Assessing cumulative effects of medication use: New insights and new challenges

Biostatistical research aims at developing new analytical methods that help investigate intricate substantive questions of empirical research using complex data structures. Consistent with this mission, analytical challenges of pharmacoepidemiological studies of real-world safety or effectiveness of medications gave stimulus to developments of several innovative study designs and analysis methods.1 Yet, the increasingly frequent use of time-varying drug exposures (TVEs) creates a need to address further methodological complexities, including careful assessments of potential cumulative effects of past drug use.2 Indeed, cumulative effects are one of the main categories of adverse drug reactions,3 and are plausible for many important health outcomes, such as cancer incidence. However, as often, the devil is in the details. In pharmacoepidemiological studies, cumulative exposure at time t during follow-up is typically represented by a TVE X(t) calculated as the sum of all doses taken up to time t. (Using TVEs is crucial to avoid serious bias toward a spurious protective effect of higher/longer cumulative exposure, similar to immortal time bias, if total cumulative dose or total exposure duration during the entire follow-up was incorrectly represented by a time-invariant covariate.) However, this imposes a strong a priori assumption that the impact of past doses/exposures on the current hazard is the same regardless of how long ago they were received, which may often be questionable, as illustrated by a recent review.4 Indeed, in many real-world studies, pharmacodynamic properties of the drug and plausible biological pathways linking past drug exposures with subsequent changes in the risk suggest that, for example, doses taken 3 months ago should have a different impact than those taken 2 years ago. In general, recency of exposure should be considered in epidemiological studies of associations, in addition to its intensity (e.g., dose) and duration.5 Because in most long-term pharmacoepidemiological studies, drug exposures occur intermittently, with their timing, dose and/or duration varying both between patients and within patients over time,2 it is preferable to construct a single TVE metric that aggregates all this information.6 The above considerations motivated our team to adapt the weighted cumulative exposure (WCE) methodology to pharmacoepidemiological studies of time-varying drug exposures, with a main focus on time-to-event analysis.7, 8 The WCE models expand the cumulative exposure metric to include a weight function that assigns differential importance weights to past doses/exposures, depending on how long ago they were received. Thus, the conventional (unweighted) cumulative dose or duration of past use become special cases of the WCE metric, with constant weights, which permits testing if differential weighting improves the model's fit to data.8 Whereas in some applications prior knowledge may suggest an analytical form of the weight function,7, 9 to allow a more widespread applications, we relied on flexible cubic spline modeling to estimate a smooth weight function that optimizes the model's fit to data.8 WCE estimates have been validated in extensive simulations.6, 8 Kelly et al. present an insightful review of both WCE methodology, including some outstanding challenges, and its real-world pharmacoepidemiological applications.4 Typical of new complex statistical methods, the uptake by other researchers was initially slow but has improved since the WCE R package was made publicly available.10 Interestingly, in 10 out of 11 real-world studies that compared the goodness of fit of alternative exposure models, the WCE model yielded the best fit.4 Even if this statistic may partly reflect publication bias, it provides an empirical support for differential weighting of past drug exposures, depending on their recency, across real-world studies covering many drugs, prescribed for various diseases, and a range of clinical outcomes. Equally salient is the fact that some real-world applications confirm specific practical advantages of flexible spline modeling. Indeed, for different drug-outcome associations, a variety of weight function shapes were estimated, including complex non-monotone curves with bi-modal11 and delayed12 effects, as well as the inverted S-shaped curve suggesting risk increases for recently initiated exposures but decreases associated with long-term use.13 Importantly, for all these complex functions substantive experts proposed potential explanations.11-13 Thus, flexible WCE modeling can help generate new hypotheses regarding the mechanisms underlying the observed cumulative effects of different drugs. Of course, ideally, further replication studies should help assess whether the conjectures suggested by WCE estimates are robust. In fact, similar weight functions were estimated for cumulative effects of oral glucocorticoids on the hazard of diabetes mellitus in independent UK and US cohorts,14 and a WCE-based spline weight function estimate was consistent with the known pharmacodynamics of a novel cancer drug.9 By improving the model's fit to data, WCE analyses may help detect an association missed with simpler models, especially if drug exposure in different time intervals is associated with either increased or