Restricted Spline Research Articles

Dietary and blood selenium are inversely associated with the prevalence of stroke among Inuit in Canada

Inuit in Canada have high selenium intake from the consumption of country food such as fish and marine mammals. The health consequence is not known. This study examines the association between blood selenium concentration and prevalence of stroke among Canadian Inuit. The International Polar Year Inuit Health Survey was conducted in 2007–2008. Among the 2077 adults participants (≥18 years old) who completed a questionnaire and gave blood samples, 49 stroke cases were reported, 31 of which were from women. The crude prevalence of stroke was 2.4% in the participants. Participants with stroke had lower blood selenium (geometric mean: 260 μg/L vs. 319 μg/L) and dietary selenium (144 μg/day vs. 190 μg/day) compared to individuals without stroke. Participants with high blood/dietary selenium exposure (quartiles 3 and 4) had a lower prevalence of stroke compared to those with low selenium exposure (quartile 1). The adjusted odds ratio ranged from 0.09 to 0.25 among subgroups (e.g. age, sex, and blood mercury). An L-shaped relationship between prevalence of stroke with blood and dietary selenium was observed, based on the cubic restricted spline and segmented regression analyses. The estimated turning points of the L-shaped curve for blood selenium and dietary selenium were 450 μg/L and 350 μg/day, respectively. Below the turning points, it was estimated that each 50-μg/L increase in blood selenium was associated with a 38% reduction in the prevalence of stroke, and each 50-μg/day increase in dietary selenium was associated with a 30% reduction in the prevalence of stroke. In conclusion, blood and dietary selenium are reversely associated with the prevalence of stroke in Inuit, which follows an L-shaped relationship. Whether this relationship applies to other population needs further investigation.

The role of maternal age in twin pregnancy outcomes

There are limited data on how maternal age is related to twin pregnancy outcomes. The purpose of this study was to assess the relationship between maternal age and risk for preterm birth, fetal death, and neonatal death in the setting of twin pregnancy. This population-based study of US birth, fetal death, and period-linked birth-infant death files from 2007-2013 evaluated neonatal outcomes for twin pregnancies. Maternal age was categorized as 15-17, 18-24, 25-29, 30-34, 35-39, and ≥40 years of age. Twin live births and fetal death delivered at 20-42 weeks were included. Primary outcomes included preterm birth (<34 weeks and <37 weeks), fetal death, and neonatal death at <28 days of life. Analyses of preterm birth at <34 and <37 weeks were adjusted for demographic and medical factors, with maternal age modeled with the use of restricted spline transformations. A total of 955,882 twin live births from 2007-2013 were included in the analysis. Preterm birth rates at <34 and <37 weeks gestation were highest for women 15-17 years of age, decreased across subsequent maternal age categories, nadired for women 35-39 years old, and then increased slightly for women ≥40 years old. Risk for fetal death generally decreased across maternal age categories. Risk for fetal death was 39.9 per 1000 live births for women 15-17 years old, 24.2 for women 18-24 years old, 17.8 for women 25-29 years old, 16.4 for women 30-34 years old, 17.2 forwomen 35-39 years old, and 15.8 for women ≥40 years old. Risk forneonatal death at <28 days was highest for neonates born to women 15-17 years old (10.0 per 1,000 live births), decreased to 7.3 for women 18-24 years old and 5.5 for women 25-29 years old and ranged from 4.3-4.6 for all subsequent maternal age categories. In adjusted models, risk for preterm birth at <34-<37 weeks gestation was not elevated for women in their mid-to-late 30s; however, risk was elevated for women <20 years old and increased progressively with age for women in their 40s. Although twin pregnancy is associated with increased risk for most adverse perinatal outcomes, this analysis did not find advanced maternal age to be an additional risk factor for fetal death and infant death. Preterm birth risk was relatively low for women in their late 30s. Risks for adverse outcomes were higher among younger women; further research is indicated to improve outcomes for this demographic group. It may be reasonable to counsel women in their 30s that their age is not a major additional risk factor for adverse obstetric outcomes in the setting of twin pregnancy.

