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)).
Usage
fit.linERR(formula, beta = NULL, data, ages, lag = 0)
Arguments
formula
An object of class formula (or one that can be coerced to that class), i.e. a symbolic description of the model to be fitted. The response must be a survival object as returned by the Surv() function, and the log-linear and linear terms are separated by the character “|”. Stratum are defined using the strata() function.
beta
Starting values for parameter estimates. Its default value is NULL.
data
Data frame that contains the cohort.
ages
Age at each exposure.
lag
Lag to be applied. Its default value is zero.
Value
An object of class fit.linERR, essentially a named list. The elements of this list are detailed below
lowb
Low boundary of the parameter in the linear part.
beta
Initial values for the estimates.
max.exp
Maximum number of exposures.
covariates1
Covariates in the loglinear part.
data_2
Original data reestructured as a list.
rsets_2
Risk sets reestructured as a list.
doses_2
Doses at each exposure reestructured as a list.
ages_2
Ages at each exposure reestructured as a list.
vcov
Variance-covariance matrix.
aic
Akaike's Information Criteria.
Call
Call to the function.
llike
Maximum log-likelihood.
deviance
Deviance of the model.
Author(s)
David Moriña, ISGlobal, Centre for Research in Environmental Epidemiology (CREAL)
References
B. Langholz and D. B. Richardson. Fitting general relative risk models for survival time and matched
case-control analysis. American journal of epidemiology, 171(3):377-383, 2010.
D. L. Preston, J. H. Lubin, D. A. Pierce, and M. E. McConney. Epicure: User's Guide. HiroSoft
International Corporation, Seattle, WA, 1993.
E. Ron, J. H. Lubin, R. E. Shore, K. Mabuchi, B. Modan, L. M. Pottern, A. B. Schneider, M. A.
Tucker, and J. D. Boice Jr. Thyroid Cancer after Exposure to External Radiation: A Pooled Analysis
of Seven Studies. Radiation Research, 141(3):259-277, 1995.