable and attributable burden based on the plausible minimum risk counterfactual distribution of exposure.     

Two denominators for one numerator: the example of neonatal mortality

Preterm delivery is one of the strongest predictors of neonatal mortality. A given exposure may increase neonatal mortality directly, or indirectly by increasing the risk of preterm birth. Efforts to assess these direct and indirect effects are complicated by the fact that neonatal mortality arises from two distinct denominators (i.e. two risk sets). One risk set comprises fetuses, susceptible to intrauterine pathologies (such as malformations or infection), which can result in neonatal death. The other risk set comprises live births, who (unlike fetuses) are susceptible to problems of immaturity and complications of delivery. In practice, fetal and neonatal sources of neonatal mortality cannot be separated—not only because of incomplete information, but because risks from both sources can act on the same newborn. We use simulations to assess the repercussions of this structural problem. We first construct a scenario in which fetal and neonatal factors contribute separately to neonatal mortality. We introduce an exposure that increases risk of preterm birth (and thus neonatal mortality) without affecting the two baseline sets of neonatal mortality risk. We then calculate the apparent gestational-age-specific mortality for exposed and unexposed newborns, using as the denominator either fetuses or live births at a given gestational age. If conditioning on gestational age successfully blocked the mediating effect of preterm delivery, then exposure would have no effect on gestational-age-specific risk. Instead, we find apparent exposure effects with either denominator. Except for prediction, neither denominator provides a meaningful way to define gestational-age-specific neonatal mortality.     

Formulating causal questions and principled statistical answers

Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline (“point exposure”) and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we describe principled definitions of causal effects and of estimation approaches classified according to whether they invoke the no unmeasured confounding assumption (including outcome regression and propensity score-based methods) or an instrumental variable with added assumptions. We mainly focus on continuous outcomes and causal average treatment effects. We discuss interpretation, challenges, and potential pitfalls and illustrate application using a “simulation learner,” that mimics the effect of various breastfeeding interventions on a child's later development. This involves a typical simulation component with generated exposure, covariate, and outcome data inspired by a randomized intervention study. The simulation learner further generates various (linked) exposure types with a set of possible values per observation unit, from which observed as well as potential outcome data are generated. It thus provides true values of several causal effects. R code for data generation and analysis is available on www.ofcaus.org , where SAS and Stata code for analysis is also provided.     

列线图法预测人群归因分值

人群归因分值（人群归因危险度百分比，PAF）是广大流行病学工作者熟悉的公共卫生学指标。PAF的计算主要根据某个危险因素对某病的相对危险度（RR）和人群中该危险因素的暴露比例（R）。文中介绍由RR和R估计PAF列线图的制作方法，以便快速简捷地估算PAF。     

Design and analysis considerations in a cohort study involving repeated measurement of both exposure and outcome: The association between genital papillomavirus infection and risk of cervical intraepithelial neoplasia

Cohort studies commonly involve a single determination of exposure, and one or more assessments of whether or not the outcome of interest has occurred. This approach is appropriate when the exposure does not change with time, and when one can readily determine the time of outcome (for example, mortality). If either of these conditions is not met, however, we may introduce bias into the estimate of effect, since we may misclassify individual members of the cohort with respect to exposure, outcome or both. We can reduce this bias by measuring exposure and outcome on more than one occasion. In this paper, we illustrate the design and analysis issues that arise in such circumstances, by reference to an ongoing prospective study of the relationship between genital papillomavirus infection and risk of cervical intraepithelial neoplasia. This study entails annual assessments of the status of the study subjects with respect to both conditions. In particular, we examine the implications that use of this design has on the statistical power of the study.     

Uncertainties about the benefit of treatment in subclinical thyroid dysfunction

The Leiden 85-plus study in the oldest old has observed (a) no relationship between thyroid function and symptoms of depression, cognitive impairment or disabilities in daily life, and (b) increased mortality in subjects with TSH < 0.3 mU/l as well as longer survival in subjects with TSH > 4.8 mU/l. Subclinical hyperthyroidism probably warrants more proactive treatment as other studies have also shown increased mortality to accompany a low TSH, although no randomised trials have been done to prove that early intervention prevents atrial fibrillation or prolongs life. The benefits of treatment for subclinical hypothyroidism at a very advanced age are uncertain, but treatment might well be beneficial in middle-aged subjects as some studies report an increased risk of cardiovascular morbidity and mortality. In all cases, however, it is recommended that underlying thyroid disease be demonstrated before treatment is started.     