Abstract 12404: Efficacy and Safety of Apixaban Compared With Warfarin in Patients With Atrial Fibrillation and Normal Renal Function over Time: Insights From the ARISTOTLE Trial

Introduction: It has been recently observed that one oral factor-Xa inhibitor (at the dose studied) might be associated with decreased efficacy in patients with atrial fibrillation (AF) and normal renal function. In the ARISTOTLE trial, apixaban compared to warfarin reduced stroke, mortality, and major bleeding irrespective of renal function at baseline. Our aim was to evaluate the efficacy and safety of apixaban vs. warfarin in patients with normal renal function over time. Methods: In ARISTOTLE, 16,971 patients had serial creatinine measurements available after randomization. There were a total of 397 stroke or systemic embolic events, 286 ischemic or unspecified strokes, and 712 major bleed events during median follow-up of 1.8 years. Normal renal function was predefined as an estimated glomerular filtration rate (eGFR) &gt;80 mL/min. The relations between renal function, treatment, and outcomes were investigated by using Cox regression with renal function as a continuous time dependent covariate, fitted using restricted splines. Hazard ratios with 95% confidence intervals (CI) were analyzed based on continuous eGFR level during follow-up using both the Cockcroft-Gault and CKD-EPI equations. Results: The relative risk of stroke or systemic embolism was consistently lower in participants randomized to apixaban compared with warfarin. The patterns were similar for the ischemic or unspecified stroke outcome as well as for major bleeding (Table). Conclusions: Apixaban, relative to warfarin, demonstrated preserved efficacy and safety in AF patients with normal renal function over time.

Associations of pre-diagnostic body mass index with overall and cancer-specific mortality in a large Austrian cohort.

Although obesity is a well-known risk factor for several cancers, its role on cancer survival is poorly understood. Within the VHM&PP cohort, 8,673 cancer patients (42.2% women) were followed over a median time of 11.9 years. Cox proportional hazard models were used to estimate the association of pre-diagnostic overweight (BMI 25.0-29.9 kg/m(2)) and obesity (BMI ≥ 30.0 kg/m(2)) with all-cause and cancer-specific mortality. Cubic restricted splines were additionally modeled. During 71,126 person-years, 4,571 deaths were observed. Compared to normal weight, overweight was associated with statistically significantly decreased all-cause mortality (HR 0.93; 95% CI 0.87-0.997) and cancer-specific mortality (HR 0.91; 95% CI 0.84-0.99). Underweight was statistically significantly associated with 28% increased overall mortality, in particular in men [HR 2.02 (95% CI 1.43-2.83) vs. HR 0.96 (95% CI 0.71-1.30) in women]. J-shaped associations were found between BMI and mortality with the nadir around a BMI of 25 kg/m(2). Analysis by cancer site showed though not statistically significantly that overweight was associated with reduced mortality, while obesity was associated with increased cancer-specific mortality except cancers of the upper digestive tract. In patients with local stage colorectal cancers, obesity was associated with increased all-cause (vs. normal weight HR 1.90; 95% CI 1.03-3.52) and cancer-specific mortality (HR 3.17; 95% CI 1.29-7.81). Overweight patients have a better overall prognosis, while for obesity no association and for underweight worse prognosis were found. Our results on common cancers indicate that there are tumor- and stage-specific differences.

Shape restricted smoothing splines via constrained optimal control and nonsmooth Newton’s methods

Shape restricted smoothing splines receive considerable attention, motivated by many important applications in science and engineering. In this paper, we consider smoothing splines subject to general linear dynamics and control constraints, and formulate them as finite-horizon constrained linear optimal control problems with unknown initial state and control. By exploring techniques from functional and variational analyses, optimality conditions are developed in terms of variational inequalities. Due to the control constraints, the optimality conditions give rise to a nonsmooth B-differentiable equation of an optimal initial condition, whose unique solution completely determines the shape restricted smoothing spline. A modified nonsmooth Newton’s algorithm with line search is used to solve this equation; detailed convergence analysis of the proposed algorithm is presented. Using techniques from nonsmooth analysis and polyhedral theory, we show the global convergence of the algorithm for shape restricted smoothing splines subject to general polyhedral control constraints.

