Selection Bias Scenarios Unmeasured Confounder Scenarios Multiple Bias Analysis, Probabilistic Methods Probabilistic Misclassification Bias Analysis Probabilistic Selection Bias Analysis Probabilistic Unmeasured Confounder Bias Analysis Probabilistic Multiple Bias Analysis Inferential Framework Caveats and Cautions Studies of social, environmental, behavioral, and molecular risk factors associated with the incidence of particular diseases lead to primary public health interventions aimed at preventing the disease from occurring.

Few studies of etiologic relations allow for the exposure to be assigned by randomization because of ethical constraints; participants cannot be randomized ethically to an exposure that might cause harm. Secondary interventions aim to reduce the disease burden by detecting disease before symptoms manifest, so that treatments can more effectively cure the disease or reduce its morbidity. While many studies of disease-screening programs are conducted by randomized designs, some have been conducted using nonrandomized designs Weiss, In addition, the efficacy of screening programs established by randomized designs is often compared with its effectiveness measured by nonrandomized designs Weiss, , and history of screening can be an important confounder of etiologic relations Weiss, Tertiary interventions, or medical interventions, aim to reduce the disease burden by curing the disease or by reducing its morbidity.

Ideally, the efficacy of medical interventions is established by randomized study designs.

## Applying Quantitative Bias Analysis to Epidemiologic Data

However, such designs are sometimes unethical when patients cannot be assigned to a valid comparison group. For example, patients cannot be assigned to receive a placebo or to receive no therapy when there are accepted medical interventions available. When such a comparison group is required, nonrandomized designs are the only alternative. The medical literature contains a continuous and vigorous discussion about the advantages and disadvantages of nonrandomized versus randomized controlled trial evidence Barton, ; Ioannidis et al.

Randomized controlled trials and nonrandomized studies have complementary roles Sorensen et al. Furthermore, nonrandomized designs T. Lash et al. Thus, nonrandomized epidemiologic research contributes to the knowledge base for disease prevention, early detection, and treatment. The Treatment of Uncertainty in Nonrandomized Research If the objective of epidemiologic research is to obtain a valid, precise, and generalizable estimate of the effect of an exposure on the occurrence of an outcome e.

First, they must design their investigations to enhance the precision and validity of the effect estimate that they obtain. Second, recognizing that no study is perfect, they must inform stakeholders collaborators, colleagues, and consumers of their research findings how near the precision and validity objectives they believe their estimate of effect might be. To enhance the precision of an effect estimate i. Even with an efficient design and analysis, epidemiologists customarily present a quantitative assessment of the remaining random error about an effect estimate.

Although there has been considerable Thompson, a, b; Poole, , b and continuing The Editors, ; Weinberg, ; Gigerenzer, debate about methods of describing random error, a consensus has emerged in favor of the frequentist confidence interval Poole, To enhance the validity of an effect estimate i. When the validity might be compromised by confounding after implementation of the design, epidemiologists employ analytic techniques such as stratification Greenland and Rothman, or regression Greenland, to improve the validity of the effect estimate.

Analytic corrections for selection forces or measurement error are seldom seen. Quantitative assessments of the remaining systematic error about an effect estimate are even more rare. Thus, the quantitative assessment of the error about an effect estimate usually reflects only the residual random error. Much has been written Poole, a, b, ; Gigerenzer, ; Lang et al. Introduction 3 The near complete absence of quantitative assessments of residual systematic error in published epidemiologic research has received much less attention.

Several reasons likely explain this inattention.

First, existing custom does not expect a quantitative assessment of the systematic error about an effect estimate. With no demand to drive development and no habit to breed familiarity, few methods are available to quantify the systematic error about an effect estimate and few epidemiologists are comfortable with the implementation of existing methods.

However, recent methods papers published in leading epidemiology Steenland and Greenland, and statistics journals Greenland, have called for routine training in bias modeling for epidemiology students, so demand for this training will hopefully grow in the near term. Second, the established methods often require presentations of systematic error that are lengthy Greenland and Lash, , so are too unwieldy to incorporate into data summarization and inference. By comparison, the quantitative assessments of random error require little additional space for presentation of an apparently rigorous measurement of residual random error.

Finally, the automated analytic tools often used by epidemiologists provide quantitative assessments of residual random error about effect estimates, but contain no such automated method of assessing residual systematic error. Objective The objective of this test is to reduce the aforementioned barriers to regular implementation of quantitative sensitivity analysis. Epidemiologic studies yield effect estimates such as the risk ratio, rate ratio, odds ratio, or risk difference; all of which compare measurements of the occurrence of an outcome in a group with some common characteristic such as an exposure with the occurrence of the outcome in a second group with some other common characteristic such as the absence of exposure.

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The error accompanying an effect estimate equals the square of its difference from the true effect, and conventionally parses into random error variance and systematic error bias squared. Under this construct, random error is that which approaches zero as the study size increases and systematic error is that which does not. The amount of random error in an effect estimate is measured by its precision, which is usually quantified by p-values or confidence intervals that accompany the effect estimate. The amount of systematic error in an effect estimate is measured by its validity, which is seldom quantified.

