Tutorial in biostatistics: spline smoothing with linear mixed models

Spatial inequalities and non-linear association of continuous variables with mortality risk of liver transplantation in Iran: a retrospective cohort study

Liver transplantation is the second most common solid organ transplant and the best option for liver failure. Of course, patient survival after transplantation depends on many risk factors. The aim of this study was to investigate the spatial and non-linear effects of continuous risk factors on patient survival after liver transplantation. This retrospective cohort study (n = 3148) used data on liver transplantation in Iran (2004-2019). A generalized additive model with spatial effects and non-linear effects of age and Model for End-Stage Liver Disease (MELD) score variables by penalized spline was used. The majority of patients were male (63.3%), with a mean (SD) age of 42.65 (13.31) and a mean (SD) MELD score of 24.43 (6.72). The 1, 5, and 10-year survival rates were 88.2%, 84.6%, and 82.5% respectively. The non-linear effect showed a steeper slope of the age effect on the hazard of death after the age of 50 (p < 0.05), and the MELD score had a direct but non-linear relationship with the hazard of death (p < 0.05). In the spatial pattern, the provinces with a greater distance from the transplant center had significantly fewer old patients than other provinces. Also, more distant provinces with an older transplant age had higher post-transplant mortality rates. Our study showed that it is better to take age and MELD score into account in postoperative care. The spatial pattern of mortality risk reflects inequalities in access to transplantation and public health services after transplantation.

Who could complete and benefit from the adjuvant chemotherapy regarding pancreatic ductal adenocarcinoma? A multivariate-adjusted analysis at the pre-adjuvant chemotherapy timing

BACKGROUND

The pre-adjuvant chemotherapy (PAC) status of postoperative pancreatic ductal adenocarcinoma (PDAC) patients has not been studied and elaborated well previously.

METHOD

The association of PAC variables and prognoses was explored using a multivariable Cox model, restricted cubic spline analysis, and correlation analysis. The main outcomes were overall survival (OS) and progression-free survival (PFS). The secondary outcome was chemotherapy completeness (CHC).

RESULTS

A total of 401 eligible patients were enrolled in sequential surgery and chemotherapy. The chemotherapy regimen, PAC fasting blood glucose (FBG), and elevated fasting blood glucose (eFBG) status were associated with CHC (regimen types: p = 0.005, continuous FBG: p = 0.014, eFBG status: p = 0.012). Early administration of adjuvant chemotherapy (<34 days) was a risk factor for the limited OS and PFS (OS: aHR: 1.61 [1.09-2.38], p = 0.016; PFS: aHR: 1.91 [1.29-2.82], p = 0.001). Patients with higher PAC body mass index (BMI), receiving Gemcap regimen, and with lower PAC tumor marker value were observed with better survival prognoses (PAC BMI: OS: 0.927 [0.875-0.983], p = 0.011; Gemcap: OS: 0.533 [0.312-0.913], p = 0.022; Gemcap: PFS: 0.560 [0.341-0.922], p = 0.023; PAC CA125: OS: 1.004 [1.002-1.006], p < 0.001; PAC CA125: PFS: 1.003 [1.000-1.005], p = 0.031; PAC CEA: OS: 1.050 [1.026-1.074], p < 0.001). The BMI decrease was mainly concentrated in the first 3 months of chemotherapy courses (first 3 months: p < 0.001; latter 3 months: p = 0.097). And CEA, compared to CA125 and CA199, was a better prognostic indicator (CEA: first 3 months: PFS p = 0.011, OS p < 0.001; latter 3 months: PFS p = 0.024, OS p = 0.041).

CONCLUSION

PDAC patients should be treated with adjuvant chemotherapy over 34 postoperative days. PAC sarcopenia was a risk factor for OS, but not PFS and limited CHC. Those with higher PAC FBG levels were more likely to finish chemotherapy. CEA, compared to CA125 and CA199, was a better prognostic indicator.

