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Statistical models are simple mathematical rules derived from empirical data describing the association between an outcome and several explanatory variables. In a typical modeling situation statistical analysis often involves a large number of potential explanatory variables and frequently only partial subject-matter knowledge is available. Therefore, selecting the most suitable variables for a model in an objective and practical manner is usually a non-trivial task. We briefly revisit the purposeful variable selection procedure suggested by Hosmer and Lemeshow which combines significance and change-in-estimate criteria for variable selection and critically discuss the change-in-estimate criterion. We show that using a significance-based threshold for the change-in-estimate criterion reduces to a simple significance-based selection of variables, as if the change-in-estimate criterion is not considered at all. Various extensions to the purposeful variable selection procedure are suggested. We propose to use backward elimination augmented with a standardized change-in-estimate criterion on the quantity of interest usually reported and interpreted in a model for variable selection. Augmented backward elimination has been implemented in a SAS macro for linear, logistic and Cox proportional hazards regression. The algorithm and its implementation were evaluated by means of a simulation study. Augmented backward elimination tends to select larger models than backward elimination and approximates the unselected model up to negligible differences in point estimates of the regression coefficients. On average, regression coefficients obtained after applying augmented backward elimination were less biased relative to the coefficients of correctly specified models than after backward elimination. In summary, we propose augmented backward elimination as a reproducible variable selection algorithm that gives the analyst more flexibility in adopting model selection to a specific statistical modeling situation.

Researchers often perform data-driven variable selection when modeling the associations between an outcome and multiple independent variables in regression analysis. Variable selection may improve the interpretability, parsimony and/or predictive accuracy of a model. Yet variable selection can also have negative consequences, such as false exclusion of important variables or inclusion of noise variables, biased estimation of regression coefficients, underestimated standard errors and invalid confidence intervals, as well as model instability. While the potential advantages and disadvantages of variable selection have been discussed in the literature for decades, few large-scale simulation studies have neutrally compared data-driven variable selection methods with respect to their consequences for the resulting models. We present the protocol for a simulation study that will evaluate different variable selection methods: forward selection, stepwise forward selection, backward elimination, augmented backward elimination, univariable selection, univariable selection followed by backward elimination, and penalized likelihood approaches (Lasso, relaxed Lasso, adaptive Lasso). These methods will be compared with respect to false inclusion and/or exclusion of variables, consequences on bias and variance of the estimated regression coefficients, the validity of the confidence intervals for the coefficients, the accuracy of the estimated variable importance ranking, and the predictive performance of the selected models. We consider both linear and logistic regression in a low-dimensional setting (20 independent variables with 10 true predictors and 10 noise variables). The simulation will be based on real-world data from the National Health and Nutrition Examination Survey (NHANES). Publishing this study protocol ahead of performing the simulation increases transparency and allows integrating the perspective of other experts into the study design.

Background Variable selection for regression models plays a key role in the analysis of biomedical data. However, inference after selection is not covered by classical statistical frequentist theory, which assumes a fixed set of covariates in the model. This leads to over-optimistic selection and replicability issues. Methods We compared proposals for selective inference targeting the submodel parameters of the Lasso and its extension, the adaptive Lasso: sample splitting, selective inference conditional on the Lasso selection (SI), and universally valid post-selection inference (PoSI). We studied the properties of the proposed selective confidence intervals available via R software packages using a neutral simulation study inspired by real data commonly seen in biomedical studies. Furthermore, we present an exemplary application of these methods to a publicly available dataset to discuss their practical usability. Results Frequentist properties of selective confidence intervals by the SI method were generally acceptable, but the claimed selective coverage levels were not attained in all scenarios, in particular with the adaptive Lasso. The actual coverage of the extremely conservative PoSI method exceeded the nominal levels, and this method also required the greatest computational effort. Sample splitting achieved acceptable actual selective coverage levels, but the method is inefficient and leads to less accurate point estimates. The choice of inference method had a large impact on the resulting interval estimates, thereby necessitating that the user is acutely aware of the goal of inference in order to interpret and communicate the results. Conclusions Despite violating nominal coverage levels in some scenarios, selective inference conditional on the Lasso selection is our recommended approach for most cases. If simplicity is strongly favoured over efficiency, then sample splitting is an alternative. If only few predictors undergo variable selection (i.e. up to 5) or the avoidance of false positive claims of significance is a concern, then the conservative approach of PoSI may be useful. For the adaptive Lasso, SI should be avoided and only PoSI and sample splitting are recommended. In summary, we find selective inference useful to assess the uncertainties in the importance of individual selected predictors for future applications.

