Reply to: Analysis Leads to Unreliable Results in Study of Vitamin D and Acute Respiratory Infection

In response to Dr. Beale’s letter to the editor,¹ we will clarify the rationale and validity of the analytic approach in our recently published clinical trial.² We randomized participants to high dose versus standard dose vitamin D supplementation to evaluate the impact of vitamin D on the primary outcome of acute respiratory infection (ARI) incidence rate (defined as the number of ARI events per person-years at risk for an ARI). We selected this primary endpoint because 1) it is a clinically relevant measure; 2) measures the total burden of disease experienced by each treatment group (i.e. some participants experience multiple ARIs); and 3) incorporates the fact that not all participants are at risk for the full 12 months by using person-years at risk in the denominator as opposed to simply the number of participants. Accordingly, this endpoint provides a more complete assessment than does the dichotomous outcome of whether or not a person experienced an ARI, which does not take into account the increased burden encountered when a person experiences multiple ARIs nor unequal time at risk among participants. For these reasons, we proposed cumulative incidence rate and the associated Poisson analysis (incidence rate ratio) in the original clinical trial proposal that was supported by the trial sponsors, listed in the original clinical trials registration (NCT01102374), and approved by the independent Data Safety and Monitoring Board. The observed effect size for our a priori primary endpoint was large (40% lower incidence of ARI in the high dose intervention group), clinically important, and statistically significant (p value of 0.02 indicates only a 2% chance that the observed treatment effect could be due to a type 1 error).

In this context, each ARI event was an independent infection (i.e., not related to a previous ARI for participants who experienced multiple ARIs), defined clearly in the clinical trial protocol. We analyzed count data from independent participants randomized to two independent treatment groups. Therefore, Poisson regression is an appropriate primary analysis for these count data. Regarding the concern of events occurring at a non-constant rate throughout the year, we designed the study with 12-month follow-up so that each participant would be followed through periods of expected seasonal variation (i.e., they are followed during the winter when more ARIs would be expected as well as the summer when fewer ARIs would be expected). Although some participants did not have a full 12 months of follow-up, an offset (natural log of months on study) was included in the model to account for different exposure levels for study participants. Furthermore, randomization created relative balance with both groups having similar average durations of follow-up (high dose group 10.4 months vs standard dose group 9.9 months; p=0.46) and similar season of trial initiation (p=0.73). Therefore, seasonal differences in outcomes would unlikely impact the primary results.

Finally, the proportion of participants with one or more ARI is indeed an important secondary endpoint. However, the trial was neither designed nor powered for this dichotomous endpoint to be the primary outcome. As correctly pointed out, there was not a statistically significant difference at the traditional α=0.05 level in the proportion of participants with one or more ARI (observed p=0.10). However, the observed rates of ARI (31% in high dose and 46% in standard dose groups) were consistent with potential for benefit for the high dose intervention as indicated by the primary endpoint, and the observed difference in the dichotomous outcome was clinically significant (15%; number needed to treat 6.6). As with the primary endpoint, these results should be confirmed with a larger, adequately powered phase III trial before implementation in routine clinical practice and public health recommendations.