THE AUTHORS REPLY

We thank Wolkewitz et al. (1) for their thoughtful comments on our article (2) and for bringing their closely related study (3) to our attention. We wish to point out that the term “prescription time-distribution matching” (PTDM) was coined by Zhou et al. (4), not by us. In their related study, Wolkewitz et al. (3) cited this PTDM method (4) but chose to use a new name, “matching for time to exposure” (MTE), to describe their time-matching method. In their letter, Wolkewitz et al. (1) claim that both of these methods use exactly the same procedure. However, there are 2 notable differences. First, MTE uses covariate information as additional matching criteria, while PTDM does not. Secondly, while selecting patients, “individual matching” (5) is used for PTDM, whereas “frequency matching” (3, 5) is used for MTE, and the process of deleting unexposed patients differs as well. In PTDM (2, 4), each ever-exposed subject is matched with 1 or more control subjects (due to sampling with replacement) who survived at least to the time of initiation of exposure (new time 0) of that ever-exposed subject. Unexposed patients who experienced an outcome before the assigned time 0 are excluded from the analysis. However, in MTE (3), a stratum of index subjects (ever-exposed patients) grouped together is created based on their time to exposure and the same number of matched control subjects who survived at least as long as the time to exposure for the index group. If more control subjects are eligible than needed, they are selected randomly for deletion. Despite these differences, we agree that these 2 approaches share the same concept of “time to exposure” matching in a broader sense. For generating survival times, Wolkewitz et al. (3) used a multistate modeling approach (6), whereas we adapted the well-established permutation algorithm (7–9). Although the simulation design approaches differed, we are pleased to learn that the results from both of these studies (2, 3) complement and support each other when the survival times are generated from an exponential distribution. In addition to extensive simulations that explored additional scenarios (e.g., for different ratios r, for more available events, and when event times are generated from gamma and Weibull distributions; see Tables 1–4 and 6 and Web Tables 1 and 2 in our paper (2)), we extended the PTDM literature by illustrating the extent of deviation from the correct parameters in a systematic way (Figure 1 in our paper (2)), by deriving a theoretical formula for quantifying the bias and by showing that the results from this theoretical quantification closely matched those from the simulations when the chosen parameters were similar (Web Appendix 3 in our paper (2)). As an alternative to this potentially biased PTDM approach, we advocated the simplified version of the “sequential Cox approach” (10), which results in unbiased estimates. This minitrial approach not only is intuitive but also is capable of providing additional information compared with a Cox proportional hazards model with time-dependent exposure (2, 10). Unlike the PTDM approach, the simplified sequential Cox approach (2) can take into account differing baselines (different times of treatment initiation) in the analysis using stratification. In a follow-up study (11), we further analyzed the properties of the sequential Cox approach (and a modified version) in more complicated scenarios where time-dependent confounding that may or may not affect future treatment is present. In the same study (11), we also compared these approaches with a marginal structural Cox model (12, 13). Because the exposure-density sampling approach also yields unbiased estimates (3) and is helpful in interpreting results in an intuitive way (1), further development and application of this approach would be valuable. M.E.K. was supported by a studentship from the Multiple Sclerosis Society of Canada and by a postdoctoral fellowship from the Canadian Network for Observational Drug Effect Studies. H.T. is the Canada Research Chair for Neuroepidemiology and Multiple Sclerosis. She currently receives research support from the National Multiple Sclerosis Society, the Canadian Institutes of Health Research, the Multiple Sclerosis Society of Canada, and the Multiple Sclerosis Scientific Research Foundation. In the last 5 years, H.T. has received research support from the Multiple Sclerosis Society of Canada (Don Paty Career Development Award), the Michael Smith Foundation for Health Research (Scholar Award), and the United Kingdom’s MS Trust. M.E.K. has had travel and accommodation costs covered by the endMS Research and Training Network to make presentations at conferences (2011, 2012) and has received financial support from the Pacific Institute for the Mathematical Sciences to attend a workshop (2013) and from the Statistical Society of Canada (2016) to present at a conference. P.G. has received consulting fees from Biogen Idec, Inc., to serve on an advisory board. Over the past 3 years, J.P. has received consulting fees and/or fees for service on Data Safety Monitoring Boards from EMD Serono, the Myelin Research Foundation, and Novartis. In the last 5 years, H.T. has received speaker honoraria and/or travel expenses to attend conferences from the Consortium of MS Centres (2013), the National Multiple Sclerosis Society (2012, 2014, 2016), Teva Pharmaceuticals (2011), the European Committee for Treatment and Research in Multiple Sclerosis (2011–2016), the MS Trust (2011), the Chesapeake Health Education Program, the US Department of Veterans Affairs (2012), Novartis Canada (2012), Biogen Idec (2014), and the American Academy of Neurology (2013–2016). All speaker honoraria offered to H.T. are either declined or donated to an MS charity or to an unrestricted grant for use by her research group.

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