No Effect of High Eating Frequency Compared with Low Eating Frequency on Appetite and Inflammation Biomarkers: Results from a Randomized Crossover Clinical Trial.

BACKGROUND: Eating frequency (EF) focuses on the total number of eating occasions per day and may influence metabolic health. OBJECTIVES: We sought to examine the effect of high compared with low EF on appetite regulation and inflammatory biomarkers among healthy adults. METHODS: Data are from a randomized, crossover trial (the Frequency of Eating and Satiety Hormones study). Participants (n = 50) completed 2 isocaloric 21-d study periods of low EF (3 eating occasions/d) and high EF (6 eating occasions/d) in random order with a 14-d washout period in between. Participants were free-living and consumed their own food, using study-directed, structured meal plans with identical foods and total energy in both study periods. On days 1 and 21 of each EF period, fasting blood was collected during in-person clinic visits to assess plasma concentrations of ghrelin, leptin, adiponectin, and high-sensitivity C-reactive protein (hs-CRP). Linear mixed models with EF, diet sequence, and period as fixed effects and participant as random effect were used to estimate the intervention effect. Interaction effects between EF and body fat percentage were examined. RESULTS: Among the 50 participants who completed the trial, 39 (78%) were women, 30 (60%) were Non-Hispanic White, and 40 (80%) had a body mass index of <25 kg/m2, and the mean age was 32.1 y. The differences between high and low EF in fasting ghrelin (geometric mean difference: 17.76 ng/mL; P = 0.60), leptin (geometric mean difference: 2.09 ng/mL; P = 0.14), adiponectin (geometric mean difference: 381.7 ng/mL; P = 0.32), and hs-CRP (geometric mean difference: -0.018 mg/dL; P = 0.08) were not statistically significant. No significant interaction was observed between EF and body fat percentage on appetite regulation and inflammatory biomarkers. CONCLUSIONS: No differences was observed in fasting ghrelin, leptin, adiponectin, and hs-CRP comparing high and low EF. Future studies are needed to understand the physiology of EF and appetite as they relate to metabolic health. This trial was registered at clinicaltrials.gov as NCT02392897.

Robust best linear weighted estimator with missing covariates in survival analysis.

Missing data in covariates can result in biased estimates and loss of power to detect associations. We consider Cox regression in which some covariates are subject to missing. The inverse probability weighted approach is often applied to regression analysis with missing covariates. Inverse probability weighted estimators typically are less efficient than likelihood-based estimators, but in general are more robust against model misspecification. In this article, we propose a robust best linear weighted estimator for Cox regression with missing covariates. Our proposed estimator is the projection of the simple inverse probability weighted estimator onto the orthogonal complement of the score space based on a working regression model of the observed data. The efficiency gain is from the use of the association between the survival outcome variable and the available covariates, which is the working regression model. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via extensive simulation studies. The methods are applied to a colorectal cancer study to assess the association of the microsatellite instability status with colorectal cancer-specific mortality.

A smoothed corrected score approach for proportional hazards model with misclassified discretized covariates induced by error-contaminated continuous time-dependent exposure.

We consider the proportional hazards model in which the covariates include the discretized categories of a continuous time-dependent exposure variable measured with error. Naively ignoring the measurement error in the analysis may cause biased estimation and erroneous inference. Although various approaches have been proposed to deal with measurement error when the hazard depends linearly on the time-dependent variable, it has not yet been investigated how to correct when the hazard depends on the discretized categories of the time-dependent variable. To fill this gap in the literature, we propose a smoothed corrected score approach based on approximation of the discretized categories after smoothing the indicator function. The consistency and asymptotic normality of the proposed estimator are established. The observation times of the time-dependent variable are allowed to be informative. For comparison, we also extend to this setting two approximate approaches, the regression calibration and the risk-set regression calibration. The methods are assessed by simulation studies and by application to data from an HIV clinical trial.

Semiparametric regression calibration for general hazard models in survival analysis with covariate measurement error; surprising performance under linear hazard.

