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 $w$.

Estimation of Treatment Policy Estimands for Continuous Outcomes Using Off-Treatment Sequential Multiple Imputation.

The estimands framework outlined in ICH E9 (R1) describes the components needed to precisely define the effects to be estimated in clinical trials, which includes how post-baseline 'intercurrent' events (IEs) are to be handled. In late-stage clinical trials, it is common to handle IEs like 'treatment discontinuation' using the treatment policy strategy and target the treatment effect on outcomes regardless of treatment discontinuation. For continuous repeated measures, this type of effect is often estimated using all observed data before and after discontinuation using either a mixed model for repeated measures (MMRM) or multiple imputation (MI) to handle any missing data. In basic form, both these estimation methods ignore treatment discontinuation in the analysis and therefore may be biased if there are differences in patient outcomes after treatment discontinuation compared with patients still assigned to treatment, and missing data being more common for patients who have discontinued treatment. We therefore propose and evaluate a set of MI models that can accommodate differences between outcomes before and after treatment discontinuation. The models are evaluated in the context of planning a Phase 3 trial for a respiratory disease. We show that analyses ignoring treatment discontinuation can introduce substantial bias and can sometimes underestimate variability. We also show that some of the MI models proposed can successfully correct the bias, but inevitably lead to increases in variance. We conclude that some of the proposed MI models are preferable to the traditional analysis ignoring treatment discontinuation, but the precise choice of MI model will likely depend on the trial design, disease of interest and amount of observed and missing data following treatment discontinuation.

Statistical analysis of actigraphy data with generalised additive models.

There is a growing interest in the use of physical activity data in clinical studies, particularly in diseases that limit mobility in patients. High-frequency data collected with digital sensors are typically summarised into actigraphy features aggregated at epoch level (e.g., by minute). The statistical analysis of such volume of data is not straightforward. The general trend is to derive metrics, capturing specific aspects of physical activity, that condense (say) a week worth of data into a single numerical value. Here we propose to analyse the entire time-series data using Generalised Additive Models (GAMs). GAMs are semi-parametric models that allow inclusion of both parametric and non-parametric terms in the linear predictor. The latter are smooth terms (e.g., splines) and, in the context of actigraphy minute-by-minute data analysis, they can be used to assess daily patterns of physical activity. This in turn can be used to better understand changes over time in longitudinal studies as well as to compare treatment groups. We illustrate the application of GAMs in two clinical studies where actigraphy data was collected: a non-drug, single-arm study in patients with amyotrophic lateral sclerosis, and a physical-activity sub-study included in a phase 2b clinical trial in patients with chronic obstructive pulmonary disease.

Estimation of a treatment policy estimand for time to event data using data collected post discontinuation of randomised treatment.

Discontinuation from randomised treatment is a common intercurrent event in clinical trials. When the target estimand uses a treatment policy strategy to deal with this intercurrent event, data after cessation of treatment is relevant to estimate the estimand and all efforts should be made to collect such data. Missing data may nevertheless occur due to participants withdrawing from the study and assumptions regarding the values for data that are missing are required for estimation. A missing-at-random assumption is commonly made in this setting, but it may not always be viewed as appropriate. Another potential approach is to assume missing values are similar to data collected after treatment discontinuation. This idea has been previously proposed in the context of recurrent event data. Here we extend this approach to time-to-event outcomes using the hazard function. We propose imputation models that allow for different hazard rates before and after treatment discontinuation and use the posttreatment discontinuation hazard to impute events for participants with missing follow-up periods due to study withdrawal. The imputation models are fitted as Andersen-Gill models. We illustrate the proposed methods with an example of a clinical trial in patients with chronic obstructive pulmonary disease.

Treatment policy estimands for recurrent event data using data collected after cessation of randomised treatment.

In the past, many clinical trials have withdrawn subjects from the study when they prematurely stopped their randomised treatment and have therefore only collected 'on-treatment' data. Thus, analyses addressing a treatment policy estimand have been restricted to imputing missing data under assumptions drawn from these data only. Many confirmatory trials are now continuing to collect data from subjects in a study even after they have prematurely discontinued study treatment as this event is irrelevant for the purposes of a treatment policy estimand. However, despite efforts to keep subjects in a trial, some will still choose to withdraw. Recent publications for sensitivity analyses of recurrent event data have focused on the reference-based imputation methods commonly applied to continuous outcomes, where imputation for the missing data for one treatment arm is based on the observed outcomes in another arm. However, the existence of data from subjects who have prematurely discontinued treatment but remained in the study has now raised the opportunity to use this 'off-treatment' data to impute the missing data for subjects who withdraw, potentially allowing more plausible assumptions for the missing post-study-withdrawal data than reference-based approaches. In this paper, we introduce a new imputation method for recurrent event data in which the missing post-study-withdrawal event rate for a particular subject is assumed to reflect that observed from subjects during the off-treatment period. The method is illustrated in a trial in chronic obstructive pulmonary disease (COPD) where the primary endpoint was the rate of exacerbations, analysed using a negative binomial model.

