A novel equivalence probability weighted power prior for using historical control data in an adaptive clinical trial design: A comparison to standard methods

A standard two-arm randomised controlled trial usually compares an intervention to a control treatment with equal numbers of patients randomised to each treatment arm and only data from within the current trial are used to assess the treatment effect. Historical data are used when designing new trials and have recently been considered for use in the analysis when the required number of patients under a standard trial design cannot be achieved. Incorporating historical control data could lead to more efficient trials, reducing the number of controls required in the current study when the historical and current control data agree. However, when the data are inconsistent, there is potential for biased treatment effect estimates, inflated type I error and reduced power. We introduce two novel approaches for binary data which discount historical data based on the agreement with the current trial controls, an equivalence approach and an approach based on tail area probabilities. An adaptive design is used where the allocation ratio is adapted at the interim analysis, randomising fewer patients to control when there is agreement. The historical data are down-weighted in the analysis using the power prior approach with a fixed power. We compare operating characteristics of the proposed design to historical data methods in the literature: the modified power prior; commensurate prior; and robust mixture prior. The equivalence probability weight approach is intuitive and the operating characteristics can be calculated exactly. Furthermore, the equivalence bounds can be chosen to control the maximum possible inflation in type I error.     

The BIAS of the maximum likelihood estimators of the von mises-fisher concentration parameters

It is shown that the bias of the maximum likelihood estimators of the concentration parameters of the von Mises and Fisher distributions is considerable. New estimators which are either nearly unbiased or nearly median unbiased are proposed.     

The impact of respondent attentiveness on reliability and validity

This study aims to assess whether respondent inattentiveness causes systematic and unsystematic measurement error that influences survey data quality. To determine the impact of (in)attentiveness on the reliability and validity of target measures, we compared respondents from a German online survey (N = 5205) who had passed two attention checks with those who had failed. Our results show that inattentiveness induces both random and systematic measurement error, which impacts estimates of the reliability and validity of multi-item scales. In addition, we conducted a sensitivity analysis, which revealed that the impact of inattentiveness on analyses can be substantial.     

Assessing efficacy in important subgroups in confirmatory trials: An example using Bayesian dynamic borrowing

Assessment of efficacy in important subgroups – such as those defined by sex, age, race and region – in confirmatory trials is typically performed using separate analysis of the specific subgroup. This ignores relevant information from the complementary subgroup. Bayesian dynamic borrowing uses an informative prior based on analysis of the complementary subgroup and a weak prior distribution centred on a mean of zero to construct a robust mixture prior. This combination of priors allows for dynamic borrowing of prior information; the analysis learns how much of the complementary subgroup prior information to borrow based on the consistency between the subgroup of interest and the complementary subgroup. A tipping point analysis can be carried out to identify how much prior weight needs to be placed on the complementary subgroup component of the robust mixture prior to establish efficacy in the subgroup of interest. An attractive feature of the tipping point analysis is that it enables the evidence from the source subgroup, the evidence from the target subgroup, and the combined evidence to be displayed alongside each other. This method is illustrated with an example trial in severe asthma where efficacy in the adolescent subgroup was assessed using a mixture prior combining an informative prior from the adult data in the same trial with a non-informative prior.     

Mixture of measurement errors and their impact on parameter inferences

A mixture measurement error model built upon skew normal distributions and normal distributions is developed to evaluate various impacts of measurement errors to parameter inferences in logistic regressions. Data generated from survey questionnaires are usually error contaminated. We consider two types of errors: person-specific bias and random errors. Person-specific bias is modelled using skew normal distribution, and the distribution of random errors is described by a normal distribution. Intensive simulations are conducted to evaluate the contribution of each component in the mixture to outcomes of interest. The proposed method is then applied to a questionnaire data set generated from a neural tube defect study. Simulation results and real data application indicate that ignoring measurement errors or misspecifying measurement error components can both produce misleading results, especially when measurement errors are actually skew distributed. The inferred parameters can be attenuated or inflated depending on how the measurement error components are specified. We expect the findings will self-explain the importance of adjusting measurement errors and thus benefit future data collection effort.     

Gauging the Impact of Growing Nonresponse on Estimates from a National RDD Telephone Survey

Declining contact and cooperation rates in random digit dial(RDD) national telephone surveys raise serious concerns aboutthe validity of estimates drawn from such research. While researchin the 1990s indicated that nonresponse bias was relativelysmall, response rates have continued to fall since then. Thecurrent study replicates a 1997 methodological experiment thatcompared results from a "Standard" 5-day survey employing thePew Research Center’s usual methodology with results froma "Rigorous" survey conducted over a much longer field periodand achieving a significantly higher response rate. As withthe 1997 study, there is little to suggest that unit nonresponsewithin the range of response rates obtained seriously threatensthe quality of survey estimates. In 77 out of 84 comparableitems, the two surveys yielded results that were statisticallyindistinguishable. While the "Rigorous" study respondents tendedto be somewhat less politically engaged, they did not reportconsistently different behaviors or attitudes on other kindsof questions. With respect to sample composition, the Standardsurvey was closely aligned with estimates from the U.S. Censusand other large government surveys on most variables. We extendour analysis of nonresponse to include comparisons with thehardest-to-reach respondents and with respondents who terminatedthe interview prior to completion.     

Small area variation in hospital admission rates: Bayesian adjustment for primary care and hospital factors

Hospital admission rates are often used as a proxy to reflect patterns of morbidity or health need in population subgroups or across geographic areas. This paper considers the estimation of small area variations in relative health need, as measured by routinely collected hospital admissions data, after allowing for variation in general practice (primary care) and hospital (supply) effects. A fully Bayesian hierarchical modelling framework is adopted, using combinations of electoral ward populations and general practice patients' lists to define catchment groups for analysis. Hospitals create a further stratum, with flows of patients between catchment groups and hospitals being represented by a gravity model. Variations in health outcomes are modelled by using a range of random-effects structures for each cross-classification of strata, together with a consideration of ward, practice, hospital and crossed level covariates. The approach is applied to case-studies of child respiratory and total emergency hospital admissions for residents in a London health authority.     

GOODNESS-OF-FIT AND DISCORDANCY TESTS FOR SAMPLES FROM THE WATSON DISTRIBUTION ON THE SPHERE

The only parametric model in current use for axial data from a rotationally symmetric bipolar or girdle distribution on the sphere is the Watson distribution. This paper develops methods for evaluating the model as a fit to data using graphical and formal goodness-of-fit tests, and tests of discordancy.