Observational epidemiological studies often confront the problem of estimating exposure-disease relationships when the exposure is not measured exactly. Regression calibration (RC) is a common approach to correct for bias in regression analysis with covariate measurement error. In survival analysis with covariate measurement error, it is well known that the RC estimator may be biased when the hazard is an exponential function of the covariates. In the paper, we investigate the RC estimator with general hazard functions, including exponential and linear functions of the covariates. When the hazard is a linear function of the covariates, we show that a risk set regression calibration (RRC) is consistent and robust to a working model for the calibration function. Under exponential hazard models, there is a trade-off between bias and efficiency when comparing RC and RRC. However, one surprising finding is that the trade-off between bias and efficiency in measurement error research is not seen under linear hazard when the unobserved covariate is from a uniform or normal distribution. Under this situation, the RRC estimator is in general slightly better than the RC estimator in terms of both bias and efficiency. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative.

Multinomial logistic regression with missing outcome data: An application to cancer subtypes.

Many diseases such as cancer and heart diseases are heterogeneous and it is of great interest to study the disease risk specific to the subtypes in relation to genetic and environmental risk factors. However, due to logistic and cost reasons, the subtype information for the disease is missing for some subjects. In this article, we investigate methods for multinomial logistic regression with missing outcome data, including a bootstrap hot deck multiple imputation (BHMI), simple inverse probability weighted (SIPW), augmented inverse probability weighted (AIPW), and expected estimating equation (EEE) estimators. These methods are important approaches for missing data regression. The BHMI modifies the standard hot deck multiple imputation method such that it can provide valid confidence interval estimation. Under the situation when the covariates are discrete, the SIPW, AIPW, and EEE estimators are numerically identical. When the covariates are continuous, nonparametric smoothers can be applied to estimate the selection probabilities and the estimating scores. These methods perform similarly. Extensive simulations show that all of these methods yield unbiased estimators while the complete-case (CC) analysis can be biased if the missingness depends on the observed data. Our simulations also demonstrate that these methods can gain substantial efficiency compared with the CC analysis. The methods are applied to a colorectal cancer study in which cancer subtype data are missing among some study individuals.

Methods for generalized change-point models: with applications to human immunodeficiency virus surveillance and diabetes data.

In many epidemiological and biomedical studies, the association between a response variable and some covariates of interest may change at one or several thresholds of the covariates. Change-point models are suitable for investigating the relationship between the response and covariates in such situations. We present change-point models, with at least one unknown change-point occurring with respect to some covariates of a generalized linear model for independent or correlated data. We develop methods for the estimation of the model parameters and investigate their finite-sample performances in simulations. We apply the proposed methods to examine the trends in the reported estimates of the annual percentage of new human immunodeficiency virus (HIV) diagnoses linked to HIV-related medical care within 3 months after diagnosis using HIV surveillance data from the HIV prevention trial network 065 study. We also apply our methods to a dataset from the Pima Indian diabetes study to examine the effects of age and body mass index on the risk of being diagnosed with type 2 diabetes.

Best linear inverse probability weighted estimation for two-phase designs and missing covariate regression.

The inverse probability weighted estimator is often applied to two-phase designs and regression with missing covariates. Inverse probability weighted estimators typically are less efficient than likelihood-based estimators but, in general, are more robust against model misspecification. In this paper, we propose a best linear inverse probability weighted estimator for two-phase designs and missing covariate regression. Our proposed estimator is the projection of the SIPW onto the orthogonal complement of the score space based on a working regression model of the observed covariate data. The efficiency gain is from the use of the association between the outcome variable and the available covariates, which is the working regression model. One advantage of the proposed estimator is that there is no need to calculate the augmented term of the augmented weighted estimator. The estimator can be applied to general missing data problems or two-phase design studies in which the second phase data are obtained in a subcohort. The method can also be applied to secondary trait case-control genetic association studies. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via extensive simulation studies. The methods are applied to a bladder cancer case-control study.

Eating behaviors and weight loss outcomes in a 12-month randomized trial of diet and/or exercise intervention in postmenopausal women.

