Introduction Goals and outline Examples Survival Analysis Basic concepts in survival analysis Censoring and truncation Parametric models Estimation of survival and hazard functions Regression models Identifiability problems Univariate Frailty Models The concept of univariate frailty Discrete frailty model Gamma frailty model Log-normal frailty model Inverse Gaussian frailty model Positive stable frailty model PVF frailty model Compound Poisson frailty model Quadratic hazard frailty model Levy-type frailty models Log-t frailty model Univariate frailty cure models Missing covariates in proportional hazard models Shared Frailty Models Marginal versus frailty model The concept of shared frailty Shared gamma frailty model Shared log-normal frailty model Shared positive stable frailty model Shared compound Poisson/PVF frailty model Shared frailty models more general Dependence measures Limitations of the shared frailty model Correlated Frailty Models The concept of correlated frailty Correlated gamma frailty model Correlated log-normal frailty model MCMC methods for the correlated log-normal frailty model Correlated compound Poisson frailty model Correlated quadratic hazard frailty model Other correlated frailty models Bivariate frailty cure models Comparison of different estimation strategies Dependent competing risks in frailty models Copula Models Shared gamma frailty copula Correlated gamma frailty copula General correlated frailty copula Cross-ratio function Different Aspects of Frailty Modeling Dependence and interaction between frailty and observed covariates Cox model with general Gaussian random effects Nested frailty models Recurrent event time data Tests for heterogeneity Log-rank test in frailty models Time-dependent frailty models Identifiability of frailty models Applications of frailty models Software for frailty models Appendix References Index

/pdf/frailty-models-in-survival-analysis-260ntqn9sj.pdf

Frailty Models in Survival Analysis

The rural-urban gap in infant mortality rates is explained by using a new decomposition method that permits identification of the contribution of unobserved heterogeneity at the household and the community level. Using Demographic and Health Survey data for six Francophone countries in Central and West sub-Saharan Africa, we find that differences in the distributions of factors that determine mortality—not differences in their effects—explain almost the entire gap. Higher infant mortality rates in rural areas mainly derive from the rural disadvantage in household characteristics, both observed and unobserved, which explain two-thirds of the gap. Among the observed characteristics, environmental factors—a safe source of drinking water, electricity, and quality of housing materials—are the most important contributors. Community characteristics explain less than one-quarter of the gap, with about two-thirds of this coming from community unobserved heterogeneity and one-third from the existence of a health facility within the community. The effect of disadvantageous environmental conditions—such as limited electricity and water supply—derives both from a lack of community-level infrastructure and from the inability of some households to exploit it when available. Policy needs to operate at both the community and household levels to correct such deficiencies.

/pdf/what-explains-the-rural-urban-gap-in-infant-mortality-2beplovdx6.pdf

What Explains the Rural-Urban Gap in Infant Mortality: Household or Community Characteristics?

https://www.rand.org/content/dam/rand/pubs/working_papers/2005/RAND_WR219.pdf

Birth-spacing, fertility and neonatal mortality in India: Dynamics, frailty, and fecundity

An Investigation of District Spatial Variations of Childhood Diarrhoea and Fever Morbidity in Malawi

Data from a range of different environments indicate that the incidence of death is not randomly distributed across families but, rather, that there is a clustering of death amongst siblings. A natural explanation of this would be that there are (observed or unobserved) differences across families, for example in genetic frailty, education or living standards. Another hypothesis of considerable interest for both theory and policy is that there is a causal process whereby the death of a child influences the risk of death of the succeeding child in the family. Drawing language from the literature on the economics of unemployment, the causal effect is referred to here as state dependence (or scarring). This paper investigates the extent of state dependence in India, distinguishing this from family-level risk factors common to siblings. It offers a number of methodological innovations upon previous research. Estimates are obtained for each of three Indian states, which exhibit dramatic differences in socio-economic and demographic variables. The results suggest a significant degree of state dependence in each of the three regions. Eliminating scarring, it is estimated, would reduce the incidence of infant mortality (among children born after the first child) by 9.8% in the state of Uttar Pradesh, 6.0% in West Bengal and 5.9% in Kerala.

/pdf/sibling-death-clustering-in-india-state-dependence-vs-4r1u8a8odk.pdf

Sibling Death Clustering in India: State Dependence vs. Unobserved Heterogeneity

The Malawi Demographic and Health Survey conducted in 1992 collected the retrospective birth histories for a national sample of 4,878 women aged between 15 and 49 years. The sample was randomly selected by a two-stage sampling design. The data consist of biological, demographic, and social variables collected for each birth. This article models the infant and early childhood survival using family and community random effect multipliers on the fixed effect proportional hazards model, which allows the dependence between observations in the same family and community into the model. A Markov chain Monte Carlo sample from the posterior distribution of the parameters given the data is found. The standard errors of the fixed effect estimates are more correct than those found from the standard model, which are underestimated because of the ignored correlation structure.

https://www.jstor.org/stable/info/2670336

Samuel O Manda

Papers

Investigating Child Mortality in Malawi Using Family and Community Random Effects