Historical controls in clinical trials: a note on linking Pocock's model with the robust mixture priors.

Several Bayesian methods have been proposed to borrow information dynamically from historical controls in clinical trials. In this note, we identify key features of the relationship between the first method proposed, the bias-variance method, which is strongly related to the commensurate prior approach, and a more recent and widely used approach called robust mixture priors (RMP). We focus on the two key terms that need to be chosen to define the RMP, namely $w$, the prior probability that the new trial differs systematically from the historical trial, and $s_v^2$, the variance of the vague component of the RMP. The relationship with Pocock's prior reveals that different combinations of these two terms can express similar prior beliefs about the amount of information provided by the historical data. This demonstrates the value of fixing $s_v^2$, e.g., so the vague component is "worth one subject." Prior belief about the relevance of the historical data is then driven by a single value, the prespecified weight $w$.

LEAP: the latent exchangeability prior for borrowing information from historical data.

It is becoming increasingly popular to elicit informative priors on the basis of historical data. Popular existing priors, including the power prior, commensurate prior, and robust meta-analytic predictive prior, provide blanket discounting. Thus, if only a subset of participants in the historical data are exchangeable with the current data, these priors may not be appropriate. In order to combat this issue, propensity score approaches have been proposed. However, these approaches are only concerned with the covariate distribution, whereas exchangeability is typically assessed with parameters pertaining to the outcome. In this paper, we introduce the latent exchangeability prior (LEAP), where observations in the historical data are classified into exchangeable and non-exchangeable groups. The LEAP discounts the historical data by identifying the most relevant subjects from the historical data. We compare our proposed approach against alternative approaches in simulations and present a case study using our proposed prior to augment a control arm in a phase 3 clinical trial in plaque psoriasis with an unbalanced randomization scheme.

Rejoinder to the discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data".

The discussions of our paper provide insights into the practical considerations of the latent exchangeability prior while also highlighting further extensions. In this rejoinder, we briefly summarize the discussions and provide comments.

A Bayesian platform trial design with hybrid control based on multisource exchangeability modelling.

Enrolling patients to the standard of care (SOC) arm in randomized clinical trials, especially for rare diseases, can be very challenging due to the lack of resources, restricted patient population availability, and ethical considerations. As the therapeutic effect for the SOC is often well documented in historical trials, we propose a Bayesian platform trial design with hybrid control based on the multisource exchangeability modelling (MEM) framework to harness historical control data. The MEM approach provides a computationally efficient method to formally evaluate the exchangeability of study outcomes between different data sources and allows us to make better informed data borrowing decisions based on the exchangeability between historical and concurrent data. We conduct extensive simulation studies to evaluate the proposed hybrid design. We demonstrate the proposed design leads to significant sample size reduction for the internal control arm and borrows more information compared to competing Bayesian approaches when historical and internal data are compatible.

Dust to Feed, Dust to Gray: The Effect of in Utero Exposure to the Dust Bowl on Old-Age Longevity.

Intensive agriculture and deep plowing caused topsoil erosion and dust storms during the 1930s, affecting agricultural income and land values for years. Given the growing literature on the relevance of in utero and early-life exposures, it is surprising that studies focusing on links between the Dust Bowl and later-life health have produced inconclusive and mixed results. We reevaluate this literature and study the long-term effects of in utero and early-life exposure to topsoil erosion caused by the 1930s Dust Bowl on old-age longevity. Specifically, using Social Security Administration death records linked with the full-count 1940 census, we conduct event studies with difference-in-differences designs to compare the longevity of individuals in high- versus low-topsoil-erosion counties before versus after 1930. We find intent-to-treat reductions in longevity of approximately 0.85 months for those born in high-erosion counties after 1930. We show that these effects are not an artifact of preexisting trends in longevity. Additional analyses suggest that the effects are more pronounced among children raised in farm households, females, and those whose mothers had lower education. We also provide suggestive evidence that reductions in adulthood income are a likely mechanism for the effects we document.

Power priors for replication studies.

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power of α, and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance I2. The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.