BACKGROUND: Certain eating behaviors are common among women with obesity. Whether these behaviors influence outcomes in weight loss programs, and whether such programs affect eating behaviors, is unclear. METHODS: Our aim was to examine the effect of baseline eating behaviors on intervention adherence and weight among postmenopausal women with overweight or obesity, and to assess intervention effects on eating behaviors. Four hundred and 39 women (BMI ≥25 kg/m2) were randomized to 12 months of: i) dietary weight loss with a 10% weight loss goal ('diet'; n = 118); ii) moderate-to-vigorous intensity aerobic exercise for 225 mins/week ('exercise'; n = 117); iii) combined dietary weight loss and exercise ('diet + exercise'; n = 117); or iv) no-lifestyle change control (n = 87). At baseline and 12 months, restrained eating, uncontrolled eating, emotional eating and binge eating were measured by questionnaire; weight and body composition were assessed. The mean change in eating behavior scores and weight between baseline and 12 months in the diet, exercise, and diet + exercise arms were each compared to controls using the generalized estimating equation (GEE) modification of linear regression adjusted for age, baseline BMI, and race/ethnicity. RESULTS: Baseline restrained eating was positively associated with change in total calories and calories from fat during the dietary intervention but not with other measures of adherence. Higher baseline restrained eating was associated with greater 12-month reductions in weight, waist circumference, body fat and lean mass. Women randomized to dietary intervention had significant reductions in binge eating (- 23.7%, p = 0.005 vs. control), uncontrolled eating (- 24.3%, p < 0.001 vs. control), and emotional eating (- 31.7%, p < 0.001 vs. control) scores, and a significant increase in restrained eating (+ 60.6%, p < 0.001 vs. control); women randomized to diet + exercise reported less uncontrolled eating (- 26.0%, p < 0.001 vs. control) and emotional eating (- 22.0%, p = 0.004 vs. control), and increased restrained eating (+ 41.4%, p < 0.001 vs. control). Women randomized to exercise alone had no significant change in eating behavior scores compared to controls. CONCLUSIONS: A dietary weight loss intervention helped women modify eating behaviors. Future research should investigate optimal behavioral weight loss interventions for women with both disordered eating and obesity. TRIAL REGISTRATION: NCT00470119 (https://clinicaltrials.gov). Retrospectively registered May 7, 2007.

Nested case-control study of telomere length and lung cancer risk among heavy smokers in the ß-Carotene and Retinol Efficacy Trial.

BACKGROUND: Telomeres protect cells from genomic instability. We examined telomere length and lung cancer risk prospectively in heavy smokers. METHODS: In a nested case-control study with 709 cases and 1313 controls, conditional logistic regression was used to evaluate associations between telomere length (global, chromosome 5p, and 13q) and lung cancer risk by histotype, controlling for detailed smoking history. RESULTS: Risks of overall lung cancer and adenocarcinoma were suggestively elevated among individuals with telomere length in the longest tertile. No clear patterns were observed for other histotypes, or for chromosome 5p or 13q telomere length. Associations with adenocarcinoma were strongest among (OR, 95% CI for longest versus shortest tertile): former smokers (2.26, 1.03-4.96), individuals <65 years (2.22, 1.13-4.35), and women (2.21, 0.99-4.93). CONCLUSIONS: Our large study of heavy smokers adds additional evidence that long telomere length prior to diagnosis is associated with risk of lung adenocarcinoma, but not other histotypes.

Cox regression with dependent error in covariates.

Many survival studies have error-contaminated covariates due to the lack of a gold standard of measurement. Furthermore, the error distribution can depend on the true covariates but the structure may be difficult to characterize; heteroscedasticity is a common manifestation. We suggest a novel dependent measurement error model with minimal assumptions on the dependence structure, and propose a new functional modeling method for Cox regression when an instrumental variable is available. This proposal accommodates much more general error contamination than existing approaches including nonparametric correction methods of Huang and Wang (2000, Journal of the American Statistical Association 95, 1209-1219; 2006, Statistica Sinica 16, 861-881). The estimated regression coefficients are consistent and asymptotically normal, and a consistent variance estimate is provided for inference. Simulations demonstrate that the procedure performs well even under substantial error contamination. Illustration with a clinical study is provided.

Methods for multivariate recurrent event data with measurement error and informative censoring.