Diabetes-related quality of life is enhanced by glycaemic improvement in older people.

To investigate the validity and reliability of the Audit of Diabetes-Dependent Quality of Life instrument in older Italians with diabetes and to test the association of diabetes-related quality of life with glycaemic control over time. A total of 558 outpatients with Type 2 diabetes from the Diabetic Unit of the Italian National Research Centre on Aging Hospital in Ancona were enrolled to complete questionnaires (Audit of Diabetes-Dependent Quality of Life-19 and the Short-Form-12), and to undergo clinical and biochemical testing at baseline and at 12 months of follow-up. The overall impact of diabetes using the average weighted impact score from the Audit of Diabetes-Dependent Quality of Life questionnaire was calculated. Participants were categorized according to this score as having either less or more negative diabetes-related quality of life. Participants had a mean ± SD age of 67.7 ± 9.2 years and 51.8% were male. Factor analysis and Cronbach's coefficient of internal consistency (Cronbach's α = 0.931) confirmed that the 19 domain-specific Audit of Diabetes-Dependent Quality of Life items could be combined into a single scale in this Italian population. The impact score correlated with the physical (r = 0.275; P < 0.001) and mental components (r = 0.291; P < 0.001) of the Short-Form-12 questionnaire. Significant differences were found according to diabetic complications in specific Audit of Diabetes-Dependent Quality of Life items and impact scores. Insulin use had a greater association with a more negative quality of life compared with other antidiabetic agents. A multivariate linear regression model with restricted linear spline application showed that the relationship between HbA1c and impact score was not linear and that the change in the impact score was associated with improved glycaemic control in those with a less negative diabetes-related quality of life at 12 months. The Audit of Diabetes-Dependent Quality of Life-19 is a valid tool for measuring the impact of diabetes on quality of life in older Italians. Perception of diabetes-related quality of life is associated with glycaemic control over time.

Menarche, menopause, years of menstruation, and the incidence of osteoporosis: the influence of prenatal exposure to diethylstilbestrol.

Estrogen is critical for bone formation and growth in women. Estrogen exposures occur throughout life, including prenatally, and change with reproductive events, such as menarche and menopause. The objective of this study was to investigate the association between age at menarche, age at menopause, and years of menstruation with incidence of osteoporosis and assess the impact of prenatal exposure to diethylstilbestrol (DES), a synthetic estrogen, on such associations. Participants were 5573 women in the National Cancer Institute Combined Cohort Study of DES (1994-2006). Data on reproductive history and medical conditions were collected through questionnaires at baseline in 1994 and subsequently in 1997, 2001, and 2006. Age-stratified Cox regression models were used to calculate multivariable incidence rate ratios (IRRs) and 95% confidence intervals (CIs). Effect measure modification by prenatal DES exposure was assessed using cubic restricted spline regression models. Osteoporosis was the main outcome measure. The IRRs for osteoporosis incidence with age at menarche less than 11 years and age at menopause of 50 years or younger were 0.82 (CI 0.59, 1.14) and 0.61 (CI 0.40, 0.92), respectively. Fewer than 25 years of menstruation was associated with an increased incidence of osteoporosis (IRR 1.80; CI 1.14, 2.86) compared with 35 years or more of menstruation. Associations were stronger among women who had not been prenatally exposed to DES. Our data support the hypothesis that lifetime cumulative exposure to estrogens is protective against osteoporosis. Furthermore, prenatal exposure to estrogen appears to modify these associations, although the mechanism by which this occurs is unknown.

