Marginal versus conditional rate estimation for count and recurrent event data with an estimand framework.

Count and recurrent event endpoints are common key efficacy endpoints in clinical research. For example, in clinical research of pulmonary diseases such as chronic obstructive pulmonary disease (COPD) or asthma, the reduction of the occurrence of a recurrent event, pulmonary exacerbation (PEx) caused by acute respiratory symptoms, is often used to measure the treatment effect. The occurrence of PEx is often analyzed with nonlinear models, such as Poisson regression or Negative Binomial regression. It is observed that model-estimated within-group PEx rates are often lower than the descriptive statistics of within-group PEx rates. Motivated by this observation, we explore their relationship mathematically and demonstrate that it is due to the difference between conditional PEx rates and population-level PEx rates (marginal rates). Our findings corroborate the recent FDA guidance (2023) [1], which discusses considerations for covariate adjustment in nonlinear models, and that conditional or subgroup treatment effects with covariate adjustment may differ from marginal treatment effects. In this article, we demonstrate how covariate adjustment impacts the estimation of event rates and rate ratios with both closed form and simulation studies. Additionally, following the ICH E9 addendum on the estimand framework [2], we discuss the estimand framework for count and recurrent event data.

Insulin-Like Growth Factor, Inflammation, and MRI Markers of Alzheimer's Disease in Predominantly Middle-Aged Adults.

BACKGROUND: Insulin-like growth factor 1 (IGF-1) signaling has been implicated in Alzheimer's disease pathogenesis, and further evidence suggests inflammation can be a moderator of this association. However, most research to date has been conducted on older adults. OBJECTIVE: To investigate the association of serum IGF-1 and IGF binding protein 3 (IGFBP-3) concentrations with MRI markers of Alzheimer's disease in predominantly middle-aged adults, and further assess moderation by chronic inflammation. METHODS: We included participants from the Framingham Heart Study (n = 1,852, mean age 46±8, 46% men) and the Study of Health in Pomerania (n = 674, mean age 50±13, 42% men) with available serum IGF-1, IFGBP-3, as well as brain MRI. IGF-1 and IFGBP-3 were related to MRI outcomes (i.e., total brain, cortical gray matter, white matter, white matter hyperintensities (WMH), and hippocampal volumes) using multivariable regression models adjusting for potential confounders. Subgroup analyses by C-reactive protein (CRP) concentrations were also performed. Cohort-specific summary statistics were meta-analyzed using random-effects models and corrected for multiple comparisons. RESULTS: Meta-analysis results revealed that higher IGF-1 concentrations were associated with lower WMH (estimate [ß] [95% CI], -0.05 [-0.09, -0.02], p = 0.006) and larger hippocampal volumes (0.07 [0.02, 0.12], p = 0.01), independent of vascular risk factors. These associations occurred predominantly in individuals with CRP concentrations < 75th percentile. We did not observe associations between IGFBP-3 and MRI outcomes. CONCLUSION: Our findings suggest that IGF-1-related signaling may be implicated in brain health as early as midlife.

A comparison of statistical methods to predict the residual lifetime risk.

Lifetime risk measures the cumulative risk for developing a disease over one's lifespan. Modeling the lifetime risk must account for left truncation, the competing risk of death, and inference at a fixed age. In addition, statistical methods to predict the lifetime risk should account for covariate-outcome associations that change with age. In this paper, we review and compare statistical methods to predict the lifetime risk. We first consider a generalized linear model for the lifetime risk using pseudo-observations of the Aalen-Johansen estimator at a fixed age, allowing for left truncation. We also consider modeling the subdistribution hazard with Fine-Gray and Royston-Parmar flexible parametric models in left truncated data with time-covariate interactions, and using these models to predict lifetime risk. In simulation studies, we found the pseudo-observation approach had the least bias, particularly in settings with crossing or converging cumulative incidence curves. We illustrate our method by modeling the lifetime risk of atrial fibrillation in the Framingham Heart Study. We provide technical guidance to replicate all analyses in R.