In multivariate recurrent event data regression, observation of recurrent events is usually terminated by other events that are associated with the recurrent event processes, resulting in informative censoring. Additionally, some covariates could be measured with errors. In some applications, an instrumental variable is observed in a subsample, namely a calibration sample, which can be applied for bias correction. In this article, we develop two non-parametric correction approaches to simultaneously correct for the informative censoring and measurement errors in the analysis of multivariate recurrent event data. A shared frailty model is adopted to characterize the informative censoring and dependence among different types of recurrent events. To adjust for measurement errors, a non-parametric correction method using the calibration sample only is proposed. In the second approach, the information from the whole cohort is incorporated by the generalized method of moments. The proposed methods do not require the Poisson-type assumption for the multivariate recurrent event process and the distributional assumption for the frailty. Moreover, we do not need to impose any distributional assumption on the underlying covariates and measurement error. Both methods perform well, but the second approach improves efficiency. The proposed methods are applied to the Nutritional Prevention of Cancer trial to assess the effect of selenium treatment on the recurrences of basal cell carcinoma and squamous cell carcinoma.

Randomized Trial Testing the Effects of Eating Frequency on Two Hormonal Biomarkers of Metabolism and Energy Balance.

BACKGROUND: Eating frequency (EF) may influence obesity-related disease risk by attenuating postprandial fluctuations in hormones involved in metabolism, appetite regulation, and inflammation. MATERIALS/METHODS: This randomized crossover intervention trial tested the effects of EF on fasting plasma insulin-like growth factor-I (IGF-1) and leptin. Fifteen subjects (4 males, 11 females) completed two eucaloric intervention phases lasting 21 days each: low EF ("low-EF"; 3 eating occasions/day) and high EF ("high-EF"; 8 eating occasions/day). Subjects were free-living and consumed their own meals using individualized structured meal plans with instruction from study staff. Subjects completed fasting blood draws and anthropometry on the first and last day of each study phase. The generalized estimated equations modification of linear regression tested the intervention effect on fasting serum IGF-1 and leptin. RESULTS: Mean (± SD) age was 28.5 ± 8.70 years, and mean (± SD) Body Mass Index was 23.3 (3.4) kg/m2. We found lower mean serum IGF-1 following the high-EF condition compared to the low-EF condition (P < 0.001). There was no association between EF and plasma leptin (P = 0.83). CONCLUSION: These results suggest that increased EF may lower serum IGF-1, which is a hormonal biomarker linked to increased risk of breast, prostate, and colorectal cancer.

Increased breast cancer screening and downstaging in Colombian women: A randomized trial of opportunistic breast-screening.

The lack of breast cancer screening in low and middle-income countries results in later stage diagnosis and worsened outcomes for women. A cluster randomized trial was performed in Bogotá, Colombia between 2008 and 2012 to evaluate effects of opportunistic breast cancer screening. Thirteen clinics were randomized to an intervention arm and 13 to a control arm. Physicians in intervention clinics were instructed to perform clinical breast examination on all women aged 50-69 years attending clinics for non-breast health issues, and then refer them for mammographic screening. Physicians in control clinics were not explicitly instructed to perform breast screening or mammography referrals, but could do so if they thought it indicated ("usual care"). Women were followed for 2-years postrandomization. 7,436 women were enrolled and 7,419 (99.8%) screened in intervention clinics, versus 8,419 enrolled and 1,108 (13.1%) screened in control clinics. Incidence ratios (IR) of early, advanced and all breast cancers were 2.9 (95% CI 1.1-9.2), 1.0 (0.3-3.5) and 1.9 (0.9-4.1) in the first (screening) year of the trial, and the cumulative IR for all breast cancers converged to 1.4 (0.7-2.8) by the end of follow-up (Year 2). Eighteen (69.2%) of 26 women with early stage disease had breast conservation surgery (BCS) versus 6 (42.5%) of 14 women with late-stage disease (p = 0.02). Fifteen (68.2%) of 22 women with breast cancer in the intervention group had BCS versus nine (50.0%) of 18 women in the control group (p = 0.34). Well-designed opportunistic clinic-based breast cancer screening programs may be useful for early breast cancer detection in LMICs.

Higher Eating Frequency Does Not Decrease Appetite in Healthy Adults.

