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What proportion of athletes sustained an injury during a prospective study? Censored observations matter
  1. Jonatan Jungmalm1,
  2. Michael Lejbach Bertelsen2,
  3. Rasmus Oestergaard Nielsen2
  1. 1 Department of Food and Nutrition and Sport Science, Center for Health and Performance, University of Gothenburg, Goteborg, Sweden
  2. 2 Department of Public Health, Section for Sport Science, Aarhus University, Aarhus, Denmark
  1. Correspondence to Mr Jonatan Jungmalm, Center for Health and Performance, Department of Food and Nutrition, and Sport Science, University of Gothenburg, Goteborg, Sweden; jonatan.jungmalm{at}gu.se

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Introduction

A common question in sports injury research is ‘what proportion of athletes sustained an injury over a certain time period?’. In cross-sectional studies, where data are collected at a single point in time, the prevalence proportion is simply the number of injured athletes divided by the total sample. In prospective cohort studies, caution is needed as the injury incidence proportion (proportion of newly injured athletes during the observation period) is likely to be underestimated by simply using the approach that is valid for cross-sectional studies. As a part of the BJSM methods matter series,1 we here compare the analytical approaches for cross-sectional studies and prospective cohort studies (ie, without censoring and with censoring, respectively) to help the reader accurately estimate incidence proportion in prospective studies.

Cumulative incidence proportion (CIP)

To describe the proportion of sports injuries occurring over a given time period, one can calculate the CIP. The CIP can be calculated with or without censoring (in this paper, we discuss the concept of ‘right censoring’, but use the term ‘censoring’ only). For instance, the number of injured runners in a 1-year prospective cohort study was 252 of 931.2 Hence, the CIP calculated without censoring is 27% ((252/931)*100); this parallels how prevalence proportion is calculated in cross-sectional studies.

Calculating CIP while ignoring censored observations relies on two assumptions: (1) that all runners were at risk of injury throughout the entire 1-year follow-up period (implying that none of the 931 runners dropped out during the study) and (2) that all injuries occurred after exactly 365 days (last day of follow-up). These assumptions are depicted in figure 1A. Because these assumptions will almost always be violated in sports medicine prospective studies, it is more appropriate to calculate the CIP using censoring.

Figure 1

(A) Data setup without censoring. Here, two assumptions are (1) that all athletes are at risk of sustaining an injury throughout the entire follow-up (eg, 1 year), which implies that none of the seven athletes dropped out during the course of the study and (2) that all injuries occurred on the last day of follow-up, day 365. (B) The dashed lines reflect the additional time-at-risk the seven athletes are followed until they sustain a injury or they leave the study (no additional time-at-risk is added). X indicates injury; black dot indicates censored athlete; arrow indicates end of follow-up; solid line indicates time under observation; dashed line indicates time not under observation.

Censored observations result from athletes dropping out without injury (eg, stop practising sport due to lack of interest, pregnancy or death) and injuries occurring at various times during the follow-up period (figure 1B). In the 931-person cohort study, the calculated CIP was 4% higher than without censoring (31% vs 27%) when using the analytical approach described by Parner and Andersen.3 To calculate the proportion of injury-free athletes while applying the concept of censored observations, you can use the following equation (survival function—you can think of ‘survival’ as remaining ‘uninjured’ in sports medicine): S(t)=pr(T>t), where S(t) is the survival at time t, T is the time to injury and pr is the probability that a participant will ‘survive’ (remain uninjured) beyond time t. In table 1, similar calculations are made across four different prospective studies. These revealed substantial differences between the CIP calculated with and without the censored observations. For instance, the CIP in ProjectRun21 is 22% pretending observations are not censored and 44% when censored observations are used.4 Clearly, the latter result of 44%, better represents the true proportion.

Table 1

Cumulative incidence proportion without and with censoring across four different studies with prospective data collection

Why is the CIP underestimated without acknowledging censored observations?

In prospective cohort studies, athletes are enrolled at baseline, and data on exposure (eg, training) and outcome (eg, injury) are collected during follow-up. Censored observations are traditionally defined in relation to a ‘failure event’ (eg, cancer incidence or death), and so in sports medicine the parallel is ‘injury’ which we will refer to as the outcome here. Censoring occurs while the participant is not under observation or if no outcome ever occurs.5 Usually, censoring occurs due to one of the following reasons: (1) the participant withdraws from the study, (2) the participant is lost during follow-up or (3) a study with prespecified length ends and not all participants experienced the event (which does not affect CIP without censoring).

In figure 1, we visualise the differences in data structure in a setup not using censoring and in a setup using censoring. In this fictitious example, three of seven athletes sustained an injury during the course of 365 days which corresponds to a CIP of 43% (not using censoring). However, only six athletes were at risk of sustaining injury when athlete #7 was injured, because athlete #5 was lost earlier. Therefore, the proportion of injured participants at that time is 1−(5/6) (16.7%) and not 1/7 (14.3%). Similarly, when athlete #6 was injured, only two athletes were at risk of sustaining injury, the others were already injured or censored and not at risk of sustaining injury. The proportion of injured participants at the time of the last injury is therefore 1−((5/6)*(4/5)*(1/2)) (66.7%). This is substantially higher than the injury proportion of 43% obtained without censoring.

We conclude that the CIP is likely underestimated in prospective studies if researchers do not take into account censoring. For more detailed information on the concept of respecting the importance of censored observations, we guide the reader to two additional publications.6 7

Acknowledgments

Daniel Ramskov and Camma Damsted are greatly acknowledged for sharing data from RunClever and ProjectRun21.

References

Footnotes

  • Contributors JJ drafted the editorial, while the remaining co-authors revised it for important intellectual content.

  • Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

  • Competing interests None declared.

  • Patient consent for publication Not required.

  • Provenance and peer review Not commissioned; externally peer reviewed.

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