Competing regression models for longitudinal data

The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretestposttest longitudinal data. In particular, we consider log-normal linear mixed models (LNLMM), generalized linear mixed models (GLMM), and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEE-based models may be preferable when the goal is to compare the marginal expected responses.

Counterbalancing effects of competition for resources and facilitation against grazing in alpine snowbed communities

Alpine snowbeds are habitats where the major limiting factors for plant growth are herbivory and a small time window for growth due to late snowmelt. Despite these limitations, snowbed vegetation usually forms a dense carpet of palatable plants due to favourable abiotic conditions for plant growth within the short growing season. These environmental characteristics make snowbeds particularly interesting to study the interplay of facilitation and competition. We hypothesised an interplay between resource competition and facilitation against herbivory. Further, we investigated whether these predicted neighbour effects were species-specific and/or dependent on ontogeny, and whether the balance of positive and negative plant–plant interactions shifted along a snowmelt gradient. We determined the neighbour effects by means of neighbour removal experiments along the snowmelt gradient, and linear mixed model analyses. The results showed that the effects of neighbour removal were weak but generally consistent among species and snowmelt dates, and depended on whether biomass production or survival was considered. Higher total biomass and increased fruiting in removal plots indicated that plants competed for nutrients, water, and light, thereby supporting the hypothesis of prevailing competition for resources in snowbeds. However, the presence of neighbours reduced herbivory and thereby also facilitated survival. For plant growth the facilitative effects against herbivores in snowbeds counterbalanced competition for resources, leading to a weak negative net effect. Overall the neighbour effects were not species-specific and did not change with snowmelt date. Our finding of counterbalancing effects of competition and facilitation within a plant community is of special theoretical value for species distribution models and can explain the success of models that give primary importance to abiotic factors and tend to overlook interrelations between biotic and abiotic effects on plants.

A prospective study of the impact of air pollution on respiratory symptoms and infections in infants

Rationale: There is increasing evidence that short-term exposure to air pollution has a detrimental effect on respiratory health, but data from healthy populations, particularly infants, are scarce. Objectives: To assess the association of air pollution with frequency and severity of respiratory symptoms and infections measured weekly in healthy infants. Methods: In a prospective birth cohort of 366 infants of unselected mothers, respiratory health was assessed weekly by telephone interviews during the first year of life (19,106 total observations). Daily mean levels of particulate matter (PM10), nitrogen dioxide (NO2), and ozone (O3) were obtained from local monitoring stations. We determined the association of the preceding week's pollutant levels with symptom scores and respiratory tract infections using a generalized additive mixed model with an autoregressive component. In addition, we assessed whether neonatal lung function influences this association and whether duration of infectious episodes differed between weeks with normal PM10 and weeks with elevated levels. Measurements and Main Results: We found a significant association between air pollution and respiratory symptoms, particularly in the week after respiratory tract infections (risk ratio, 1.13 [1.02-1.24] per 10 μg/m(3) PM10 levels) and in infants with premorbid lung function. During times of elevated PM10 (>33.3 μg/m(3)), duration of respiratory tract infections increased by 20% (95% confidence interval, 2-42%). Conclusions: Exposure to even moderate levels of air pollution was associated with increased respiratory symptoms in healthy infants. Particularly in infants with premorbid lung function and inflammation, air pollution contributed to longer duration of infectious episodes with a potentially large socioeconomic impact.

Clinical and molecular characterization of the potential CF disease modifier syntaxin 1A

