Comparison of confidence intervals for adjusted attributable risk estimates under multinomial sampling

The epidemiologic concept of the adjusted attributable risk is a useful approach to quantitatively describe the importance of risk factors on the population level. It measures the proportional reduction in disease probability when a risk factor is eliminated from the population, accounting for effects of confounding and effect-modification by nuisance variables. The computation of asymptotic variance estimates for estimates of the adjusted attributable risk is often done by applying the delta method. Investigations on the delta method have shown, however, that the delta method generally tends to underestimate the standard error, leading to biased confidence intervals. We compare confidence intervals for the adjusted attributable risk derived by applying computer intensive methods like the bootstrap or jackknife to confidence intervals based on asymptotic variance estimates using an extensive Monte Carlo simulation and within a real data example from a cohort study in cardiovascular disease epidemiology. Our results show that confidence intervals based on bootstrap and jackknife methods outperform intervals based on asymptotic theory. Best variants of computer intensive confidence intervals are indicated for different situations.     

A Generalized Estimator of the Attributable Benefit of an Optimal Treatment Regime

Summary For many diseases where there are several treatment options often there is no consensus on the best treatment to give individual patients. In such cases, it may be necessary to define a strategy for treatment assignment; that is, an algorithm that dictates the treatment an individual should receive based on their measured characteristics. Such a strategy or algorithm is also referred to as a treatment regime. The optimal treatment regime is the strategy that would provide the most public health benefit by minimizing as many poor outcomes as possible. Using a measure that is a generalization of attributable risk (AR) and notions of potential outcomes, we derive an estimator for the proportion of events that could have been prevented had the optimal treatment regime been implemented. Traditional AR studies look at the added risk that can be attributed to exposure of some contaminant; here we will instead study the benefit that can be attributed to using the optimal treatment strategy. We will show how regression models can be used to estimate the optimal treatment strategy and the attributable benefit of that strategy. We also derive the large sample properties of this estimator. As a motivating example, we will apply our methods to an observational study of 3856 patients treated at the Duke University Medical Center with prior coronary artery bypass graft surgery and further heart‐related problems requiring a catheterization. The patients may be treated with either medical therapy alone or a combination of medical therapy and percutaneous coronary intervention without a general consensus on which is the best treatment for individual patients.     

Average attributable fractions: a coherent theory for apportioning excess risk to individual risk factors and subpopulations

The attributable fraction in a population and the attributable fraction in exposed are different epidemiologic measures for quantifying the contribution of a risk factor to the risk of disease. While the attributable fraction in a population depends on both the relative risk of disease and the risk of being exposed in the population, the attributable fraction in exposed depends only on the relative risk. Similar relationships apply to the combined attributable fraction in a population and in exposed, respectively, for quantifying the total contribution of a group of risk factors. Eide and Gefeller (1995) showed how the sequential and average attributable fractions could be applied to quantify the contributions of the individual risk factors to a combined attributable fraction in a population. The present paper shows how this methodology can be extended to the combined attributable fraction in exposed. The resulting average attributable fractions in exposed are compared to other proposed methods. The relationship between the average attributable fractions in a population and in exposed is outlined, thus establishing a coherent theory for apportioning attributable fractions in individuals, groups of individuals and populations, to single risk factors or groups of risk factors like modifiable versus nonmodifiable factors.     

On the conversion of solid cancer excess relative risk into lifetime attributable risk

Risk coefficients representing the lifetime radiation-induced cancer mortality (or incidence) attributable to an exposure to ionizing radiation, have been published by major international scientific committees. The calculations involve observations in an exposed population and choices of a standard population (for risk transportation), of suitable numerical models, and of computational techniques. The present lack of a firm convention for these choices makes it difficult to inter-compare risk estimates presented by different scientific bodies. Some issues that relate to a necessary harmonization and standardization of risk estimates are explored here. Computational methods are discussed and, in line with the approach utilized by ICRP, conversion factors from excess relative risk (ERR) to lifetime attributable risk (LAR) are exemplified for exposures at all ages and for occupational exposures. A standard population is specified to illustrate the possibility of a simplified standard for risk transportation computations. It is suggested that a more realistic perception of lifetime risk could be gained by the use of coefficients scaled to the lifetime spontaneous cancer rates in the standard population. The resulting quantity lifetime fractional risk (LFR) is advantageous also because it depends much less on the choice of the reference population than the lifetime attributable risk (LAR). Received: 5 April 2001 / Accepted: 1 July 2001     

