SAS Macro for Causal Mediation Analysis with Survival Data

Abstract

To the Editor: Mediation analysis investigates the mechanisms that underlie an observed relation between an exposure variable and an outcome variable and examines the role of an intermediate factor, the mediator. Such an analysis can help explain biological and social mechanisms and inform policy making. In 2013, we released a SAS (SAS Institute Inc, Cary, NC) macro for causal mediation analysis for binary, continuous and count outcomes, and binary and continuous mediators,1 implementing the regression-based results of VanderWeele and Vansteeland,2,3 and Valeri and VanderWeele1 for natural direct and indirect effects.4–6 Here, we have extended the SAS macro for mediation analysis to survival outcomes. The methods for causal mediation analysis yield valid inferences for natural direct and natural indirect effects under the assumptions that the measured covariates control for confounding of the (1) exposure–outcome, (2) mediator–outcome, and (3) exposure–mediator relations, and (4) that none of the mediator–outcome confounders are affected by the exposure. The methods also require correct specification of the model for the outcome given exposure, mediator and confounders, as well as correct specification of the model for the mediator given the exposure and confounders. Unlike traditional approaches to mediation, the causal inference methods allow for effect decomposition even in the presence of exposure–mediator interaction. Lange and Hansen7 and VanderWeele8 extended these approaches to survival outcomes and continuous mediator. We show that estimators of direct and indirect causal effects derived in Valeri and VanderWeele1 for the case of binary outcome and binary or continuous mediator are valid with a failure time outcome (see eAppendix, https://links.lww.com/EDE/A877, sections 1 and 4 and VanderWeele6). We extend the SAS statistical software in Valeri and VanderWeele1 to allow for survival outcomes modeled under the Cox proportional hazard or accelerated failure time models (AFT) assuming exponential or Weibull distributions. The causal effects are estimated on the hazard ratio scale if the Cox proportional hazard is employed and on the mean survival ratio scale if the AFT model is chosen. The Cox proportional hazards model mediation results require a rare outcome at the end of follow-up to be valid; the AFT model does not require this assumption. See eAppendix (https://links.lww.com/EDE/A877) for more details. In eAppendix (https://links.lww.com/EDE/A877) section 2, we provide the macro user manual, and in section 3, we provide an example of mediation analysis with survival data of colorectal cancer patients from Surveillance, Epidemiology, and End Results Program carried out using the macro.9 We highlight that the present example is for illustration purposes only, as several of the identification conditions are not met. We might, for example, want to investigate whether socio-economic position, measured by percentage of people living below the poverty line in the county of residence, affects survival of colorectal cancer patients and whether stage at diagnosis may mediate some of this effect. In this example, stage at diagnosis may be a potential mediator of the relation between residing in poor counties and the survival outcome. Here, we briefly present the results of the analyses. An AFT regression assuming exponential distribution is run for survival among colorectal cancer patients on the exposure (county percent below poverty line), adjusting for the mediator (stage at diagnosis: advanced versus non-advanced) and potential confounders (age at diagnosis, year at diagnosis, race-ethnicity, cancer registry). A logistic regression model for stage at diagnosis on the exposure adjusting for potential confounders is fitted. The Table displays the output of the estimated direct and indirect effects at the mean level of the covariates. The analysis, presented in full in the eAppendix (https://links.lww.com/EDE/A877) indicates a negative significant effect of poverty on survival. A positive, significant interaction between stage at diagnosis and poverty is detected. The socio-economic position measure displays a positive and significant association with stage at diagnosis. We find that the mean survival time of individuals living in counties with 30% of the population living below the poverty level is 11% lower than that of individuals living in counties that have no people living below the poverty line. On the mean survival-time ratio scale, the direct effect is 0.94 (95% confidence interval = 0.87–0.99) and the indirect effect is 0.95 (95% confidence interval = 0.93–0.97). Stage at diagnosis is estimated to mediate 42% of the effect of poverty on survival.TABLE: Output of Estimated Indirect, Indirect, Total Effects and Proportion Mediated from the SAS MacroTo the best of our knowledge, this is the first automated macro software for mediation for survival data allowing for exposure–mediator interactions. We anticipate that this additional feature of our SAS macro will foster the application of causal mediation analysis in life course studies. The macro was developed under SAS 9.3 and is available for download at the authors’ websites. Further details are available in the eAppendix (https://links.lww.com/EDE/A877). ACKNOWLEDGEMENTS The authors acknowledge Jarvis Chen and Brent Coull for assistance with the Surveillance Epidemiology End Results (SEER) cancer registry data and helpful discussions. Linda Valeri Department of Biostatistics Harvard School of Public Health Boston, MA [email protected] Tyler J. VanderWeele Departments of Biostatistics and Epidemiology Harvard School of Public Health Boston, MA