Clinical prediction models are commonly utilized in clinical practice to screen high-risk patients. This enables healthcare professionals to initiate interventions aimed at delaying or preventing adverse medical events. Nevertheless, the majority of these models focus on calculating probabilities or risk scores for medical events. This information can pose challenges for patients to comprehend, potentially causing delays in their treatment decision-making process. Our paper presents a statistical methodology and protocol for the utilization of a Weibull accelerated failure time (AFT) model in predicting the time until a health-related event occurs. While this prediction technique is widely employed in engineering reliability studies, it is rarely applied to medical predictions, particularly in the context of predicting survival time. Furthermore, we offer a practical demonstration of the implementation of this prediction method using a publicly available dataset.

Summary Hip fractures in elderly women pose significant healthcare challenges. Promoting walking for exercise as a cost-effective intervention may help reduce the risk of fractures in this population. Purpose This study aimed to examine the relationship between walking and hip fracture risk among women aged 65 years and older. Methods A 20-year prospective study (1986–2006) included 9704 women from the Study of Osteoporotic Fractures (SOF) in the USA. Participants were followed biennially, and walking exposure was assessed by the number of city blocks walked for exercise, routine activity, and total blocks walked daily. Cox regression models with time-varying covariates assessed associations, with competing risks addressed using Fine and Gray models. Penalized splines were used to explore dose–response relationships. Results In total, 1419 hip fractures were identified through the study period. The mean and median follow-up times for hip fractures or censoring were 15.0 and 15.8 years in the walking for exercise group, vs. 13.2 and 13.7 years in the not walking for exercise group. The hip fracture incidence rate was 10.0 cases per 1000 person-years (py) in the walking for exercise group compared to 10.9 per 1000 py in the not walking for exercise group. All-cause mortality was 37.1 per 1000 py in the walking for exercise group compared to 46.4 per 1000 py in the not walking for exercise group. Adjusted models showed that walking for exercise significantly reduced hip fracture risk (HR, 0.864; 95% CI, 0.762–0.980; P = 0.0230), with each additional block walked for exercise reducing risk (HR per block, 0.986; 95% CI, 0.978–0.995; P = 0.0022). Walking for routine activities showed no significant association. Spline analysis indicated walking 16 blocks (≈3200 steps) daily significantly lowered hip fracture risk. Conclusion Walking for exercise is linked to a reduced risk of hip fractures in elderly women. Walking the equivalent of 16 blocks or more (> 3200 steps) per day might be an effective way to reduce the risk of hip fractures in this vulnerable population.

Detecting interactions is a critical aspect of medical research. When interactions are present, it is essential to calculate confidence intervals for both the main effect and the interaction effect. This requires determining the covariance between the two effects. In a two-stage individual patient data (IPD) meta-analysis, the coefficients, as well as their variances and covariances, can be calculated for each study. These coefficients can then be combined into an overall estimate using either a fixed-effect or random-effects meta-analysis model. The overall variance of the combined coefficient is typically derived using the inverse-variance method. The most commonly used method for calculating the overall covariance between the main effect and the interaction effect in meta-analysis is multivariate meta-analysis. In this paper, we propose an alternative, straightforward, and transparent method for calculating this covariance when interactions are considered in a meta-analysis. To facilitate implementation, we have developed an R package, ‘covmeta’.

Background/Objectives: Evidence regarding the associations between coffee and tea consumption and bone mineral density (BMD) in postmenopausal women remains inconclusive. Prior studies have not examined these relationships using repeated measures of both beverage intake and BMD over an extended follow-up. This study aimed to evaluate the longitudinal associations of coffee and tea consumption with BMD in older women. Methods: Data were drawn from the Study of Osteoporotic Fractures (SOF), a prospective cohort of 9704 women aged ≥65 years. Coffee and tea intake were repeatedly assessed via self-administered questionnaires at visits 2, 4, 5, and 6, spanning approximately 10 years. Femoral neck and total hip BMD were repeatedly measured by dual-energy X-ray absorptiometry. Linear mixed-effects models with random intercepts were used to estimate associations, adjusting for demographic, physical activity, comorbidities, and medication use. Nonlinear relationships were assessed using natural splines, and subgroup analyses were conducted using exposure-by-covariate interaction terms. Results: During the 10-year follow-up, tea consumption was positively associated with total hip BMD (least squares mean: 0.718 vs. 0.715 g/cm²; mean difference: 0.003; 95% CI: 0.000–0.005; p = 0.026). No significant overall association was observed on coffee consumption with femoral neck or total hip BMD. However, spline analyses suggested that consuming more than five cups of coffee per day may be associated with lower BMD. Interaction analyses indicated significant interactions between coffee and alcohol intake (p = 0.0147) and between tea consumption and BMI (p = 0.0175). Conclusions: Tea consumption was associated with higher total hip BMD in postmenopausal women, whereas excessive coffee intake (>5 cups/day) may adversely affect BMD. Coffee consumption was negatively associated with femoral neck BMD in women with higher alcohol intake, while tea consumption appeared particularly beneficial for those with obesity.

Detecting interactions is a critical aspect of medical research. When interactions are present, it is essential to calculate confidence intervals for both the main effect and the interaction effect. This requires determining the covariance between the two effects. In a two-stage individual patient data (IPD) meta-analysis, the coefficients, as well as their variances and covariances, can be calculated for each study. These coefficients can then be combined into an overall estimate using either a fixed-effect or random-effect meta-analysis model. The overall variance of the combined coefficient is typically derived using the inverse-variance method.However, to the best of our knowledge, no existing studies have addressed how to calculate the overall covariance between the main effect and the interaction effect in the context of meta-analysis. In this paper, we propose a straightforward and transparent method for calculating this covariance when interactions are considered in a meta-analysis. To facilitate implementation, we have developed an R package, covmeta, which is available at https://github.com/enwuliu/covmeta.