Variance calculations and confidence intervals for estimates of the attributable risk based on logistic models

The attributable risk (AR), defined as AR = [Pr(disease) - Pr(disease/no exposure)]/Pr(disease), measures the proportion of disease risk that is attributable to an exposure. Recently Bruzzi et al. (1985, American Journal of Epidemiology 122, 904-914) presented point estimates of AR based on logistic models for case-control data to allow for confounding factors and secondary exposures. To produce confidence intervals, we derived variance estimates for AR under the logistic model and for various designs for sampling controls. Calculations for discrete exposure and confounding factors require covariances between estimates of the risk parameters of the logistic model and the proportions of cases with given levels of exposure and confounding factors. These covariances are estimated from Taylor series expansions applied to implicit functions. Similar calculations for continuous exposures are derived using influence functions. Simulations indicate that those asymptotic procedures yield reliable variance estimates and confidence intervals with near nominal coverage. An example illustrates the usefulness of variance calculations in selecting a logistic model that is neither so simplified as to exhibit systematic lack of fit nor so complicated as to inflate the variance of the estimate of AR.     

A scaled linear mixed model for multiple outcomes

We propose a scaled linear mixed model to assess the effects of exposure and other covariates on multiple continuous outcomes. The most general form of the model allows a different exposure effect for each outcome. An important special case is a model that represents the exposure effects using a common global measure that can be characterized in terms of effect sizes. Correlations among different outcomes within the same subject are accommodated using random effects. We develop two approaches to model fitting, including the maximum likelihood method and the working parameter method. A key feature of both methods is that they can be easily implemented by repeatedly calling software for fitting standard linear mixed models, e.g., SAS PROC MIXED. Compared to the maximum likelihood method, the working parameter method is easier to implement and yields fully efficient estimators of the parameters of interest. We illustrate the proposed methods by analyzing data from a study of the effects of occupational pesticide exposure on semen quality in a cohort of Chinese men.     

The Fraction of Cancer Attributable to Ways of Life,Infections, Occupation,and Environmental Agents in Brazil in 2020

Many human cancers develop as a result of exposure to risk factors related to the environment and ways of life. The aim of this study was to estimate attributable fractions of 25 types of cancers resulting from exposure to modifiable risk factors in Brazil. The prevalence of exposure to selected risk factors among adults was obtained from population-based surveys conducted from 2000 to 2008. Risk estimates were based on data drawn from meta-analyses or large, high quality studies. Population-attributable fractions (PAF) for a combination of risk factors, as well as the number of preventable deaths and cancer cases, were calculated for 2020. The known preventable risk factors studied will account for 34% of cancer cases among men and 35% among women in 2020, and for 46% and 39% deaths, respectively. The highest attributable fractions were estimated for tobacco smoking, infections, low consumption of fruits and vegetables, excess weight, reproductive factors, and physical inactivity. This is the first study to systematically estimate the fraction of cancer attributable to potentially modifiable risk factors in Brazil. Strategies for primary prevention of tobacco smoking and control of infection and the promotion of a healthy diet and physical activity should be the main priorities in policies for cancer prevention in the country.     

An Annotated Bibliography on the Attributable Risk

The attributable risk constitutes an important epidemiologic risk measure. In epidemiologic studies it quantifies the proportion of cases of disease due to the exposure factor under study. Hence, it assesses the public health importance of an exposure factor in the study population. The literature on the concept of attributable risk is diverse, appears in a variety of journals from different specialities, and most papers cite only a very limited part of it. In addition, it suffers from a substantial confusion in terminology and algebraic formulation. As a consequence, it is difficult to obtain an overview with respect to the statistical results relating to the concept. To remedy this problem, this paper provides an annotated bibliography containing a complete list of all references dealing with methodological aspects of the attributable risk.     