Bayesian model to detect phenotype-specific genes for copy number data.

BACKGROUND: An important question in genetic studies is to determine those genetic variants, in particular CNVs, that are specific to different groups of individuals. This could help in elucidating differences in disease predisposition and response to pharmaceutical treatments. We propose a Bayesian model designed to analyze thousands of copy number variants (CNVs) where only few of them are expected to be associated with a specific phenotype. RESULTS: The model is illustrated by analyzing three major human groups belonging to HapMap data. We also show how the model can be used to determine specific CNVs related to response to treatment in patients diagnosed with ovarian cancer. The model is also extended to address the problem of how to adjust for confounding covariates (e.g., population stratification). Through a simulation study, we show that the proposed model outperforms other approaches that are typically used to analyze this data when analyzing common copy-number polymorphisms (CNPs) or complex CNVs. We have developed an R package, called bayesGen, that implements the model and estimating algorithms. CONCLUSIONS: Our proposed model is useful to discover specific genetic variants when different subgroups of individuals are analyzed. The model can address studies with or without control group. By integrating all data in a unique model we can obtain a list of genes that are associated with a given phenotype as well as a different list of genes that are shared among the different subtypes of cases.

Bayesian shared spatial-component models to combine and borrow strength across sparse disease surveillance sources.

When analyzing the geographical variations of disease risk, one common problem is data sparseness. In such a setting, we investigate the possibility of using Bayesian shared spatial component models to strengthen inference and correct for any spatially structured sources of bias, when distinct data sources on one or more related diseases are available. Specifically, we apply our models to analyze the spatial variation of risk of two forms of scrapie infection affecting sheep in Wales (UK) using three surveillance sources on each disease. We first model each disease separately from the combined data sources and then extend our approach to jointly analyze diseases and data sources. We assess the predictive performances of several nested joint models through pseudo cross-validatory predictive model checks.

Assessing gut microbial diversity from feces and rectal mucosa.

Gut microbiota is the most complex bacterial community in the human body and its study may give important clues to the etiology of different intestinal diseases. Most studies carried out so far have used fecal samples, assuming that these samples have a similar distribution to the communities present throughout the colon. The present study was designed to test this assumption by comparing samples from the rectal mucosa and feces of nine healthy volunteers by sequencing libraries of 16S rRNA genes. At the family taxonomic level, where rarefaction curves indicate that the observed number of taxa is close to the expected one, we observe under different statistical analyses that fecal and mucosal samples cluster separately. The same is found at the level of species considering phylogenetic information. Consequently, it cannot be stated that both samples from a given individual are of similar composition. We believe that the evidence in support of this statement is strong and that it would not change by increasing the number of individuals and/or performing massive sequencing. We do not expect clinicians to stop using feces for research, but we think it is important to caution them on their potential lack of representativeness with respect to the bacterial biofilm on the rectal mucosa.

Environmental inequity in England: small area associations between socio-economic status and environmental pollution.

Recent studies have suggested that more deprived people tend to live in areas characterised by higher levels of environmental pollution. If generally true, these environmental inequities may combine to cause adverse effects on health and also exacerbate problems of confounding in epidemiological studies. Previous studies of environmental inequity have nevertheless indicated considerable complexity in the associations involved, which merit further investigation using more detailed data and more advanced analytical methods. This study investigates the ways in which environmental inequity in England varies in relation to: (a) different environmental pollutants (measured in different ways); (b) different aspects of socio-economic status; and (c) different geographical scales and contexts (urban vs. rural). Associations were analysed between the Index of Multiple Deprivation (IMD2004) and its domains and five sets of environmental pollutants (relating to road traffic, industry, electro-magnetic frequency radiation, disinfection by-products in drinking water and radon), measured in terms of proximity, emission intensity and environmental concentration. Associations were assessed using bivariate and multivariate correlation, and by comparing the highest and lowest quintiles of deprivation using Student's t-test and Hotelling's T2. Associations are generally weak (R(2) < 0.10), and vary depending on the specific measures used. Strongest associations occur with what can be regarded as contingent components of deprivation (e.g. crime, living environment, health) rather than causative factors such as income, employment or education. Associations also become stronger with increasing level of spatial aggregation. Overall, the results suggest that any triple jeopardy for health, and problems of confounding, associated with environmental inequities are likely to be limited.

Bayesian spatio-temporal analysis of joint patterns of male and female lung cancer risks in Yorkshire (UK).

Recent advances in disease mapping have focused first on including the time dimension, thus giving rise to spatio-temporal analysis of the variation of disease risk and, secondly, on carrying out joint analysis of two diseases that share common environmental risk factors and are, therefore, related. Here, we try to combine both issues and present a joint analysis of the spatio-temporal variation of the risks of two related diseases processes-male and female lung cancer incidence-in a region of England. To do so, we use a Bayesian hierarchical model that splits the risk of disease into two spatio-temporal components: a shared component and a specific component that calibrates the differential between the two diseases.