Covariate adjusted meta-analytic predictive (CA-MAP) prior for historical borrowing using patient-level data.

Utilization of historical data is increasingly common for gaining efficiency in the drug development and decision-making processes. The underlying issue of between-trial heterogeneity in clinical trials is a barrier in making these methods standard practice in the pharmaceutical industry. Common methods for historical borrowing discount the borrowed information based on the similarity between outcomes in the historical and current data. However, individual clinical trials and their outcomes are intrinsically heterogenous due to differences in study design, patient characteristics, and changes in standard of care. Additionally, differences in covariate distributions can produce inconsistencies in clinical outcome data between historical and current data when there may be a consistent covariate effect. In such scenario, borrowing historical data is still advantageous even though the population level outcome summaries are different. In this paper, we propose a covariate adjusted meta-analytic-predictive (CA-MAP) prior for historical control borrowing. A MAP prior is assigned to each covariate effect, allowing the amount of borrowing to be determined by the consistency of the covariate effects across the current and historical data. This approach integrates between-trial heterogeneity with covariate level heterogeneity to tune the amount of information borrowed. Our method is unique as it directly models the covariate effects instead of using the covariates to select a similar population to borrow from. In summary, our proposed patient-level extension of the MAP prior allows for the amount of historical control borrowing to depend on the similarity of covariate effects rather than similarity in clinical outcomes.

Upslope migration of snow avalanches in a warming climate.

Snow is highly sensitive to atmospheric warming. However, because of the lack of sufficiently long snow avalanche time series and statistical techniques capable of accounting for the numerous biases inherent to sparse and incomplete avalanche records, the evolution of process activity in a warming climate remains little known. Filling this gap requires innovative approaches that put avalanche activity into a long-term context. Here, we combine extensive historical records and Bayesian techniques to construct a 240-y chronicle of snow avalanching in the Vosges Mountains (France). We show evidence that the transition from the late Little Ice Age to the early twentieth century (i.e., 1850 to 1920 CE) was not only characterized by local winter warming in the order of +1.35 °C but that this warming also resulted in a more than sevenfold reduction in yearly avalanche numbers, a severe shrinkage of avalanche size, and shorter avalanche seasons as well as in a reduction of the extent of avalanche-prone terrain. Using a substantial corpus of snow and climate proxy sources, we explain this abrupt shift with increasingly scarcer snow conditions with the low-to-medium elevations of the Vosges Mountains (600 to 1,200 m above sea level [a.s.l.]). As a result, avalanches migrated upslope, with only a relict activity persisting at the highest elevations (release areas >1,200 m a.s.l.). This abrupt, unambiguous response of snow avalanche activity to warming provides valuable information to anticipate likely changes in avalanche behavior in higher mountain environments under ongoing and future warming.

Unequal before death: The effect of paternal education on children's old-age mortality in the United States.

A growing body of research documents the relevance of parental education as a marker of family socio-economic status for children's later-life health outcomes. A strand of this literature evaluates how the early-life environment shapes mortality outcomes during infancy and childhood. However, the evidence on mortality during the life course and old age is limited. This paper contributes to the literature by analysing the association between paternal education and children's old-age mortality. We use data from Social Security Administration death records over the years 1988-2005 linked to the United States 1940 Census. Applying a family(cousin)- fixed-effects model to account for shared environment, childhood exposures, and common endowments that may confound the long-term links, we find that having a father with a college or high-school education, compared with elementary/no education, is associated with a 4.6- or 2.6-month-higher age at death, respectively, for the child, conditional on them surviving to age 47.

Bayesian sample size determination using commensurate priors to leverage preexperimental data.