A quantitative assessment of the systematic error about an effect estimate can be made using bias analysis.

## Applying Quantitative Bias Analysis to Epidemiologic Data

In this text, we have collected existing methods of quantitative bias analysis, explained them, illustrated them with examples, and linked them to tools for implementation. The software tools automate the analysis in familiar software and provide output that reduces the resources required for presentation. Probabilistic bias analysis and multiple biases modeling, for example, yield output that is no more complicated to present and interpret than the conventional point estimate and its associated confidence interval. For example, we have not addressed model misspecification or bias from missing data.

We have not addressed empirical methods of bias analysis or Bayesian methods of bias analysis, although these methods are related to many of the methods we do present.

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The interested reader can find textbooks and journal articles that describe these methods, some of which can be implemented by freely available software that can be downloaded from the internet. We have not presented these methods for several reasons. The alternative methods often require more sophisticated computer programming than required to implement the methods we present. Second, the empirical methods often require assumptions about the accuracy of the data source used to inform the bias analysis, which we believe can seldom be supported.

We prefer to recognize that the validation data are often themselves measured with error, and that this error should be incorporated into the bias analysis. The methods we present more readily accommodate this preference. Third, the Bayesian methods are similar to the probabilistic bias analysis methods and probabilistic multiple bias analysis methods we present toward the end of this text. The primary difference is that the Bayesian methods require specification of a prior for the parameter to be estimated i.

While we recognize and even agree with this Bayesian approach to data analysis and inference, particularly compared with the inherent frequentist prior that any association is equally likely, this text is not the forum to continue that debate. An Alternative As stated earlier, epidemiologic research is an exercise in measurement. Its objective is to obtain a valid and precise estimate of either the occurrence of disease in a population or the effect of an exposure on the occurrence of disease. Conventionally, epidemiologists present their measurements in three parts: a point estimate e.

Without randomization of study subjects to exposure groups, point estimates, confidence intervals, and p-values lack their correct frequentist interpretations An Alternative 5 Greenland, Randomization and a hypothesis about the expected allocation of outcomes — such as the null hypothesis — allow one to assign probabilities to the possible outcomes.

One can then compare the observed association, or a test statistic related to it, with the probability distribution to estimate the probability of the observed association, or associations more extreme, under the initial hypothesis. This comparison provides an important aid to causal inference Greenland, because it provides a probability that the outcome distribution is attributable to chance as opposed to the effects of exposure. The comparison is therefore at the root of frequentist statistical methods and inferences from them.

## Epidemiology - Wikipedia

When the exposure is not assigned by randomization, as is the case for nonrandomized epidemiologic research and for randomized trials with withdrawals or classification errors , the comparison provides a probability that the outcome distribution is attributable to chance as opposed to the combined effects of exposure and systematic errors. Causal inference therefore requires an educated guess about the strength of the systematic errors compared with the strength of the exposure effects.

http://tf.nn.threadsol.com/savon-best-mobile-phone.php These educated guesses can be accomplished quantitatively by likelihood methods Espeland and Hui, , Bayesian methods Gustafson, , regression calibration Spiegelman et al. Some of these methods will be described in later chapters. An assessment of the strength of systematic errors, compared with the strength of exposure effects, therefore becomes an exercise in reasoning under uncertainty. Human ability to reason under uncertainty has been wellstudied and shown to be susceptible to systematic bias resulting in predictable mistakes.

A brief review of this literature, focused on situations analogous to epidemiologic inference, suggests that the qualitative approach will frequently fail to safeguard against tendencies to favor exposure effects over systematic errors as an explanation for observed associations. The aforementioned quantitative methods have the potential to safeguard against these failures. Heuristics The Dual-Process Model of Cognition A substantial literature from the field of cognitive science has demonstrated that humans are frequently biased in their judgments about probabilities and at choosing between alternative explanations for observations Piattelli-Palmarini, b; Kahneman et al.

Some cognitive scientists postulate that the mind uses dual processes to solve problems that require such evaluations or choices Kahneman and Frederick, ; Sloman, We can think of this system as reason, although the label alone should not connote that this system is superior.

The Associative System is in constant action, while the Rule-Based System is constantly monitoring the Associative System to intervene when necessary. The process used by the Associative System to reach a solution relies on heuristics. A heuristic reduces the complex problem of assessing probabilities or predicting uncertain values to simpler judgmental operations Tversky and Kahneman, b. An example of a heuristic often encountered in epidemiologic research is the notion that nondifferential misclassification biases an association toward the null.

Heuristics often serve us well because their solutions are correlated with the truth, but they can sometimes lead to systematic and severe errors Tversky and Kahneman, b. Nondifferential and nondependent misclassification of a dichotomous exposure leads to the expectation that an association will be biased toward the null, but many exceptions exist.

For example, any particular association influenced by nondifferential misclassification may not be biased toward the null Jurek et al. Application of the misclassification heuristic without deliberation can lead to errors in an estimate of the strength and direction of the bias Lash and Fink, a , as is true for more general cognitive heuristics Tversky and Kahneman, b. Cognitive scientists have identified several classes of general heuristics, three of which are described below because they may be most relevant to causal inference based on nonrandomized epidemiologic results.