Developing Immune Profiles of Endangered Australian Sea Lion (Neophoca cinerea) Pups Within the Context of Endemic Hookworm (Uncinaria sanguinis) Infection

As a top predator, the endangered Australian sea lion (Neophoca cinerea) is a sentinel of ecosystem change, where population trends can reflect broader shifts in the marine environment. The population of this endemic pinniped was historically diminished by commercial sealing, and recovery has been slowed by fishery interactions, disease and, potentially, pollutants. Hookworm infects 100% of neonatal pups and has been identified as a contributor to population decline. Here, a multivariable approach using traditional serological and novel molecular tools such as qPCR and ddPCR was used to examine immune phenotypes of developing Australian sea lion pups infected with the endemic hookworm (Uncinaria sanguinis) from two South Australian colonies. Results show changing immunophenotypes throughout the patent period of infection represented by pro-inflammatory cytokines (IL-6), IgG and acute-phase proteins. Although cytokines may prove useful as markers of resistance, in this study, IL-6 is determined to be an early biomarker of inflammation in Australian sea lion pups, excluding the alternative hypothesis. Additionally, immunological differences between animals from high- and low-intensity hookworm seasons, as well as ivermectin-treated animals, indicate hookworm infection modulation of the host immune response, as evidenced by a lower IL-6 mRNA expression in the non-treated groups. This study of the Australian sea lion is an example of an ecoimmunological approach to disease investigation, which can be applied to evaluate the impact of environmental and anthropogenic factors on susceptibility to infectious diseases in free-ranging species

A time-varying GARCH mixed-effects model for isolating high- and low- frequency volatility and co-volatility

This article studies long-term, short-term volatility and co-volatility in stock markets by introducing modelling strategies to the multivariate data analysis that deal with serially correlated innovations and cross-section dependence. In particular, it presents an innovative mixed-effects model through a GARCH process, allowing for heterogeneity effects and time-series dynamics. We propose a non-parametric regression model of the penalized low-rank smoothing spline to present time trends into the variance and covariance equations. The strategy provides flexible modelling of the low-frequency volatility and co-volatility in equity markets. The decomposed low-frequency matrix was modelled using the modified Cholesky factorization. The Hamiltonian Monte Carlo technique is implemented as a Bayesian computing process for estimating parameters and latent factors. The advantage of our modelling strategy in empirical studies is highlighted by examining the effect of latent financial factors on a panel across 10 equities over 110 weekly series. The model can differentiate non-parametrically dynamic patterns of high and low frequencies of variance–covariance structural equations and incorporate economic features to predict variabilities in stock markets regarding time-series evidence.

Higher body mass index indicated better overall survival in pancreatic ductal adenocarcinoma patients: a real-world study of 2010 patients

BACKGROUND

The association between body mass index (BMI) and the overall survival (OS) of pancreatic ductal adenocarcinoma (PDAC) patients remains controversial and unclear, METHOD: A total of 2010 patients from a high-volume center were enrolled in the study. The OS of PDAC patients was evaluated based on restricted cubic spline (RCS), propensity score (PS) and multivariable risk adjustment analyses.

RESULT

BMI was linearly related to the OS (total P = 0.004, nonlinear P = 0.124). BMI was analyzed as categorical data based on X-tile software-defined cutoffs and World Health Organization (WHO)-recommended cutoffs. Adjusted with confounding covariates, higher BMI manifested as a positive prognostic predictor. Furthermore, BMI was proven to be associated with the OS in the PS analysis. (UnderweightXtile vs. NormalXtileP = 0.003, OverweightXtile vs. NormalXtileP = 0.019; UnderweightWHO vs. NormalWHOP < 0.001, OverweightWHO vs. NormalWHOP = 0.024). It was also revealed that patients with higher BMI benefitted more from chemotherapy. (Adjusted hazard ratio (aHR): UnderweightXtile vs. NormalXtile vs. OverweightXtile: 0.565 vs. 0.474 vs. 0.409; UnderweightWHO vs. NormalWHO vs. OverweightWHO: 0.613 vs. 0.464 vs. 0.425).

CONCLUSION

Among PDAC patients, there was a positive association between BMI and the OS, especially in patients treated with chemotherapy.

LASSO type penalized spline regression for binary data

BACKGROUND

Generalized linear mixed models (GLMMs), typically used for analyzing correlated data, can also be used for smoothing by considering the knot coefficients from a regression spline as random effects. The resulting models are called semiparametric mixed models (SPMMs). Allowing the random knot coefficients to follow a normal distribution with mean zero and a constant variance is equivalent to using a penalized spline with a ridge regression type penalty. We introduce the least absolute shrinkage and selection operator (LASSO) type penalty in the SPMM setting by considering the coefficients at the knots to follow a Laplace double exponential distribution with mean zero.