This paper develops Bayesian sample size formulae for experiments comparing two groups, where relevant preexperimental information from multiple sources can be incorporated in a robust prior to support both the design and analysis. We use commensurate predictive priors for borrowing of information and further place Gamma mixture priors on the precisions to account for preliminary belief about the pairwise (in)commensurability between parameters that underpin the historical and new experiments. Averaged over the probability space of the new experimental data, appropriate sample sizes are found according to criteria that control certain aspects of the posterior distribution, such as the coverage probability or length of a defined density region. Our Bayesian methodology can be applied to circumstances that compare two normal means, proportions, or event times. When nuisance parameters (such as variance) in the new experiment are unknown, a prior distribution can further be specified based on preexperimental data. Exact solutions are available based on most of the criteria considered for Bayesian sample size determination, while a search procedure is described in cases for which there are no closed-form expressions. We illustrate the application of our sample size formulae in the design of clinical trials, where pretrial information is available to be leveraged. Hypothetical data examples, motivated by a rare-disease trial with an elicited expert prior opinion, and a comprehensive performance evaluation of the proposed methodology are presented.

SAM: Self-adapting mixture prior to dynamically borrow information from historical data in clinical trials.

Mixture priors provide an intuitive way to incorporate historical data while accounting for potential prior-data conflict by combining an informative prior with a noninformative prior. However, prespecifying the mixing weight for each component remains a crucial challenge. Ideally, the mixing weight should reflect the degree of prior-data conflict, which is often unknown beforehand, posing a significant obstacle to the application and acceptance of mixture priors. To address this challenge, we introduce self-adapting mixture (SAM) priors that determine the mixing weight using likelihood ratio test statistics or Bayes factors. SAM priors are data-driven and self-adapting, favoring the informative (noninformative) prior component when there is little (substantial) evidence of prior-data conflict. Consequently, SAM priors achieve dynamic information borrowing. We demonstrate that SAM priors exhibit desirable properties in both finite and large samples and achieve information-borrowing consistency. Moreover, SAM priors are easy to compute, data-driven, and calibration-free, mitigating the risk of data dredging. Numerical studies show that SAM priors outperform existing methods in adopting prior-data conflicts effectively. We developed R package "SAMprior" and web application that are freely available at CRAN and www.trialdesign.org to facilitate the use of SAM priors.

Elastic priors to dynamically borrow information from historical data in clinical trials.

Use of historical data and real-world evidence holds great potential to improve the efficiency of clinical trials. One major challenge is to effectively borrow information from historical data while maintaining a reasonable type I error and minimal bias. We propose the elastic prior approach to address this challenge. Unlike existing approaches, this approach proactively controls the behavior of information borrowing and type I errors by incorporating a well-known concept of clinically significant difference through an elastic function, defined as a monotonic function of a congruence measure between historical data and trial data. The elastic function is constructed to satisfy a set of prespecified criteria such that the resulting prior will strongly borrow information when historical and trial data are congruent, but refrain from information borrowing when historical and trial data are incongruent. The elastic prior approach has a desirable property of being information borrowing consistent, that is, asymptotically controls type I error at the nominal value, no matter that historical data are congruent or not to the trial data. Our simulation study that evaluates the finite sample characteristic confirms that, compared to existing methods, the elastic prior has better type I error control and yields competitive or higher power. The proposed approach is applicable to binary, continuous, and survival endpoints.

The scale transformed power prior for use with historical data from a different outcome model.

We develop the scale transformed power prior for settings where historical and current data involve different data types, such as binary and continuous data. This situation arises often in clinical trials, for example, when historical data involve binary responses and the current data involve some other type of continuous or discrete outcome. The power prior, proposed by Ibrahim and Chen, does not address the issue of different data types. Herein, we develop a new type of power prior, which we call the scale transformed power prior (straPP). The straPP is constructed by transforming the power prior for the historical data by rescaling the parameter using a function of the Fisher information matrices for the historical and current data models, thereby shifting the scale of the parameter vector from that of the historical to that of the current data. Examples are presented to motivate the need for such a transformation, and simulation studies are presented to illustrate the performance advantages of the straPP over the power prior and other informative and noninformative priors. A real dataset from a clinical trial undertaken to study a novel transitional care model for stroke survivors is used to illustrate the methodology.

The written history of plant phenology: shaping primary sources for secondary publications.

