Usual approaches to the analysis of cohort and case control data often follow from risk-set sampling designs, where at each failure time a new risk set is defined, including the index case and all the controls that were at risk at that time. That kind of sampling designs are usually related to the Cox proportional hazards model, available in most standard statistical packages but limited to log-linear models (except Epicure, (Preston et al., 1993)) of the form log(φ(z, β)) = β_1 cdot z_1 + … β_k cdot z_k, where z is a vector of explanatory variables and φ is the rate ratio. This implies exponential dose-response trends and multiplicative interactions, which may not be the best exposure-response representation in some cases, such as radiation exposures. One model of particular interest, especially in radiation environmental and occupational epidemiology is the ERR model, φ(z, β) = 1 + α cdot f(dose). The ERR model represents the excess relative rate per unit of exposure and z_1, …, z_k are covariates. Estimation of a dose-response trend under a linear relative rate model implies that for every 1-unit increase in the exposure metric, the rate of disease increases (or decreases) in an additive fashion. The modification of the effect of exposure in linear relative rate models by a study covariate m can be assessed by including a log-linear subterm for the linear exposure effect (Preston et al., 2003; Ron et al., 1995), implying a model of the form φ(z, β) = e^{β_0 + β_1 cdot z_1 + … + β_k cdot z_k} (1 + α cdot f(dose)).
Usual approaches to the analysis of cohort and case control data often follow from risk-set sampling designs, where at each failure time a new risk set is defined, including the index case and all the controls that were at risk at that time. That kind of sampling designs are usually related to the Cox proportional hazards model, available in most standard statistical packages but limited to log-linear models (except Epicure, (Preston et al., 1993)) of the form log(φ(z, β)) = β_1 cdot z_1 + … β_k cdot z_k, where z is a vector of explanatory variables and φ is the rate ratio. This implies exponential dose-response trends and multiplicative interactions, which may not be the best exposure-response representation in some cases, such as radiation exposures. One model of particular interest, especially in radiation environmental and occupational epidemiology is the ERR model, φ(z, β) = 1 + α cdot f(dose). The ERR model represents the excess relative rate per unit of exposure and z_1, …, z_k are covariates. Estimation of a dose-response trend under a linear relative rate model implies that for every 1-unit increase in the exposure metric, the rate of disease increases (or decreases) in an additive fashion. The modification of the effect of exposure in linear relative rate models by a study covariate m can be assessed by including a log-linear subterm for the linear exposure effect (Preston et al., 2003; Ron et al., 1995), implying a model of the form φ(z, β) = e^{β_0 + β_1 cdot z_1 + … + β_k cdot z_k} (1 + α cdot f(dose)).
ERRci
(Package: linERR) :
Profile likelihood based confidence intervals
The standard procedure for computing a confidence interval for a parameter β (Wald-type CI), based on hat{β} pm z_{1-frac{α}{2}} SE(hat{β}) may work poorly if the distribution of the parameter estimator is markedly skewed or if the standard error is a poor estimate of the standard deviation of the estimator. Profile likelihood confidence intervals doesn't assume normality of the estimator and perform better for small sample sizes or skewed estimates than Wald-type confidence intervals.
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