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Appendices 218 9.3 Explanation of time-varying covariate format of Chapter 6 Several variables in Chapter 6 were time-varying in the sense that respondents could have multiple measurements. For instance, employees received their first performance and potential ratings after some time on the job and these ratings were updated annually. Additionally, employees were assigned and repatriated from STIA and thereby accumulated international experience and had changing mobility status. Not accounting for these time dependencies causes serious implications, most importantly immortal time 19 . For example, graduate recruits with a performance rating inherently survive until the start of their (first) performance evaluation and, retrospectively, appear immortal as none leaves the organization. If this immortal time is not accounted for, models incorrectly estimate strong positive effects of time-varying covariates. Immortal time is prevented by encoding time-dependent covariates with a (start, stop] format (Fox & Weisberg, 2011; Therenau, Crowson, & Atkinson, 2017). Here, a record is duplicated whenever a covariate changes. The original record is right-censored at the moment of change, after all, there is no observation of what would have happened if the change had not occurred. The duplicate record is left-censored at the moment of change, after all, there is no observation of what would have happened had the change occurred earlier. The duplicate record ends as usual: either at another change of a covariate, at the end of the observational timeframe, or at turnover. Figure 9.3.1 displays this transformation on simplified example data. Despite appearances, this transformation does not cause multicollinearity because the survival analysis techniques are programmed to only use a single record per subject, depending on the point in time (Therenau et al., 2017). Figure 9.3.1: A simplified example of the transformation to a time-varying covariates format. 19 Suissa, S. (2007). Immortal time bias in pharmacoepidemiology. American Journal of Epidemiology , 167 (4), 492-499.
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