Phenological research establishes the science of nature's natural calendar. This research, the monitoring and analysis of seasonal rhythms of plants and animals, is commonly based on citizen science data. Such data may be digitized from primary sources provided by the citizen scientist's original phenological diaries. Secondary data sources are formed by historical publications (for example, yearbooks and climate bulletins). While primary data has the advantage of first-hand notetaking, its digitization may, in practice, be time-consuming. Contrastingly, secondary data can contain well-organized typesetting, making digitization less labour-intensive. However, secondary data can be reshaped by the motivations of the historical actors who were collating the data. This study compared data from 1876-1894 gathered originally by citizen scientists (primary data) and the secondary data founded upon the previous primary data, later published by the Finnish Society of Sciences and Letters as a series of phenological yearbooks. In the secondary data, the recorded numbers of taxa and their phenological stages appeared to be fewer and phenological events standardized, with an increased prevalence of agricultural phenology (at the cost of autumn phenology). Moreover, it seems the secondary data had been screened for potential outliers. While secondary sources may provide current phenologists with coherent sets of relevant data, future users must be aware of potential data reshaping resulting from the preferences of historical actors. These actors may weigh and limit the original observations according to their own criteria and preferences.

Childhood exposure to birth registration laws and old-age mortality.

This paper studies the effects of the enactment of birth registration laws, as the official universal and uniform method of recording births, across US states in the first decades of the 20th century on old-age longevity for children affected by these laws. We show that establishing birth registration laws has long-term benefits for old-age health. The benefits are primarily driven by states with an effective child labor policy, suggesting that registering births helps the enforcement of child labor laws which in turn operate as the mechanism channel to improve old-age longevity. A treatment-on-treated calculation suggests an increase of 0.6 years of longevity from not working during childhood due to the birth registration law.

Long-run intergenerational health benefits of women empowerment: Evidence from suffrage movements in the US.

An ongoing body of research documents that women empowerment is associated with improved outcomes for children. However, little is known about the long-run effects on health outcomes. This paper adds to this literature and studies the association between maternal exposure to suffrage reforms and children's old-age longevity. We utilize changes in suffrage laws across US states and over time as a source of incentivizing maternal investment in children's health and education. Using the universe of death records in the US over the years 1979-2020 and implementing a difference-in-difference econometric framework, we find that cohorts exposed to suffrage throughout their childhood live 0.6 years longer than unexposed cohorts. Furthermore, we show that these effects are not driven by preexisting trends in longevity, endogenous migration, selective fertility, and changes in the demographic composition of the sample. Additional analysis reveals that improvements in education and income are candidate mechanisms. Moreover, we find substantial improvements in early-adulthood socioeconomic standing, height, and height-for-age outcomes due to childhood exposure to suffrage movements. A series of state-level analyses suggest reductions in infant and child mortality following suffrage law change. We also find evidence that counties in states that passed the law experienced new openings of County Health Departments and increases in physicians per capita.

BASIC: A Bayesian adaptive synthetic-control design for phase II clinical trials.

BACKGROUND: Randomized controlled trials are considered the gold standard for evaluating experimental treatments but often require large sample sizes. Single-arm trials require smaller sample sizes but are subject to bias when using historical control data for comparative inferences. This article presents a Bayesian adaptive synthetic-control design that exploits historical control data to create a hybrid of a single-arm trial and a randomized controlled trial. METHODS: The Bayesian adaptive synthetic control design has two stages. In stage 1, a prespecified number of patients are enrolled in a single arm given the experimental treatment. Based on the stage 1 data, applying propensity score matching and Bayesian posterior prediction methods, the usefulness of the historical control data for identifying a pseudo sample of matched synthetic-control patients for making comparative inferences is evaluated. If a sufficient number of synthetic controls can be identified, the single-arm trial is continued. If not, the trial is switched to a randomized controlled trial. The performance of The Bayesian adaptive synthetic control design is evaluated by computer simulation. RESULTS: The Bayesian adaptive synthetic control design achieves power and unbiasedness similar to a randomized controlled trial but on average requires a much smaller sample size, provided that the historical control data patients are sufficiently comparable to the trial patients so that a good number of matched controls can be identified in the historical control data. Compared to a single-arm trial, The Bayesian adaptive synthetic control design yields much higher power and much smaller bias. CONCLUSION: The Bayesian adaptive synthetic-control design provides a useful tool for exploiting historical control data to improve the efficiency of single-arm phase II clinical trials, while addressing the problem of bias when comparing trial results to historical control data. The proposed design achieves power similar to a randomized controlled trial but may require a substantially smaller sample size.