Estimation and modeling of the restricted mean time lost in the presence of competing risks.

Survival data with competing or semi-competing risks are common in observational studies. As an alternative to cause-specific and subdistribution hazard ratios, the between-group difference in cause-specific restricted mean times lost (RMTL) gives the mean difference in life expectancy lost to a specific cause of death or in disease-free time lost, in the case of a nonfatal outcome, over a prespecified period. To adjust for covariates, we introduce an inverse probability weighted estimator and its variance for the marginal difference in RMTL. We also introduce an inverse probability of censoring weighted regression model for the RMTL. In simulation studies, we examined the finite sample performance of the proposed methods under proportional and nonproportional subdistribution hazards scenarios. We illustrated both methods with competing risks data from the Framingham Heart Study. We estimated sex differences in atrial fibrillation (AF)-free times lost over 40 years. We also estimated sex differences in mean lifetime lost to cardiovascular disease (CVD) and non-CVD death over 10 years among individuals with AF.

Growth Differentiation Factor 15 and NT-proBNP as Blood-Based Markers of Vascular Brain Injury and Dementia.

Background GDF15 (growth differentiation factor 15) and NT-proBNP (N-terminal pro-B-type natriuretic peptide) may offer promise as biomarkers for cognitive outcomes, including dementia. We determined the association of these biomarkers with cognitive outcomes in a community-based cohort. Methods and Results Plasma GDF15 (n=1603) and NT-proBNP levels (n=1590) (53% women; mean age, 68.7 years) were measured in dementia-free Framingham Offspring cohort participants at examination 7 (1998-2001). Participants were followed up for incident dementia. Secondary outcomes included Alzheimer disease dementia, magnetic resonance imaging structural brain measures, and neurocognitive performance. During a median 11.8-year follow-up, 131 participants developed dementia. On multivariable Cox proportional-hazards analysis, higher circulating GDF15 was associated with an increased risk of incident all-cause and Alzheimer disease dementia (hazard ratio [HR] per SD increment in natural log-transformed biomarker value, 1.54 [95% CI, 1.22-1.95] and 1.37 [95% CI, 1.03-1.81], respectively), whereas higher plasma NT-proBNP was also associated with an increased risk of all-cause dementia (HR, 1.32; 95% CI, 1.05-1.65). Elevated GDF15 was associated with lower total brain and hippocampal volumes, greater white matter hyperintensity volume, and poorer cognitive performance. Elevated NT-proBNP was associated with greater white matter hyperintensity volume and poorer cognitive performance. Addition of both biomarkers to a conventional risk factor model improved dementia risk classification (net reclassification improvement index, 0.25; 95% CI, 0.05-0.45). Conclusions Elevated plasma GDF15 and NT-proBNP were associated with vascular brain injury on magnetic resonance imaging, poorer neurocognitive performance, and increased risk of incident dementia in individuals aged >60 years. Both biomarkers improved dementia risk classification beyond that of traditional clinical risk factors, indicating their potential value in predicting incident dementia.

Mid-life and late-life vascular risk factor burden and neuropathology in old age.