Calculation of the 1995 lung cancer incidence in the Netherlands and Sweden caused by smoking and radon: risk implications for radon

A two-mutation carcinogenesis model was used to calculate the expected lung cancer incidence caused by both smoking and exposure to radon in two populations, i.e. those of the Netherlands and Sweden. The model parameters were taken from a previous analysis of lung cancer in smokers and uranium miners and the model was applied to the two populations taking into account the smoking habits and exposure to radon. For both countries, the smoking histories and indoor radon exposure data for the period 1910-1995 were reconstructed and used in the calculations. Compared with the number of lung cancer cases observed in 1995 among both males and females in the two countries, the calculations show that between 72% and 94% of the registered lung cancer cases may be attributable to the combined effects of radon and smoking. In the Netherlands, a portion of about 4% and in Sweden, a portion of about 20% of the lung cancer cases (at ages 0-80 years) may be attributable to radon exposure, the numbers for males being slightly lower than for females. In the Netherlands, the proportions of lung cancers attributable to smoking are 91% for males and 71% for females; in Sweden, the figures are 70% and 56%, respectively. The risk from radon exposure is dependent on gender and cigarette smoking: the excess absolute risk for continuous exposure to 100 Bq m-3 ranges between 0.003 and 0.006 and compares well with current estimates, e.g. 0.0043 of the International Commission on Radiological Protection (ICRP). The excess relative risk for continuous exposure to 100 Bq m-3 shows a larger variation, ranging generally between 0.1 for smokers and 1.0 for non-smokers. The results support the assumption that exposure to (indoor) radon, even at a level as low as background radiation, causes lung cancer proportional to the dose and is consistent with risk factors derived from the miners data.     

Tuberculosis incidence in prisons: a systematic review

Background

Transmission of tuberculosis (TB) in prisons has been reported worldwide to be much higher than that reported for the corresponding general population.

Methods and Findings

A systematic review has been performed to assess the risk of incident latent tuberculosis infection (LTBI) and TB disease in prisons, as compared to the incidence in the corresponding local general population, and to estimate the fraction of TB in the general population attributable (PAF%) to transmission within prisons. Primary peer-reviewed studies have been searched to assess the incidence of LTBI and/or TB within prisons published until June 2010; both inmates and prison staff were considered. Studies, which were independently screened by two reviewers, were eligible for inclusion if they reported the incidence of LTBI and TB disease in prisons. Available data were collected from 23 studies out of 582 potentially relevant unique citations. Five studies from the US and one from Brazil were available to assess the incidence of LTBI in prisons, while 19 studies were available to assess the incidence of TB. The median estimated annual incidence rate ratio (IRR) for LTBI and TB were 26.4 (interquartile range [IQR]: 13.0–61.8) and 23.0 (IQR: 11.7–36.1), respectively. The median estimated fraction (PAF%) of tuberculosis in the general population attributable to the exposure in prisons for TB was 8.5% (IQR: 1.9%–17.9%) and 6.3% (IQR: 2.7%–17.2%) in high- and middle/low-income countries, respectively.

Conclusions

The very high IRR and the substantial population attributable fraction show that much better TB control in prisons could potentially protect prisoners and staff from within-prison spread of TB and would significantly reduce the national burden of TB. Future studies should measure the impact of the conditions in prisons on TB transmission and assess the population attributable risk of prison-to-community spread. Please see later in the article for the Editors'' Summary     

Avoiding biohazards in medical,veterinary and research laboratories

Personnel in medical, veterinary or research laboratories may be exposed to a wide variety of pathogens that range from deadly to debilitating. For some of these pathogens, no treatment is available, and in other cases the treatment does not fully control the disease. It is important that personnel in laboratories that process human or microbiological specimens follow universal precautions when handling tissues, cells, or microbiological specimens owing to the increasing numbers of individuals infected with hepatitis C and HIV in the US and the possibility that an individual may be asymptomatic when a specimen is obtained. Similar precautions must be followed in laboratories that use animal tissues owing to the possibility of exposure to agents that are pathogenic in humans. Personnel with conditions associated with immunosuppression should evaluate carefully whether or not specific laboratory environments put them at increased risk of disease. We offer here some general approaches to identifying biohazards and to minimizing the potential risk of exposure. The issues discussed can be used to develop a general safety program as required by regulatory or accrediting agencies, including the Occupational Safety and Health Administration.     

