Evidence
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Individualized treatment effect prediction instead targets the difference in expected outcome under treatment versus control for a given set of covariate values, and thus requires a model that explicitly allows the treatment effect to vary across individuals.
Passages supplied to the Evidence version
Card 1 · The Choice of Effect Measure for Binary Outcomes: Introducing Counterfactual Outcome State Transition Parameters
Standard measures of effect, including the risk ratio, the odds ratio, and the risk difference, are associated with a number of well-described shortcomings, and no consensus exists about the conditions under which investigators should choose one effect measure over another. In this paper, we introdu…
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Standard measures of effect, including the risk ratio, the odds ratio, and the risk difference, are associated with a number of well-described shortcomings, and no consensus exists about the conditions under which investigators should choose one effect measure over another. In this paper, we introduce a new framework for reasoning about choice of effect measure by linking two separate versions of the risk ratio to a counterfactual causal model. In our approach, effects are defined in terms of "counterfactual outcome state transition parameters", that is, the proportion of those individuals who would not have been a case by the end of follow-up if untreated, who would have responded to treatment by becoming a case; and the proportion of those individuals who would have become a case by the end of follow-up if untreated who would have responded to treatment by not becoming a case. Although counterfactual outcome state transition parameters are generally not identified from the data witho …
Card 2 · Disagreement Concerning Effect-Measure Modification
Stratifying factors, like age and gender, can modify the effect of treatments and exposures on risk of a studied outcome. Several effect measures, including the relative risk, hazard ratio, odds ratio, and risk difference, can be used to measure this modification. It is known that choice of effect m…
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Stratifying factors, like age and gender, can modify the effect of treatments and exposures on risk of a studied outcome. Several effect measures, including the relative risk, hazard ratio, odds ratio, and risk difference, can be used to measure this modification. It is known that choice of effect measure may determine the presence and direction of effect-measure modification. We show that considering the opposite outcome -- for example, recovery instead of death -- may similarly influence effect-measure modification. In fact, if the relative risk for the studied outcome and the relative risk for the opposite outcome agree about the direction of effect-measure modification, then so will the two cumulative hazard ratios, the risk difference, and the odds ratio. When risks are randomly sampled from the uniform (0,1) distribution, the probability of this happening is 5/6. Disagreement is probable enough that researchers considering one relative risk should also consider the other and furt …
Card 3 · Subtleties in the interpretation of hazard ratios
The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by (Hernan, 2010) in commentary, which emphasised that the hazard ratio contrasts populations of treated and untreated individu…
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The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by (Hernan, 2010) in commentary, which emphasised that the hazard ratio contrasts populations of treated and untreated individuals who survived a given period of time, populations that will typically fail to be comparable - even in a randomised trial - as a result of different pressures or intensities acting on both populations. The commentary has been very influential, but also a source of surprise and confusion. In this note, we aim to provide more insight into the subtle interpretation of hazard ratios and differences, by investigating in particular what can be learned about treatment effect from the hazard ratio becoming 1 after a certain period of time. Throughout, we will focus on the analysis of randomised experiments, but our results have immediate implications for the interpretation of hazard ratios in obse …
Card 4 · The statistical properties of RCTs and a proposal for shrinkage
Abstract We abstract the concept of a randomized controlled trial as a triple , where is the primary efficacy parameter, b the estimate, and s the standard error (). If the parameter is either a difference of means, a log odds ratio or a log hazard ratio, then it is reasonable to assume that b is un…
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Abstract We abstract the concept of a randomized controlled trial as a triple , where is the primary efficacy parameter, b the estimate, and s the standard error (). If the parameter is either a difference of means, a log odds ratio or a log hazard ratio, then it is reasonable to assume that b is unbiased and normally distributed. This then allows us to estimate the joint distribution of the z‐value and the signal‐to‐noise ratio from a sample of pairs . We have collected 23 551 such pairs from the Cochrane database. We note that there are many statistical quantities that depend on only through the pair . We start by determining the estimated distribution of the achieved power. In particular, we estimate the median achieved power to be only 13%. We also consider the exaggeration ratio which is the factor by which the magnitude of is overestimated. We find that if the estimate is just significant at the 5% level, we would expect it to overestimate the true effect by a factor of 1.7. This …
Card 5 · A Small Sample Correction for Estimating Attributable Risk in Case-Control Studies
The attributable risk, often called the population attributable risk, is in many epidemiological contexts a more relevant measure of exposure-disease association than the excess risk, relative risk, or odds ratio. When estimating attributable risk with case-control data and a rare disease, we presen…
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The attributable risk, often called the population attributable risk, is in many epidemiological contexts a more relevant measure of exposure-disease association than the excess risk, relative risk, or odds ratio. When estimating attributable risk with case-control data and a rare disease, we present a simple correction to the standard approach making it essentially unbiased, and also less noisy. As with analogous corrections given in Jewell (1986) for other measures of association, the adjustment often won't make a substantial difference unless the sample size is very small or point estimates are desired within fine strata, but we discuss the possible utility for applications.
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