The selection of covariates for the relationship between blood-lead and ability

This thesis arose from a problem in the analysis of data from the Edinburgh Lead Study. The data were to be used to estimate the influence of children's blood lead levels on their mental abilities, controlling for other factors which might confound this relationship. The other factors were summarised as a set of covariate scores, and the question arose as to which of these scores should be included in a multiple regression whose purpose was to estimate the coefficient of blood-lead. This problem has arisen in other studies of the influence of lead on ability, and a variety of solutions have been implemented. The statistical and epidemiological literature offers little guidance.The problem is formalised by proposing regression models with various assumptions. Expressions are derived for the mean-square-error of the parameter of special interest (here the blood-lead coefficient) in terms of quantities which can be calculated from the data. Various stepwise procedures are proposed for selecting a sub-set of covariates to include in the regression equation. These include the usual stepwise procedures, as well as new ones based on the various meansquare-error criteria and on changes in the coefficient of interest. These procedures are studied for the data from the Edinburgh Lead Study and evaluated by simulation in different ways.The potential for variance reduction from sub-models, compared to including all covariates, is a function of the multiple correlation between the variable of special interest and the variables which could be omitted from the model. The results suggest that, unless this correlation exceeds 0.2, inferences should be based on a regression with the full set of covariates. The greatest benefit is obtained from sub-set selection procedures when the multiple correlation is increased as a result of a decrease in the residual degrees of freedom. In these circumstances the multiple correlation will be high, but its value will fall when the usual adjustment for degrees of freedom is applied. The simulation results suggest that sub-set selection will be beneficial when the residual degrees of freedom for the full model are less than three time the number of covariates.The method which performed best was to select, at each step, the variable which made the largest change in the coefficient of interest. Stopping rules for this criterion are propped. This method was less prone than the other methods to underestimate the variance of the coefficient of interest, when this is evaluated in the usual way for the final model. But it performed badly and underestimated this variance, for artificial data where the population multiple correlation between the variable of special interest and the covariates was high. This suggests that sub-set selection should not be used when the estimated multiple correlation adjusted for degrees of freedom is high.These criteria applied to the Lead Study data would suggest that the effect of lead on ability should be assessed by adjusting for all the covariate scores

Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL) trial: Health-related quality of life outcomes, resource utilization, and cost-effectiveness analysis

BackgroundThe Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL) trial showed that survival in patients with severe lower limb ischemia (rest pain, tissue loss) who survived postintervention for >2 years after initial randomization to bypass surgery (BSX) vs balloon angioplasty (BAP) was associated with an improvement in subsequent amputation-free and overall survival of about 6 and 7 months, respectively. We now compare the effect on hospital costs and health-related quality of life (HRQOL) of the BSX-first and BAP-first revascularization strategies using a within-trial cost-effectiveness analysis.MethodsWe measured HRQOL using the Vascular Quality of Life Questionnaire (VascuQol), the Short Form 36 (SF-36), and the EuroQol (EQ-5D) health outcome measure up to 3 years from randomization. Hospital use was measured and valued using United Kingdom National Health Service hospital costs over 3 years. Analysis was by intention-to-treat. Incremental cost-effectiveness ratios were estimated for cost per quality-adjusted life-year (QALY) gained. Uncertainty was assessed using nonparametric bootstrapping of incremental costs and incremental effects.ResultsNo significant differences in HRQOL emerged when the two treatment strategies were compared. During the first year from randomization, the mean cost of inpatient hospital treatment in patients allocated to BSX ($34,378) was estimated to be about$8469 (95% confidence interval, $2,417-$14,522) greater than that of patients allocated to BAP ($25,909). Owing to increased costs subsequently incurred by the BAP patients, this difference decreased at the end of follow-up to$5521 ($45,322 for BSX vs$39,801 for BAP) and was no longer significant. The incremental cost-effectiveness ratio of a BSX-first strategy was $184,492 per QALY gained. The probability that BSX was more cost-effective than BAP was relatively low given the similar distributions in HRQOL, survival, and hospital costs.ConclusionsAdopting a BSX-first strategy for patients with severe limb ischemia does result in a modest increase in hospital costs, with a small positive but insignificant gain in disease-specific and generic HRQOL. However, the real-world choice between BSX-first and BAP-first revascularization strategies for severe limb ischemia due to infrainguinal disease cannot depend on costs alone and will require a more comprehensive consideration of individual patient preferences conditioned by expectations of survival and other health outcomes

Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL) trial: A survival prediction model to facilitate clinical decision making

BackgroundAn intention-to-treat analysis of the Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL) trial showed that in patients with severe lower limb ischemia (SLI) due to infrainguinal disease who survived for 2 years after intervention, initial randomization to a bypass surgery (BSX)-first vs balloon angioplasty (BAP)-first revascularization strategy was associated with improvements in subsequent overall survival (OS) and amputation-free survival (AFS) of about 7 and 6 months, respectively. This study explored the value of baseline factors to estimate the likelihood of survival to 2 years for the trial cohort (Cox model) and for individual BASIL trial patients (Weibull model) as an aid to clinical decision making.MethodsOf 452 patients presenting to 27 United Kingdom hospitals, 228 were randomly assigned to a BSX-first and 224 to a BAP-first revascularization strategy. Patients were monitored for at least 3 years. Baseline factors affecting the survival of the entire cohort were examined with a multivariate Cox model. The chances of survival at 1 and 2 years for patients with given baseline characteristics were estimated with a Weibull parametric model.ResultsAt the end of follow-up, 172 patients (38%) were alive without major limb amputation of the trial leg, and 202 (45%) were alive. Baseline factors that were significant in the Cox model were BASIL randomization stratification group, below knee Bollinger angiogram score, body mass index, age, diabetes, creatinine level, and smoking status. Using these factors to define five equally sized groups, we identified patients with 2-year survival rates of 50% to 90%. The factors that contributed to the Weibull predictive model were age, presence of tissue loss, serum creatinine, number of ankle pressure measurements detectable, maximum ankle pressure measured, a history of myocardial infarction or angina, a history of stroke or transient ischemia attack, below knee Bollinger angiogram score, body mass index, and smoking status.ConclusionsPatients in the BASIL trial were at high risk of amputation and death regardless of revascularization strategy. However, baseline factors can be used to stratify those risks. Furthermore, within a parametric Weibull model, certain of these factors can be used to help predict outcomes for individuals. It may thus be possible to define the clinical and anatomic (angiographic) characteristics of SLI patients who are likely—and not likely—to live for >2 years after intervention. Used appropriately in the context of the BASIL trial outcomes, this may aid clinical decision making regarding a BSX- or BAP-first revascularization strategy in SLI patients like those randomized in BASIL

Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL) trial: An intention-to-treat analysis of amputation-free and overall survival in patients randomized to a bypass surgery-first or a balloon angioplasty-first revascularization strategy

