Caution: Time‐Varying Exposures Ahead

Time-fixed exposures are measured at a single point in time, most often at study baseline, and their value is assumed to remain constant throughout the follow-up period. Some exposures are truly time-fixed, such as age at menarche or the date of a pregnancy loss. In other instances, investigators choose to analyse an exposure as time-fixed, even though the value of the exposure actually changes over time. Consider a fictitious study that examines the effect of reproductive hormones and lifestyle behaviours on bone mineral density in perimenopausal women. In this study, the investigators measured reproductive hormones (e.g., estradiol) and collected information on lifestyle behaviours (e.g., physical activity, diet) during a clinic visit at study baseline. They then examined the relationship between reproductive hormone levels and lifestyle behaviours as time-fixed exposures based on the single measurement at baseline, despite the fact that the values of these variables may change over time. By choosing to analyse these time-varying variables as time-fixed exposures, the investigators are making an implicit assumption that changes in the exposure over time are irrelevant or substantively unimportant. The validity of any analysis examining a time-varying variable as a time-fixed exposure rests on the degree to which this assumption is true. In contrast, time-varying exposures are variables whose value can change over follow-up time. An individual's value of the exposure may be different at each exposure measurement time point. Extending the example above, if investigators chose to measure reproductive hormones monthly, corresponding with a woman's menstrual cycle, and ask women to complete a self-report physical activity questionnaire at the same time, there could be as many exposure values as there are measurement time points. Analyses with time-varying exposures must appropriately account for temporal ordering and consider time-varying confounders, particularly time-varying confoundings that are affected by prior exposure. An important advantage of considering time-varying exposures is that they enable the examination of exposure history, including patterns, timing, duration of past exposure, or cumulative exposures. There are many examples wherein the biological effect of an exposure may accumulate over time, and investigators are interested in studying the number of years exposed, cumulative dose, or exposure burden. In this issue of Paediatric and Perinatal Epidemiology, Wang and colleagues [1] employ a time-varying exposure approach to investigate the association between physical activity and the risk of injury among Danish school children. They use a flexible weighted cumulative exposure (WCE) method [2] to model physical activity over time. We commend them for considering physical activity as a time-varying exposure and using a complex exposure modelling approach that captures how past exposure contributes to current injury risk. The WCE approach [2] used by Wang and colleagues is one of several options for investigators interested in analysing time-varying exposures. In Table 1, we briefly describe some methodological approaches for modelling time-varying exposures. Each approach has distinct strengths, limitations, and underlying assumptions that should be evaluated in relation to the available data and the research question of interest. Repeated measures models are the simplest approach to implement and preserve temporal ordering. Lagged exposure models [3, 4] attempt to capture biologically or etiologically relevant exposure windows and consider timing of the exposure. However, they often rely on arbitrary lag choices and the modelling may be affected by collinearity across adjacent time points. Distributed lag models [5, 6] mitigate some of these concerns by smoothing exposure–response relationships across lags, although they require densely measured data and are sensitive to specification and smoothing assumptions. Cumulative and unweighted moving average models [7] assume equal contributions of past exposure and ignore timing; exponentially weighted moving average models [8] consider recency but require assumptions about decay functions. Finally, trajectory models [9] summarise exposure histories into latent classes and are primarily descriptive. WCE models [2] estimate data-driven weights that can identify etiologically relevant windows and accommodate non-monotonic effects. Wang and colleagues use the WCE approach with cubic splines to avoid the need to impose pre-specified functional forms or assumptions. This approach also allows past exposure to contribute differentially to current risk as a function of recency, which seems biologically plausible in this case given the interest in examining physical activity and injury risk. WCE presents a balance between flexibility and interpretability, but is computationally intensive, requires large sample size, exposure variability, and is sensitive to choices about spline form, knot placement, and window length. They also increase the risk of overfitting, particularly in small samples or when exposure histories are long relative to the number of outcome events. Interpretation of the estimated weight function may also be challenging, especially when weights fluctuate or cross zero, complicating translation into biologically meaningful exposure periods. WCE and other methods designed to examine time varying exposures have the potential to meaningfully advance science and inform clinical or public health interventions. However, it is still critical to consider key sources of bias (e.g., confounding, measurement, selection) when