Cystic fibrosis (CF) is caused by mutations in the CF transmembrane conductance regulator gene (CFTR). Disease severity in CF varies greatly, and sibling studies strongly indicate that genes other than CFTR modify disease outcome. Syntaxin 1A (STX1A) has been reported as a negative regulator of CFTR and other ion channels. We hypothesized that STX1A variants act as a CF modifier by influencing the remaining function of mutated CFTR. We identified STX1A variants by genomic resequencing patients from the Bernese CF Patient Data Registry and applied linear mixed model analysis to establish genotype-phenotype correlations, revealing STX1A rs4363087 (c.467-38A>G) to significantly influence lung function. The same STX1A risk allele was recognized in the European CF Twin and Sibling Study (P=0.0027), demonstrating that the genotype-phenotype association of STX1A to CF disease severity is robust enough to allow replication in two independent CF populations. rs4363087 is in linkage disequilibrium to the exonic variant rs2228607 (c.204C>T). Considering that neither rs4363087 nor rs2228607 changes the amino-acid sequence of STX1A, we investigated their effects on mRNA level. We show that rs2228607 reinforces aberrant splicing of STX1A mRNA, leading to nonsense-mediated mRNA decay. In conclusion, we demonstrate the clinical relevance of STX1A variants in CF, and evidence the functional relevance of STX1A variant rs2228607 at molecular level. Our findings show that genes interacting with CFTR can modify CF disease progression.European Journal of Human Genetics advance online publication, 10 April 2013; doi:10.1038/ejhg.2013.57.

Whither PQL?

Generalized linear mixed models (GLMM) are generalized linear models with normally distributed random effects in the linear predictor. Penalized quasi-likelihood (PQL), an approximate method of inference in GLMMs, involves repeated fitting of linear mixed models with “working” dependent variables and iterative weights that depend on parameter estimates from the previous cycle of iteration. The generality of PQL, and its implementation in commercially available software, has encouraged the application of GLMMs in many scientific fields. Caution is needed, however, since PQL may sometimes yield badly biased estimates of variance components, especially with binary outcomes. Recent developments in numerical integration, including adaptive Gaussian quadrature, higher order Laplace expansions, stochastic integration and Markov chain Monte Carlo (MCMC) algorithms, provide attractive alternatives to PQL for approximate likelihood inference in GLMMs. Analyses of some well known datasets, and simulations based on these analyses, suggest that PQL still performs remarkably well in comparison with more elaborate procedures in many practical situations. Adaptive Gaussian quadrature is a viable alternative for nested designs where the numerical integration is limited to a small number of dimensions. Higher order Laplace approximations hold the promise of accurate inference more generally. MCMC is likely the method of choice for the most complex problems that involve high dimensional integrals.

Semiparametric Estimation in General Repeated Measures Problems

This paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal/clustered data, conditional logistic regression for matched case-control studies, multivariate measurement error models, generalized linear mixed models with a semiparametric component, and many others. We propose profile-kernel and backfitting estimation methods for these problems, derive their asymptotic distributions, and show that in likelihood problems the methods are semiparametric efficient. While generally not true, with our methods profiling and backfitting are asymptotically equivalent. We also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm. The proposed methods are evaluated using simulation studies and applied to the Kenya hemoglobin data.

MODELING DIFFERENTIATED TREATMENT EFFECTS FOR MULTIPLE OUTCOMES DATA

Multiple outcomes data are commonly used to characterize treatment effects in medical research, for instance, multiple symptoms to characterize potential remission of a psychiatric disorder. Often either a global, i.e. symptom-invariant, treatment effect is evaluated. Such a treatment effect may over generalize the effect across the outcomes. On the other hand individual treatment effects, varying across all outcomes, are complicated to interpret, and their estimation may lose precision relative to a global summary. An effective compromise to summarize the treatment effect may be through patterns of the treatment effects, i.e. "differentiated effects." In this paper we propose a two-category model to differentiate treatment effects into two groups. A model fitting algorithm and simulation study are presented, and several methods are developed to analyze heterogeneity presenting in the treatment effects. The method is illustrated using an analysis of schizophrenia symptom data.

Long-term gas exchange characteristics as marker of deterioration in patients with cystic fibrosis