Body Mass Index Is Associated With Hospital Mortality in Critically Ill Patients

Obesity is associated with a variety of diseases, which results in a decreased overall life expectancy. Nevertheless, some studies suggest that being overweight may reduce hospital mortality of certain patient groups, referred to as obesity paradox. Conflicting results for critically ill patients are reported. Therefore, we wished to investigate the association of body mass index and hospital mortality in critically ill patients. Observational cohort study in Dutch critically ill patients. A dataset from the Dutch National Intensive Care Evaluation registry that includes patients admitted to Dutch ICUs was used. One hundred fifty-four thousand three hundred and eight ICU patients of teaching and nonteaching units in urban and nonurban hospitals. None. We used logistic regression analysis, correcting for case mix (Simplified Acute Physiology Score II, age, gender, admission type, neoplasm, AIDS, hematologic malignancy, immunologic insufficiency, mechanical ventilation, and calendar year), to determine the relationship between body mass index and hospital mortality. Body mass index was included in the model as a continuous nonlinear covariate in a restricted regression spline transformation. To facilitate interpretation, adjusted odds ratios were calculated for the World Health Organization-based body mass index classes. Body mass index was found to be significantly associated with hospital mortality, with risks quickly increasing for underweight patients (body mass index < 18.5 kg/m). Obese and seriously obese patients, with a body mass index of 30-39.9 kg/m, had the lowest risk of death with an adjusted odds ratio of 0.86 (0.83-0.90). This large observational database shows an inverse association between obesity and hospital mortality in critically ill patients that could not be explained by a variety of known confounders.

Abstract MP23: Urinary Magnesium Excretion and Risk of Incident Hypertension

Background: Observational studies on dietary magnesium and risk of hypertension have reported mixed findings, but have lacked direct measures of magnesium uptake. Urinary excretion of magnesium, an indicator of dietary uptake, may clarify these discrepant findings. Methods: We examined 4,070 participants aged 28-75 years free of hypertension, kidney disease, and cardiovascular disease in the PREVEND Study, a prospective population-based cohort study. Urinary magnesium excretion was measured in two 24-hour urine collections at baseline. Incident hypertension was defined as blood pressure ≥140/90 mm Hg or initiation of antihypertensive medication. Results: During a median follow-up of 7.5 years (interquartile range: 5.5-9.2 years), 1,001 participants developed incident hypertension. Mean 24-hour urinary magnesium excretion was 4.35 ± 1.61 mmol for men and 3.65 ± 1.35 mmol for women. Urinary magnesium excretion was associated with risk of hypertension in a log-linear fashion (Figure) after adjustment for age, body mass index, sex, smoking status, alcohol intake, family history of hypertension, and urinary excretion of sodium, potassium, and calcium. Each 1-unit increment in ln-transformed urinary magnesium excretion was associated with a 26% lower risk of incident hypertension after multivariable adjustment (adjusted hazard ratio, 0.74; 95% confidence interval, 0.65-0.84). Conclusion: Urinary magnesium excretion is inversely and independently associated with risk of incident hypertension. Increasing dietary intake of magnesium could reduce the risk of hypertension. Figure legend: Natural log-transformed urinary magnesium concentrations and adjusted risk of hypertension. Magnesium levels were back-transformed to original values for ease of interpretation. Association estimated by Cox regression based on restricted splines with three knots. Dashed lines represent the 95% confidence interval. The spline curve is truncated at the 0.5 percentile and 99.5 percentile of the distribution curve.

Statins and risk of treated incident diabetes in a primary care population

(i) To examine the incidence of new onset treated diabetes in patients treated with different types of statins and (ii) the relationship between the duration and dose of statins and the subsequent development of new onset treated diabetes. A retrospective cohort study was performed using the Irish Health Services Executive Primary Care Reimbursement Services national pharmacy claims database. Individuals who received any medicines were identified from January 2001 to January 2009 (n = 1 235 671). Patients newly treated with statins from 1 January 2002 to 31 December 2007 were identified (n = 239 628). Cases were identified as individuals newly treated with antidiabetic medication (n = 38 503). Adjusted hazards ratios (HR) with 95% confidence intervals (CI) were calculated to examine the association between statins (any vs. none) and time to new onset treated diabetes using Cox proportional hazard regression. The dose and duration response relationship between statins and new onset treated diabetes was examined using restricted spline functions to assess the linearity of the relationship. Statin use was associated with an increased risk of new onset treated diabetes (HR = 1.18, 95% CI 1.15, 1.22). Increased risk of new onset treated diabetes was found with rosuvastatin (HR = 1.41, 95% CI 1.31, 1.52), atorvastatin (HR = 1.23, 95% CI 1.19, 1.27) and simvastatin (HR = 1.15, 95% CI 1.05, 1.25). There were statistically significant overall dose and duration effects for all statins, excepting fluvastatin, which only demonstrated a duration effect. An increased risk of new onset treated diabetes was found in those treated with statins showing significant duration and dose effect. Further study is required to confirm this association.