METHODS

We adopt a Bayesian approach and use the Markov Chain Monte Carlo (MCMC) algorithm for model fitting. Through simulations, we compare the performance of curve fitting in a SPMM using a LASSO type penalty to that of using ridge penalty for binary data. We apply the proposed method to obtain smooth curves from data on the relationship between the amount of pack years of smoking and the risk of developing chronic obstructive pulmonary disease (COPD).

RESULTS

The LASSO penalty performs as well as ridge penalty for simple shapes of association and outperforms the ridge penalty when the shape of association is complex or linear.

CONCLUSION

We demonstrated that LASSO penalty captured complex dose-response association better than the Ridge penalty in a SPMM.

Effectiveness of Sequential Compression Devices in Prevention of Venous Thromboembolism in Medically Ill Hospitalized Patients: A Retrospective Cohort Study

Objective:

To evaluate the effectiveness of sequential compression devices (SCDs) for venous thromboembolism (VTE) prevention in medically ill hospitalized patients.

Materials and Methods:

Adult patients admitted to a teaching hospital from April 2015 to March 2016 were included. Patients on anticoagulants with or without SCDs were excluded. We analyzed VTE risk, length of hospital stay, and other comorbidities among propensity score-matched patients on SCDs and those without thromboprophylaxis (NONE).

Results:

Among 30,824 patients, 67 patients (0.22%) developed VTE during their hospital stays, with deep vein thrombosis (DVT) in 55 cases and pulmonary embolism (PE) in 12. VTE was seen in 47 out of 20,018 patients on SCDs (41 DVT, 6 PE) and 20 out of 10,819 patients without SCDs (14 DVT, 6 PE). Risk-adjusted analysis showed no significant difference in VTE incidence in the SCD group compared to NONE (odds ratio 0.99, 95% confidence interval 0.57-1.73, p=0.74).

Conclusion:

Compared to the NONE group, SCDs are not associated with decreased VTE incidence during hospital stay.

Neutrophil-lymphocyte ratio, gamma-glutamyl transpeptidase, lipase, high-density lipoprotein as a panel of factors to predict acute pancreatitis in pregnancy

Acute pancreatitis in pregnancy (APIP) is a rare but dangerous complication. APIP has common symptoms with acute abdomen. Assessment of an acute abdomen is more complicated during pregnancy because the gravid uterus could mask most of symptomatic signs. It has been a challenge to diagnose APIP by physical examination or diagnostic imaging. Case studies on APIP are also limited for analysis on the risk factors associated with the disease. This retrospective study evaluated a series of risk factors from a relatively substantial number of APIP cases to determine early predictors or prognosis markers for APIP.Fifty-nine APIP patients together with 179 random normal pregnant women in Shengjing Affiliated Hospital of China Medical University were included for this retrospective study. Medical parameters of blood test in biochemistry and hematology were compared between 2 groups using t test. Multivariate logistic regression analysis was performed to investigate the relationship between various factors and APIP using Statistical Applied Software (SAS student version).Compared with normal pregnant women, APIP patients have elevated values in alanine aminotransferase (ALT), aspartate aminotransferase (AST), blood urea nitrogen, creatinine, C-reactive protein, direct bilirubin, fibrin degradation products, gamma-glutamyl transpeptidase (GGT), glucose, lipase, pH and decreased values in albumin, fibrinogen, high-density lipoprotein (HDL), hemoglobin, low-density lipoprotein cholesterol (LDL-D), and total proteins from their blood tests. In addition, APIP patients have decreased numbers in red cells but increased numbers in white blood cells and increased ratio of neutrophil/lymphocyte (N/L). Among these factors, N/LR, GGT, lipase, and HDL are significantly associated with APIP. This study suggests that the combination of those factors serve as a panel of indicators for early-onset prognosis of APIP.GGT, lipase, HDL, and N/LR can serve as a panel of factors to predict APIP. More case studies are important to further evaluate the predicting power of this panel factors in APIP.