Background and Aim In patients with cystic fibrosis (CF) the architecture of the developing lungs and the ventilation of lung units are progressively affected, influencing intrapulmonary gas mixing and gas exchange. We examined the long-term course of blood gas measurements in relation to characteristics of lung function and the influence of different CFTR genotype upon this process. Methods Serial annual measurements of PaO2 and PaCO2 assessed in relation to lung function, providing functional residual capacity (FRCpleth), lung clearance index (LCI), trapped gas (VTG), airway resistance (sReff), and forced expiratory indices (FEV1, FEF50), were collected in 178 children (88 males; 90 females) with CF, over an age range of 5 to 18 years. Linear mixed model analysis and binary logistic regression analysis were used to define predominant lung function parameters influencing oxygenation and carbon dioxide elimination. Results PaO2 decreased linearly from age 5 to 18 years, and was mainly associated with FRCpleth, (p < 0.0001), FEV1 (p < 0.001), FEF50 (p < 0.002), and LCI (p < 0.002), indicating that oxygenation was associated with the degree of pulmonary hyperinflation, ventilation inhomogeneities and impeded airway function. PaCO2 showed a transitory phase of low PaCO2 values, mainly during the age range of 5 to 12 years. Both PaO2 and PaCO2 presented with different progression slopes within specific CFTR genotypes. Conclusion In the long-term evaluation of gas exchange characteristics, an association with different lung function patterns was found and was closely related to specific genotypes. Early examination of blood gases may reveal hypocarbia, presumably reflecting compensatory mechanisms to improve oxygenation.

Changes in the PQRST intervals and heart rate variability associated with rewarming in two newborns undergoing hypothermia therapy.

BACKGROUND: Little is known about the effects of hypothermia therapy and subsequent rewarming on the PQRST intervals and heart rate variability (HRV) in term newborns with hypoxic-ischemic encephalopathy (HIE). OBJECTIVES: This study describes the changes in the PQRST intervals and HRV during rewarming to normal core body temperature of 2 newborns with HIE after hypothermia therapy. METHODS: Within 6 h after birth, 2 newborns with HIE were cooled to a core body temperature of 33.5 degrees C for 72 h using a cooling blanket, followed by gradual rewarming (0.5 degrees C per hour) until the body temperature reached 36.5 degrees C. Custom instrumentation recorded the electrocardiogram from the leads used for clinical monitoring of vital signs. Generalized linear mixed models were calculated to estimate temperature-related changes in PQRST intervals and HRV. Results: For every 1 degrees C increase in body temperature, the heart rate increased by 9.2 bpm (95% CI 6.8-11.6), the QTc interval decreased by 21.6 ms (95% CI 17.3-25.9), and low and high frequency HRV decreased by 0.480 dB (95% CI 0.052-0.907) and 0.938 dB (95% CI 0.460-1.416), respectively. CONCLUSIONS: Hypothermia-induced changes in the electrocardiogram should be monitored carefully in future studies.

An index to identify stroke-related vs incidental patent foramen ovale in cryptogenic stroke

OBJECTIVE We aimed to create an index to stratify cryptogenic stroke (CS) patients with patent foramen ovale (PFO) by their likelihood that the stroke was related to their PFO. METHODS Using data from 12 component studies, we used generalized linear mixed models to predict the presence of PFO among patients with CS, and derive a simple index to stratify patients with CS. We estimated the stratum-specific PFO-attributable fraction and stratum-specific stroke/TIA recurrence rates. RESULTS Variables associated with a PFO in CS patients included younger age, the presence of a cortical stroke on neuroimaging, and the absence of these factors: diabetes, hypertension, smoking, and prior stroke or TIA. The 10-point Risk of Paradoxical Embolism score is calculated from these variables so that the youngest patients with superficial strokes and without vascular risk factors have the highest score. PFO prevalence increased from 23% (95% confidence interval [CI]: 19%-26%) in those with 0 to 3 points to 73% (95% CI: 66%-79%) in those with 9 or 10 points, corresponding to attributable fraction estimates of approximately 0% to 90%. Kaplan-Meier estimated stroke/TIA 2-year recurrence rates decreased from 20% (95% CI: 12%-28%) in the lowest Risk of Paradoxical Embolism score stratum to 2% (95% CI: 0%-4%) in the highest. CONCLUSION Clinical characteristics identify CS patients who vary markedly in PFO prevalence, reflecting clinically important variation in the probability that a discovered PFO is likely to be stroke-related vs incidental. Patients in strata more likely to have stroke-related PFOs have lower recurrence risk.