OBJECTIVE: To determine whether vascular risk factor burden in mid- or late-life associates with postmortem vascular and neurodegenerative pathologies in a community-based sample. METHODS: We studied participants from the Framingham Heart Study who participated in our voluntary brain bank program. Overall vascular risk factor burden was calculated using the Framingham Stroke Risk Profile (FSRP). Mid-life FSRP was measured at 50 to 60 years of age. Following death, brains were autopsied and semi-quantitatively assessed by board-certified neuropathologists for cerebrovascular outcomes (cortical infarcts, subcortical infarcts, atherosclerosis, arteriosclerosis) and Alzheimer's disease pathology (Braak stage, cerebral amyloid angiopathy, and neuritic plaque score). We estimated adjusted odds ratios between vascular risk burden (at mid-life and before death) and neuropathological outcomes using logistic and proportional-odds logistic models. RESULTS: The median time interval between FSRP and death was 33.4 years for mid-life FSRP and 4.4 years for final FSRP measurement before death. Higher mid-life vascular risk burden was associated with increased odds of all cerebrovascular pathology, even with adjustment for vascular risk burden before death. Late-life vascular risk burden was associated with increased odds of cortical infarcts (OR [95% CI]: 1.04 [1.00, 1.08]) and arteriosclerosis stage (OR [95% CI]: 1.03 [1.00, 1.05]). Mid-life vascular risk burden was not associated with Alzheimer's disease pathology, though late-life vascular risk burden was associated with increased odds of higher Braak stage (OR [95% CI]: 1.03 [1.01, 1.05]). INTERPRETATION: Mid-life vascular risk burden was predictive of cerebrovascular but not Alzheimer's disease neuropathology, even after adjustment for vascular risk factors before death.

Circulating IGFBP-2: a novel biomarker for incident dementia.

OBJECTIVE: To determine the association between plasma insulin-like growth factor binding protein 2 (IGFBP-2) and cognitive outcomes. METHODS: We measured plasma IGFBP-2 levels in 1596 (53% women, mean age 68.7 [SD 5.7] years) dementia-free Framingham Offspring cohort participants between 1998 and 2001. Multivariable Cox proportional hazards models related plasma IGFBP-2 to subsequent risk of incident dementia and Alzheimer's disease. MRI brain measures and cognitive performance were included as secondary outcomes. RESULTS: During a median follow-up of 11.8 (Q1, Q3: 7.1, 13.3) years, 131 participants developed incident dementia, of whom 98 were diagnosed with Alzheimer's disease. The highest tertile of IGFBP-2, compared to the lowest tertile, was associated with an increased risk of incident all-cause dementia (hazard ratio [HR] 2.89, 95% CI 1.63-5.13) and Alzheimer's disease (HR 3.63, 95% CI 1.76-7.50) in multivariable analysis. Higher circulating IGFBP2 levels were also cross-sectionally associated with poorer performance on tests of abstract reasoning but not with MRI-based outcomes. After adding plasma IGFBP-2 levels to a conventional dementia prediction model, 32% of individuals with dementia were correctly assigned a higher predicted risk, while 8% of individuals without dementia were correctly assigned a lower predicted risk (overall net reclassification improvement index, 0.40, 95% CI 0.22-0.59). INTERPRETATION: Elevated circulating IGFBP-2 levels were associated with an increased risk of both all-cause dementia and Alzheimer's disease. Addition of IGFBP2 plasma levels to a model of traditional risk factors significantly improved dementia risk classification. Manipulation of insulin-like growth factor signaling via IGFBP-2 may be a promising therapeutic target for dementia.

Refining the Association Between Body Mass Index and Atrial Fibrillation: G-Formula and Restricted Mean Survival Times.

Background Previous studies assessing the association between body mass index (BMI) and atrial fibrillation (AF) did not account for time-varying covariates, which may be affected by previous BMI. We illustrate how the g-formula can account for time-varying confounding. Methods and Results We included 4392 participants from the Framingham Heart Study who were AF free at ages 45 to 55 years, and followed them for up to 20 years. We estimated hazard ratios (HRs) comparing time-varying nonobese versus obese with Cox models. We used the g-formula to compare nonobese versus obese and 10% annual decrease in BMI (until normal weight is reached) versus natural course. We estimated HRs and differences in restricted mean survival times, the mean difference in time alive and AF free. We adjusted for sex, age, and time-varying risk factors. Cox models indicated that nonobese participants had a decreased rate of AF versus obese participants (HR, 0.83; 95% CI, 0.72-0.97). G-formula analyses comparing everyone had they been nonobese versus obese yielded stronger associations (HR, 0.73; 95% CI, 0.58-0.91). The restricted mean survival time was 19.22 years had everyone been nonobese and 19.03 years had everyone been obese (difference, 2.25 months; 95% CI, -0.66 to 5.16). When assessing a 10% annual decrease in BMI, the association was weaker (HR 0.96; 95% CI, 0.86-1.08). Conclusions Decreased BMI was associated with a lower rate of AF after accounting for time-varying covariates that depend on previous exposure using the g-formula, which Cox models cannot accommodate. Absolute measures like the restricted mean survival time difference offer context to relative measures of association.