Avoiding biohazards in medical, veterinary and research laboratories

Personnel in medical, veterinary or research laboratories may be exposed to a wide variety of pathogens that range from deadly to debilitating. For some of these pathogens, no treatment is available, and in other cases the treatment does not fully control the disease. It is important that personnel in laboratories that process human or microbiological specimens follow universal precautions when handling tissues, cells, or microbiological specimens owing to the increasing numbers of individuals infected with hepatitis C and HIV in the US and the possibility that an individual may be asymptomatic when a specimen is obtained. Similar precautions must be followed in laboratories that use animal tissues owing to the possibility of exposure to agents that are pathogenic in humans. Personnel with conditions associated with immunosuppression should evaluate carefully whether or not specific laboratory environments put them at increased risk of disease. We offer here some general approaches to identifying biohazards and to minimizing the potential risk of exposure. The issues discussed can be used to develop a general safety program as required by regulatory or accrediting agencies, including the Occupational Safety and Health Administration.     

Beyond Attributable Burden: Estimating the Avoidable Burden of Disease Associated with Household Air Pollution

Background

The Global Burden of Disease (GBD) studies have transformed global understanding of health risks by producing comprehensive estimates of attributable disease burden, or the current disease that would be eliminated if a risk factor did not exist. Yet many have noted the greater policy significance of avoidable burden, or the future disease that could actually be eliminated if a risk factor were eliminated today. Avoidable risk may be considerably lower than attributable risk if baseline levels of exposure or disease are declining, or if a risk factor carries lagged effects on disease. As global efforts to deliver clean cookstoves accelerate, a temporal estimation of avoidable risk due to household air pollution (HAP) becomes increasingly important, particularly in light of the rapid uptake of modern stoves and ongoing epidemiologic transitions in regions like South and Southeast Asia.

Methods and Findings

We estimate the avoidable burden associated with HAP using International Futures (IFs), an integrated forecasting system that has been used to model future global disease burdens and risk factors. Building on GBD and other estimates, we integrated a detailed HAP exposure estimation and exposure-response model into IFs. We then conducted a counterfactual experiment in which HAP exposure is reduced to theoretical minimum levels in 2015. We evaluated avoidable mortality and DALY reductions for the years 2015 to 2024 relative to a Base Case scenario in which only endogenous changes occurred. We present results by cause and region, looking at impacts on acute lower respiratory infection (ALRI) and four noncommunicable diseases (NCDs). We found that just 2.6% of global DALYs would be averted between 2015 and 2024, compared to 4.5% of global DALYs attributed to HAP in the 2010 GBD study, due in large part to the endogenous tendency towards declining traditional stove usage in the IFs base case forecast. The extent of diminished impact was comparable for ALRI and affected NCDs, though for different reasons. ALRI impacts diminish due to the declining burden of ALRI in the base case forecast, particularly apparent in South Asia and Southeast Asia. Although NCD burdens are rising in regions affected by HAP, the avoidable risk of NCD nonetheless diminishes due to lagged effects. Because the stove transition and the decline of ALRI are proceeding more slowly in Sub-Saharan Africa, avoidable impacts would also be more persistent (3.9% of total DALY due to HAP) compared to South Asia (3.6%) or Southeast Asia (2.5%).

Conclusions

Our results illustrate how a temporal dynamic calculation of avoidable risk may yield different estimates, compared to a static attributable risk estimate, of the global and regional burden of disease. Our results suggest a window of rising and falling opportunity for HAP interventions that may have already closed in Southeast Asia and may be closing quickly in South Asia, but may remain open longer in Sub-Saharan Africa. A proper accounting of global health priorities should apply an avoidable risk framework that considers the role of ongoing social, economic and health transitions in constantly altering the disease and risk factor landscape.     

Demonstration of the facts and research of the causes in environmental epidemiology: methodological aspects