decreased current risks.8, 12, 13 By revealing such complex cumulative effects, WCE results may also help understand the reasons for possibly contradictory results of some earlier studies.13 Furthermore, WCE estimates help quantify how the risks vary depending on drug use patterns. For example, among current glucocorticoid users, the adjusted odds ratio (OR) for serious infections varies from miniscule OR = 1.03 (95% confidence interval [CI]: 1.02–1.11) for a 5-mg daily dose taken for a week, to at least a threefold odds increase associated with 3-month use of a 30-mg dose (OR = 4.82, 95% CI: 3.12–9.29).11 In contrast, conventional analyses with all current users pooled together yielded OR = 1.84 (1.64–2.06),11 masking very important risk differences related to treatment duration, dose and recency. Reporting hazard or odds ratio estimates for different time-varying patterns of past exposures/doses, in addition to the weight function estimate, facilitates the interpretation of WCE analyses, addressing a potential barrier against their more widespread use identified by Kelly et al.4 Kelly et al.4 correctly identify some limitations of the currently available WCE models and, especially, of the current R package.10 Still, a few issues require additional comments. Most importantly, WCE methods work better with (a) stronger associations, (b) high numbers of events, and (c) marked within-person variation of exposure over time. Simulations demonstrate that (a) for a moderate association, (b) at least 250 uncensored events are necessary to get reasonably stable and accurate weight function estimates.6, 8 With fewer events and/or weaker cumulative effects, it is difficult to assess if WCE models fit the data better than conventional models, and to identify the best-fitting WCE model,6 so that WCE analyses may be considered “exploratory” or “hypothesis generating.” (c) Finally, if doses vary considerably only between but not within persons, it is impossible to separate the effects of, nearly collinear, doses taken at different times, and conventional unweighted cumulative dose should be used. Some issues pointed out by Kelly et al.4 can be addressed using the current WCE package.10 To test (i) the proportional hazards (PH) assumption or (ii) an interaction with a potential effect modifier, one can employ a two-step approach. At step one, the WCE model is estimated assuming the association strength is constant across, respectively, (i) all follow-up times or (ii) all values of the modifier. Then, WCE i u = ∑ w ̂ u − t X i t $$ {WCE}_i(u)=\sum \hat{w}\left(u-t\right){X}_i(t) $$ values are calculated for all participants i and all times u, using the estimated weights w ̂ $$ \hat{w} $$ and observed exposures X i t $$ {X}_i(t) $$ . At step two, WCE i u $$ {WCE}_i(u) $$ is treated as a known time-varying covariate, and standard software for estimating the Cox model can be used to test (i) the PH hypothesis or (ii) its interaction with another covariate, as illustrated by Danieli et al.15 Furthermore, soon we will release an updated WCE package with new options for (iii) assigning external weights, for example, IPT time-varying weights to allow marginal structural model analyses; and (iv) robust variance estimation. Choosing the WCE model most appropriate for a given association may be challenging,4 and involves selecting the number of interior knots, the time window within which past exposures affect the current hazard, and whether the weight function is either unconstrained or constrained to decay to 0 at the window end.8 With a large number of events, different combinations of these meta-parameters may be compared to select the best-fitting model (see e.g., Dixon et al.11). With 300 or less events, it is preferable to consider only one-knot models, to reduce the over-fit bias, and first fit unconstrained and constrained models for the longest time window considered a priori plausible. If the unconstrained model fits better, this suggests that exposures that occurred further in the past contribute to the current hazard, so the window should be extended. If this occurs even for the window equal to the maximum follow-up duration, then cumulative effects are likely underestimated due to insufficiently long follow-up. Otherwise, if the constrained model fits better, it should be re-estimated using two or three shorter time windows, to select the best-fitting window. Often, especially for smaller datasets and weaker associations, a few models can yield similar AIC/BIC and then the corresponding weight functions should be presented, for example, in Supplementary materials. In conclusion, the evidence presented by Kelly et al.4 should stimulate more frequent use of WCE modeling in those pharmacoepidemiologic studies where cumulative effects are plausible. In parallel with new extensions of the methodology, to address some important issues identified in their review,4 these trends will hopefully advance further our understanding of the different ways patterns of drug use affect specific health outcomes. Michal Abrahamowicz is a James McGill Professor at McGill University. The author thanks Dr. Marie-Eve Beauchamp for careful revisions of earlier drafts. This work was supported by the Canadian Institutes of Health Research (grant no. PJT-180634). The author declares no conflict of interest.

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