Effect of Smoothing in Generalized Linear Mixed Models on the Estimation of Covariance Parameters for Longitudinal Data

Besides being mainly used for analyzing clustered or longitudinal data, generalized linear mixed models can also be used for smoothing via restricting changes in the fit at the knots in regression splines. The resulting models are usually called semiparametric mixed models (SPMMs). We investigate the effect of smoothing using SPMMs on the correlation and variance parameter estimates for serially correlated longitudinal normal, Poisson and binary data. Through simulations, we compare the performance of SPMMs to other simpler methods for estimating the nonlinear association such as fractional polynomials, and using a parametric nonlinear function. Simulation results suggest that, in general, the SPMMs recover the true curves very well and yield reasonable estimates of the correlation and variance parameters. However, for binary outcomes, SPMMs produce biased estimates of the variance parameters for high serially correlated data. We apply these methods to a dataset investigating the association between CD4 cell count and time since seroconversion for HIV infected men enrolled in the Multicenter AIDS Cohort Study.

Unraveling the associations of age and menopause with cardiovascular risk factors in a large population-based study

BACKGROUND

Although the association between menopause and cardiovascular disease (CVD) risk has been studied extensively, the simultaneous role of chronological aging herein remains underexposed. This study aims to disentangle the relationships of menopausal status and chronological aging with CVD risk factors in the largest study population to date.

METHODS

In this cross-sectional study, CVD risk factors were compared between women with a different menopausal status within the same yearly age strata. The study population comprised female participants of the baseline visit of the population-based LifeLines Cohort Study. A total of 63,466 women, aged between 18 and 65 years, was included. Of them, 39,379 women were considered to be premenopausal, 8669 were perimenopausal, 14,514 were naturally postmenopausal, and 904 were surgically postmenopausal.

RESULTS

Compared to postmenopausal women aged 45 years, average total cholesterol (TC) and low-density lipoprotein cholesterol (LDL-c) were 0.5 and 0.4 mmol/L higher, respectively, in postmenopausal women aged 50. Systolic and diastolic blood pressure levels were 4 and 1 mmHg higher, respectively. At all ages between 46 and 55 years, and after adjustment for confounders, naturally postmenopausal women had 0.2 to 0.4 mmol/L higher TC and 0.1 to 0.3 mmol/L higher LDL-c levels compared to premenopausal women in the same age range. Systolic blood pressure levels were up to 4 mmHg lower in naturally post- compared to premenopausal women at all ages between 29 and 52 years. Body mass index levels were up to 3.2 kg/m² higher in women with surgical menopause compared to all other women between the ages 32 and 52 years. All aforementioned results were statistically significant.

CONCLUSIONS

Chronological age and menopausal status are both independently associated with CVD risk factors. Based on the comparatively smaller observed differences associated with menopausal status than with chronological aging, the significance of a more unfavorable lipid profile in a later reproductive stage may be less obvious than previously thought.

Modelling retinal pulsatile blood flow from video data

Modern day datasets continue to increase in both size and diversity. One example of such 'big data' is video data. Within the medical arena, more disciplines are using video as a diagnostic tool. Given the large amount of data stored within a video image, it is one of most time consuming types of data to process and analyse. Therefore, it is desirable to have automated techniques to extract, process and analyse data from video images. While many methods have been developed for extracting and processing video data, statistical modelling to analyse the outputted data has rarely been employed. We develop a method to take a video sequence of periodic nature, extract the RGB data and model the changes occurring across the contiguous images. We employ harmonic regression to model periodicity with autoregressive terms accounting for the error process associated with the time series nature of the data. A linear spline is included to account for movement between frames. We apply this model to video sequences of retinal vessel pulsation, which is the pulsatile component of blood flow. Slope and amplitude are calculated for the curves generated from the application of the harmonic model, providing clinical insight into the location of obstruction within the retinal vessels. The method can be applied to individual vessels, or to smaller segments such as 2 × 2 pixels which can then be interpreted easily as a heat map.

Comparing Smoothing Techniques for Fitting the Nonlinear Effect of Covariate in Cox Models

BACKGROUND AND OBJECTIVE

Cox model is a popular model in survival analysis, which assumes linearity of the covariate on the log hazard function, While continuous covariates can affect the hazard through more complicated nonlinear functional forms and therefore, Cox models with continuous covariates are prone to misspecification due to not fitting the correct functional form for continuous covariates. In this study, a smooth nonlinear covariate effect would be approximated by different spline functions.

MATERIAL AND METHODS

We applied three flexible nonparametric smoothing techniques for nonlinear covariate effect in the Cox models: penalized splines, restricted cubic splines and natural splines. Akaike information criterion (AIC) and degrees of freedom were used to smoothing parameter selection in penalized splines model. The ability of nonparametric methods was evaluated to recover the true functional form of linear, quadratic and nonlinear functions, using different simulated sample sizes. Data analysis was carried out using R 2.11.0 software and significant levels were considered 0.05.