There are usually three major steps in the study of the possible impact of environmental factors on health: 1) to demonstrate that there is an association between exposure to the factor and the disease under study; 2) to demonstrate that this association is causal; 3) to evaluate the health benefit that could be obtained by removing the source of exposure. Statistical methods are commonly assumed to provide an objective way of achieving these three steps. This paper reviews some of the conditions that have to be met to allow proper interpretations and to avoid some of the controversies that are often found in health-environment studies. First, it should be remembered that the so-called P value which is used to qualify 'statistically significant' associations between risk factors and diseases does not give any indication of the probability that this association is actual, while far too often it is believed that it does. The probability that an association between an environmental factor and a disease is real could, however, be estimated by using Bayesian methods. These methods require that the a priori probabilities be stated, which is difficult to do in practice. Some directions to overcome this difficulty are presented. Second, the analysis of causality cannot be carried out on statistical grounds alone and the so-called 'causality criteria' are of limited practical interest. Definition of what is a cause, and upon which conditions a candidate factor of a disease can be considered as a cause, deserves much research effort, and careful consideration of the huge literature (mostly outside of the epidemiological field, for example in logic) which is devoted to this subject. Finally, the measurement of the role of a factor in a disease is very often assessed through the use of 'attributable fraction' or 'attributable mortality'. This should be done only when it is demonstrated that the considered factor is causal. Moreover, the interpretation of attributable fractions to a specific factor may be difficult in the (general) case where there are multiple causal factors implied in the development of the disease. Demographic measures of 'potential years (or days, etc.) of life lost' should in general be used, rather than 'numbers of deaths' to quantify the possible impact of environmental factors. Also, as the personal factors are generally extremely important in the determinism of the causes of death associated to environmental factors, and as they cannot be controlled through ecological studies, epidemiological designs where these cofactors can be evaluated individually on cases and controls should be preferred.     

Biostatistics and epidemiology: measuring the risk attributable to an environmental or genetic factor

Disease frequency is measured through estimating incidence rates or disease risk. Several measures are used for assessing exposure-disease association, with adjusted estimates based on standardization, stratification, or more flexible regression techniques. Several measures are available to assess an exposure impact in terms of disease occurrence at the population level, including the commonly used attributable risk (AR). Adjusted AR estimation relies on stratification or regression techniques. Sequential and partial ARs have been proposed to handle the situation of multiple exposures and circumvent the associated non-additivity problem. Despite remaining issues in properly interpreting AR, AR remains a useful guide to assess prevention strategies.     

Excess Relative Risk as an Effect Measure in Case-Control Studies of Rare Diseases

Epidemiologists often use ratio-type indices (rate ratio, risk ratio and odds ratio) to quantify the association between exposure and disease. By comparison, less attention has been paid to effect measures on a difference scale (excess rate or excess risk). The excess relative risk (ERR) used primarily by radiation epidemiologists is of peculiar interest here, in that it involves both difference and ratio operations. The ERR index (but not the difference-type indices) is estimable in case-control studies. Using the theory of sufficient component cause model, the author shows that when there is no mechanistic interaction (no synergism in the sufficient cause sense) between the exposure under study and the stratifying variable, the ERR index (but not the ratio-type indices) in a rare-disease case-control setting should remain constant across strata and can therefore be regarded as a common effect parameter. By exploiting this homogeneity property, the related attributable fraction indices can also be estimated with greater precision. The author demonstrates the methodology (SAS codes provided) using a case-control dataset, and shows that ERR preserves the logical properties of the ratio-type indices. In light of the many desirable properties of the ERR index, the author advocates its use as an effect measure in case-control studies of rare diseases.     

Attributable risk function in the proportional hazards model for censored time-to-event

Time-to-event endpoints are often used in clinical and epidemiological studies to evaluate disease association with hazardous exposures. In the statistical literature of time-to-event analysis, such association is usually measured by the hazard ratio in the proportional hazards model. In public health, it is also of important interest to assess the excess risk attributable to an exposure in a given population. In this article, we extend the notion of 'population attributable fraction' for the binary outcomes to the attributable risk function for the event times in prospective studies. A simple estimator of the time-varying attributable risk function is proposed under the proportional hazards model. Its inference procedures are established. Monte-Carlo simulation studies are conducted to evaluate its validity and performance. The proposed methodology is motivated and demonstrated by the data collected in a multicenter acquired immunodeficiency syndrome (AIDS) cohort study to estimate the attributable risk of human immunodeficiency virus type 1 (HIV-1) infections due to several potential risk factors.     

Investigation on circular asymmetry of geographical distribution in cancer mortality of Hiroshima atomic bomb survivors based on risk maps: analysis of spatial survival data

While there is a considerable number of studies on the relationship between the risk of disease or death and direct exposure from the atomic bomb in Hiroshima, the risk for indirect exposure caused by residual radioactivity has not yet been fully evaluated. One of the reasons is that risk assessments have utilized estimated radiation doses, but that it is difficult to estimate indirect exposure. To evaluate risks for other causes, including indirect radiation exposure, as well as direct exposure, a statistical method is described here that evaluates risk with respect to individual location at the time of atomic bomb exposure instead of radiation dose. In addition, it is also considered to split the risks into separate risks due to direct exposure and other causes using radiation dose. The proposed method is applied to a cohort study of Hiroshima atomic bomb survivors. The resultant contour map suggests that the region west to the hypocenter has a higher risk compared to other areas. This in turn suggests that there exists an impact on risk that cannot be explained by direct exposure.     

