fit.linERR {linERR}

Fits linear ERR model

Description

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(\phi(z, \beta)) = \beta_1 \cdot z_1 + \ldots \beta_k \cdot z_k, where z is a vector of explanatory variables and \phi 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, \phi(z, \beta) = 1 + \alpha \cdot f(dose). The ERR model represents the excess relative rate per unit of exposure and z_1, \ldots, 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 \phi(z, \beta) = e^{\beta_0 + \beta_1 \cdot z_1 + \ldots + \beta_k \cdot z_k} (1 + \alpha \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.

See Also

ERRci, linERR-package

Examples

  data(cohort1) 
  fit.1 <- fit.linERR(Surv(entryage, exitage, leu)~sex|dose1+dose2+dose3+dose4+dose5+dose6+
                      dose7+dose8+dose9+dose10+dose11+dose12+dose13+dose14+dose15+dose16+
                      dose17+dose18+dose19+dose20+dose21+dose22+dose23+dose24+dose25+dose26+
                      dose27+dose28+dose29+dose30+dose31+dose32, data=cohort1, beta=NULL, 
                      ages=cohort1[, 7:38], lag=2)