September 25, 2024

This article focused how changing living arrangements was associated with suicide risk using survival analysis along with causal inference. The authors admitted that traditional methods like Cox model analysis were not sufficient to handle time-varying variables so they linked up applying g-methods (Hernán and Robins, 2020) such as inverse probability weighting which they said is necessary. Traditionally the hazard ratio (HR) is instantaneous or averaged over time but an actual HR would change over time. Therefore in their study they used data from the Japan Public Health Center (JPHC)-based Prospective Study to account for time-fixed and time-varying confounders in the analyses. They had two cohorts, Cohort I of people aged 40-59 years and Cohort II of people aged 40-69 years. They have two wave: Wave 1 used data collection from 1995-1999 with specific timing dependent on each public health center and Wave 2 was defined as the period 5 years after wave 1, from 2000-2004.

Their primary outcome was suicide death, evaluated up to 14 years after wave 2. They also looked at non-suicide death and all-cause mortality. They evaluated covariates at wave 1 to use as potential confounders in analyses. For all statistical analyses they used R 4.3.1. They used inverse probability weighted pooled logistic regression models for discrete-time hazards. They used random forest imputation to impute missing data for covariates but not for living arrangements for which they did not describe why. They predicted counterfactual hazard at each year and calculated survival probability from pooled logistic regression models without weighting and compared this to the Kaplan-Meier curve.

They examined the robustness of estimates to potential unmeasured confounding by calculating E-values (VanderWelle and Ding, 2017). This involved determining minimum strength of association that an unmeasured confounder would require to have above and beyond the measured covariates. Finally, they evaluated age-stratified and gender-stratified associations, fitting pooled logistic regression models with inverse probability weighting for each stratum.

They had 103,880 participants in their study. Persons living alone consistently showed a higher risk of suicide death, even an observed four-fold increase in risk at the end of the followup period. The calculated E-values showed some observed associations between living arrangements and suicide death, non-suicide death, and all-cause mortality were reasonably robust to unmeasured confounders. Overall their use of the pooled logistic regression and cumulative incidence allowed them to evaluate the impact of time-varying living arrangements over time, controlling for time-varying confounders. To address the time-varying issue, they employed a discrete-time hazard model showing cumulative incidence over time and calculated risk difference and relative risk at multiple time points.

The authors had not well described their discrete-time hazard modeling. Also, they did not describe how did they calculate survival from pooled logistic regression? None of that was explained and also it seemed like they were equating RR or RD as HRs even though these are still different measures. Also, it was unclear why they did not use time-varying covariates in a Cox model and compare that to what they had done. They also used causal modeling without really explaining its results.

Written by,

Usha Govindarajulu, PhD

**Keywords: **survival, pooled logistic regression, hazard ratio, causal inference

** **

**References**

Narita Z, Shinozaki T, Goto A, et al. Time-varying living arrangements and suicide death in the general population sample: 14-year causal survival analysis via pooled logistic regression. *Epidemiology and Psychiatric Sciences*. 2024;33:e30. doi:10.1017/S2045796024000325

Hernán, M, and Robins, J (2020) *Causal Inference: What If*, Boca, R (ed.). FL: Chapman & Hall/CRC, 257–275.Google Scholar

VanderWeele, TJ and Ding, P (2017) Sensitivity analysis in observational research: Introducing the E-value. *Annals of Internal Medicine.* 167, 268–274.CrossRefGoogle ScholarPubMed

https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240522135708624-0552:S2045796024000325:S2045796024000325_fig2.png