Basic quantitative risk assessment of light sources: Comparison of light exposure assessment and endpoint life cycle impact assessment

Human Health Area of Protection (HHAoP) has been receiving greater emphasis in recent years in the scope of Environmental Impact Assessment (EIA) of products or services with more impact categories specifically dedicated to include different dimensions of HHAoP. Human health impacts of light sources, however, have received less attention despite their prevalent use for backlighting, general lighting and architectural purposes. Currently, Environmental Product Declarations (EPDs) of lighting devices and electronic devices with backlit screens do not address endpoint impacts nor do they specify technical properties of the light that can enable such an assessment. This study investigates endpoint impacts of eleven lighting devices (1) due to light exposure during the use phase and (2) due to emissions throughout their life cycle. Impacts are quantified as disease burden in terms of disability adjusted life years (DALY). The burden of exposure was calculated using attributable fraction (AF) method. The burden due to life cycle emissions was quantified using GaBi software and built-in life cycle impact assessment (LCIA) method ReCiPe. Endpoint impact categories included were climate change human health, human toxicity, ionizing radiation, ozone depletion, particulate matter formation, and photochemical oxidant formation. The disease burden due to light exposure of all light sources is of two orders of magnitude greater than the disease burden due to life cycle emissions pointing to the need for its treatment.     

Power Analysis for Population-Based Longitudinal Studies Investigating Gene-Environment Interactions in Chronic Diseases: A Simulation Study

Conventional methods for sample size calculation for population-based longitudinal studies tend to overestimate the statistical power by overlooking important determinants of the required sample size, such as the measurement errors and unmeasured etiological determinants, etc. In contrast, a simulation-based sample size calculation, if designed properly, allows these determinants to be taken into account and offers flexibility in accommodating complex study design features. The Canadian Longitudinal Study on Aging (CLSA) is a Canada-wide, 20-year follow-up study of 30,000 people between the ages of 45 and 85 years, with in-depth information collected every 3 years. A simulation study, based on an illness-death model, was conducted to: (1) investigate the statistical power profile of the CLSA to detect the effect of environmental and genetic risk factors, and their interaction on age-related chronic diseases; and (2) explore the design alternatives and implementation strategies for increasing the statistical power of population-based longitudinal studies in general. The results showed that the statistical power to identify the effect of environmental and genetic risk exposures, and their interaction on a disease was boosted when: (1) the prevalence of the risk exposures increased; (2) the disease of interest is relatively common in the population; and (3) risk exposures were measured accurately. In addition, the frequency of data collection every three years in the CLSA led to a slightly lower statistical power compared to the design assuming that participants underwent health monitoring continuously. The CLSA had sufficient power to detect a small (1<hazard ratio (HR)≤1.5) or moderate effect (1.5< HR≤2.0) of the environmental risk exposure, as long as the risk exposure and the disease of interest were not rare. It had enough power to detect a moderate or large (2.0<HR≤3.0) effect of the genetic risk exposure when the prevalence of the risk exposure was not very low (≥0.1) and the disease of interest was not rare (such as diabetes and dementia). The CLSA had enough power to detect a large effect of the gene-environment interaction only when both risk exposures had relatively high prevalence (0.2) and the disease of interest was very common (such as diabetes). The minimum detectable hazard ratios (MDHR) of the CLSA for the environmental and genetic risk exposures obtained from this simulation study were larger than those calculated according to the conventional sample size calculation method. For example, the MDHR for the environmental risk exposure was 1.15 according to the conventional method if the prevalence of the risk exposure was 0.1 and the disease of interest was dementia. In contrast, the MDHR was 1.61 if the same exposure was measured every 3 years with a misclassification rate of 0.1 according to this simulation study. With a given sample size, higher statistical power could be achieved by increasing the measuring frequency in participants with high risk of declining health status or changing risk exposures, and by increasing measurement accuracy of diseases and risk exposures. A properly designed simulation-based sample size calculation is superior to conventional methods when rigorous sample size calculation is necessary.