Investigating treatment-effect modification by a continuous covariate in IPD meta-analysis: an approach using fractional polynomials

Background: In clinical trials, there is considerable interest in investigating whether a treatment effect is similar in all patients, or that one or more prognostic variables indicate a differential response to treatment. To examine this, a continuous predictor is usually categorised into groups according to one or more cutpoints. Several weaknesses of categorization are well known. To avoid the disadvantages of cutpoints and to retain full information, it is preferable to keep continuous variables continuous in the analysis. To handle this issue, the Subpopulation Treatment Effect Pattern Plot (STEPP) was proposed about two decades ago, followed by the multivariable fractional polynomial interaction (MFPI) approach. Provided individual patient data (IPD) from several studies are available, it is possible to investigate for treatment heterogeneity with meta-analysis techniques. Meta-STEPP was recently proposed and in patients with primary breast cancer an interaction of estrogen receptors with chemotherapy was investigated in eight randomized controlled trials (RCTs). Methods: We use data from eight randomized controlled trials in breast cancer to illustrate issues from two main tasks. The first task is to derive a treatment effect function (TEF), that is, a measure of the treatment effect on the continuous scale of the covariate in the individual studies. The second is to conduct a meta-analysis of the continuous TEFs from the eight studies by applying pointwise averaging to obtain a mean function. We denote the method metaTEF. To improve reporting of available data and all steps of the analysis we introduce a three-part profile called MethProf-MA. Results: Although there are considerable differences between the studies (populations with large differences in prognosis, sample size, effective sample size, length of follow up, proportion of patients with very low estrogen receptor values) our results provide clear evidence of an interaction, irrespective of the choice of the FP function and random or fixed effect models. Conclusions: In contrast to cutpoint-based analyses, metaTEF retains the full information from continuous covariates and avoids several critical issues when performing IPD meta-analyses of continuous effect modifiers in randomised trials. Early experience suggests it is a promising approach. Trial registration: Not applicable

Reporting of prognostic studies of tumour markers: a review of published articles in relation to REMARK guidelines

Background: Poor reporting compromises the reliability and clinical value of prognostic tumour marker studies. We review articles to assess the reporting of patients and events using REMARK guidelines, at the time of guideline publication. Methods: We sampled 50 prognostic tumour marker studies from higher impact cancer journals between 2006 and 2007. The inclusion criteria were cancer; focus on single biological tumour marker; survival analysis; multivariable analysis; and not gene array or proteomic data. Articles were assessed for the REMARK profile and other REMARK guideline items. We propose a reporting aid, the REMARK profile, motivated by the CONSORT flowchart. Results: In 50 studies assessed for the REMARK profile, the number of eligible patients (56% of articles), excluded patients (54%) and patients in analyses (98%) was reported. Only 50% of articles reported the number of outcome events. In multivariable analyses, 54% and 30% of articles reported patient and event numbers for all variables. Of the studies, 66% used archival samples, indicating a potentially biased patient selection. Only 36% of studies reported clearly defined outcomes. Conclusions: Good reporting is critical for the interpretability and clinical applicability of prognostic studies. Current reporting of key information, such as the number of outcome events in all patients and subgroups, is poor. Use of the REMARK profile would greatly improve reporting and enhance prognostic research

Exploration of the variability of variable selection based on distances between bootstrap sample results

It is well known that variable selection in multiple regression can be unstable and that the model uncertainty can be considerable. The model uncertainty can be quantified and explored by bootstrap resampling, see Sauerbrei et al. (Biom J 57:531–555, 2015). Here approaches are introduced that use the results of bootstrap replications of the variable selection process to obtain more detailed information about the data. Analyses will be based on dissimilarities between the results of the analyses of different bootstrap samples. Dissimilarities are computed between the vector of predictions, and between the sets of selected variables. The dissimilarities are used to map the models by multidimensional scaling, to cluster them, and to construct heatplots. Clusters can point to different interpretations of the data that could arise from different selections of variables supported by different bootstrap samples. A new measure of variable selection instability is also defined. The methodology can be applied to various regression models, estimators, and variable selection methods. It will be illustrated by three real data examples, using linear regression and a Cox proportional hazards model, and model selection by AIC and BIC

