Discrete Time Survival Analysis Via Latent Variable Modeling: A Note on Lagged Depression Links to Stroke in Middle and Late Life

Abstract

This article is concerned with a latent variable modeling approach to discrete time survival analysis that includes both time-invariant and time-varying covariates. The approach is illustrated with data from the Health and Retirement Study, which are utilized to study further the relationship of depression to stroke in middle and late life. Employing lag-1 depression scores as time-varying covariates, in addition to a set of relevant medical and demographic variables as time-invariant covariates collected at baseline, the article addresses a particular aspect of the prominent vascular depression hypothesis representing an important area in aging research, gerontology, geriatrics, and medicine. The results indicate considerable links of immediately prior depression levels to subsequent occurrences of stroke in middle-aged and older adults. The findings complement those reported by Raykov, Gorelick, Zajacova, and Marcoulides (2017), and are consistent with that hypothesis implying depression as a potential warning sign of an impending stroke.

Keywords:

• depression
• discrete time survival analysis
• latent variable modeling
• time-invariant covariate
• time-varying covariate
• vascular depression hypothesis

ACKNOWLEDGMENTS

We are indebted to B. O. Muthén and K. Masyn for helpful discussions on survival analysis, as well as to P. Lichtenberg and D. Paulson for informative comments on the VDH.

Notes

¹ The depression measure employed in this article is the overall score resulting from a short form of the widely used Center for Epidemiologic Studies Depression scale (CES–D; Radloff, 1977; cf. Raykov, Gorelick, et al., 2017). The CES–D measure used here comprised eight indicators of a respondent’s feelings during the week prior to the interview. Six negative indicators measure whether the respondent experienced feeling depressed, like everything is an effort, sleep is restless, felt alone, felt sad, and could not get going. The remaining two, positive indicators (reverse coded) include having felt happy and enjoyed life. At Wave 1, the response categories for all items were all or almost all of the time, most of the time, some of the time, or none or almost none of the time. At all following waves, the same seven indicators were assessed but the questions were phrased in terms of how the respondents felt “much of the time” over the week prior to the interview and the response categories were dichotomous: yes–no. The CES–D scale has high internal consistency, acceptable test–retest reliability, and excellent concurrent validity with clinical and self-report criteria across population subgroups and thus is a useful tool for population studies of depression (Radloff, 1977). Acceptable validity and reliability have also been shown for the short forms of the CES–D scale such as those used by the HRS (Andersen, Malmgren, Carter, & Patrick, 1994; Levine, 2013).

² Due to the change in the original scoring of the CES–D items, which was introduced after Wave 1 by the team conducting the HRS (in 1994), the variance (as well as mean) of the resulting depression scores after baseline is nearly three times smaller relative to that of the Wave 1 depression measure. This substantial loss in variability in the key independent variables could well have contributed to the lack of significance finding for the remaining six near-contemporaneous effects of depression on stroke occurrence that are found in Table 2. Similarly, this article differs from Raykov, Gorelick, et al. (2017) also in the following aspect. In the latter source, initial depression was assumed to be predictive of the propensity to experience first stroke during the 22 years of the study with analyzed data, whereas here baseline depression is only assumed to be (directly) predictive of the probability of first stroke at Wave 2 (see Table 2 in this article and compare with Table 2 in Raykov, Gorelick, et al., 2017; compare also Equation 5 for the model underlying the present note, with Equation 5 in Raykov, Gorelick, et al. (2017), for the model on which that article was based).