Christensen et al. question whether our recent study regarding seasonal variance to the occurrence of venous thrombotic events, and its conclusion, is valid [1, 2]. We appreciate the authors' concern and would like to commend the authors' way of discussing our findings by contrasting these to findings from Denmark on seasonal variance and venous thrombosis risk. We studied 5343 patients with thrombosis from Milan, Leiden and Tromsø, spanning a nearly 3000-km long north-south axis over Europe, and found a 2.3% lower incidence in spring than in summer. Christensen et al. included 152 548 patients from Denmark, and found an incidence rate ratio of winter over summer of 1.19. We offer four points with which to contend Christensen claims on the origin of our different findings, and their clinical relevance.
- Christensen's et al. main argument is that we did not use the statistical analysis applied by them, and that this is the reason why we only found a small difference in venous thrombosis events that was 2.3% lower in spring than in the other seasons. With the method of Christensen et al. (which is a Poisson regression model that describes seasonal variation as a weighted sum of four sinusoids), the authors found a 19% higher rate of venous thrombosis occurrence in winter than in summer. When they used our method (in which we simply counted events within the four seasons) they also found a difference of only a few percent in winter as compared with summer. Here, the authors seem to directly compare our 2.3% with their 19%. However, although both are percentages, our finding relates to a risk difference, whereas their finding relates to a relative risk. To be precise, if 25% of the events occur in one season and 22% in another, we would present a difference of 3% in the actual number of events occurring, whereas Chirstensen would find a 25/22 × 100 = 13.6 higher rate. These are just different ways of presenting the same observation. Our risk difference can easily be transformed into a relative risk. For example, when we consider spring as our reference season (23.2% of all events occurred in spring), and compare this finding with winter (25.9% of all events occurred in winter). we would have found a 25.9/23.2 × 100 = 12% higher rate of venous thrombosis in winter than in spring. So, the magnitude of the rate ratios found in both studies, and with both approaches, is in fact quite similar between the Danish and the tri-country study.
- The Poisson regression model of Christensen et al. seems to have the advantage over our model (where we just simply counted events over the four seasons) that it provides incidence rates of venous thrombosis on a day-to-day basis. Nevertheless, their model assumes that seasonal variance follows a sinusoid pattern. This assumption is not necessarily true. We do not want to completely disregard the model of Christensen et al., but believe such parametric models mainly serve a purpose when actual data are scarce. However, the study of Christensen et al. is very large. It has information on more than 150 000 venous thrombotic events over 30 years of time. Therefore, a statistical model with model constraints seems redundant.
- Christensen et al. claim that their relative risk increases over the seasons are clinically relevant while we conclude from our study and from the study from Christensen et al. that a relative risk increase of 12–19% on first venous thrombosis occurrence over the seasons is not clinically relevant. Perhaps, a number needed to treat (NNT)  can help here to explain why we do not believe that a relative increase of a first venous thrombosis of even 19% on a bad winter day as compared with a good summer day can ever be clinically useful. As the absolute risk of venous thrombosis is 1 in 1000 persons per year or 1/365.25 in 1000 persons per day, a relative increase of 19% of a bad winter day as compared with a good summer day would mean that about 5000 persons (1000/0.19) would need to be treated with a good summer day annually to prevent 1 venous thrombotic event which is about 1.8 million per day to prevent one venous thrombosis event. If we could give one person a summer season instead of a winter season, we would need to give this to 400 000 people to prevent one thrombotic event, and likewise for other interventions. Even if we were able to completely replace 3 months of Danish, or Dutch, winter by summer, for 3 months, we would need to maintain this for hundreds of years to prevent one case of thrombosis. Not only is this NNT exceptionally large, but also the intervention ‘good summer day’, however desirable, seems a difficult tool to introduce into clinical practice.
- There is a problem with the registration of venous events in Denmark, which is acknowledged by the authors. That is that only 75% of venous events in which patients are admitted to hospital, are objectively confirmed venous thrombotic events . As a deep vein thrombosis is nowadays usually treated outside of the hospital, there will be an excess of a pulmonary embolism in the study from Christensen et al., or events that are misclassified as such. Because the differential diagnosis of a pulmonary embolism includes seasonal-related diseases such as pneumonia or myocardial infarction , it is possible that the seasonal pattern that the authors observed is flawed by misclassified pulmonary embolisms that were actually pneumonia or myocardial infarctions. Another limitation that could be present in the study is the possibility of an increased number of clinical diagnostics of venous thrombosis or pulmonary embolism in patients hospitalized for other reasons in the early 1980s, which authors also included in their analysis. At that time, objective radiologic techniques were not as widely available as is currently the case, and a diagnosis was often made by clinical suspicion only. As the number of hospitalizations increase during the winter time the chance of misclassification increases. In our study, we did not have this problem as our observation time started in 1993 and all events were objectively confirmed by radiologic techniques.
Due to these four reasons, we believe that the study of Christensen et al. does not disconfirm our findings. That is that the risk of a venous thrombosis is different between the seasons, with the lowest prevalence noted in spring. The percentage difference in the number of events in spring as compared with the other seasons is small (2%) and is without any clinical relevance , Table 1 allows us to compare the percentage of events per seasons between Denmark and Leiden, Tromsø, Milan, Belo Horizonte, Brazil and Leiden, the Netherlands, 31 December 2012.
|Seasons||Denmark||Leiden, Tromso and Milan|
|% (95% CI)||% (95% CI)|
|Winter||26.07 (25.85 – 26.29)||25.88 (24.73 – 27.08)|
|Spring||24.98 (24.76 – 25.20)||23.25 (22.13 – 24.40)|
|Summer||23.72 (23.51 – 23.93)||25.47 (24.32 – 26.66)|
|Autumn||25.22 (25.00 – 25.44)||25.40 (24.25 – 26.58)|