Improving the Prognostic Ability through Better Use of Standard Clinical Data - The Nottingham Prognostic Index as an Example

Background Prognostic factors and prognostic models play a key role in medical research and patient management. The Nottingham Prognostic Index (NPI) is a well-established prognostic classification scheme for patients with breast cancer. In a very simple way, it combines the information from tumor size, lymph node stage and tumor grade. For the resulting index cutpoints are proposed to classify it into three to six groups with different prognosis. As not all prognostic information from the three and other standard factors is used, we will consider improvement of the prognostic ability using suitable analysis approaches. Methods and Findings Reanalyzing overall survival data of 1560 patients from a clinical database by using multivariable fractional polynomials and further modern statistical methods we illustrate suitable multivariable modelling and methods to derive and assess the prognostic ability of an index. Using a REMARK type profile we summarize relevant steps of the analysis. Adding the information from hormonal receptor status and using the full information from the three NPI components, specifically concerning the number of positive lymph nodes, an extended NPI with improved prognostic ability is derived. Conclusions The prognostic ability of even one of the best established prognostic index in medicine can be improved by using suitable statistical methodology to extract the full information from standard clinical data. This extended version of the NPI can serve as a benchmark to assess the added value of new information, ranging from a new single clinical marker to a derived index from omics data. An established benchmark would also help to harmonize the statistical analyses of such studies and protect against the propagation of many false promises concerning the prognostic value of new measurements. Statistical methods used are generally available and can be used for similar analyses in other diseases

Magnetic order in GdBiPt studied by x-ray resonant magnetic scattering

Rare earth (R) half-Heusler compounds, RBiPt, exhibit a wide spectrum of novel ground states. Recently, GdBiPt has been proposed as a potential antiferromagnetic topological insulator (AFTI). We have employed x-ray resonant magnetic scattering to elucidate the microscopic details of the magnetic structure in GdBiPt below T_N = 8.5 K. Experiments at the Gd L_2 absorption edge show that the Gd moments order in an antiferromagnetic stacking along the cubic diagonal [1 1 1] direction satisfying the requirement for an AFTI, where both time-reversal symmetry and lattice translational symmetry are broken, but their product is conserved.Comment: 4 pages, 4 figure

Meta‐analysis of non‐linear exposure‐outcome relationships using individual participant data: A comparison of two methods

Non‐linear exposure‐outcome relationships such as between body mass index (BMI) and mortality are common. They are best explored as continuous functions using individual participant data from multiple studies. We explore two two‐stage methods for meta‐analysis of such relationships, where the confounder‐adjusted relationship is first estimated in a non‐linear regression model in each study, then combined across studies. The “metacurve” approach combines the estimated curves using multiple meta‐analyses of the relative effect between a given exposure level and a reference level. The “mvmeta” approach combines the estimated model parameters in a single multivariate meta‐analysis. Both methods allow the exposure‐outcome relationship to differ across studies. Using theoretical arguments, we show that the methods differ most when covariate distributions differ across studies; using simulated data, we show that mvmeta gains precision but metacurve is more robust to model mis‐specification. We then compare the two methods using data from the Emerging Risk Factors Collaboration on BMI, coronary heart disease events, and all‐cause mortality (>80 cohorts, >18 000 events). For each outcome, we model BMI using fractional polynomials of degree 2 in each study, with adjustment for confounders. For metacurve, the powers defining the fractional polynomials may be study‐specific or common across studies. For coronary heart disease, metacurve with common powers and mvmeta correctly identify a small increase in risk in the lowest levels of BMI, but metacurve with study‐specific powers does not. For all‐cause mortality, all methods identify a steep U‐shape. The metacurve and mvmeta methods perform well in combining complex exposure‐disease relationships across studies

Review of guidance papers on regression modeling in statistical series of medical journals