Total Adiponectin and Risk of Symptomatic Lower Extremity Peripheral Artery Disease in Men

Lower concentrations of adiponectin have been linked to subsequent risk of coronary heart disease in healthy individuals. Whether similar relationships exist for the development of systemic atherosclerosis, such as peripheral artery disease (PAD), is uncertain. We investigated the association between total adiponectin and risk of lower extremity PAD. We performed a prospective, nested case-control study among 18,225 male participants of the Health Professionals Follow-up Study who were free of diagnosed cardiovascular disease at the time of blood draw (1993-1995). During 14 years of follow-up, 143 men developed PAD. Using risk set sampling, controls were selected in a 3:1 ratio and matched on age, smoking status, fasting status, and date of blood draw (n=429). Median (interquartile range) adiponectin concentrations at baseline were lower among cases compared with controls (4.1 [3.2-5.5] versus 5.4 [3.8-7.5] µg/mL; P<0.001). A log-linear inverse association was evident over the full spectrum of adiponectin concentrations with PAD risk after controlling for baseline cardiovascular risk factors using restricted spline conditional logistic regression. Adiponectin was associated with a 42% lower risk of PAD per SD increase in natural log-transformed adiponectin (relative risk, 0.58; 95% confidence interval, 0.45-0.74) after adjustment for cardiovascular risk factors. The relative risk was attenuated (relative risk, 0.68; 95% confidence interval, 0.51-0.92) after further accounting for high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, C-reactive protein, and cystatin C. Additional adjustment for hemoglobin A(1c), triglycerides, and γ-glutamyltransferase had little impact on this association (relative risk, 0.68; 95% confidence interval, 0.50-0.92). Total adiponectin is inversely associated with risk of symptomatic lower extremity PAD in men.

Localized Bases for Kernel Spaces on the Unit Sphere

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of $N$ scattered sites, the standard basis for such a space utilizes $N$ \emph{globally} supported kernels; computing with it is prohibitively expensive for large $N$. Easily computable, well-localized bases, with "small-footprint" basis elements - i.e., elements using only a small number of kernels -- have been unavailable. Working on $\sphere$, with focus on the restricted surface spline kernels (e.g. the thin-plate splines restricted to the sphere), we construct easily computable, spatially well-localized, small-footprint, robust bases for the associated kernel spaces. Our theory predicts that each element of the local basis is constructed by using a combination of only $\mathcal{O}((\log N)^2)$ kernels, which makes the construction computationally cheap. We prove that the new basis is $L_p$ stable and satisfies polynomial decay estimates that are stationary with respect to the density of the data sites, and we present a quasi-interpolation scheme that provides optimal $L_p$ approximation orders. Although our focus is on $\mathbb{S}^2$, much of the theory applies to other manifolds - $\mathbb{S}^d$, the rotation group, and so on. Finally, we construct algorithms to implement these schemes and use them to conduct numerical experiments, which validate our theory for interpolation problems on $\mathbb{S}^2$ involving over one hundred fifty thousand data sites.

Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation

This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and SO(3), we establish, using techniques involving differential geometry and Lie groups, that the kernels obtained as fundamental solutions of certain partial differential operators generate Lagrange functions that are uniformly bounded and decay away from their center at an algebraic rate, and in certain cases, an exponential rate. An immediate corollary is that the corresponding Lebesgue constants for interpolation as well as for $L_2$ minimization are uniformly bounded with a constant whose only dependence on the set of data sites is reflected in the mesh ratio, which measures the uniformity of the data. The kernels considered here include the restricted surface splines on spheres, as well as surface splines for SO(3), both of which have elementary closed-form representations that are computationally implementable. In addition to obtaining bounded Lebesgue constants in this setting, we also establish a "zeros lemma" for domains on compact Riemannian manifolds -- one that holds in as much generality as the corresponding Euclidean zeros lemma (on Lipschitz domains satisfying interior cone conditions) with constants that clearly demonstrate the influence of the geometry of the boundary (via cone parameters) as well as that of the Riemannian metric.

Spline methods for degressive proportionality in the composition of the European Parliament

This paper contains a proposal to determine the distribution of seats of the European Parliament among the member states by using linear spline functions. The Lisbon Treaty establishes that such an allotment must be done under degressive proportion to the population, and that every member state must receive no less than 6 and no more than 96 seats. A definition of degressive proportion was given in 2007 by Lamassoure and Severin as that, the ratio between population and assigned seats should not increase when population decreases. In addition, the Parliament size cannot surpass 751 seats.With these limitations, we first study some linear spline functions leading to allotments verifying limitations on minimum, maximum and size, and unrounded degressive proportionality (before rounding to integers). Next, restricted linear spline functions are used to obtain allotments verifying all four properties including rounded degressive proportionality, although sometimes a slightly smaller EP size must be considered.

Splines for Trend Analysis and Continuous Confounder Control

Spline regression often represents a less biased and more efficient alternative to standard linear, curvilinear, or categorical analyses of continuous exposures and confounders. Benefits of restricted cubic and quadratic splines have been described in the epidemiologic and biomedical literature.1-2 Analogous to the SAS (SAS Institute, Inc., Cary, North Carolina) code provided by Harrell3 for estimating restricted cubic splines, we present straightforward SAS code for estimating restricted quadratic splines. Using data from the HIV clinical cohort at the University of North Carolina Center for AIDS Research,4 we illustrate use of restricted quadratic splines in regression modeling for trend analysis and control of a continuous confounder. Details regarding the functional form of the restricted quadratic splines as well as SAS code for estimating restricted quadratic spline functions are provided in the eAppendix (http://links.lww.com). The data and SAS code used to generate the results included in this paper are also in the eAppendix. First, we illustrate the use of a restricted quadratic splines when estimating the association between log10 HIV-1 viral load centered at 2.301 log10 copies/ml and mortality. Figures S1 A-1C show the unadjusted association between centered log10 HIV-1 viral load at therapy initiation and the relative hazard of death estimated from several Cox proportional hazards models that (A) assume a log-linear relationship, (B) use indicators corresponding to quartiles of centered log10 HIV-1 viral load, or (C) include restricted quadratic splines with 4 equal knots based on the case distribution. Figure 1 Unadjusted associations between centered log10 HIV-1 viral load at therapy initiation and relative hazard of death among 557 male participants in the University of North Carolina Center for AIDS Research HIV clinical cohort, 1999-2010. HIV-1 viral load ... Based on the Akaike information criterion (AIC),5 presented in Figure 1, the restricted quadratic splines model provides the best fit to the data. The P- value for a joint Wald test of the three restricted quadratic splines basis functions included in the model was 0.010. The restricted quadratic splines model suggests a non-log-linear relationship between centered log10 HIV-1 viral load at therapy initiation and the relative hazard of death. Second, we illustrate the use of restricted quadratic splines when controlling for centered log10 HIV-1 viral load as a confounder using a Cox model. The table shows the hazard ratios for the association between an indicator of CD4 cell count ≤350 cells/mm3 at therapy initiation and hazard of death, both unadjusted and adjusted for confounding by viral load at therapy initiation. Adjusting for viral load using a log-linear term attenuated the point estimate corresponding to the CD4 cell count indicator by 26%. Adjustment using restricted quadratic splines with 4 equal knots based on the case distribution attenuated the point estimate by 30%. Attenuation upon control for viral load is expected given that higher viral load was associated with lower CD4 cell count (http://links.lww.com), and an elevated risk of subsequent mortality. Similar results were observed when restricted cubic splines was used instead of a restricted quadratic splines with the same degrees of freedom and comparable knot locations (http://links.lww.com). Table Hazard ratio for association between CD4 cell count less than or equal to 350 cells/mm3 versus greater than 350 cells/mm3 at therapy initiation and death among 557 male participants in the University of North Carolina Center for AIDS Research HIV clinical ... For the first example, use of restricted quadratic splines rather than linear terms or indicators provided a better fit, revealing non-linear relationships that otherwise may have not been apparent. In the second example, use of a restricted quadratic spline resulted in stronger attenuation of a crude association, which likely represents better control of confounding by viral load. The macro presented here offers users a straightforward SAS option for implementing restricted quadratic splines regression. This code is intended to aid in model selection as well as assessing robustness of inferences when comparing various modeling strategies.3,6-7 Furthermore, we hope the examples and code will facilitate the use of splines among researchers hesitant to employ less intuitive but largely equivalent modeling strategies,3,7 and in turn broaden the use of splines in applied epidemiologic research.

