Flexible regression models with cubic splines

Durrleman, Sylvain; Simon, Richard

doi:10.1002/sim.4780080504

Cited by 2,283 publications

(1,629 citation statements)

References 18 publications

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“…Time in study was modeled using restricted cubic splines (Durrleman & Simon, 1989). A restricted cubic spline is a piecewise function, joined together by knots, and constrained to be linear before the first knot and after the last knots, otherwise taking the shape of cubic polynomials.…”

Section: Methodsmentioning

confidence: 99%

Cellular aging dynamics after acute malaria infection: A 12‐month longitudinal study

et al. 2017

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SummaryAccelerated cellular aging and reduced lifespan have recently been shown in birds chronically infected with malaria parasites. Whether malaria infection also affects cellular aging in humans has not been reported. Here, we assessed the effect of a single acute Plasmodium falciparum malaria infection on cellular aging dynamics in travelers prospectively followed over one year in Sweden. DNA and RNA were extracted from venous blood collected at the time of admission and repeatedly up to one year. Telomere length was measured using real‐time quantitative PCR, while telomerase activity and CDKN2A expression were measured by reverse transcriptase (RT)–qPCR. Our results show that acute malaria infection affects cellular aging as reflected by elevated levels of CDKN2A expression, lower telomerase activity, and substantial telomere shortening during the first three months postinfection. After that CDKN2A expression declined, telomerase activity increased and telomere length was gradually restored over one year, reflecting that cellular aging was reversed. These findings demonstrate that malaria infection affects cellular aging and the underlying cellular mechanism by which pathogens can affect host cellular aging and longevity need to be elucidated. Our results urge the need to investigate whether repeated malaria infections have more pronounced and long‐lasting effects on cellular aging and lifespan (similarly to what was observed in birds) in populations living in malaria endemic areas.

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Section: Methodsmentioning

confidence: 99%

Cellular aging dynamics after acute malaria infection: A 12‐month longitudinal study

et al. 2017

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“…Then, restricted cubic spline models were used. Cubic splines are smoothly joined piecewise third-order polynomials [19]. Polynomials are fitted within intervals delimited by knots, and restrictions are placed on the resulting curve to ensure a smooth appearance at the knot points.…”

Section: Methodsmentioning

confidence: 99%

Modeling the relationship between circulating tumour cells number and prognosis of metastatic breast cancer

Botteri

Sandri

Bagnardi

et al. 2009

Breast Cancer Res Treat

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Modeling the relationship between circulating tumour cells number and prognosis of metastatic breast cancer. Breast Cancer Research and Treatment, Springer Verlag, 2009, 122 (1), pp.211-217. <10.1007/s10549-009-0668-7>. EPIDEMIOLOGYModeling the relationship between circulating tumour cells number and prognosis of metastatic breast cancer Abstract Circulating tumor cell (CTC) count has been shown to be an independent predictor of progression in metastatic breast, prostate, and colorectal cancer. A cutpoint is generally used to identify favorable and unfavorable response groups. In this study, we propose an approach in which the number of CTCs is analyzed as a continuous predictor, to detect the shape of the relationship between CTCs and prognosis of metastatic breast cancer. We evaluated the association of baseline CTC with progression-free survival (PFS) and overall survival (OS) in a series of 80 patients treated for advanced breast cancer at the European Institute of Oncology, Milan. The association between CTCs and prognosis was analyzed with standard categorical survival analysis and spline regression models. At baseline, median age was 55 years; 33 patients were newly diagnosed with metastatic breast cancer (41%), while 28 (35%) and 19 (24%) were pretreated with one and two previous chemotherapy lines, respectively. After a median follow-up of 28 months, 76 disease progressions and 44 deaths were observed. Kaplan-Meier curves showed a clear association between CTCs and PFS (P-value 0.03) and OS (Pvalue \ 0.01). Patients with no CTC at baseline had a significantly better prognosis. When analyzing the CTCs as a continuous variable, we found an increase in risk with increasing number of CTCs, for both PFS and OS. The increase rate lessened after approximately 5 CTCs. CTCs represent a robust prognostic factor in the metastatic breast cancer setting. A nonlinear increase in risk of both progression and death with increasing number of CTCs was observed, with a lessening increase after approximately 5 CTCs. If distinct prognostic groups are to be identified, women with no CTC could plausibly represent a distinct favorable one.

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“…In preliminary analyses, we used plots created by fitting restricted cubic splines 18 to allow us to inspect and formally test the 'shape' of the relationship between BMI and liver disease mortality. Both the plots for liver disease versus BMI, and the tests for non-linearity (all P-values 40.25), indicated that the relationship was well described using a single linear BMI term.…”

Section: Methodsmentioning

confidence: 99%

Obesity and overweight in relation to liver disease mortality in men: 38 year follow-up of the original Whitehall study

et al. 2008

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Obesity has been implicated in the aetiology of liver disease. However, to date, evidence is largely drawn from cross-sectional studies, where interpretation is hampered by reverse causality, and from studies on clinical populations that have limited generalisability. In this prospective cohort study, data on body mass index (BMI) and covariates were collected at baseline on 18 863 male government employees (aged 40-69 years). Respondents were then followed up for a maximum of 38 years of age. Mortality surveillance gave rise to 13 129 deaths, 122 of which were due to liver disease (57 cancers; 65 non-cancers). In ageadjusted analyses, BMI was positively related to total liver disease mortality (hazards ratio per 1 s.d. increase in BMI; 95% confidence interval (CI): 1.36; 1.14, 1.62) in a graded fashion across the weight categories (P-value for trend: 0.01). The magnitude of this association was somewhat stronger for non-cancer liver disease deaths (1.47; 1.16, 1.86) than for cancer liver disease deaths (1.25; 0.96, 1.62). Excluding deaths in the first 10 years of follow-up somewhat strengthened the BMIFnoncancer liver disease association. Adjustment for socioeconomic position, other candidate confounders and mediating factors led to the modest attenuation of these associations. Further investigation in prospective cohort studies with more detailed data on liver disease, for instance using biochemical tests of liver function or hepatic ultrasonography, is warranted.

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Flexible regression models with cubic splines

Cited by 2,283 publications

References 18 publications

Cellular aging dynamics after acute malaria infection: A 12‐month longitudinal study

Cellular aging dynamics after acute malaria infection: A 12‐month longitudinal study

Modeling the relationship between circulating tumour cells number and prognosis of metastatic breast cancer

Obesity and overweight in relation to liver disease mortality in men: 38 year follow-up of the original Whitehall study

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