Adjusted restricted mean survival times in observational studies.

In observational studies with censored data, exposure-outcome associations are commonly measured with adjusted hazard ratios from multivariable Cox proportional hazards models. The difference in restricted mean survival times (RMSTs) up to a pre-specified time point is an alternative measure that offers a clinically meaningful interpretation. Several regression-based methods exist to estimate an adjusted difference in RMSTs, but they digress from the model-free method of taking the area under the survival function. We derive the adjusted RMST by integrating an adjusted Kaplan-Meier estimator with inverse probability weighting (IPW). The adjusted difference in RMSTs is the area between the two IPW-adjusted survival functions. In a Monte Carlo-type simulation study, we demonstrate that the proposed estimator performs as well as two regression-based approaches: the ANCOVA-type method of Tian et al and the pseudo-observation method of Andersen et al. We illustrate the methods by reexamining the association between total cholesterol and the 10-year risk of coronary heart disease in the Framingham Heart Study.

Circulating fibroblast growth factor 23 levels and incident dementia: The Framingham heart study.

BACKGROUND: Fibroblast growth factor 23 is an emerging vascular biomarker, recently associated with cerebral small vessel disease and poor cognition in patients on dialysis. It also interacts with klotho, an anti-aging and cognition enhancing protein. OBJECTIVE: To determine if circulating Fibroblast growth factor 23 (FGF23) is associated with new-onset cognitive outcomes in a community-based cohort of cognitively healthy adults with long-term follow-up. METHODS: We measured serum FGF23 levels in 1537 [53% women, mean age 68.7 (SD 5.7)] dementia-free Framingham Offspring participants at their 7th quadrennial examination (1998-2001), and followed these participants for the development of clinical all-cause dementia and Alzheimer's disease (AD). Secondary outcomes included MRI-based structural brain measures, and neurocognitive test performance at exam 7. RESULTS: During a median (Q1, Q3) 12-year (7.0, 13.3) follow up, 122 (7.9%) participants developed dementia, of whom 91 (5.9%) had AD. Proportional-hazards regression analysis, adjusted for age, sex, education, systolic blood pressure, antihypertensive medication, prevalent cardiovascular disease, diabetes mellitus, smoking status and apoE ε4 carrier status, revealed that higher serum FGF23 levels were associated with an increased risk of incident dementia and AD (Hazard ratio [HR] per 1 standard deviation increment in inverse transformed FGF23 level 1.25, 95% CI 1.02-1.53, and 1.32, 95% CI 1.04-1.69, respectively). There was no significant interaction according to presence/absence of significant renal impairment (eGFR <30 versus ≥30ml/min) and risk of dementia (based on 1537; p = 0.97). CONCLUSIONS: Higher circulating FGF23 is associated with an increased risk of dementia, suggesting that FGF23-related biological pathways may play a role in the development of dementia.

Methionine Sulfoxide Reductase-B3 Risk Allele Implicated in Alzheimer's Disease Associates with Increased Odds for Brain Infarcts.

