Estimation of causal effect measures with the R-package stdReg

Abstract

Measures of causal effects play a central role in epidemiology. A wide range of measures exist, which are designed to give relevant answers to substantive epidemiological research questions. However, due to mathematical convenience and software limitations most studies only report odds ratios for binary outcomes and hazard ratios for time-to-event outcomes. In this paper we show how logistic regression models and Cox proportional hazards regression models can be used to estimate a wide range of causal effect measures, with the R-package stdReg. For illustration we focus on the attributable fraction, the number needed to treat and the relative excess risk due to interaction. We use two publicly available data sets, so that the reader can easily replicate and elaborate on the analyses. The first dataset includes information on 487 births among 188 women, and the second dataset includes information on 2982 women diagnosed with primary breast cancer.

Keywords: Attributable fraction; Causal effect; Cox proportional hazards regression; Logistic regression; Number needed to treat; Relative excess risk due to interaction.

Fig. 1

The estimated AF (solid line) as a function of time since diagnosis, together with point-wise 95% confidence intervals (dashed lines)

Fig. 2

The estimated NNT (solid line) as a function of time since diagnosis, together with point-wise 95% confidence intervals (dashed lines)

Fig. 3

The estimated RERI (solid line) as a function of time since diagnosis, together with point-wise 95% confidence intervals (dashed lines)