Parametric Frailty and Shared Frailty Survival Models

Abstract

Frailty models are the survival data analog to regression models, which account for heterogeneity and random effects. A frailty is a latent multiplicative effect on the hazard function and is assumed to have unit mean and variance θ, which is estimated along with the other model parameters. A frailty model is an heterogeneity model where the frailties are assumed to be individual-or spell-specific. A shared frailty model is a random effects model where the frailties are common (or shared) among groups of individuals or spells and are randomly distributed across groups. Parametric frailty models were made available in Stata with the release of Stata 7, while parametric shared frailty models were made available in a recent series of updates. This article serves as a primer to those fitting parametric frailty models in Stata via the streg command. Frailty models are compared to shared frailty models, and both are shown to be equivalent in certain situations. The user-specified form of the distribution of the frailties (whether gamma or inverse Gaussian) is shown to subtly affect the interpretation of the results. Methods for obtaining predictions that are either conditional or unconditional on the frailty are discussed. An example that analyzes the time to recurrence of infection after catheter insertion in kidney patients is studied.

Speed of adoption of improved maize varieties in Tanzania: An application of duration analysis

“…To address this shared frailty model was estimated but we found no basic difference with the findings estimated with frailty model. As noted by (Gutierrez, 2002), both the frailty and shared frailty models can be equivalent in certain situations. The estimation results are available up on request from the authors.…”

“…In standard duration models, which fail to account adequately for all the variability in the observed failure times, a hazard ratio is interpreted as a proportional shift in the hazard function corresponding to one unit change in the covariate. However, the hazard ratio in a frailty model carries this usual interpretation only if comparing two hazards conditional on a given α, which is unobservable multiplicative effect (Gutierrez, 2002). A hazard ratio greater than one indicates an increase in the hazard of failure (i.e.…”

“…This shows that unobserved heterogeneity is an important feature of adoption decisions, and it is therefore appropriate to employ a frailty model in order to capture unobserved heterogeneity in both models. Frailty models are essentially random effects duration models that account for unobserved heterogeneity (Gutierrez, 2002). The Weibull model with gamma frailty does not converge and thus we estimated the inverse Gaussian frailty model.…”

Survival of high tech firms: The effects of diversity of product–market portfolios, patents, and trademarks

“…Based on the Consistent Akaike's Information Criterion, the Inverse Gaussian distribution outperformed the Gamma distribution for both types of exits, and we report the results for the Inverse Gaussian model (Table 3). In the Inverse Gaussian models (unlike in the Gamma model), the effects of covariates persisted, suggesting that, over time, both intrinsic firm characteristics (unobserved characteristics) and the effect of covariates (in this case, firm strategy) play an important role on influencing the firm's exit, either by acquisition or dissolution (Gutierrez, 2002). Empirical support for the Inverse Gaussian distribution of frailty is consistent with findings in the strategy literature (Bourgeois, 1984), which stress the important role of both choice (e.g., firm strategy) and determinism (intrinsic firm characteristics) on firm performance.…”

Bloodstream infections and inpatient length of stay among pediatric cancer patients with febrile neutropenia in Mexico City

“…The shared frailty component (random effect) of the model addresses withinperson dependence for individuals with multiple episodes of febrile neutropenia during the study period. 8 Our models were also adjusted for age, sex, cancer type (leukemia, lymphomas, solid tumors), and prophylaxis (yes or no) to reduce confounding bias. Persistent fever, an intermediate on the causal pathway, was not adjusted in the model to avoid potential overadjustment bias.…”