Sensitivity Analysis

Sensitivity analysis is useful in assessing how robust an association is to potential unmeasured or uncontrolled confounding. This article introduces a new measure called the "E-value," which is related to the evidence for causality in observational studies that are potentially subject to confounding. The E-value is defined as the minimum strength of association, on the risk ratio scale, that an unmeasured confounder would need to have with both the treatment and the outcome to fully explain away a specific treatment-outcome association, conditional on the measured covariates. A large E-value implies that considerable unmeasured confounding would be needed to explain away an effect estimate. A small E-value implies little unmeasured confounding would be needed to explain away an effect estimate. The authors propose that in all observational studies intended to produce evidence for causality, the E-value be reported or some other sensitivity analysis be used. They suggest calculating the E-value for both the observed association estimate (after adjustments for measured confounders) and the limit of the confidence interval closest to the null. If this were to become standard practice, the ability of the scientific community to assess evidence from observational studies would improve considerably, and ultimately, science would be strengthened.

I have performed monte carlo simulation of a VCO circuit and checked the sensitivity analysis. There are around 50 process parameters, whose individual variance contributions are listed in a tabular form for some performance parameters(Phase noise and Frequency of oscillations of VCO). I want to explore a minimum subset out of these 50 process parameters combinedly which should explain the performance parameters(Phase noise and frequency of oscillation of VCO) with a good accuracy. Any idea/suggestions in this regard please. Also i need to know more about this sensitivity analysis in Monte carlo simulations. Any documentations on this would be highly helpful to me.

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Sensitivity analysis allows analysts to explore the impact of uncertainty on their findings. It is an important part of any economic evaluation, and a lack of analysis is evidence of a poor quality study. Sensitivity analysis helps the analyst evaluate the reliability of conclusions for the context of the evaluation and can also facilitate consideration of the generalizability of results to other settings. The variety of one and multi-way sensitivity analyses offer simple and complementary approaches to evaluating the impact of uncertainty on the results and conclusions of economic evaluations. The paper begins with a brief discussion of the types of uncertainty that can arise in economic evaluation, and follows with suggestions of how to plan a justified sensitivity analysis. A number of specific techniques are worked through with examples, followed by a discussion of when it is best to use them. The main weakness associated with sensitivity analysis is the control that the analyst retains over three parts of the process: the choice of which variables to vary and which to treat as known or fixed; the amount of variation around the base value of the parameter that is considered clinically meaningful or policy-relevant; and the determination of what constitutes a sensitive or robust finding. It is therefore essential that the approach of the analyst is clear and justified. It is likely that the future will see further developments in the approaches and training of statistical analysis. But in the meantime, an increase in the number of evaluators undertaking a wider range of sensitivity analysis would improve the quality of evidence for, and outcomes of, decision-making.

This chapter considers the forms of sensitivity analysis that can be included in the analysis of an observational comparative effectiveness study, provides examples, and offers recommendations about the use of sensitivity analyses.

An underlying assumption of all epidemiological studies is that there is no unmeasured confounding, as unmeasured confounders cannot be accounted for in the analysis and including all confounders is a necessary condition for an unbiased estimate. Thus, inferences drawn from an epidemiologic study depend on this assumption. However, it is widely recognized that some potential confounding variables may not have been measured or available for analysis: the unmeasured confounding variable could either be a known confounder that is not present in the type of data being used (e.g., obesity is commonly not available in prescription claims databases) or an unknown confounder where the confounding relation is unsuspected. Quantifying the effect that an unmeasured confounding variable would have on study results provides an assessment of the sensitivity of the result to violations of the assumption of no unmeasured confounding. The robustness of an association to the presence of a confounder,1-2 can alter inferences that might be drawn from a study, which then might change how the study results are used to influence translation into clinical or policy decisionmaking. Methods for assessing the potential impact of unmeasured confounding on study results, as well as quasi-experimental methods to account for unmeasured confounding, are discussed later in the chapter.

Establishing a time window that appropriately captures exposure during etiologically relevant time periods can present a challenge in study design when decisions need to be made in the presence of uncertainty.5 Uncertainty about the most appropriate way to define drug exposure can lead to questions about what would have happened if the exposure had been defined a different way. A substantially different exposure-outcome association observed under different definitions of exposure (such as different time windows or dose [e.g., either daily or cumulative]) might provide insight into the biological mechanisms underlying the association or provide clues about potential confounding or unaddressed bias. As such, varying the exposure definition and re-analyzing under different definitions serves as a form of sensitivity analysis.

The association between exposure and outcome can also be assessed under different definitions of the outcome. Often a clinically relevant outcome in a data source can be ascertained in several ways (e.g., a single diagnosis code, multiple diagnosis codes, a combination of diagnosis and procedure codes). The analysis can be repeated using these different definitions of the outcome, which may shed light on the how well the original outcome definition truly reflects the condition of interest.

Beyond varying a single outcome definition, it is also possible to evaluate the association between the exposure and clinically different outcomes. If the association between the exposure and one clinical outcome is known from a study with strong validity (such as from a clinical trial) and can be reproduced in the study, the observed association between the exposure of interest and an outcome about which external data are not available becomes more credible. Since some outcomes might not be expected to occur immediately after exposure (e.g., cancer), the study could employ different lag (induction) periods between exposure and the first outcomes to be analyzed in order to assess the sensitivity of the result to the definition. This result can lead either to insight into potential unaddressed bias or confounding, or it could be used as a basis for discussion about etiology (e.g., does the outcome have a long onset period?).

Covariate definitions can also be modified to assess how well they address confounding in the analysis. Although a minimum set of covariates may be used to address confounding, there may be an advantage to using a staged approach where groups of covariates are introduced, leading to progressively greater adjustment. If done transparently, this approach may provide insight into which covariates have relatively greater influences on effect estimates, permitting comparison with known or expected associations or permitting the identification of possible intermediate variables.

The assessment of selection bias through sensitivity analysis involves assumptions regarding inclusion or participation by potential subjects, and results can be highly sensitive to assumptions. For example, the oversampling of cases exposed to one of the drugs under study (or, similarly, an undersampling) can lead to substantial changes in effect measures over ranges that might plausibly be evaluated. Even with external validation data, which may work for unmeasured confounders,9 it is difficult to account for more than a trivial amount of selection bias. Generally, if there is strong evidence of selection bias in a particular data set it is best to seek out alternative data sources.

The first section of this chapter covered traditional sensitivity analysis to test basic assumptions such as variable definitions and to consider the impact of an unmeasured confounder. These issues should be considered in every observational study of comparative effectiveness research. However, there are some additional sensitivity analyses that should be considered, depending on the nature of the epidemiological question and the data available. Not every analysis can (or should) consider these factors, but they can be as important as the more traditional sensitivity analysis approaches.

For many comparative effectiveness studies, the data used for the analysis were not specifically collected for the purpose of the research question. Instead, the data may have been obtained as part of routine care or for administrative purposes such as medical billing. In such cases, it may be possible to acquire multiple data sources for a single analysis (and use the additional data sources as a sensitivity analysis). Where this is not feasible, it may be possible to consider differences between study results and results obtained from other papers that use different data sources. 2351a5e196