BACKGROUND: Consumption of small, frequent meals is suggested as an effective approach to control appetite and food intake and might be a strategy for weight loss or healthy weight maintenance. Despite much speculation on the topic, scientific evidence is limited to support such a relation in the absence of changes to diet composition. OBJECTIVE: We examined the effects of high compared with low eating frequency (EF) on self-reported appetite as a secondary outcome in a controlled trial. METHODS: We conducted a randomized, crossover intervention trial in 12 participants (4 men, 8 women) who completed 2 isocaloric 3-wk intervention phases of low EF (3 eating occasions/d) compared with high EF (8 eating occasions/d). On the last morning of each study phase, participants completed a 4-h appetite testing session. During the appetite testing session, participants completing the low EF phase consumed a meal at 0800. Participants completing the high EF intervention consumed the same meal spread evenly over 2 eating occasions at 0800 and 1030. Standardized ratings of hunger, desire to eat, fullness, thirst, and nausea were completed every 30 min with the use of paper-and-pencil semianchored 100-mm visual analog scales. A composite appetite score was calculated as the mean of hunger, desire to eat, and the inverse of fullness (calculated as 100-fullness rating). Linear regression analysis compared ratings between low EF and high EF conditions. RESULTS: The mean composite appetite score was higher in the high EF condition for the total testing period (baseline through 1200) (P < 0.05) and for the time period from baseline through 1030 (P < 0.001). CONCLUSION: The results from this study in 12 healthy adults do not support the popularized notion that small, frequent meals help to decrease overall appetite. This trial was registered at clinicaltrials.gov as NCT02548026.

Augmented case-only designs for randomized clinical trials with failure time endpoints.

Under suitable assumptions and by exploiting the independence between inherited genetic susceptibility and treatment assignment, the case-only design yields efficient estimates for subgroup treatment effects and gene-treatment interaction in a Cox model. However it cannot provide estimates of the genetic main effect and baseline hazards, that are necessary to compute the absolute disease risk. For two-arm, placebo-controlled trials with rare failure time endpoints, we consider augmenting the case-only design with random samples of controls from both arms, as in the classical case-cohort sampling scheme, or with a random sample of controls from the active treatment arm only. The latter design is motivated by vaccine trials for cost-effective use of resources and specimens so that host genetics and vaccine-induced immune responses can be studied simultaneously in a bigger set of participants. We show that these designs can identify all parameters in a Cox model and that the efficient case-only estimator can be incorporated in a two-step plug-in procedure. Results in simulations and a data example suggest that incorporating case-only estimators in the classical case-cohort design improves the precision of all estimated parameters; sampling controls only in the active treatment arm attains a similar level of efficiency.

Methods to adjust for misclassification in the quantiles for the generalized linear model with measurement error in continuous exposures.

In many biomedical studies, covariates of interest may be measured with errors. However, frequently in a regression analysis, the quantiles of the exposure variable are often used as the covariates in the regression analysis. Because of measurement errors in the continuous exposure variable, there could be misclassification in the quantiles for the exposure variable. Misclassification in the quantiles could lead to bias estimation in the association between the exposure variable and the outcome variable. Adjustment for misclassification will be challenging when the gold standard variables are not available. In this paper, we develop two regression calibration estimators to reduce bias in effect estimation. The first estimator is normal likelihood-based. The second estimator is linearization-based, and it provides a simple and practical correction. Finite sample performance is examined via a simulation study. We apply the methods to a four-arm randomized clinical trial that tested exercise and weight loss interventions in women aged 50-75 years.

Repletion of vitamin D associated with deterioration of sleep quality among postmenopausal women.

Reduced health-related quality of life (HRQOL), depressive symptoms and poor sleep quality are important health issues among postmenopausal women and may be associated with low vitamin D status. Overweight postmenopausal women, with serum 25-hydroxyvitamin D [25(OH)D] 10-32ng/m, were recruited in Seattle, WA (2010-2012) and randomly assigned to 12months of weight loss +2000IU oral vitamin D3/day or weight loss+daily placebo. The weight-loss program included a reduced-calorie diet and 225min/week of moderate-to-vigorous aerobic activity. Eight subscales of HRQOL were assessed by the MOS 36-Item Short-Form Health Survey. Depressive symptoms were assessed using the Brief Symptom Inventory-18, and sleep quality was assessed using the Pittsburg Sleep Quality Index (PSQI). Mean 12-month changes in HRQOL, depressive symptoms and sleep quality were compared between groups (intent-to-treat) using generalized estimating equations. Compared to placebo, women receiving vitamin D did not experience any significant change in depressive symptoms (p=0.78), HRQOL subscales (all p>0.05), or overall sleep quality (p=0.21). However, a greater magnitude of change in serum 25(OH)D was associated with an increased need to take medications to sleep (ptrend=0.01) and overall worse sleep quality (ptrend<0.01). Women who became vitamin D replete (≥32ng/mL) also showed a deterioration in total PSQI sleep quality score compared to women who remained <32ng/mL despite supplementation, even after adjusting for relevant covariates (Non-Replete: -5.7% vs. Replete: +6.2%, p<0.01). Vitamin D supplementation of 2000IU/d may result in overall worse sleep quality for postmenopausal women with low circulating vitamin D undergoing weight loss.