Should radon be reduced in homes? A cost-effect analysis

BACKGROUND: Radon is a radioactive gas that may leak into buildings from the ground. Radon exposure is a risk factor for lung cancer. An intervention against radon exposure in homes may consist of locating homes with high radon exposure (above 200 Bq m(-3)) and improving these, and protecting future houses. The purpose of this paper is to calculate the costs and the effects of this intervention. METHODS: We performed a cost-effect analysis from the perspective of the society, followed by an uncertainty and sensitivity analysis. The distribution of radon levels in Norwegian homes is lognormal with mean = 74.5 Bq m(-3), and 7.6% above 200 Bq m(-3). RESULTS: The preventable attributable fraction of radon on lung cancer was 3.8% (95% uncertainty interval: 0.6%, 8.3%). In cumulative present values the intervention would cost $238 (145, 310) million and save 892 (133, 1981) lives; each life saved costs $0.27 (0.09, 0.9) million. The cost-effect ratio was sensitive to the radon risk, the radon exposure distribution, and the latency period of lung cancer. Together these three parameters explained 90% of the variation in the cost-effect ratio. CONCLUSIONS: The uncertainty in the estimated cost per life is large, mainly due to uncertainty in the risk of lung cancer from radon. Based on estimates from road construction, the Norwegian society has been willing to pay $1 million to save a life. This is above the upper uncertainty limit of the cost per life. The intervention against radon in homes, therefore, seems justifiable.     

Bootstrap analysis of multivariate failure time data

Multivariate failure time data often arise in research. Cox proportional hazards modelling is a widely used method of analysing failure time data for independent observations. However, when failure times are correlated the Cox proportional hazards model does not yield valid estimates of standard errors or significance tests. Many methods for the analysis of multivariate failure time data have been proposed. These methods commonly test hypotheses about the regression parameters, a practice which averages the treatment effect across time. The purpose of this paper is to examine the bootstrap method for obtaining standard errors in the multivariate failure time case, particularly when the focus is the survival probability or the treatment effect at a single time point such as in a surgical trial. Our motivating example comes from the Asymptomatic Carotid and Atherosclerosis Study (ACAS) in which the outcome of stroke or perioperative complications could be observed for either or both carotid arteries within each patient. Extensive simulation studies were conducted to examine the bootstrap procedure for analysing correlated failure time data under a variety of conditions including a range of treatment effects, cluster sizes, intercluster correlation values and for both proportional and non-proportional data. We found that the bootstrap method was able to estimate the standard error adequately for survival probabilities at a specific time and the standard error for the survival difference and the relative risk at a specific time. We illustrated the bootstrap method for calculating the standard error for the survival probability and statistical testing at a specific time value by analysing the two arteries per patient from the ACAS study.     

The impact of educational interventions on primary health care workers' knowledge of occupational exposure to blood or body fluids

AIM: To assess the impact of educational interventions on primary health care workers' knowledge of management of occupational exposure to blood or body fluids. METHODS: Cluster-randomized trial of educational interventions in two National Health Service board areas in Scotland. Medical and dental practices were randomized to four groups; Group A, a control group of practices where staff received no intervention, Group B practices where staff received a flow chart regarding the management of blood and body fluid exposures, Group C received an e-mail alert containing the flow chart and Group D practices received an oral presentation of information in the flow chart. Staff knowledge was assessed on one occasion, following the educational intervention, using an anonymous postal questionnaire. RESULTS: Two hundred and fifteen medical and dental practices were approached and 114 practices participated (response rate 53%). A total of 1120 individual questionnaires were returned. Face to face training was the most effective intervention with four of five outcome measures showing better than expected knowledge. Seventy-seven percent of staff identified themselves as at risk of exposure to blood and body fluids. Twenty-one percent of staff believed they were not at risk of exposure to blood-borne viruses although potentially exposed and 16% of exposed staff had not been immunized against hepatitis B. Of the 856 'at risk' staff, 48% had not received training regarding blood-borne viruses. CONCLUSIONS: We found greater knowledge regarding management of exposures to blood and body fluids following face to face training than other educational interventions. There is a need for education of at risk primary health care workers.     

Analysing malaria drug trials on a per‐individual or per‐clone basis: a comparison of methods

There are a variety of methods used to estimate the effectiveness of antimalarial drugs in clinical trials, invariably on a per‐person basis. A person, however, may have more than one malaria infection present at the time of treatment. We evaluate currently used methods for analysing malaria trials on a per‐individual basis and introduce a novel method to estimate the cure rate on a per‐infection (clone) basis. We used simulated and real data to highlight the differences of the various methods. We give special attention to classifying outcomes as cured, recrudescent (infections that never fully cleared) or ambiguous on the basis of genetic markers at three loci. To estimate cure rates on a per‐clone basis, we used the genetic information within an individual before treatment to determine the number of clones present. We used the genetic information obtained at the time of treatment failure to classify clones as recrudescence or new infections. On the per‐individual level, we find that the most accurate methods of classification label an individual as newly infected if all alleles are different at the beginning and at the time of failure and as a recrudescence if all or some alleles were the same. The most appropriate analysis method is survival analysis or alternatively for complete data/per‐protocol analysis a proportion estimate that treats new infections as successes. We show that the analysis of drug effectiveness on a per‐clone basis estimates the cure rate accurately and allows more detailed evaluation of the performance of the treatment. Copyright © 2012 John Wiley & Sons, Ltd.