The summer heatwave in 2022 and its role in changing permafrost and periglacial conditions at a historic mountain pass in the Eastern Alps (Hochtor, Hohe Tauern Range, Austria).

Air temperatures in Europe in 2022 had been the highest on record for the meteorological summer season [June, July and August (JJA)], with +1.3°C above the 1991-2020 average. We studied the effects of recent warming on permafrost and periglacial conditions at a historical mountain pass in the Eastern Alps (Hochtor, 2,576 m asl, 47.08°N, 12.84°E). We used ground temperature data (2010-2022), repeated electrical resistivity tomography measurements (2019, 2022) and auxiliary data dating back to Roman times. We quantified permafrost conditions, evaluated frost-related weathering and slope processes and assessed the impact of atmospheric warming on it. Results show that summer ground surface temperatures increased by 2.5°C between 1891-1920 and 1991-2020, whereas frost-related weathering and periglacial processes decreased. The summers of 2003, 2015, 2019 and 2022 were the four warmest ones in 1887-2022. Hochtor changed in 2010-2022 from an active permafrost site to an inactive one with supra-permafrost talik. A general three-layer structure was quantified for all three ERT profiles measured. The middle, 5-10 m thick layer is ice-poor permafrost detected in 2019, whose existence, although smaller, was confirmed in 2022. Resistivity decreased at the three profiles by 3.9% to 5.2% per year, suggesting permafrost degradation. We interpret the resistivity changes between the summers of 2019 and 2022 as a long-term signal of permafrost degradation and not as the single effect of the summer heatwave in 2022. As our data show how rapidly permafrost degrades and as we face an even warmer climate for the remaining part of the 21st century, we expect that near-surface permafrost at the Hochtor site will soon be history.

Ten best practices for effective phenological research.

The number and diversity of phenological studies has increased rapidly in recent years. Innovative experiments, field studies, citizen science projects, and analyses of newly available historical data are contributing insights that advance our understanding of ecological and evolutionary responses to the environment, particularly climate change. However, many phenological data sets have peculiarities that are not immediately obvious and can lead to mistakes in analyses and interpretation of results. This paper aims to help researchers, especially those new to the field of phenology, understand challenges and practices that are crucial for effective studies. For example, researchers may fail to account for sampling biases in phenological data, struggle to choose or design a volunteer data collection strategy that adequately fits their project's needs, or combine data sets in inappropriate ways. We describe ten best practices for designing studies of plant and animal phenology, evaluating data quality, and analyzing data. Practices include accounting for common biases in data, using effective citizen or community science methods, and employing appropriate data when investigating phenological mismatches. We present these best practices to help researchers entering the field take full advantage of the wealth of available data and approaches to advance our understanding of phenology and its implications for ecology.

Bayesian borrowing from historical control data in a vaccine efficacy trial.

In the context of vaccine efficacy trial where the incidence rate is very low and a very large sample size is usually expected, incorporating historical data into a new trial is extremely attractive to reduce sample size and increase estimation precision. Nevertheless, for some infectious diseases, seasonal change in incidence rates poses a huge challenge in borrowing historical data and a critical question is how to properly take advantage of historical data borrowing with acceptable tolerance to between-trials heterogeneity commonly from seasonal disease transmission. In this article, we extend a probability-based power prior which determines the amount of information to be borrowed based on the agreement between the historical and current data, to make it applicable for either a single or multiple historical trials available, with constraint on the amount of historical information to be borrowed. Simulations are conducted to compare the performance of the proposed method with other methods including modified power prior (MPP), meta-analytic-predictive (MAP) prior and the commensurate prior methods. Furthermore, we illustrate the application of the proposed method for trial design in a practical setting.