Using fractional polynomials and restricted cubic splines to model non‐proportional hazards or time‐varying covariate effects in the Cox regression model

Austin, Peter C.; Fang, Jiming; Lee, Douglas S.

doi:10.1002/sim.9259

Cited by 28 publications

(15 citation statements)

References 38 publications

(70 reference statements)

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“…Restricted cubic spline, a widely used method, is applied to fit and analyze the non-linear relationship between variables and outcomes (44)(45)(46). When using restricted cubic spline to draw curve relation, it is usually necessary to set the number of knots.…”

Section: Discussionmentioning

confidence: 99%

Associations between novel anthropometric measures and the prevalence of hypertension among 45,853 adults: A cross-sectional study

Kong²,

Shi³

et al. 2022

Front. Cardiovasc. Med.

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AimsTraditional anthropometric measures, including body mass index (BMI), are insufficient for evaluating the risk of hypertension. We aimed to investigate the association between novel anthropometric indices and hypertension risk in a large population in the United States.MethodsForty-five thousand eight hundred fifty-three participants from the National Health and Nutrition Examination Survey (NHANES) (1999–2018) were enrolled. Social demographic information, lifestyle factors, blood biochemical measurements and anthropometric indices, including body weight, body mass index (BMI), waist circumference, waist-to-height ratio (WtHR), conicity index (CI), a body shape index (ABSI), body roundness index (BRI) and lipid accumulation product (LAP) were collected. Multivariable logistic regression and restricted cubic spline were adopted to investigate the associations between hypertension risk and anthropometric indices. We also performed receiver operating characteristic (ROC) curve analyses to further evaluate the discriminatory powers of anthropometric measurements for screening hypertension risk. Moreover, participants were randomly assigned to the training group and the validation group in a ratio of 3 to 1. A nomogram model based on anthropometric measures was established and validated in the training group and validation group, respectively.ResultsAll of the anthropometric measurements investigated were positively and independently associated with the hypertension risk. Among all anthropometric indices, per-SD increment in ABSI had the highest OR (OR: 3.4; 95% CI: 2.73–4.24) after adjusting for age, sex, race/ethnicity, education, smoking, drinking, diabetes, and eGFR. Moreover, results from restricted cubic splines revealed the non-linear association between anthropometric measurements and hypertension risk. In ROC analyses, CI had superior discriminatory power for hypertension (area under the curve: 0.71; 95% CI: 0.706–0.715; optimal cutoff value: 1.3) compared with other indices. Nomogram model based on age, sex, diabetes, CI and LAP showed favorable predicting ability of hypertension risk with an AUC (95% CI) in training group of 80.2% (79.7–80.6%), and the AUC (95% CI) in validation group was 79.5% (78.3–80.1%). Meanwhile, calibration plot showed good consistency.ConclusionsAnthropometric measurements including BMI, WtHR, CI, ABSI, BRI and LAP are closely associated with hypertension risk in the present study. For better prevention and treatment of hypertension, more attention should be paid to anthropometric indices, especially novel anthropometric indices.

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Section: Discussionmentioning

confidence: 99%

Associations between novel anthropometric measures and the prevalence of hypertension among 45,853 adults: A cross-sectional study

Kong²,

Shi³

et al. 2022

Front. Cardiovasc. Med.

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“…If the researcher includes many variables that affect survival time and assesses each one's effects separately, assumes only linear relationships between predictors, and ignores interactions, the study results might not match predictions. 19 By eliminating the linear, non-linear, and interaction effects of predictors that have an impact on survival times, the recently created SM model presents a new perspective that makes interpretation easier.…”

Section: Discussionmentioning

confidence: 99%

Use of Survival Data in Multivariate Adaptive Regression Analysis: Simulation Study

