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1.  How to interpret a small increase in AUC with an additional risk prediction marker: Decision analysis comes through 
Statistics in medicine  2014;33(22):3946-3959.
An important question in the evaluation of an additional risk prediction marker is how to interpret a small increase in the area under the receiver operating characteristic curve (AUC). Many researchers believe that a change in AUC is a poor metric because it increases only slightly with the addition of a marker with a large odds ratio. Because it is not possible on purely statistical grounds to choose between the odds ratio and AUC, we invoke decision analysis, which incorporates costs and benefits. For example a timely estimate of the risk of later non-elective operative delivery can help a woman in labor decide if she wants an early elective cesarean section to avoid greater complications from possible later non-elective operative delivery. A basic risk prediction model for later non-elective operative delivery involves only antepartum markers. Because adding intrapartum markers to this risk prediction model increases AUC by 0.02, we questioned whether this small improvement is worthwhile. A key decision-analytic quantity is the risk threshold, here the risk of later non-elective operative delivery at which a patient would be indifferent between an early elective cesarean section and usual care. For a range of risk thresholds, we found that an increase in the net benefit of risk prediction requires collecting intrapartum marker data on 68 to 124 women for every correct prediction of later non-elective operative delivery. Because data collection is non-invasive, this test tradeoff of 68 to 124 is clinically acceptable, indicating the value of adding intrapartum markers to the risk prediction model.
doi:10.1002/sim.6195
PMCID: PMC4156533  PMID: 24825728
AUC; cesarean section; decision curves; receiver operating characteristic curves; relative utility curves
2.  Clarifying the Role of Principal Stratification in the Paired Availability Design 
The paired availability design for historical controls postulated four classes corresponding to the treatment (old or new) a participant would receive if arrival occurred during either of two time periods associated with different availabilities of treatment. These classes were later extended to other settings and called principal strata. Judea Pearl asks if principal stratification is a goal or a tool and lists four interpretations of principal stratification. In the case of the paired availability design, principal stratification is a tool that falls squarely into Pearl's interpretation of principal stratification as “an approximation to research questions concerning population averages.” We describe the paired availability design and the important role played by principal stratification in estimating the effect of receipt of treatment in a population using data on changes in availability of treatment. We discuss the assumptions and their plausibility. We also introduce the extrapolated estimate to make the generalizability assumption more plausible. By showing why the assumptions are plausible we show why the paired availability design, which includes principal stratification as a key component, is useful for estimating the effect of receipt of treatment in a population. Thus, for our application, we answer Pearl's challenge to clearly demonstrate the value of principal stratification.
doi:10.2202/1557-4679.1338
PMCID: PMC3114955  PMID: 21686085
principal stratification; causal inference; paired availability design
3.  The Paired Availability Design for Historical Controls 
Background
Although a randomized trial represents the most rigorous method of evaluating a medical intervention, some interventions would be extremely difficult to evaluate using this study design. One alternative, an observational cohort study, can give biased results if it is not possible to adjust for all relevant risk factors.
Methods
A recently developed and less well-known alternative is the paired availability design for historical controls. The paired availability design requires at least 10 hospitals or medical centers in which there is a change in the availability of the medical intervention. The statistical analysis involves a weighted average of a simple "before" versus "after" comparison from each hospital or medical center that adjusts for the change in availability.
Results
We expanded requirements for the paired availability design to yield valid inference. (1) The hospitals or medical centers serve a stable population. (2) Other aspects of patient management remain constant over time. (3) Criteria for outcome evaluation are constant over time. (4) Patient preferences for the medical intervention are constant over time. (5) For hospitals where the intervention was available in the "before" group, a change in availability in the "after group" does not change the effect of the intervention on outcome.
Conclusion
The paired availability design has promise for evaluating medical versus surgical interventions, in which it is difficult to recruit patients to a randomized trial.
doi:10.1186/1471-2288-1-9
PMCID: PMC57808  PMID: 11602018

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