RESULTS

Based on AIC, the penalized spline method had consistently lower mean square error compared to others to selection of smoothed parameter. The same result was obtained with real data.

CONCLUSION

Penalized spline smoothing method, with AIC to smoothing parameter selection, was more accurate in evaluate of relation between covariate and log hazard function than other methods.

Estimating time-varying drug adherence using electronic records: extending the proportion of days covered (PDC) method

PURPOSE

Accurate measurement of drug adherence is essential for valid risk-benefit assessments of pharmacologic interventions. To date, measures of drug adherence have almost exclusively been applied for a fixed-time interval and without considering changes over time. However, patients with irregular dosing behaviour commonly have a different prognosis than patients with stable dosing behaviour.

METHODS

We propose a method, based on the proportion of days covered (PDC) method, to measure time-varying drug adherence and drug dosage using electronic records. We compare a time-fixed PDC method with the time-varying PDC method through detailed examples and through summary statistics of 100 randomly selected patients on statin therapy.

RESULTS

We demonstrate that time-varying PDC method better distinguishes an irregularly dosing patient from a stably dosing patient and demonstrate how the time-fixed method can result in a biassed estimate of drug adherence. Furthermore, the time-varying PDC method may be better used to reduce certain types of confounding and misclassification of exposure.

CONCLUSIONS

The time-varying PDC method may improve longitudinal and time-to-event studies that associate adherence with a clinical outcome or (intervention) studies that seek to describe changes in adherence over time.

The impact of sleep restriction while performing simulated physical firefighting work on cortisol and heart rate responses

PURPOSE

Physical work and sleep restriction are two stressors faced by firefighters, yet the combined impact these demands have on firefighters' acute stress responses is poorly understood. The purpose of the present study was to assess the effect firefighting work and sleep restriction have on firefighters' acute cortisol and heart rate (HR) responses during a simulated 3-day and 2-night fire-ground deployment.

METHODS

Firefighters completed multiple days of simulated physical work separated by either an 8-h (control condition; n = 18) or 4-h sleep opportunity (sleep restriction condition; n = 17). Salivary cortisol was sampled every 2 h, and HR was measured continuously each day.

RESULTS

On day 2 and day 3 of the deployment, the sleep restriction condition exhibited a significantly higher daily area under the curve cortisol level and an elevated cortisol profile in the afternoon and evening when compared with the control condition. Firefighters' HR decreased across the simulation, but there were no significant differences found between conditions.

CONCLUSION

Findings highlight the protective role an 8-h sleep opportunity between shifts of firefighting work has on preserving normal cortisol levels when compared to a 4-h sleep opportunity which resulted in elevated afternoon and evening cortisol. Given the adverse health outcomes associated with chronically high cortisol, especially later in the day, future research should examine how prolonged exposure to firefighting work (including restricted sleep) affects firefighters' cortisol levels long term. Furthermore, monitoring cortisol levels post-deployment will determine the minimum recovery time firefighters need to safely return to the fire-ground.

Developing emergency department physician shift schedules optimized to meet patient demand

Objectives: 1) To assess temporal patterns in historical patient arrival rates in an emergency department (ED) to determine the appropriate number of shift schedules in an acute care area and a fast-track clinic and 2) to determine whether physician scheduling can be improved by aligning physician productivity with patient arrivals using an optimization planning model.

Methods: Historical data were statistically analyzed to determine whether the number of patients arriving at the ED varied by weekday, weekend, or holiday weekend. Poisson-based generalized additive models were used to develop models of patient arrival rate throughout the day. A mathematical programming model was used to produce an optimal ED shift schedule for the estimated patient arrival rates. We compared the current physician schedule to three other scheduling scenarios: 1) a revised schedule produced by the planning model, 2) the revised schedule with an additional acute care physician, and 3) the revised schedule with an additional fast-track clinic physician.

Results: Statistical modelling found that patient arrival rates were different for acute care versus fast-track clinics; the patterns in arrivals followed essentially the same daily pattern in the acute care area; and arrival patterns differed on weekdays versus weekends in the fast-track clinic. The planning model reduced the unmet patient demand (i.e., the average number of patients arriving at the ED beyond the average physician productivity) by 19%, 39%, and 69% for the three scenarios examined.

Conclusions: The planning model improved the shift schedules by aligning physician productivity with patient arrivals at the ED.