ŞENGÜL¹,

Temel²,

Kaya³

2023

Turkiye Klinikleri J Biostat

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The multivariate adaptive regression splines (MARS) is very effective in order to model linear or nonlinear relationships. The Cox regression residuals-based MARS model, which integrates Cox regression and MARS approaches, was created to assess the relationships between efficient risk factors on the survival. The purpose of this study is to introduce the Survival-MARS (SM) model which uses the Cox-Snell, Martingale, and deviance residuals. Also,our aim is to compare the performance of the models created with residuals at different sample sizes and correlation levels with the simulation study in order to determine the most effective residual type that can be used in the SM model. Material and Methods: Performances of SM models that use Cox-Snell,Martingale, and deviance residual types were compared at different sample sizes (n = 30, 100, 150, 250, 500, 1.000), with both no correlation (r = 0.00) and medium (r = 0.50) and high (r = 0.90) correlations between predictors. SM model performances were compared via minimum generalized cross-validation and the sum of mean squared error values.. Results: In all scenarios, SM models with Cox-Snell residuals have the best performance compared to other models established with other residuals. Martingale and deviance residuals were affected by high correlation and low sample sizes. Conclusion: In case of linear relationship between risk factors, SM models with Cox-Snell residuals are quite successful in explaining these relationship structures and enable the effects on the dependent variable to easily interpret.

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“…The assumption is not met where the residuals correlated with time ( P <0.05), and we used restricted cubic splines to model the log-hazard ratio as a function of time to present the time-varying hazard ratios (HR) and associated 95% CIs. 23 All data analyses were performed using SAS Enterprise Guide version 9.4 (SAS Institute, Inc, Cary, NC). This article follows the STROBE (Strengthening The Reporting of OBservational studies in Epidemiology) reporting guideline.…”

Section: Methodsmentioning

confidence: 99%

Maternal Health Outcomes After Pregnancy-Associated Stroke: A Population-Based Study With 19 Years of Follow-Up

Nerenberg

Diong³

et al. 2023

Stroke

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Background: Pregnancy-associated stroke carries high short-term morbidity and mortality, but data on subsequent maternal outcomes are limited. We evaluated long-term maternal health outcomes after pregnancy-associated stroke. Methods: In this retrospective cohort study, we used administrative data to identify pregnant adults aged ≤49 years with stroke between 2002-2020 in Ontario, Canada and 2 comparison groups: (1) non-pregnant female patients with stroke and (2) pregnant patients without stroke. Patients who survived the index admission were followed until 2021. After propensity score matching, we used Cox regression with a robust variance estimator to compare pregnant patients with stroke and the 2 comparison groups for the composite outcome of death and all-cause non-pregnancy readmission. Where proportional hazard assumption was not met, we reported time-varying hazard ratios (HR) with 95% CIs by modeling the log-hazard ratio as a function of time using restricted cubic splines. Results: We identified 217 pregnant patients with stroke, 7604 non-pregnant patients with stroke, and 1 496 256 pregnant patients without stroke. Of the 202 pregnant patients with stroke who survived the index stroke admission, 41.6% (6.8 per 100 person-years) subsequently died or were readmitted during follow-up. Median follow-up times were 5 years (pregnancy-associated stroke), 3 years (non-pregnant stroke), and 8 years (pregnant without stroke). Pregnant patients with stroke had a lower hazard of death and all-cause readmission compared with non-pregnant patients with stroke at 1-year follow-up (HR, 0.64 [95% CI, 0.44–0.94]), but this association did not persist during longer-term follow-up. Conversely, pregnant patients with stroke had higher hazard of death and readmission compared with pregnant patients without stroke at 1-year follow-up (HR, 5.70 [95% CI, 3.04–10.66]), and this association persisted for a decade. Conclusions: Stroke during pregnancy is associated with long-term health consequences. It is essential to transition care postpartum to primary or specialty care to optimize vascular health.

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Using fractional polynomials and restricted cubic splines to model non‐proportional hazards or time‐varying covariate effects in the Cox regression model

Cited by 28 publications

References 38 publications

Associations between novel anthropometric measures and the prevalence of hypertension among 45,853 adults: A cross-sectional study

Associations between novel anthropometric measures and the prevalence of hypertension among 45,853 adults: A cross-sectional study

Use of Survival Data in Multivariate Adaptive Regression Analysis: Simulation Study

Maternal Health Outcomes After Pregnancy-Associated Stroke: A Population-Based Study With 19 Years of Follow-Up

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