Assessing the social class of children from parental information to study possible social inequalities in health outcomes.

PURPOSE: When the subjects are children, the assessment of social class must be made indirectly from parental data. We propose correspondence analysis as a method for combining parental information. METHODS: Four assessment methods were used: father's occupation, mother's occupation, dominant occupation of both, and both combined by means of a correspondence analysis. The results were used to explore social inequalities in dental health. We used data from a survey performed on school children (12- and 15-16-year olds) in the Comunitat Valenciana (Spain). Dental health was measured through prevalence of caries, number of teeth with caries, number of caries in permanent teeth, decayed, missing, and filled teeth score (DMF-T), decayed, missing, and filled surface score (DMF-S), prevalence of DMF>0, community periodontal index of treatment needs (CPITN) and prevalence of CPITN>0. RESULTS: Correspondence analysis methods reflect the impact of social class on health indicators. They were able to assign a social group to all individuals. The association between social class and oral health was found to be sensitive to the method used. CONCLUSIONS: Pooling information from both parents is important. Evidence of social inequalities in oral health may or may not be obtained depending on the method used.

Spatial analysis of the relationship between mortality from cardiovascular and cerebrovascular disease and drinking water hardness.

Previously published scientific papers have reported a negative correlation between drinking water hardness and cardiovascular mortality. Some ecologic and case-control studies suggest the protective effect of calcium and magnesium concentration in drinking water. In this article we present an analysis of this protective relationship in 538 municipalities of Comunidad Valenciana (Spain) from 1991-1998. We used the Spanish version of the Rapid Inquiry Facility (RIF) developed under the European Environment and Health Information System (EUROHEIS) research project. The strategy of analysis used in our study conforms to the exploratory nature of the RIF that is used as a tool to obtain quick and flexible insight into epidemiologic surveillance problems. This article describes the use of the RIF to explore possible associations between disease indicators and environmental factors. We used exposure analysis to assess the effect of both protective factors--calcium and magnesium--on mortality from cerebrovascular (ICD-9 430-438) and ischemic heart (ICD-9 410-414) diseases. This study provides statistical evidence of the relationship between mortality from cardiovascular diseases and hardness of drinking water. This relationship is stronger in cerebrovascular disease than in ischemic heart disease, is more pronounced for women than for men, and is more apparent with magnesium than with calcium concentration levels. Nevertheless, the protective nature of these two factors is not clearly established. Our results suggest the possibility of protectiveness but cannot be claimed as conclusive. The weak effects of these covariates make it difficult to separate them from the influence of socioeconomic and environmental factors. We have also performed disease mapping of standardized mortality ratios to detect clusters of municipalities with high risk. Further standardization by levels of calcium and magnesium in drinking water shows changes in the maps when we remove the effect of these covariates.

Instability of the faecal microbiota in diarrhoea-predominant irritable bowel syndrome.

The irritable bowel syndrome (IBS) is a functional gastrointestinal disorder with a largely unknown aetiology and a wide range of symptoms. Most cross-sectional studies carried out so far suggest subtle alterations in the structure of the intestinal microbiota that are barely reproduced, partly because of the high inter-subject variation in the community composition and disorder-specific features. We performed a longitudinal study to explore the within-subject variation in the faecal microbiota in two patients with IBS classified into the diarrhoea subtype and the healthy spouse of one of them. Faecal communities were monitored over 6-8 weeks and analysed through metagenomic and metatranscriptomic approaches. We found a higher temporal instability in the fraction of active microbiota related to the IBS condition and fluctuating symptoms. Strong and quick shifts in the distribution of the active microbiota and changes in the global pattern of gene expression were detected in association with acute diarrhoea, whereas microbial composition and encoded functions were more stable. The specific alterations in the microbiota were barely reproduced within and between patients. Further research is needed to assess whether these changes are a consequence of the abnormal gut function in acute diarrhoeic episodes and the potential usefulness of tackling them.

Structural alterations of faecal and mucosa-associated bacterial communities in irritable bowel syndrome.

Irritable bowel syndrome (IBS) is the most common functional gastrointestinal disorder in western countries. Previous studies on IBS, mostly based on faecal samples, suggest alterations in the intestinal microbiota. However, no consensus has been reached regarding the association between specific bacteria and IBS. We explore the alterations of intestinal bacterial communities in IBS using massive sequencing of amplified 16S rRNA genes. Mucosal biopsies of the ascending and descending colon and faeces from 16 IBS patients and 9 healthy controls were analysed. Strong inter-individual variation was observed in the composition of the bacterial communities in both patients and controls. These communities showed less diversity in IBS cases. There were larger differences in the microbiota composition between biopsies and faeces than between patients and controls. We found a few over-represented and under-represented taxa in IBS cases with respect to controls. The detected alterations varied by site, with no changes being consistent across sample types.