using these approaches. Using time-varying exposures allows us to explicitly account for exposure dynamics and align our analytic models with underlying aetiologic processes. However, making the decision to model an exposure as time-varying requires caution, as time-varying biases must be considered. Time-varying measurement bias [10] occurs when the accuracy or validity of exposure, outcome, or covariate measurement changes over time, typically in ways related to prior exposure, disease status, or study participation. It goes without saying that using a time-varying exposure requires a valid measure of exposure at each measurement time point. The effects of measurement bias can be compounded when examining multiple measurement time points. Measurement error or misclassification can distort both the estimated levels of exposure and the temporal pattern of exposure effects. Inaccurate measurement of exposure can lead to biased conclusions about changes in exposure status over time, the presence of dose–response relationships, and the occurrence of lagged or cumulative effects. The study by Wang and colleagues describes time-varying physical activity as the exposure of interest, measured from weekly parent-report counts of their children's participation in sports (“How many times did [child] engage in sports during the last week”?) and a count of the number of school-based physical education classes. All informal forms of physical activity, such as a game of tag at school recess, playing basketball in a local park after school, or walking to school, are not counted. There is no information on duration, type, or intensity of physical activity. The injury risk associated with any sports activity session is considered equal, regardless of whether the activity is a high-risk contact sport, such as hockey, or a low-risk non-contact sport, like tennis. Sports during summer months are not counted in the exposure, despite this being ostensibly the most active time for school-aged children. The lack of information on summer sports also means that this is not a truly cumulative exposure, as exposures prior to the start of the school year do not contribute to cumulative risk. This study takes an important step forward by recognising physical activity as a time-varying exposure; however, there is still a great deal of work to be done to understand the complex relationship between physical activity and injury risk in children. Any study examining time-varying exposures must consider the potential for time-varying confounding [10]. Time-varying confounding arises when a covariate changes over time, is predictive of the exposure, and is associated with the outcome [10]. Time-varying confounding is especially problematic when confounders are affected by prior exposure, as this requires specialised analytic approaches, such as marginal structural models or g-methods. Wang et al. controlled for confounding by sex and school grade (as a proxy for age). The analysis did not control for time-varying confounding despite using a time-varying exposure. For example, consider pain as one potential confounder of the association between physical activity and injury risk. At a single point in time, pain likely affects participation in sports (e.g., taking part in activities, duration, types, and intensity) and injury risk. Children experiencing pain could have an undiagnosed chronic injury and/or increased risk for acute injury. In Figure 1, we extend this example to the setting of a time-varying exposure. Pain experienced in prior year(s) could predict whether children engage in sports in the current school year, as well as whether they experience pain in the current school year. Current pain could also be influenced by recent physical activity and persist into subsequent weeks of physical activity, as well as diagnosed injury, making pain both a time-varying confounder and an intermediate variable. Failing to appropriately control for a time-varying confounder, like pain, results in residual confounding. In this case, there is no measure of pain in this analysis, so this could also be described as unmeasured confounding. This bias may distort the relationship between current physical activity and diagnosed injury, as students who have pain in prior weeks may not engage in as much physical activity and are at a higher risk for injury diagnosis since they are experiencing pain. Accounting for this bias would require a valid measure of pain in the dataset and methods to control for a time-varying exposure affected by prior exposure. In situations where there is no measure of an important unmeasured confounder, quantitative bias analysis approaches should be considered. Valid inference in the setting of time-varying exposures requires appropriate modelling strategies and consideration of potential threats to validity. Even the most sophisticated longitudinal modelling approaches cannot produce unbiased effect estimates when the exposure is mismeasured or there is residual confounding. Consideration of potential biases and the use of appropriate modelling strategies are necessary; without both, inferences about time-varying exposure risk may be incomplete, uninterpretable, or inaccurate. We look forward to future studies that combine flexible modelling approaches with consideration of time-varying biases to further understand the important questions regarding injury risk in school-aged children. H.R.B. and A.R. both conceptualized and contributed to the article. The authors have nothing to report. The authors declare no conflicts of interest. Data sharing not applicable to this article as no data sets were generated or analysed during the current study.