## Calculation of nnts in rcts with time-to-event outcomes a literature review gender pregnancy

The NNT is used as effect measure to present the results from RCTs with binary and time-to-event outcomes in the current medical literature. In the case of time-to-event data incorrect methods were frequently applied. Confidence intervals for NNTs were given in one third of the NNT reporting articles only. In summary, there is much room for improvement in the application of NNTs to present results of RCTs, especially where the outcome is time to an event.

Articles published in the years 2003 to 2005 in the following four frequently cited journals were evaluated: BMJ, JAMA, New England Journal of Medicine (NEJM), and Lancet. The search was limited to articles with available abstracts and publication date 2003/01/01 to 2005/12/31. In a first step, each journal was searched using PubMed to identify articles reporting results of RCTs.

Eligible articles included single studies that reported a parallel group design and an individual randomisation process; other articles were excluded (Figure (Figure1). 1) usd news. All titles and abstracts of the retrieved articles were screened to exclude obviously non-eligible articles. In a second step, the full texts of all eligible articles were then analysed to identify RCTs presenting NNTs (for any outcome) and RCTs investigating time-to-event outcomes. The articles were screened using the text search function us stock **market futures** contract. The terms used to identify the number needed to treat were "number", "need", "treat", and "NNT". The terms used to identify survival time data were: "survival", "Kaplan", "Cox", "life", and "time". If the screening results were negative or unclear, the methods sections of the articles were also reviewed manually to identify any use of NNTs and survival data.

Study selection procedure to identify randomised controlled trials (RCTs) reporting the number needed to treat (NNT) in leading medical journals in the years 2003–2005.

We assessed, whether the methods used to calculate NNTs from time-to-event outcomes were appropriate. According to the methodology described in the literature [ 12, 14- 16, 18] we considered a method as appropriate if the NNT was calculated either from survival probabilities estimated by means of the Kaplan-Meier method or the Cox regression model [ 14] or if it was calculated as the inverse of the hazard difference and both assumptions mentioned above are met (constant hazard difference and low event rates) [ 15, 16, 18]. When the method to calculate NNTs was not described in the article, we tried to verify the reported NNTs by recalculation from the presented data. The use of an appropriate method to calculate NNTs was possible if the corresponding Kaplan-Meier survival or incidence curves were presented. In this case we were able to recalculate the NNT as follows. At first we identified the point of time at which the NNT was estimated binary dictionary. If no time point was given we used the latest time point of the Kaplan-Meier graph. From this time point we draw a vertical line to the top of the graph so that the curves of the treatment arms were crossed. From these cross points we draw horizontal lines to the y-axis and read off the corresponding survival probabilities for the different treatment arms as accurate as possible usd to ringgit. These probabilities were then used for NNT calculation. When it was clear that an inappropriate method was used either by statements given in the text or by comparing the presented with the recalculated NNT, the method was classified as "inappropriate", otherwise as "appropriate".

We also assessed whether confidence intervals for the number needed to treat were provided. If the numbers at risk were given together with the Kaplan-Meier curve or were inferable because of lost-to-follow-up information or a hazard ratio with confidence interval was presented we were able to calculate also a confidence interval for the recalculated NNT by using one of methods proposed by Altman & Andersen [ 14]. If numbers at risk were given but not exactly for the required time point we used the numbers at risk for the corresponding nearest time point.

Additionally, we investigated the reporting of absolute risk reduction with corresponding confidence interval. To characterise the studies we further evaluated the median sample size of the studies reporting NNTs and whether the outcome for which the NNT was calculated was a primary or secondary endpoint.

Reported and recalculated NNTs with 95% confidence intervals (CIs) from 17 studies using inappropriate methods to calculate NNTs for time-to-event data

To explain the methods of our calculations we present one typical example. One study provided the information "The number needed to treat to prevent 1 cardiovascular event would be 40 patients with IGT over 3.3 years". Additionally, the naive proportions of patients experiencing an event were given as 32/686 in the placebo group and 15/682 in the intervention group. Obviously, the result of NNT = 40 is based upon these naive proportions, because 1/(32/686-15/682)≈1/0.025 = 40. However, due to varying follow-up times and censoring, the naive proportions represent no valid estimates of the corresponding risks at time point 3.3 years, which is only the mean follow-up time inc connector. An adequate approach to estimate the required risks for a specified time point is given by the Kaplan-Meier method.

We enlarged the Kaplan-Meier incidence curve given in the paper and determined the corresponding risk estimates at time point 1200 days visually as accurate as possible. We found the risk values 0.0410 and 0.0235 for the placebo and the intervention group, respectively. Thus, the recalculated NNT is given by 1/(0.0410 – 0.0235) = 1/0.0175 = 57.1 and the reported NNT of 40 is about 30% too low.

In the 62 NNT-reporting articles, corresponding confidence intervals were presented in 21 studies (6 of the 34 studies with time-to-event outcomes and 15 of the 28 studies with binary outcomes). Among the 62 NNT-reporting articles, 1 article used the term "number needed to screen" (NNS), 2 articles used the terminology "number needed to treat for one patient to benefit" (NNTB) and harm (NNTH), respectively, and 1 article used the term "number needed to harm" (NNH).