Cigarette smoking and lung cancer in women: Results of the French ICARE case–control study

BackgroundThe incidence of female lung cancer in developed countries has been increasing since 1950. In order to have recent and reliable data on the association between cigarette smoking and the risk of lung cancer in women, we analysed cases from a French population-based case–control study. MethodsThe ICARE study is a multicenter case–control study on respiratory cancers (lung and UADT cancers), set up in 10 départements that include a general cancer registry. We included 648 women lung cancer cases up to 76 years of age, with a histologically confirmed primary lung cancer. The 775 controls were randomly selected from the general population and frequency-matched with cases by age and département. ResultsOverall, smoking cigarettes at some time was associated with a 8-fold increase in lung cancer risk (OR=8.2, 95% CI 6.0–11.4). A dose–response relationship was observed as a function of duration, intensity and pack-years. Using restricted splines cubic models, we have shown that intensity dose-response departed significantly from linearity while the risk increased linearly with duration and decreased linearly with time since cessation. The following characteristics were associated with a higher relative risk: smoke inhalation, smoking non-filter cigarettes, smoking dark tobacco cigarettes and starting at a young age. In addition, duration, intensity and time since cessation was significantly related with histological type. This was not the case for characteristics such as the use of a filter or not, the inhalation pattern, or the type of tobacco smoked. The proportion of lung cancer cases attributable to cigarette smoking was 55% (95% CI: [47–63%]). ConclusionsOur results confirm that cigarette smoking is by far the most important cause of the current epidemic of lung cancer among French women and that the most important smoking-related variables for varying the risk of lung cancer are the duration, the intensity and the time since cessation.

Prospective weight change and colon cancer risk in male US health professionals.

Epidemiological studies are remarkably consistent, especially among men, in showing that overweight and obesity [body mass index (BMI) >25] are associated with increased risk of colon cancer. However, no prospective studies address the influence of weight change in adulthood on subsequent colon cancer risk. In this study, we investigated whether weight change influences colon cancer risk utilizing prospectively collected weight data. We included 46,349 men aged 40-75 participating in the Health Professionals Follow-Up Study. Questionnaires including items on weight were completed every second year during follow-up from 1986 to 2004. Updated weight change between consecutive questionnaires during follow-up and recalled weight gain since age 21 was evaluated. All eligible men were cancer-free at baseline. Proportional hazard and restricted spline regression models were implemented. Over an 18-year period, we documented 765 cases of colon cancer. Cumulative mean BMI >22.5 was associated with significantly increased risk of colon cancer. The short-term weight change in the prior 2 to 4 years was positively and significantly associated with risk [HR = 1.14 (95% confidence interval, 1.00-1.29) for 4.54 kg (10 pounds) increment, p = 0.04 for overall trend]. Weight gain per 10 years since age 21 was associated with significantly increased risk [HR = 1.33 (1.12-1.58) for 4.54 kg increase per 10 years, p = 0.001]. We estimated that 29.5% of all colon cancer cases was attributable to BMI above 22.5. Our results add support that overweight and obesity are modifiable risk factors for colon cancer among men and suggest that weight has an important influence on colon cancer risk even in later life.