Robust best linear estimator for Cox regression with instrumental variables in whole cohort and surrogates with additive measurement error in calibration sample.

Biomedical researchers are often interested in estimating the effect of an environmental exposure in relation to a chronic disease endpoint. However, the exposure variable of interest may be measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies an additive measurement error model, but it may not have repeated measurements. The subset in which the surrogate variables are available is called a calibration sample. In addition to the surrogate variables that are available among the subjects in the calibration sample, we consider the situation when there is an instrumental variable available for all study subjects. An instrumental variable is correlated with the unobserved true exposure variable, and hence can be useful in the estimation of the regression coefficients. In this paper, we propose a nonparametric method for Cox regression using the observed data from the whole cohort. The nonparametric estimator is the best linear combination of a nonparametric correction estimator from the calibration sample and the difference of the naive estimators from the calibration sample and the whole cohort. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via intensive simulation studies. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative.

The effects of separate and combined dietary weight loss and exercise on fasting ghrelin concentrations in overweight and obese women: a randomized controlled trial.

OBJECTIVE: Compensatory metabolic changes that accompany weight loss, for example, increased ghrelin, contribute to weight regain and difficulty in long-term weight loss maintenance; however, the separate effects of long-term caloric restriction and exercise on total circulating ghrelin in humans are unknown. DESIGN: A 12-month randomized controlled trial comparing: i) dietary weight loss with a 10% weight loss goal ('diet'; n = 118); ii) moderate-to-vigorous intensity aerobic exercise for 45 min/day, 5 days/week ('exercise'; n = 117); iii) dietary weight loss and exercise ('diet + exercise'; n = 117); or iv) no-lifestyle-change control (n = 87). PARTICIPANTS: 439 overweight or obese postmenopausal women (50-75 y). MEASUREMENTS: Fasting total serum ghrelin was measured by radioimmunoassay at baseline and 12 months. Fasting serum leptin, adiponectin and insulin were also measured. RESULTS: Fasting total ghrelin significantly increased in the diet + exercise arm (+7·4%, P = 0·008) but not in either the diet (+6·5%, P = 0·07) or exercise (+1·0%, P = 0·53) arms compared with control. Greater weight loss was associated with increased ghrelin concentrations, regardless of intervention. Neither baseline ghrelin nor body composition modified the intervention effects on changes in total ghrelin. The 12-month change in total ghrelin was inversely associated with changes in leptin, insulin and insulin resistance, and positively associated with change in adiponectin. CONCLUSIONS: Greater weight loss, achieved through a reduced calorie diet or exercise, is associated with increased total ghrelin concentrations in overweight or obese postmenopausal women.

Variable selection for zero-inflated and overdispersed data with application to health care demand in Germany.

In health services and outcome research, count outcomes are frequently encountered and often have a large proportion of zeros. The zero-inflated negative binomial (ZINB) regression model has important applications for this type of data. With many possible candidate risk factors, this paper proposes new variable selection methods for the ZINB model. We consider maximum likelihood function plus a penalty including the least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and minimax concave penalty (MCP). An EM (expectation-maximization) algorithm is proposed for estimating the model parameters and conducting variable selection simultaneously. This algorithm consists of estimating penalized weighted negative binomial models and penalized logistic models via the coordinated descent algorithm. Furthermore, statistical properties including the standard error formulae are provided. A simulation study shows that the new algorithm not only has more accurate or at least comparable estimation, but also is more robust than the traditional stepwise variable selection. The proposed methods are applied to analyze the health care demand in Germany using the open-source R package mpath.