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• W1643127116 abstract "This comment only addresses the response by Mathes et al. 1 to the letter by de Bruin et al. 2 with respect to the statistical analysis in de Bruin et al. 3. Below I have pasted the paragraph at issue from Mathes et al. 1. I have split this into two parts, as my comment will address each part in turn. de Bruin et al. stated in the statistical analysis section that the study ‘treatment effects were analysed using repeated measures ANOVA’ and that the ‘mean baseline (month 1–2), intervention (month 4–5), and follow-up (month 8–9) adherence scores were computed over 8-week periods’ [11]. In the results section, they wrote that ‘the repeated measures ANOVA showed no Treatment by Time interaction’. No treatment by time interaction means that the treatment differences did not change over time. Consequently, if the mean adherence is the average for both time periods, there are no differences between the average for the intervention period and the average for the follow-up period. Mathes et al. appear to misunderstand either the repeated measures analysis of variance (ANOVA) as carried out, or its meaning. So I will clarify both. There are two methods that can be used to examine the presence of an intervention effect in repeated measures ANOVA when the dependent variable is assessed at baseline (month 1–2), post-intervention (month 4–5), and follow-up (month 8–9). Method 1. Include baseline, post-intervention and follow-up as repeated measures in the model, and examine whether there is a significant treatment by time interaction. In this case a nonsignificant interaction term means that there is no change in the group difference in adherence from baseline to post-intervention and follow-up, and thus that there is no intervention effect. Method 2. Include baseline as a covariate in the model to increase power 4, and include post-intervention and follow-up as repeated measures. In this case, testing for a treatment by time interaction is not testing for the presence/absence of an intervention effect; rather, it examines whether there is a change in the group difference in adherence from post-intervention to follow-up. A nonsignificant interaction term now means that any group difference (= intervention effect) observed at post-intervention was maintained at follow-up (which would be a good thing in behavioural trials; i.e. no relapse). With method 2, which is more powerful than method 1, the presence/absence of an intervention effect is tested as follows. In the case of a nonsignificant treatment by time interaction term (see above: the difference between groups is the same at post-intervention and follow-up), the statistical model can be made more parsimonious by first computing per patient the average of post-intervention and follow-up adherence, and then testing the difference between treatment groups with respect to this average. If the treatment by time interaction is significant, this implies that the difference in adherence between the two groups is different at post-intervention and follow-up, implying that one has to test the intervention effect (i.e. the group difference in adherence) separately at each time-point. In both instances (a significant or nonsignificant treatment by time interaction term), the model simplifies from a repeated measures ANOVA to an ANOVA of a single outcome (either the average of both time-points or the outcome per time-point). In both instances, adding the baseline as a covariate turns the ANOVA into an analysis of covariance (ANCOVA) and increases the power to detect an intervention effect if it exists. Re our specific analysis as reported in de Bruin et al. 3, note that the baseline measurement of adherence (months 1–2) was included as a covariate and not as a repeated measure (see de Bruin et al. 3, page 423, right column, last six lines). So only the post-intervention (month 4–5) and follow-up (month 8–9) measures were included as levels of the within-subject factor time. So, of the two methods above, we used method 2, not method 1. Re the meaning of our analysis, as explained above, absence of a treatment by time interaction in method 2 means that the group difference in adherence is the same at post-intervention and follow-up (in epidemiological terminology: that the treatment effect is not modified by time). It does not mean that there is no difference in adherence between the two groups. Instead, the absence of a time by treatment interaction means that we can legitimately test the adherence difference between the two treatment arms by first taking per patient the average of the post-intervention and follow-up adherence, and then testing the difference between treatment arms with respect to this average, always including baseline adherence as a covariate. This is exactly what is done by the ANCOVA reported on page 424, right column, lines 5–15, which shows a highly significant adherence difference between the intervention and control arms. In short, using repeated measures ANOVA (with treatment arm, time and baseline adherence as independent variables, and with adherence at post-test and follow-up as outcomes), we found no treatment arm by time interaction. This justified the averaging of adherence over post-intervention and follow-up, and then using that average as outcome in an ANCOVA (without repeated measures). This ANCOVA showed a highly significant treatment effect. The mistake Mathes and colleagues seem to make both in their review and in the commentary is that they treat the interaction term as if it includes baseline (analysis method 1), whereas baseline was included as a covariate (method 2), and therefore the interaction does not test for an intervention effect. Just to prevent a possible further misunderstanding, note that de Bruin et al. 3 also report subgroup analyses in view of the finding of a treatment by covariate (baseline adherence) interaction (not to be confused with a treatment by time interaction). We do not think that the confusion arises from these analyses (also because Mathes and colleagues focus on the full sample of 133 patients, and not on the additional subgroup analysis). However, if the Editor thinks this is needed, we can provide additional clarification on these subgroup analyses as well. Furthermore, results were only presented for two [analysis of covariance (ANCOVA) and mixed linear regression] out of the three statistical analysis strategies that were used to test the treatment effect. But the results were not presented for the ANOVA, which is described as the primary analysis. Thus, we had – as suggested in the Cochrane Handbook – the ‘particular concern (. . .) that statistically non-significant results might be selectively withheld from publication’ [10]. This again reflects a misreading of de Bruin et al. 3 by Mathes et al. In the analysis section, we write (page 423, right column, last 7 lines, and page 424, left column, lines 7–12): Treatment effects were analyzed using repeated measures ANOVA, with treatment as between-subjects factor and time (intervention, follow-up) as within-subject factor, and baseline timing adherence as covariate to increase power 4. If no Treatment by Time interaction was found (i.e., if the effects of the intervention was similar at the intervention and follow-up assessment), treatment effects were analyzed averaged across both periods. [….] The adherence analyses were conducted on all complete cases and with an intention-to-treat procedure for patients dropping out (last observation carried forward). We also conducted a mixed linear regression that mimics the repeated measures ANCOVA (for details, see 4), using only the available data (i.e., without imputing missing values). Hence, de Bruin et al. state that they performed three analyses of adherence: (1) a repeated measures ANOVA on the complete cases; (2) the same ANOVA but now on all cases (with missing values replaced by the last observation because ANOVA cannot handle missing data); (3) a mixed linear regression (which can include incomplete cases without replacing missing values). Note that the last two of these analyses are intention-to-treat (ITT) analyses, and that we conducted the mixed-effects analysis in addition to the ITT ANOVA to enhance confidence in the robustness of the results. Now, contrary to what Mathes and colleagues write in their response, the primary analysis (i.e. the repeated measures ANOVA based on ITT with baseline as covariate, which simplifies into an ANCOVA after averaging post-intervention to follow-up data) is fully reported in the Results section (page 424, right column, lines 6–15). As all three analyses led to the same conclusion of a beneficial treatment effect on adherence, differing in small details of P-value and effect size only, for the sake of brevity and simplicity de Bruin et al. 3 only briefly state that the results were similar for the complete case and mixed-effects regression analyses (2010, page 424, right column, halfway). We are willing to submit a short report with the details of all three analyses performed to the Editor upon request, but we do not think that this is why Mathes and colleagues state that de Bruin et al. 3 are withholding nonsignificant results (as they state in their response that de Bruin et al. do report the results from the mixed-effects analysis, suggesting that this statement is considered as sufficient). Instead, although it is a bit hard to infer from the response by Mathes and colleagues, it seems that the confusion has arisen because analysis method 2 described above was unclear to them based on the article describing the trial results 3. This can be deduced from their response in which they state that we report the ANCOVA but not the primary repeated measures ANOVA results, while, in fact, the ANCOVA is the endpoint of the repeated measures ANOVA analysis method 2. In short, we conducted three analyses. The primary analysis started with a repeated measures ANOVA on all cases (by replacing missing values using last observation carried forward) and, in view of the absence of a treatment by time interaction, ended with an ANCOVA testing the between-group difference after averaging post-intervention and follow-up data (note that both analyses were performed with baseline as covariate). The results of this primary analysis are reported. As the additional complete case ANOVA and the mixed-effects analyses yielded similar results, this was stated in the text. Hence, there is no instance of any selective reporting, and there are no nonsignificant results to be hidden in the first place. The editors have received this additional rebuttal from the team lead by de Bruin et al. 3 on their publication from 2010. The editors conclude that Van Breukelen & De Bruin (2015) convincingly argue for how they have analyzed and reported their findings. The editors agree that de Bruin and colleagues did report their findings in a transparent way and that the publication from 2010 did show a beneficial effect from the intervention studied." @default.
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• W1643127116 title "Incorrect interpretation of AIMS trial analyses: comment on Mathes et al .'s ‘Response to letter …’ (HIV Medicine 2014, 15, 383-384)" @default.
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