Use of Spline Regression in an Analysis of Maternal Prepregnancy Body Mass Index and Adverse Birth Outcomes: Does It Tell Us More Than We Already Know?

Categorical analyses of prepregnancy body mass index (BMI) have shown that maternal overweight and obesity are associated with adverse pregnancy outcomes. It is unclear whether further insight into these associations can be gained from spline regression. We used spline regression to examine the relations between prepregnancy BMI and five adverse pregnancy outcomes in the Baltimore-Washington Infant Study, a case-control study of congenital cardiac defects. Analyses included 3,226 singleton live-born control infants delivered 1981 through 1989. We modeled BMI using (a) traditional categories of underweight, average weight, overweight, and obese and (b) restricted quadratic splines. We confirmed that overweight status and obesity were associated with increased risk of macrosomia and large for gestational age. For these outcomes, splines provided detail about the associations at the ends of the BMI distribution and within the average BMI category. Spline analyses also showed that underweight status was associated with increased risk of preterm delivery. Analyses of traditional categories of BMI provide good understanding of the associations with several adverse birth outcomes. For three outcomes, modeling with splines provided additional insight regarding dose-response relations within categories. Results suggest the need for further analyses of average BMI and adverse pregnancy outcomes.

Parsimonious analysis of time‐dependent effects in the Cox model

Cox's proportional hazards model can be extended to accommodate time-dependent effects of prognostic factors. We briefly review these extensions along with their varying degrees of freedom. Spending more degrees of freedom with conventional procedures (a priori defined interactions with simple functions of time, restricted natural splines, piecewise estimation for partitions of the time axis) allows the fitting of almost any shape of time dependence but at an increased risk of over-fit. This results in increased width of confidence intervals of time-dependent hazard ratios and in reduced power to confirm any time-dependent effect or even any effect of a prognostic factor. By means of comparative empirical studies the consequences of over-fitting time-dependent effects have been explored. We conclude that fractional polynomials, and similarly penalized likelihood approaches, today are the methods of choice, avoiding over-fit by parsimonious use of degrees of freedom but also permitting flexible modelling if time dependence of a usually a priori unknown shape is present in a data set. The paradigm of a parsimonious analysis of time-dependent effects is exemplified by means of a gastric cancer study.

Folate intake and the risk of neural tube defects: an estimation of dose-response.

Studies have shown that folic acid supplementation in early pregnancy markedly reduces the risk of neural tube defects (NTDs). Investigation of the relation between relative dose of supplemental folic acid or total folate intake and NTD risk is limited. We used data from 23,228 women, predominantly from the northeastern United States, enrolled between October 1984 and June 1987 in a prospective study of early prenatal exposures and pregnancy outcomes. Diet and vitamin intake data were gathered in the early second trimester. NTDs were ascertained through prenatal testing and by report of the delivering physician. Data analyses included multiple logistic regression and restricted spline regression modeling. For each additional 500 dietary folate equivalents consumed per day, the prevalence of NTDs decreased by 0.78 cases (95% confidence interval [CI] = 0.47-1.09) per 1,000 pregnancies. Compared with women having the lowest total folate intakes (0-149 folate equivalents per day), the prevalence of NTDs declined by 34%, 30%, 56% and 77% among the offspring of those women consuming 150-399, 400-799, 800-1199 and > or = 1200 folate equivalents per day, respectively (P-value for linear trend = 0.016). Our results suggest that NTD risk declines markedly with modest increases of total folate in early pregnancy. Total folate dose, rather than supplemental folate alone, should be considered in formulating public health guidelines for NTD prevention.