Genome-wide association studies identified a single nucleotide polymorphism (SNP) in the MSRB3 gene encoding Methionine Sulfoxide Reductase-B3 (MsrB3) to be associated with the risk for low hippocampal volume and late onset Alzheimer's disease (AD). Subsequently, we identified AD-associated abnormal patterns of neuronal and vascular MsrB3 expression in postmortem hippocampi. The present study investigated the relationship between the MSRB3 SNP rs61921502, G (minor/risk allele) and MRI measures of brain injury including total brain volume, hippocampal volume, and white matter hyperintensities using linear regression models; the presence of brain infarcts using logistic regression models; and the incidence of stroke, dementia, and AD using Cox proportional hazards models in 2,038 Framingham Heart Study Offspring participants with MRI administered close to examination cycle 7 (1998-2001). Participants with neurological conditions that impede evaluation of vascular pathology by MRI, i.e., brain tumors, multiple sclerosis, and major head trauma, were excluded from the study. When adjusted for age and age squared at MRI exam, sex, and presence of Apolipoproteinɛ4 allele (APOE4), individuals with MSRB3 rs61921502 minor allele had increased odds for brain infarcts on MRI compared to those with no minor allele. However, in stratified analyses, MSRB3 rs61921502 minor allele was significantly associated with increased odds for MRI brain infarcts only in the absence of APOE4.

Circulating cortisol and cognitive and structural brain measures: The Framingham Heart Study.

OBJECTIVE: To assess the association of early morning serum cortisol with cognitive performance and brain structural integrity in community-dwelling young and middle-aged adults without dementia. METHODS: We evaluated dementia-free Framingham Heart Study (generation 3) participants (mean age 48.5 years, 46.8% men) who underwent cognitive testing for memory, abstract reasoning, visual perception, attention, and executive function (n = 2,231) and brain MRI (n = 2018) to assess total white matter, lobar gray matter, and white matter hyperintensity volumes and fractional anisotropy (FA) measures. We used linear and logistic regression to assess the relations of cortisol (categorized in tertiles, with the middle tertile as referent) to measures of cognition, MRI volumes, presence of covert brain infarcts and cerebral microbleeds, and voxel-based microstructural white matter integrity and gray matter density, adjusting for age, sex, APOE, and vascular risk factors. RESULTS: Higher cortisol (highest tertile vs middle tertile) was associated with worse memory and visual perception, as well as lower total cerebral brain and occipital and frontal lobar gray matter volumes. Higher cortisol was associated with multiple areas of microstructural changes (decreased regional FA), especially in the splenium of corpus callosum and the posterior corona radiata. The association of cortisol with total cerebral brain volume varied by sex (p for interaction = 0.048); higher cortisol was inversely associated with cerebral brain volume in women (p = 0.001) but not in men (p = 0.717). There was no effect modification by the APOE4 genotype of the relations of cortisol and cognition or imaging traits. CONCLUSION: Higher serum cortisol was associated with lower brain volumes and impaired memory in asymptomatic younger to middle-aged adults, with the association being evident particularly in women.

Circulating Vascular Growth Factors and Magnetic Resonance Imaging Markers of Small Vessel Disease and Atrophy in Middle-Aged Adults.

Background and Purpose- Little is known about associations between vascular growth factors and magnetic resonance imaging (MRI) markers in midlife. We investigated the association of serum VEGF (vascular endothelial growth factor), Ang2 (angiopoietin 2), sTie2 (soluble tyrosine kinase with immunoglobulin-like and EGF-like domains 2), and HGF (hepatocyte growth factor) concentrations with MRI markers of brain aging in middle-aged adults. Methods- We evaluated 1853 participants (mean age, 46±9 years; 46% men) from the Framingham Heart Study. Serum growth factor concentrations were measured using standardized immunoassays. Outcomes included total brain, cortical and subcortical gray matter, white matter, cerebrospinal fluid, and white matter hyperintensity volumes derived from MRI; as well as fractional anisotropy in white matter tracts from diffusion tensor imaging. We related VEGF, Ang2, sTie2, and HGF to MRI measures using multivariable regression models adjusting for vascular risk factors. We tested for interactions with APOE (apolipoprotein E) genotype and CRP (C-reactive protein). Results were corrected for multiple comparisons. Results- Higher sTie2 was associated with smaller total brain (estimate by SD unit±SE=-0.08±0.02, P=0.002) and larger white matter hyperintensity (0.08±0.02, P=0.002) volumes. Furthermore, higher Ang2 (0.06±0.02, P=0.049) and HGF (0.09±0.02, P=0.001) were associated with larger cerebrospinal fluid volumes. Finally, higher Ang2 was associated with decreased fractional anisotropy, in APOE-ε4 carriers only. Conclusions- Vascular growth factors are associated with early MRI markers of small vessel disease and neurodegeneration in middle-aged adults.