Although regression models play a central role in the analysis of medical research projects, there still exist many misconceptions on various aspects of modeling leading to faulty analyses. Indeed, the rapidly developing statistical methodology and its recent advances in regression modeling do not seem to be adequately reflected in many medical publications. This problem of knowledge transfer from statistical research to application was identified by some medical journals, which have published series of statistical tutorials and (shorter) papers mainly addressing medical researchers. The aim of this review was to assess the current level of knowledge with regard to regression modeling contained in such statistical papers. We searched for target series by a request to international statistical experts. We identified 23 series including 57 topic-relevant articles. Within each article, two independent raters analyzed the content by investigating 44 predefined aspects on regression modeling. We assessed to what extent the aspects were explained and if examples, software advices, and recommendations for or against specific methods were given. Most series (21/23) included at least one article on multivariable regression. Logistic regression was the most frequently described regression type (19/23), followed by linear regression (18/23), Cox regression and survival models (12/23) and Poisson regression (3/23). Most general aspects on regression modeling, e.g. model assumptions, reporting and interpretation of regression results, were covered. We did not find many misconceptions or misleading recommendations, but we identified relevant gaps, in particular with respect to addressing nonlinear effects of continuous predictors, model specification and variable selection. Specific recommendations on software were rarely given. Statistical guidance should be developed for nonlinear effects, model specification and variable selection to better support medical researchers who perform or interpret regression analyses

Systematic review of education and practical guidance on regression modeling for medical researchers who lack a strong statistical background: Study protocol

In the last decades, statistical methodology has developed rapidly, in particular in the field of regression modeling. Multivariable regression models are applied in almost all medical research projects. Therefore, the potential impact of statistical misconceptions within this field can be enormous Indeed, the current theoretical statistical knowledge is not always adequately transferred to the current practice in medical statistics. Some medical journals have identified this problem and published isolated statistical articles and even whole series thereof. In this systematic review, we aim to assess the current level of education on regression modeling that is provided to medical researchers via series of statistical articles published in medical journals. The present manuscript is a protocol for a systematic review that aims to assess which aspects of regression modeling are covered by statistical series published in medical journals that intend to train and guide applied medical researchers with limited statistical knowledge. Statistical paper series cannot easily be summarized and identified by common keywords in an electronic search engine like Scopus. We therefore identified series by a systematic request to statistical experts who are part or related to the STRATOS Initiative (STRengthening Analytical Thinking for Observational Studies). Within each identified article, two raters will independently check the content of the articles with respect to a predefined list of key aspects related to regression modeling. The content analysis of the topic-relevant articles will be performed using a predefined report form to assess the content as objectively as possible. Any disputes will be resolved by a third reviewer. Summary analyses will identify potential methodological gaps and misconceptions that may have an important impact on the quality of analyses in medical research. This review will thus provide a basis for future guidance papers and tutorials in the field of regression modeling which will enable medical researchers 1) to interpret publications in a correct way, 2) to perform basic statistical analyses in a correct way and 3) to identify situations when the help of a statistical expert is required

Supply driven mortgage choice

Variable mortgage contracts dominate the UK mortgage market (Miles, 2004). The dominance of the variable rate mortgage contracts has important consequences for the transmission mechanism of monetary policy decisions and systemic risks (Khandani et al., 2012; Fuster and Vickery, 2013). This raises an obvious concern that a mortgage market such as that in the UK, where the major proportion of mortgage debt is either at a variable or fixed for less than two years rate (Badarinza, et al., 2013; CML, 2012), is vulnerable to alterations in the interest rate regime. Theoretically, mortgage choice is determined by demand and supply factors. So far, most of the existing literature has focused on the demand side perspective, and what is limited is consideration of supply side factors in empirical investigation on mortgage choice decisions. This paper uniquely explores whether supply side factors may partially explain observed/ex-post mortgage type decisions. Empirical results detect that lenders’ profit motives and mortgage funding/pricing issues may have assisted in preferences toward variable rate contracts. Securitisation is found to positively impact upon gross mortgage lending volumes while negatively impacting upon the share of variable lending flows. This shows that an increase in securitisation not only improves liquidity in the supply of mortgage funds, but also has the potential to shift mortgage choices toward fixed mortgage debt. The policy implications may involve a number of measures, including reconsideration of the capital requirements for the fixed, as opposed to the variable rate mortgage debt, growing securitisation and optimisation of the mortgage pricing policies