Two Theories on the best Bench: Internal and External Validity of the Theories of Ronald Inglehart and Shalom Schwartz
Randomized controlled trials (RCTs) are considered gold standard in generating judicious evidence to support treatment decisions. Ideal-typical trials are called explanatory trials to distinguish it from trials completed under real-world conditions. The four most prevalent types of bias (selection-, performance-, attrition-, and detection-bias) can be avoided and internal validity of a study can be increased if all requested quality criteria will be met. The external validity can be neither investigated not can it be confirmed by randomized trials. But the confirmation of external validity is as important as the confirmation of internal validity because knowledge that has been generated in RCTs will be valuable only if it can be successfully applied to patients under real-world conditions. For confirmation of external validity the mentioned four types of bias have to be avoided. In addition, it has to be confirmed that the individuals from whom the evidence was derived are comparable to the individuals to whom the evidence should be applied. Violation of this simple appearing requirement is called 'sampling bias'. A two-step procedure seems to be useful to confirm internal as well as external evidence. As first step the efficacy of a therapeutic principle may be confirmed under ideal study conditions by using an explanatory trial without demanding the confirmation of external validity. In a second step the benefit for the investigated group of patients is examined under real-world conditions (pragmatic trial). The design and established methods for evaluation of these studies are discussed. The two-step approach offers three advantages: it reduces the risk to over-interpret the results of RCTs as explanatory trials can only demonstrate efficacy under ideal conditions. The benefit which is requested by our authorities can be demonstrated only by pragmatic trials which consider the external validity. Progress may possibly achieved only if controlled pragmatic trials will be used which can compare the influence of the intended (specific treatment effect) intervention with not-intended (confounder) interventions. Examples for these methods are the propensity score matching or structural equation models.
Non-responses caused by refusals became the main reason for surveys’ failure to provide representative data. Refusals do not occur randomly and they distort representation of certain social groups and subgroups in survey data. Criteria for external validity are seldom mentioned in publications dealing with nonresponse bias in surveys. We propose the method for estimating certain biases of sampling by calculating indicators based on sample data, which could be compared with reliable statistical data from some independent source.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.