Incidence of hospital-acquired pressure ulcers - a population-based cohort study

Our study sought to estimate the association between race, gender, comorbidity and body mass index (BMI) on the incidence of hospital-acquired pressure ulcer (PU) from a population-based retrospective cohort comprising 242 745 unique patient hospital discharges in two fiscal years from July 2009 to June 2010 from 15 general and tertiary care hospitals. Cases were patients with a single inpatient encounter that led to an incident PU. Controls were patients without a PU at any encounter during the two fiscal years with the earliest admission retained for analysis. Logistic regression models quantified the association of potential risk factors for PU incidence. Spline functions captured the non-linear effects of age and comorbidity. Overall 2·68% of patients experienced an incident PU during their inpatient stay. Unadjusted analyses revealed statistically significant associations by age, gender, race, comorbidity, BMI, admitted for a surgical procedure, source of admission and fiscal year, but differences by gender and race did not persist in adjusted analyses. Interactions between age, comorbidity and BMI contributed significantly to the likelihood of PU incidence. Patients who were older, with multiple comorbidities and admitted for a surgical diagnosis-related groups (DRG) were at greater risk of experiencing a PU during their stay.

Renal function and outcomes in anticoagulated patients with non-valvular atrial fibrillation: the AMADEUS trial

AIMS

Limited data are available on the impact of renal function on the outcome of patients with atrial fibrillation (AF).

METHODS AND RESULTS

AMADEUS was a multicentre, randomized, open-label non-inferiority study that compared fixed-dose idraparinux with conventional anticoagulation by dose-adjusted vitamin K antagonists. We performed a post hoc analysis to assess the impact of renal function on the outcomes of anticoagulated AF patients. The primary efficacy outcome was the composite of stroke/systemic embolism (SE). The principal safety outcome of this analysis was major bleeding. We calculated c-indexes, reflecting the ability for discriminating diseased vs. non-diseased patients, and the net reclassification improvement (NRI, an index of inferior/superior performance of risk estimation scores). Of 4576 patients, 45 strokes and 103 major bleeding events occurred following an average follow-up of 325 ± 164 days. Patients with CrCl >90 mL/min had an annual stroke/SE rate of 0.6% compared with 0.8% for those with CrCl 60-90 mL/min and 2.2% for those with CrCl <60 mL/min (P < 0.001 for linear association). After adjusting for stroke risk factors, patients with CrCl <60 mL/min had more than two-fold higher risk of stroke/SE and almost 60% higher risk of major bleeding compared with those with CrCl ≥60. In patients with the CHA2DS2VASc score 1-2, CrCl <60 mL/min was associated with eight-fold higher stroke risk. When added to the CHA2DS2VASc or CHADS2 scores, CrCl <60 mL/min did not improve the c-indexes for CHADS2 (P = 0.054) or CHA2DS2VASc (P = 0.63) but resulted in significant NRI (0.26, P = 0.02) in this anticoagulated trial cohort.

CONCLUSION

Renal impairment (CrCl <60 mL/min) doubles the risk of stroke and increased the risk of major bleeding by almost 60% in anticoagulated patients with AF. Renal impairment was additive to stroke risk prediction scores based on a significant NRI, but no significant improvement in discrimination ability (based on c-indexes) for CHA2DS2VASc or CHADS2 was observed.

Environmental and lunar cues are predictive of the timing of river entry and spawning-site arrival in lake sturgeon Acipenser fulvescens

The associations were quantified between daily and interannual variation in the timing of a closed population of lake sturgeon Acipenser fulvescens migration and arrival at spawning sites with stream environmental and lunar covariates. Spawning data were gathered from 1262 fish in Black Lake, Michigan 2001 to 2008 and by video monitoring 2000 to 2002. Sex-specific variation in responses to external cues was also tested. Results showed that a greater number of individuals initiated migration from lake to riverine habitats at dawn and dusk relative to other times of the day. Current and lagged effects of water temperature and river discharge, and periods in the lunar cycle were important variables in models quantifying movements into the river and timing of adult arrival at spawning sites. Different suites of covariates were predictive of A. fulverscens responses during different periods of the spawning season. The timing of initiation of migration and spawning, and the importance of covariates to the timing of these events, did not differ between sexes. Stream flow and temperature covaried with other variables including day length and the lunar cycle. Anthropogenic disruption of relationships among variables may mean that environmental cues may no longer reliably convey information for Acipenseriformes and other migratory fishes.