Determinants of antithrombotic choice for patent foramen ovale in cryptogenic stroke

Objective: We examined the influence of clinical, radiologic, and echocardiographic characteristics on antithrombotic choice in patients with cryptogenic stroke (CS) and patent foramen ovale (PFO), hypothesizing that features suggestive of paradoxical embolism might lead to greater use of anticoagulation. Methods: The Risk of Paradoxical Embolism Study combined 12 databases to create the largest dataset of patients with CS and known PFO status. We used generalized linear mixed models with a random effect of component study to explore whether anticoagulation was preferentially selected based on the following: (1) younger age and absence of vascular risk factors, (2) “high-risk” echocardiographic features, and (3) neuroradiologic findings. Results: A total of 1,132 patients with CS and PFO treated with anticoagulation or antiplatelets were included. Overall, 438 participants (39%) were treated with anticoagulation with a range (by database) of 22% to 54%. Treatment choice was not influenced by age or vascular risk factors. However, neuroradiologic findings (superficial or multiple infarcts) and high-risk echocardiographic features (large shunts, shunt at rest, and septal hypermobility) were predictors of anticoagulation use. Conclusion: Both antithrombotic regimens are widely used for secondary stroke prevention in patients with CS and PFO. Radiologic and echocardiographic features were strongly associated with treatment choice, whereas conventional vascular risk factors were not. Prior observational studies are likely to be biased by confounding by indication.

Only Neochordoplasty Achieves Physiological Trans-valvular Pressure Gradients After Repair Of Acute Posterior Leaflet Prolapse In Porcine Mitral Valves

Objective: Minimizing resection and preserving leaflet tissue has been previously shown to be beneficial for mitral valve function and leaflet kinematics after repair of acute posterior leaflet prolapse in porcine valves. We examined the effects of different additional methods of mitral valve repair (neochordoplasty, ring annuloplasty, edge-to-edge repair and triangular resection) on hemodynamics at different heart rates in an experimental model. Methods: Severe acute P2 prolapse was created in eight porcine mitral valves by resecting the posterior marginal chordae. Valve hemodynamics was quantified under pulsatile conditions in an in vitro heart simulator before and after surgical manipulation. Mitral regurgitation was corrected using four different methods of repair on the same valve: neochordoplasty with expanded polytetrafluoroethylene sutures alone and together with ring annuloplasty, edge-to-edge repair and triangular resection, both with non-restrictive annuloplasty. Residual mitral valve leak, trans-valvular pressure gradients, flow and cardiac output were measured at 60 and 80 beats/min. A validated statistical linear mixed model was used to analyze the effect of treatment. The p values were calculated using a two-sided Wald test. Results: Only neochordoplasty with expanded polytetrafluoroethylene sutures but without ring annuloplasty achieved similar hemodynamics compared to those of the native mitral valve (p range 0.071-0.901). Trans-valvular diastolic pressure gradients were within a physiologic range but significantly higher than those of the native valve following neochordoplasty with ring annuloplasty (p=0.000), triangular resection (p=0.000) and edge-to-edge repair (p=0.000). Neochordoplasty alone was significantly better in terms of hemodynamic than neochordoplasty with a ring annuloplasty (p=0.000). These values were stable regardless of heart rate or ring size. Conclusions: Neochordoplasty without ring annuloplasty is the only repair technique able to achieve almost native physiological hemodynamics after correction of leaflet prolapse in a porcine experimental model of acute chordal rupture.

Effect of an intervertebral disk spacer on stiffness after monocortical screw/polymethylmethacrylate fixation in simulated and cadaveric canine cervical vertebral columns.