Is employment status in adults over 25 years old associated with nonmedical prescription opioid and stimulant use?

PURPOSE: Nonmedical use of prescription opioid and stimulants (NMUPO and NMUPS, respectively) has declined in recent years, but remains an important public health problem. Evidence regarding their relationships with employment status remains unclear. We determined the relationship between employment status and NMUPO and NMUPS. METHODS: We analyzed a cross-sectional, nationally representative, weighted sample of 58,486 adults, ages 26 years and older, using combined 2011-2013 data from the National Survey on Drug Use and Health (NSDUH). We fit two crude and two adjusted multivariable logistic regression models to assess the relationship between our two different outcomes of interest: (1) past-year NMUPO and (2) past-year NMUPS, and our exposure of interest: employment status, categorized as (1) full time, (2) part time, (3) unemployed, and (4) not in the workforce. Our adjusted models featured the following covariates: sex, race, age, marital status, and psychological distress, and other nonmedical use. RESULTS: Prevalence of NMUPO was higher than NMUPS (3.48 vs. 0.72%). Unemployed participants had the highest odds of NMUPO [aOR 1.45, 95% CI (1.15-1.82)], while those not in the workforce had the highest odds of NMUPS [aOR 1.71, 95% CI (1.22-2.37)]. Additionally, part-time and unemployed individuals had increased odds of NMUPS [aORs, 95% CI 1.59 (1.09-2.31) and 1.67 (1.11-2.37) respectively], while those not in the workforce had decreased odds of NMUPO [aOR 0.82, 95% CI (0.68-0.99)] relative to full-time participants. CONCLUSIONS: There is a need for adult prevention and deterrence programs that target nonmedical prescription drug use, especially among those unemployed or not in the workforce.

Comparison of Treatment Effects Measured by the Hazard Ratio and by the Ratio of Restricted Mean Survival Times in Oncology Randomized Controlled Trials.

PURPOSE: We aimed to compare empirically the treatment effects measured by the hazard ratio (HR) and by the difference (and ratio) of restricted mean survival times (RMST) in oncology randomized trials. METHODS: We selected oncology randomized controlled trials from five leading journals during the last 6 months of 2014. We reconstructed individual patient data for one time-to-event outcome from each trial, preferably the primary outcome. We reanalyzed each trial and compared the treatment effect estimated by the HR with that by the difference (and ratio) of RMST. We estimated an average ratio of the HR to the ratio of RMST; an average ratio less than one indicates more optimistic assessments with HRs. RESULTS: We analyzed 54 randomized controlled trials totaling 33,212 patients. The selected outcome was overall survival in 21 (39%) trials. There was evidence of nonproportionality of hazards in 13 (24%) trials. The HR and RMST-based measures were in agreement regarding the statistical significance of the effect, except in one case. The median HR was 0.84 (Q1 to Q3 range, 0.67 to 0.97) and the median difference in RMST was 1.12 months (range, 0.22 to 2.75 months). The average ratio of the HR to the ratio of RMST was 1.11 (95% CI, 1.07 to 1.15), with substantial between-trial variability (I(2) = 86%). Results were consistent by outcome type (overall survival v other outcomes) and whether the proportional hazard assumption held or not. CONCLUSION: On average, the HR provided significantly larger treatment effect estimates than the ratio of RMST. The HR may seem large when the absolute effect is small. RMST-based measures should be routinely reported in randomized trials with time-to-event outcomes.