The absolute risk reduction was given in 33 (53.2%) of the 62 NNT-reporting articles (17 with time-to-event data and 16 with binary data), a corresponding confidence interval for the absolute risk reduction was given in 21 (63.6%) of 33 articles (7 with time-to-event data and 14 with binary data).

The number needed to treat is used as effect measure to present the results from randomised controlled trials with binary and time-to-event outcomes. We found that in the case of survival time data incorrect methods were frequently applied. As the explanatory document of the CONSORT statement [ 13] described the number needed to treat in addition to other effect measures (risk ratio or risk reduction) as helpful for expressing results of both binary and survival time data, appropriate methods are required for the calculation of NNTs also for the situation of time-to-event data. Our finding that 50% of the NNT-reporting articles with survival time data used inadequate calculation methods underlines the requirement to point out that special methods based on survival time techniques have to be used to calculate NNTs in this situation convert aud to usd. This observed proportion probably underestimates the true proportion because we classified the method to calculate NNTs as "appropriate" if the method used was unclear and the reported NNT equalled the recalculated NNT from survival probabilities. It could be that in fact naive proportions have been used (i.e. an inappropriate method) but the result haphazardly equalled the correct result based upon survival probabilities usd aud exchange rate. Thus, the true proportion of NNT-reporting articles with survival time data and inadequate calculation methods may be even higher than the observed proportion of 50%. As the considered journals represent the leading journals in medical research it can be expected that a broader review containing also medical journals of lower rank would lead to even a higher proportion of papers with inadequate NNT calculation.

In this paper we did not judge whether the application of NNTs was helpful or useful in the specific situation. For example, it was argued that in the case of chronic diseases and continuous treatments the calculation of NNTs by inverting the risk differences is not useful because the duration of treatment is not taken into account [ 15]. We agree that in the case of continuous treatments one should be careful if a cost-effectiveness analysis shall be made on the basis of NNTs. The treatment costs depend on the duration of treatment and this is shorter than the follow-up time for patients having an event before the end of the study. Thus, simple NNTs are insufficient for cost-effectiveness analyses in the case of chronic diseases and continuous treatments. If the duration of treatment is important, more complicated methods are required, e.g. survival techniques for time dependent covariates. These methods are not considered in this paper because the problem of treatment duration is independent from the type of outcome (binary or time-to-event data) **us futures market** live. If the treatment duration plays a role in the analysis, it has to be considered in addition to the effect measure used, regardless of whether the effect measure is the NNT or any other measure (risk difference, odds ratio, hazard ratio). In general it is highly subjective whether NNTs are useful or not. Therefore, we did not judge the usefulness of reported NNTs in the specific situation but considered the frequency of NNT applications in RCTs published in major medical journals in the years 2003 to 2005 and verified whether the applied calculation methods were technically appropriate in the case of time-to-event outcomes.

The error produced by using an inadequate method to calculate NNTs is unpredictable *msn news* usa. In a number of cases, there was no substantial difference between adequately and inadequately calculated NNTs. For example, one trial with inappropriate NNT calculation presented a number needed to treat of 39 which is nearly the same as the correct result of 38.2 obtained by the appropriate method proposed by Altman & Andersen [ 14]. However, in another trial the published NNT of 23 is 26.4% too large (absolute difference: +4.8) compared with the correct result of 18.2. In another example the published NNT of 10 is 32% too small (absolute difference: -4.7) compared with the correct result of 14.7 (Table (Table3). 3). It has been argued that clinicians should not be overly concerned about inaccuracies that may arise from estimating NNTs inadequately from naive proportions, especially when using data from large RCTs with high rates of follow-up [ 20]. We agree that in the case of equal censoring in the two groups the difference between adequately and inadequately calculated NNTs is negligible in practice. However, if the amount of censoring is quite different between the experimental and control group, relevant differences between adequately and inadequately calculated NNTs can be obtained. Moreover, confidence intervals for NNTs will be too narrow if censoring is not taken into account because the values used for the effective sample sizes are too large. This is demonstrated in Table Table3 3 where the recalculated confidence interval covers the reported confidence interval completely euro dollar exchange rate chart. Unfortunately, there was only one study in which a confidence interval for NNT was reported and a recalculation of the confidence interval was possible. As the application of survival techniques is standard in the analysis of RCTs with varying follow-up times to account for censoring there is no reason to accept inaccurate point or interval estimates for NNTs due to neglecting censoring.

According to the CONSORT statement [ 21] confidence intervals should be reported for estimated effect measures to indicate the precision of the estimates. Due to the unusual scale of NNTs their confidence intervals are difficult to describe if the effect is not significant [ 22]. This may be one reason why confidence intervals for the number needed to treat were given in one third of the investigated articles only (time-to-event and binary data). Nevertheless, the methodology to calculate confidence intervals for NNTs is described and explained in the statistical as well as in the medical literature [ 12, 22- 27], so that the unusual scale of NNTs should be no argument to disregard the CONSORT statement.

In summary, there is much room for improvement in the application of the number needed to treat to present results of randomised controlled trials, especially where the outcome is time to an event. To account for censoring survival time techniques have to be used to calculate the number needed to treat. The common standard to provide confidence intervals to indicate the uncertainty of estimated effect measures should also be applied to the number needed to treat. In general, it should be carefully considered whether the use of the number needed to treat is sensible in the specific context. If the number needed to treat is applied the use of correct calculation methods is required as well as the presentation of point and interval estimates.