frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation

Frailty models are very useful for analysing correlated survival data, when observations are clustered into groups or for recurrent events. The aim of this article is to present the new version of an R package called frailtypack. This package allows to fit Cox models and four types of frailty models (shared, nested, joint, additive) that could be useful for several issues within biomedical research. It is well adapted to the analysis of recurrent events such as cancer relapses and/or terminal events (death or lost to follow-up). The approach uses maximum penalized likelihood estimation. Right-censored or left-truncated data are considered. It also allows stratification and time-dependent covariates during analysis

How to use frailtypack for validating failure-time surrogate endpoints using individual patient data from meta-analyses of randomized controlled trials

BACKGROUND AND OBJECTIVE:The use of valid surrogate endpoints can accelerate the development of phase III trials. Numerous validation methods have been proposed with the most popular used in a context of meta-analyses, based on a two-step analysis strategy. For two failure time endpoints, two association measures are usually considered, Kendall's τ at individual level and adjusted R2 ([Formula: see text]) at trial level. However, [Formula: see text] is not always available mainly due to model estimation constraints. More recently, we proposed a one-step validation method based on a joint frailty model, with the aim of reducing estimation issues and estimation bias on the surrogacy evaluation criteria. The model was quite robust with satisfactory results obtained in simulation studies. This study seeks to popularize this new surrogate endpoints validation approach by making the method available in a user-friendly R package.METHODS:We provide numerous tools in the frailtypack R package, including more flexible functions, for the validation of candidate surrogate endpoints using data from multiple randomized clinical trials.RESULTS:We implemented the surrogate threshold effect which is used in combination with [Formula: see text] to make decisions concerning the validity of the surrogate endpoints. It is also possible thanks to frailtypack to predict the treatment effect on the true endpoint in a new trial using the treatment effect observed on the surrogate endpoint. The leave-one-out cross-validation is available for assessing the accuracy of the prediction using the joint surrogate model. Other tools include data generation, simulation study and graphic representations. We illustrate the use of the new functions with both real data and simulated data.CONCLUSION:This article proposes new attractive and well developed tools for validating failure time surrogate endpoints

Tutorial in Joint Modeling and Prediction: A Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event

Extensions in the field of joint modeling of correlated data and dynamic predictions improve the development of prognosis research. The R package frailtypack provides estimations of various joint models for longitudinal data and survival events. In particular, it fits models for recurrent events and a terminal event (frailtyPenal), models for two survival outcomes for clustered data (frailtyPenal), models for two types of recurrent events and a terminal event (multivPenal), models for a longitudinal biomarker and a terminal event (longiPenal) and models for a longitudinal biomarker, recurrent events and a terminal event (trivPenal). The estimators are obtained using a standard and penalized maximum likelihood approach, each model function allows to evaluate goodness-of-fit analyses and provides plots of baseline hazard functions. Finally, the package provides individual dynamic predictions of the terminal event and evaluation of predictive accuracy. This paper presents the theoretical models with estimation techniques, applies the methods for predictions and illustrates frailtypack functions details with examples

Survival Analysis to Estimate Association between Short-Term Mortality and Air Pollution

BACKGROUND: Ecologic studies are commonly used to report associations between short-term air pollution and mortality. In such studies, the unit of observation is the day rather than the individual. Moreover, individual data on the subjects are rarely available, which limits the assessment of individual risk factors. These associations can also be investigated using case–crossover studies. However, by definition, individual risk factors are not studied, and such studies analyze only dead subjects, which limits the statistical power. OBJECTIVE: We suggest that the survival analysis is more suitable when cohorts are examined with a time-dependent ecologic exposure. To our knowledge, to date this type of analysis has never been proposed. DESIGN, PARTICIPANTS, MEASUREMENTS: In the present study we used a Cox proportional hazards model to investigate the distribution over time of the short-term effect of black smoke and sulfur dioxide in 439 nonaccidental and 158 cardiorespiratory deaths among the 1,469 subjects of the Personnes Agées QUID (PAQUID) cohort in Bordeaux, France. The model has a delayed entry and a polynomial distributed lag from 0 to 5 days. Results are adjusted for individual risk factors, temperature, relative humidity, weekday, season, influenza epidemics, and a time function to control temporal trends. RESULTS: We identified a positive and significant association between cardiorespiratory mortality and black smoke, with a 24% increase in deaths 3 days after a 10-μg/m(3) increase in black smoke (95% confidence interval, 4–47%). CONCLUSIONS: We conclude that the Cox proportional hazards model with time-dependent covariates is very suitable to investigate simultaneously the short-term effect of air pollution on health and the effect of individual risk factors on a cohort study

The thermoelastic Hertzian contact problem

AbstractA numerical solution is obtained for the steady-state thermoelastic contact problem in which heat is conducted between two elastic bodies of dissimilar materials at different temperatures with arbitrary quadratic profiles. Thermoelastic deformation causes the initially elliptical contact area to be reduced in size and to become more nearly circular as the temperature difference is increased. There is also a small but identifiable deviation from exact ellipticity at intermediate temperature differences. An approximate analytical solution is obtained, based on approximating the contact area by an ellipse

Socioeconomic status and its relation with breast cancer recurrence and survival in young women in the Netherlands

BACKGROUND: Associations between socioeconomic status (SES) and breast cancer survival are most pronounced in young patients. We further investigated the relation between SES, subsequent recurrent events and mortality in breast cancer patients < 40 years. Using detailed data on all recurrences that occur between date of diagnosis of the primary tumor and last observation, we provide a unique insight in the prognosis of young breast cancer patients according to SES. METHODS: All women < 40 years diagnosed with primary operated stage I-III breast cancer in 2005 were selected from the nationwide population-based Netherlands Cancer Registry. Data on all recurrences within 10 years from primary tumor diagnosis were collected directly from patient files. Recurrence patterns and absolute risks of recurrence, contralateral breast cancer (CBC) and mortality - accounting for competing risks - were analysed according to SES. Relationships between SES, recurrence patterns and excess mortality were estimated using a multivariable joint model, wherein the association between recurrent events and excess mortality (expected mortality derived from the general population) was included. RESULTS: We included 525 patients. The 10-year recurrence risk was lowest in high SES (18.1%), highest in low SES (29.8%). Death and CBC as first events were rare. In high, medium and low SES 13.2%, 15.3% and 19.1% died following a recurrence. Low SES patients had shorter median time intervals between diagnosis, first recurrence and 10-year mortality (2.6 and 2.7 years, respectively) compared to high SES (3.5 and 3.3 years, respectively). In multivariable joint modeling, high SES was significantly related to lower recurrence rates over 10-year follow-up, compared to low SES. A strong association between the recurrent event process and excess mortality was found. CONCLUSIONS: High SES is associated with lower recurrence risks, less subsequent events and better prognosis after recurrence over 10 years than low SES. Breast cancer risk factors, adjuvant treatment adherence and treatment of recurrence may possibly play a role in this association