Generic medications offer substantial potential cost savings to health systems compared to their branded counterparts. In Europe and the US, they are only approved if they are bioequivalent to the respective originator product. Nevertheless, the lack of clinical outcomes is sometimes used as the reason for hesitancy in prescribing generics. We performed an observational retrospective study on 17 branded vs. generic pharmaceutical substances for the treatment of hypertension/heart failure, hyperlipidemia, and diabetes mellitus in a dataset of 9,413,620 insured persons, representing nearly the full population of Austria, from 2007 to 2012. We compared generic vs. branded medications using hazard ratios for all-cause death and major adverse cardiac and cardiovascular events (MACCE) as outcomes of interest. Using patient demographics, health characteristics from hospitalization records, and pharmacy records as covariates, we controlled for confounding in Cox models through inverse probability of treatment weighting (IPTW) using high-dimensional propensity scores. We observed that the unadjusted hazard ratios strongly favor generic drugs for all three pooled treatment indications (hypertension/heart failure, hyperlipidemia, diabetes mellitus), but were attenuated towards unity with increasingly larger covariate sets used for confounding control. We found that after IPTW adjustment the generic formulation was associated with significantly fewer deaths in 10 of 17 investigated drugs, and with fewer MACCE in 11 of 17 investigated drugs. This result favoring generic drugs was also present in a number of sub-analyses based on gender, prior disease status, and treatment discontinuation. E-value sensitivity analyses suggested that only strong unmeasured confounding could fully explain away the observed results. In conclusion, generic medications were at least similar, and in some cases superior, to their branded counterparts regarding mortality and major cardiovascular events.

Equations predicting the risk of occurrence of cardiovascular disease (CVD) are used in primary care to identify high-risk individuals among the general population. To improve the predictive performance of such equations, we updated the Framingham general CVD 1991 and 2008 equations and the Pooled Cohort equations for atherosclerotic CVD within five years in a contemporary cohort of individuals who participated in the Austrian health-screening program from 2009–2014. The cohort comprised 1.7 M individuals aged 30–79 without documented CVD history. CVD was defined by hospitalization or death from cardiovascular cause. Using baseline and follow-up data, we recalibrated and re-estimated the equations. We evaluated the gain in discrimination and calibration and assessed explained variation. A five-year general CVD risk of 4.61% was observed. As expected, discrimination c-statistics increased only slightly and ranged from 0.73–0.79. The two original Framingham equations overestimated the CVD risk, whereas the original Pooled Cohort equations underestimated it. Re-estimation improved calibration of all equations adequately, especially for high-risk individuals. Half of the individuals were reclassified into another risk category using the re-estimated equations. Predictors in the re-estimated Framingham equations explained 7.37% of the variation, whereas the Pooled Cohort equations explained 5.81%. Age was the most important predictor.

Patients are often advised to reduce sodium and potassium intake, but supporting evidence is limited. To help provide such evidence we estimated 24h urinary sodium and potassium excretion in 28,879 participants at high cardiovascular risk who were followed for a mean of 4.5 years in the ONTARGET and TRANSCEND trials. The primary outcome was eGFR decline of 30% or more or chronic dialysis. Secondary outcomes were eGFR decline of 40% or more or chronic dialysis, doubling of serum creatinine or chronic dialysis, an over 5%/year loss of eGFR, progression of albuminuria, and hyperkalemia. Multinomial logit regression with multivariable fractional polynomials, adjusted for confounders, determined the association between urinary sodium and potassium excretion and renal outcomes, with death as a competing risk. The primary outcome occurred in 2,052 (7.6%) patients. There was no significant association between sodium and any renal outcome (primary outcome odds ratio 0.99; 95% CI 0.89–1.09 for highest [median 6.2g/day] vs. lowest third [median 3.3g/day]). Higher potassium was associated with lower odds of all renal outcomes (primary outcome odds ratio 0.74; 95% CI 0.67–0.82 for highest [median 2.7g/day] vs. lowest third [median 1.7g/day], except hyperkalemia nonsignificant. Thus, urinary potassium, but not sodium, excretion predicted clinically important renal outcomes. Our findings do not support routine low sodium and potassium diets for prevention of renal outcomes in people with vascular disease with or without chronic kidney disease.