Age-dependent recombination rates in human pedigrees

In humans, chromosome-number abnormalities have been associated with altered recombination and increased maternal age. Therefore, age-related effects on recombination are of major importance, especially in relation to the mechanisms involved in human trisomies. Here, we examine the relationship between maternal age and recombination rate in humans. We localized crossovers at high resolution by using over 600,000 markers genotyped in a panel of 69 French-Canadian pedigrees, revealing recombination events in 195 maternal meioses. Overall, we observed the general patterns of variation in fine-scale recombination rates previously reported in humans. However, we make the first observation of a significant decrease in recombination rates with advancing maternal age in humans, likely driven by chromosome-specific effects. The effect appears to be localized in the middle section of chromosomal arms and near subtelomeric regions. We postulate that, for some chromosomes, protection against non-disjunction provided by recombination becomes less efficient with advancing maternal age, which can be partly responsible for the higher rates of aneuploidy in older women. We propose a model that reconciles our findings with reported associations between maternal age and recombination in cases of trisomies.

An Assessment of Mixed-Modeling Approaches for Characterizing Profiles of Time-Varying Response and Predictor Variables

A general statistical modeling approach was tested for characterizing the relationship between pathogen inoculum density (or other biological response variables) and environmental variables when the data are collected as temporal profiles of observations within multiple locations or years. The approach, based on the use of linear mixed models, simultaneously accounts for serial correlations of the observations within each time profile, the random effects of location–year (or other grouping factors), and the cross-correlation of the environmental variables, and is appropriate when the environmental effects on the response variable or its transformation (Y) are distributed over several times (e.g., days). Stability and precision of parameter estimates for environmental effects over multiple time lags were achieved through the use of polynomial constraints within a likelihood-based full mixed-model fit; from the parameter estimates, marginal effects of environmental variables and weights for individual time lags were determined. The mixed model was directly expanded, through the incorporation of smoothing functions, to potentially account for possible longer-term trends in the temporal profiles unrelated to the environmental variables being considered. The new approach described here (with or without a smoothing function) generalizes a previously used—and computationally less demanding—two-stage (composite) approach. In the previous approach, constrained parameter estimates and associated weights were first determined without consideration of serial correlation, cross-correlation of environmental variables, and the random effects of location–year; then, a mixed-model fit was accomplished using the fixed time-lag weights derived in the first step. Using data for inoculum density of Gibberella zeae on wheat spikes from 27 location–years, similar results were achieved with the full mixed model and the two-stage approaches, in terms of both the calculated parameters and predictions of Y. With the use of smoothing functions, the precision of the predictions was improved but the general conclusions regarding environmental effects on Y were not affected. Thus, in the particular example data set, previously derived conclusions regarding environmental effects on inoculum density were robust in terms of the statistical methodology used in analysis; most researchers will find the two-stage approach much easier to implement for the analysis of multiple profiles of time-varying observations.

Modeling the volume-effectiveness relationship in the case of hip fracture treatment in Finland

Background

A common argument in the recent health policy debate is that treatment is more effective among care providers with large volumes. It is challenging, however, to examine the volume-effectiveness relationship empirically. Several suggestions have recently been made for methodological improvements in the examination of the volume-effectiveness relationship. The aim of this study is to develop an extended methodology for examining the volume-effectiveness relationship and demonstrate it for the case of hip fracture treatment.

Methods

Data consisting of 22,857 hip fracture patients from 52 hospitals in Finland in 1998-2001 were extracted from the administrative registers. The relationship between hospital and rehabilitation unit volumes and effectiveness was examined using a statistical model that allowed risk adjustments and hierarchical modeling of volume trends, developed for the purposes of this study. Four-month mortality and the alternative register-based measure of maintainability were used as effectiveness indicators.

Results

No clear relationship was found between hospital volume and the effectiveness of hip fracture treatment, but a novel result showing an association between the rehabilitation unit volume and effectiveness was detected. The face validity of the maintainability indicator seemed to be acceptable.

Conclusions

The methodological ideas presented allow for improved examination of the volume-effectiveness relationship. There are no indications that patients with hip fractures should only be treated in high-volume hospitals, though it may be beneficial to centralize the rehabilitation of hip fracture patients to specialized units.

Semiparametric regression during 2003-2007

Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology - thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.