From the authors:
First of all, we thank the editors of European Respiratory Journal (ERJ), for giving us the opportunity to respond to the correspondence by J. Swigris and D. Fairclough. We also thank J. Swigris and D. Fairclough that they read our paper 1 with interest and sent a correspondence letter to the editors of the ERJ. We were deeply encouraged to know that our paper had been received with interest.
As J. Swigris and D. Fairclough point out, as has Collard 2 in the past, analyses of clinical trial data, especially those of longitudinal data, can be affected by the methods by which missing data are handled. It is true that there is no perfect method for handling missing values, and we are always annoyed with challenging issues in selecting the method. We would like to agree with the suggestion in the letter that a mixed model approach should be used for the analyses of longitudinal data. We also understand that last observation carried forward (LOCF) is not necessarily the best method, and is rather a problematic one, since the assumption that observation at the time of drop-out will remain at the same level to the last observational time, needed in the estimation without bias for LOCF, is very stringent and may underestimate the true variability of missing data and inflate the type 1 error 3.
The primary reason we adopted the LOCF method in this study is that we adopted the same method in the previous study. Other reasons are as follows: LOCF is widely accepted and its principle or procedure is relatively simple, and since the analysis is done using the last observed measurement of each patient, we might interpret the results of LOCF analysis in many cases, considering the direction of bias if any. We planned to adopt the LOCF method in the primary analysis; however, for assurance, we also planned available case analysis (or observed value analysis) based on repeated measures of changes in vital capacity (VC), as described in the Discussion section of our maunscript. Due to the limited space of the paper, we only presented the conclusion: “Mixed model approach using repeated measures of changes in VC without LOCF imputation as a sensitivity analysis also showed significant or marginally significant treatment effects and supported the LOCF analysis.”
Here, we will present the results of mixed model based analysis. Incidentally, all the analyses were performed in full analysis set, and significance level was set at 0.1 both-sided. In the mixed model, we used the change in VC as response, and specified treatment, time (visit) and treatment by visit interaction as fixed effects, and patient as random effect. Covariance structure used was first-order autoregressive (AR(1)). Results are shown in tables 1, 2 and 3. Table 2 shows that effects of high and low-dose pirfenidone were significantly superior to one of placebo (p-values were 0.0494 and 0.0461 for the comparisons between high-dose and placebo, and low-dose and placebo groups, respectively). Table 3 also shows the marginally and significant effects of high- and low-dose pirfenidone (p-values were 0.1062 and 0.0435 for the comparisons between high-dose and placebo, and low-dose and placebo groups, respectively). Mixed model approach using the raw VC data as response, also shows similar results obtained with the changes in VC (see tables E1 A, B and C in the online supplementary material). In addition, we tried to analyse the repeated measures of VC using covariance structure other than AR(1), such as compound variance components or heterogeneous first-order autoregressive (ARH(1)) and obtained similar results.
Then, we examined the affections of trajectories prior to drop-out by reasons of discontinuing the study and the last visit, which was requested by J. Swigris and D. Fairclough. At first, table 2 in our paper 1 was modified to include the last visit (or the time of drop-out) of patients. The number of patients in each cell classified by reasons of discontinuing the study, treatment drug and the last visit is shown in table E2 in the online supplementary material. The transitional plots of the means of VC by the reasons of discontinuing the study and the last visit are shown in figure E1 (in the online supplementary material) and figure 1, respectively.
It was found from the transitional plots by the reasons, i.e. figure E1, that there was no clear upward or downward trajectory in each of the strata. For reference, the transitional plots of the means of VC by treatment group and the reasons of discontinuing the study are shown in figures A–F and tables A–F in the appendix to the online supplement. There seems to be no specific trend in trajectory of each treatment group. Transitional profiles seem different for drop-out patients with last visit ≤16 and >40 weeks. Namely, the mean of the former patients decreased at week 16, and mean of the latter patients increased at week 48. But, careful examination suggested the decrease and the increase in the means of VC in these patients depended on of the number of VC observations. Indeed, the number of the observations decreased at week 16 and week 48 for patients with last visit ≤16 and >40 weeks, respectively (table 4). As a result, this was thought to be one of the reasons of little difference between the results from LOCF and mixed model based analyses.
We will be happy if the results of the examination described in this article assist in showing the efficacy of pirfenidone in any way. Quite a few patients dropped out over the course of this study; in such studies, the handling of missing data plays important role. We thank again the ERJ editors and J. Swigris and D. Fairclough for rousing attention to the issues on missing data.
Footnotes
This article has supplementary material available from www.erj.ersjournals.com
Statement of Interest
None declared.
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