IntroductionRecent data suggest that margins ≥2 mm after breast-conserving surgery may improve local control in invasive breast cancer (BC). By allowing large resection volumes, oncoplastic breast-conserving surgery (OBCII; Clough level II/Tübingen 5-6) may achieve better local control than conventional breast conserving surgery (BCS; Tübingen 1-2) or oncoplastic breast conservation with low resection volumes (OBCI; Clough level I/Tübingen 3-4).MethodsData from consecutive high-risk BC patients treated in 15 centers from the Oncoplastic Breast Consortium (OPBC) network, between January 2010 and December 2013, were retrospectively reviewed.ResultsA total of 3,177 women were included, 30% of whom were treated with OBC (OBCI n = 663; OBCII n = 297). The BCS/OBCI group had significantly smaller tumors and smaller resection margins compared with OBCII (pT1: 50% vs. 37%, p = 0.002; proportion with margin <1 mm: 17% vs. 6%, p < 0.001). There were significantly more re-excisions due to R1 (“ink on tumor”) in the BCS/OBCI compared with the OBCII group (11% vs. 7%, p = 0.049). Univariate and multivariable regression analysis adjusted for tumor biology, tumor size, radiotherapy, and systemic treatment demonstrated no differences in local, regional, or distant recurrence-free or overall survival between the two groups.ConclusionsLarge resection volumes in oncoplastic surgery increases the distance from cancer cells to the margin of the specimen and reduces reexcision rates significantly. With OBCII larger tumors are resected with similar local, regional and distant recurrence-free as well as overall survival rates as BCS/OBCI.

Background While machine learning (ML) algorithms may predict cardiovascular outcomes more accurately than statistical models, their result is usually not representable by a transparent formula. Hence, it is often unclear how specific values of predictors lead to the predictions. We aimed to demonstrate with graphical tools how predictor-risk relations in cardiovascular risk prediction models fitted by ML algorithms and by statistical approaches may differ, and how sample size affects the stability of the estimated relations. Methods We reanalyzed data from a large registry of 1.5 million participants in a national health screening program. Three data analysts developed analytical strategies to predict cardiovascular events within 1 year from health screening. This was done for the full data set and with gradually reduced sample sizes, and each data analyst followed their favorite modeling approach. Predictor-risk relations were visualized by partial dependence and individual conditional expectation plots. Results When comparing the modeling algorithms, we found some similarities between these visualizations but also occasional divergence. The smaller the sample size, the more the predictor-risk relation depended on the modeling algorithm used, and also sampling variability played an increased role. Predictive performance was similar if the models were derived on the full data set, whereas smaller sample sizes favored simpler models. Conclusion Predictor-risk relations from ML models may differ from those obtained by statistical models, even with large sample sizes. Hence, predictors may assume different roles in risk prediction models. As long as sample size is sufficient, predictive accuracy is not largely affected by the choice of algorithm.

Quality indicators including cecal intubation rate (CIR) and adenoma detection rate (ADR) are established. Sex differences of quality indicators are observed, but the influence of sedation has not been investigated so far. The objective of this study is to assess the impact of sedation on quality indicators, including CIR and ADR, according to sex. We analyzed data of 52,506 screening colonoscopies performed by 196 endoscopists between November 2007 and April 2011 according to the Austrian \"quality management for colon cancer prevention\" program. Sedation did not affect polyp detection rate (women P=0.7972, men P=0.3711) or ADR for both sexes (women P=0.2773, men P=0.8676). ADR was not significantly influenced by sedation (P=0.1272), but by age and sex (both P<0.0001), when the executing endoscopist was considered. Although women were more often sedated than men (90.70 vs. 81.83%; P<0.0001), CIR was slightly lower in women than in men (94.69 vs. 96.58%; P<0.0001). Sedation improved the CIR in women by 2.95% (94.96 vs. 92.01%; P<0.0001), whereas in men it was just by 1.28% (96.81 vs. 95.53%; P<0.0001). Sedated women only reached the CIR of unsedated men (94.96 vs. 95.53%; P=0.1005). Accounting for the intra-observer influence of the endoscopist, the overall CIR was influenced by the interaction of sex and age (P=0.0049), but not by sedation (P=0.1435). Sedation does not increase adenoma or polyp detection, although it leads to an increase in CIR in men and women. This effect is more pronounced in women, yet CIR of men remains higher compared with women. Quality indicators are mainly influenced by the patient's age, sex, and the endoscopists' individual performance, rather than the endoscopists' subspeciality or procedural experience.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.An amendment to this paper has been published and can be accessed via a link at the top of the paper.