BackgroundA 2005 interim analysis of the Bypass versus Angioplasty in Severe Ischaemia of the Leg (BASIL) trial showed that in patients with severe lower limb ischemia (SLI; rest pain, ulceration, gangrene) due to infrainguinal disease, bypass surgery (BSX)-first and balloon angioplasty (BAP)-first revascularization strategies led to similar short-term clinical outcomes, although BSX was about one-third more expensive and morbidity was higher. We have monitored patients for a further 2.5 years and now report a final intention-to-treat (ITT) analysis of amputation-free survival (AFS) and overall survival (OS).MethodsOf 452 enrolled patients in 27 United Kingdom hospitals, 228 were randomized to a BSX-first and 224 to a BAP-first revascularization strategy. All patients were monitored for 3 years and more than half for >5 years.ResultsAt the end of follow-up, 250 patients were dead (56%), 168 (38%) were alive without amputation, and 30 (7%) were alive with amputation. Four were lost to follow-up. AFS and OS did not differ between randomized treatments during the follow-up. For those patients surviving 2 years from randomization, however, BSX-first revascularization was associated with a reduced hazard ratio (HR) for subsequent AFS of 0.85 (95% confidence interval [CI], 0.5-1.07; P = .108) and for subsequent OS of 0.61 (95% CI, 0.50-0.75; P = .009) in an adjusted, time-dependent Cox proportional hazards model. For those patients who survived for 2 years after randomization, initial randomization to a BSX-first revascularization strategy was associated with an increase in subsequent restricted mean overall survival of 7.3 months (95% CI, 1.2-13.4 months, P = .02) and an increase in restricted mean AFS of 5.9 months (95% CI, 0.2-12.0 months, P = .06) during the subsequent mean follow-up of 3.1 years (range, 1-5.7 years).ConclusionsOverall, there was no significant difference in AFS or OS between the two strategies. However, for those patients who survived for at least 2 years after randomization, a BSX-first revascularization strategy was associated with a significant increase in subsequent OS and a trend towards improved AFS

DataSHIELD: taking the analysis to the data, not the data to the analysis

Research in modern biomedicine and social science requires sample sizes so large that they can often only be achieved through a pooled co-analysis of data from several studies. But the pooling of information from individuals in a central database that may be queried by researchers raises important ethico-legal questions and can be controversial. In the UK this has been highlighted by recent debate and controversy relating to the UK's proposed 'care.data' initiative, and these issues reflect important societal and professional concerns about privacy, confidentiality and intellectual property. DataSHIELD provides a novel technological solution that can circumvent some of the most basic challenges in facilitating the access of researchers and other healthcare professionals to individual-level data. Commands are sent from a central analysis computer (AC) to several data computers (DCs) storing the data to be co-analysed. The data sets are analysed simultaneously but in parallel. The separate parallelized analyses are linked by non-disclosive summary statistics and commands transmitted back and forth between the DCs and the AC. This paper describes the technical implementation of DataSHIELD using a modified R statistical environment linked to an Opal database deployed behind the computer firewall of each DC. Analysis is controlled through a standard R environment at the AC. Based on this Opal/R implementation, DataSHIELD is currently used by the Healthy Obese Project and the Environmental Core Project (BioSHaRE-EU) for the federated analysis of 10 data sets across eight European countries, and this illustrates the opportunities and challenges presented by the DataSHIELD approach. DataSHIELD facilitates important research in settings where: (i) a co-analysis of individual-level data from several studies is scientifically necessary but governance restrictions prohibit the release or sharing of some of the required data, and/or render data access unacceptably slow; (ii) a research group (e.g. in a developing nation) is particularly vulnerable to loss of intellectual property-the researchers want to fully share the information held in their data with national and international collaborators, but do not wish to hand over the physical data themselves; and (iii) a data set is to be included in an individual-level co-analysis but the physical size of the data precludes direct transfer to a new site for analysis

Sectarianism in Scotland, myth or reality? Evidence from mixed partnerships in Scotland.

International audienceThis article explores the contested issue of whether sectarianism divides Catholics and Protestants in Scotland. The conclusions are based on an analysis of 111,627 couples from the 2001 Census. Young adults are much more likely than older people to have been raised with no religion This is largely due to a decline in the Protestant group, with Catholics remaining stable. The socio-economic disadvantage of older Catholics compared to Potestants has eroded at the youngest ages. Those with no religious upbringing are disadvantaged at all ages. Catholics are more likely than Protestants to form couples outside their religious group, and this is not simply because their minority status restricts available partners. We also describe how inter-sectarian marriage influences current religious practice. The pattern of inter-sectarian partnerships are such that many young Protestants and Catholics in Scotland will have those with the opposite background among their extended families, and this should contribute to undermining sectarian divisions