OBJECTIVE To determine the biomechanical effect of an intervertebral spacer on construct stiffness in a PVC model and cadaveric canine cervical vertebral columns stabilized with monocortical screws/polymethylmethacrylate (PMMA). STUDY DESIGN Biomechanical study. SAMPLE POPULATION PVC pipe; cadaveric canine vertebral columns. METHODS PVC model-PVC pipe was used to create a gap model mimicking vertebral endplate orientation and disk space width of large-breed canine cervical vertebrae; 6 models had a 4-mm gap with no spacer (PVC group 1); 6 had a PVC pipe ring spacer filling the gap (PCV group 2). Animals-large breed cadaveric canine cervical vertebral columns (C2-C7) from skeletally mature dogs without (cadaveric group 1, n = 6, historical data) and with an intervertebral disk spacer (cadaveric group 2, n = 6) were used. All PVC models and cadaver specimens were instrumented with monocortical titanium screws/PMMA. Stiffness of the 2 PVC groups was compared in extension, flexion, and lateral bending using non-destructive 4-point bend testing. Stiffness testing in all 3 directions was performed of the unaltered C4-C5 vertebral motion unit in cadaveric spines and repeated after placement of an intervertebral cortical allograft ring and instrumentation. Data were compared using a linear mixed model approach that also incorporated data from previously tested spines with the same screw/PMMA construct but without disk spacer (cadaveric group 1). RESULTS Addition of a spacer increased construct stiffness in both the PVC model (P < .001) and cadaveric vertebral columns (P < .001) compared to fixation without a spacer. CONCLUSIONS Addition of an intervertebral spacer significantly increased construct stiffness of monocortical screw/PMMA fixation.

Effects of Breastfeeding on Respiratory Symptoms in Infancy.

OBJECTIVE To assess the impact of potential risk factors on the development of respiratory symptoms and their specific modification by breastfeeding in infants in the first year of life. STUDY DESIGN We prospectively studied 436 healthy term infants from the Bern-Basel Infant Lung Development cohort. The breastfeeding status, and incidence and severity of respiratory symptoms (score) were assessed weekly by telephone interview during the first year of life. Risk factors (eg, pre- and postnatal smoking exposure, mode of delivery, gestational age, maternal atopy, and number of older siblings) were obtained using standardized questionnaires. Weekly measurements of particulate matter <10 μg were provided by local monitoring stations. The associations were investigated using generalized additive mixed model with quasi Poisson distribution. RESULTS Breastfeeding reduced the incidence and severity of the respiratory symptom score mainly in the first 27 weeks of life (risk ratio 0.70; 95% CI 0.55-0.88). We found a protective effect of breastfeeding in girls but not in boys. During the first 27 weeks of life, breastfeeding attenuated the effects of maternal smoking during pregnancy, gestational age, and cesarean delivery on respiratory symptoms. There was no evidence for an interaction between breastfeeding and maternal atopy, number of older siblings, child care attendance, or particulate matter <10 μg. CONCLUSIONS This study shows the risk-specific effect of breastfeeding on respiratory symptoms in early life using the comprehensive time-series approach.

Determinants of CD4 cell count decline after treatment interruption

Patients who had started HAART (Highly Active Anti-Retroviral Treatment) under previous aggressive DHHS guidelines (1997) underwent a life-long continuous HAART that was associated with many short term as well as long term complications. Many interventions attempted to reduce those complications including intermittent treatment also called pulse therapy. Many studies were done to study the determinants of rate of fall in CD4 count after interruption as this data would help guide treatment interruptions. The data set used here was a part of a cohort study taking place at the Johns Hopkins AIDS service since January 1984, in which the data were collected both prospectively and retrospectively. The patients in this data set consisted of 47 patients receiving via pulse therapy with the aim of reducing the long-term complications. ^ The aim of this project was to study the impact of virologic and immunologic factors on the rate of CD4 loss after treatment interruption. The exposure variables under investigation included CD4 cell count and viral load at treatment initiation. The rates of change of CD4 cell count after treatment interruption was estimated from observed data using advanced longitudinal data analysis methods (i.e., linear mixed model). Using random effects accounted for repeated measures of CD4 per person after treatment interruption. The regression coefficient estimates from the model was then used to produce subject specific rates of CD4 change accounting for group trends in change. The exposure variables of interest were age, race, and gender, CD4 cell counts and HIV RNA levels at HAART initiation. ^ The rate of fall of CD4 count did not depend on CD4 cell count or viral load at initiation of treatment. Thus these factors may not be used to determine who can have a chance of successful treatment interruption. CD4 and viral load were again studied by t-tests and ANOVA test after grouping based on medians and quartiles to see any difference in means of rate of CD4 fall after interruption. There was no significant difference between the groups suggesting that there was no association between rate of fall of CD4 after treatment interruption and above mentioned exposure variables. ^