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Suggestions on the use of statistical methodologies in studies of the European Group for Blood and Marrow Transplantation

Bone Marrow Transplantation volume 48, pages S1–S37 (2013)Cite this article

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Abstract

This document explains some of the relevant methodological issues involved in planning a clinical study using survival and time-to-event outcome data, particularly in the field of haematopoietic stem cell transplantation, and indicates the appropriate statistical methods to use for the analysis. As the majority of these methods are commonly used in survival and event-history analysis, this document discusses their potential and limitations with reference to common SCT research situations. Some reference is given to methods, recently appearing in the literature that may be capable of handling complex investigations. These guidelines also address various practical issues, such as recoding or transforming variables in regression models or reporting results.

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Notes

  1. Other outcome variables in longitudinal studies, such as recurrent events or repeated measurements, are not common in current SCT research. Thus, we provide only one example of analysis in a situation characterised by multiple recurrences of relapse, which will be approached in the context of multi-state models (the analysis of current leukaemia-free survival). However, other statistical approaches may be more suitable in other situations. Methods for longitudinal data and for multivariate survival outcomes are not illustrated in these Guidelines. Even less common is analysing a continuous outcome variable, such as the level of WBC. Methods for the analysis of this type of outcome (t-test, analysis of variance, multiple regression and so on) can be found in any statistics textbook. A few are mentioned in Section 3.1.

  2. EBMT internal guidelines for the conduct of studies are available for the investigators through the EBMT study offices.

  3. This terminology might create some confusion for statisticians, as the perspective is ‘prospective’, that is, longitudinal. In statistics and epidemiology, the term ‘retrospective study’ is often used with a different meaning, as for example in the case–control study.

  4. The discussion of these issues is beyond the scope of these Guidelines. EBMT adopts the ICH guidelines for the design of clinical trials.

  5. In SCT trials, the comparison between treatments is usually made as parallel groups. In other settings, popular designs include the crossover, the factorial design and others.

  6. In PCT comparing two or more treatments, randomisation, that is, the assignment of a patient to a treatment arm following a random process and independently of the patient's characteristics, is designed to (ideally) produce groups similar in terms of known and unknown risk factors. Blinding is adopted to reduce biased assessments of clinical responses.

  7. A further ‘traditional’ possibility is a case-matched study, in which each patient from group A is matched to one or more patients from group B who are identical, or nearly so, with respect to one or more potential confounders. The analysis must apply specific methods for matched pairs. This method is more difficult to apply than the others, it is less efficient (using only a part of the available information) and it has less potential than regression methods for investigating the role of all possible confounders. Matching does have a function in the propensity score method (Section 4.4).

  8. Recent literature proposes other approaches to the specific problem of removing potential confounding. In the context of the comparison of two treatment groups in a non-intention to treat non-randomised study (where, for example, propensity scores are used, Section 4.4), it is worth mentioning the use of adjusted survival curves.[42] This method uses inverse probability weights to create adjusted survival curves to artificially create comparable groups in terms of all factors that could have influenced the choice of treatment.

  9. A different yet frequent goal of many studies is proposing a new risk score, or building a ‘good’ prognostic model for outcome prediction in general. Although this problem can also be approached using the methods described in this document (regression models), a proper investigation requires specific validation techniques whose illustration would be beyond the scope of these Guidelines. Throughout the document, we will identify issues such as this and suggest texts[28] that can be consulted that illustrate methods for assessing the predictive value of the model.

  10. As indicated, the refinements of the study population (and of the statistical analysis plan) apply only (or especially) to RBS.

  11. In a two-sided test, H1 states that there is a difference of whatever sign, positive or negative. A one-sided test fixes the sign of the expected difference.

  12. Another important parameter whose meaning is worth recalling is the power (1−beta), which is the probability that the decision rule leads to ‘proving’ the presence of a difference that is actually present in the target population. Of course, this parameter should be high; it is, however, limited by the requirement of having a small alpha. The power is a key parameter in determining the sample size of a study.

  13. What is described in this section is actually right-censoring, observations that are incomplete in the sense that, if we indicate with T the time to the event of interest, and with C the time to loss to follow-up, we have T>C. Situations with left- or interval-censoring are less common in practice, and the methods for addressing them become more complicated. Refer to Kalbfleisch and Prentice[43] (Section 3.2) for the theory on different patterns of censoring.

  14. To be precise, this assumption can be slightly relaxed (see Kalbfleisch and Prentice[43]), but the substantial, interpretative meaning is the one reported here.

  15. In this context, NRM is more appropriate than TRM, which stands for transplant-related mortality or, in non-transplant settings, treatment-related mortality, because TRM suggests classifying the cause of death as either transplant-related or not, while here we specifically mean ‘death without ever experiencing a prior relapse’. See also the remarks below in the ‘common mistakes’ subsection.

  16. In fact, by NRM we mean mortality without prior relapse, and not mortality due to causes other than relapse.

  17. Although it is customary to report these events in terms of simple percentages of occurrence and to neglect the competing events, this is often the wrong approach. Appropriate approaches are discussed in Section 2.2.3.

  18. There is a semantic problem also for the event competing with relapse/progression: usually the acronym NRM is used, but more precisely we should use something like NRPM. In any case, it is important to specify (in presentations and in Statistical Methods sections) that we mean death without prior progression or relapse.

  19. This is true unless the time between transplant and CR is included among the covariates.

  20. This approach is also sometimes termed clock-forward, especially in the framework of multi-state models[5].

  21. In practice, not all statistical software programs allow the researcher to apply left-truncation. With this approach, the survival data need to be arranged in the counting process form, that is, they must be represented as a triplet (entry time, final time and failure indicator).

  22. The time threshold x should be chosen so that the most relevant part of the information is acquired by time x.

  23. Recent statistical methods approach the estimation of the marginal survival function. Such efforts can be found in the work of Fine and others,[44] who introduced the term ‘semi-competing risks’ for settings where the role of two events is asymmetric, as it is here where death prevents relapse (‘truly competing’ events), but the converse is not true.

  24. In statistics and epidemiology, ‘rate’ refers to a quantity that is not interpretable as a probability. However, in these Guidelines we follow the traditional practice of the medical literature and use this term to in fact mean ‘probability’.

  25. An interesting example of grouped survival data is when it is not known precisely when the event occurred, but only that it occurred during a certain period, such as between two different scheduled follow-up times. Useful remarks can be found in the books by Kalbfleish and Prentice[43] and Marubini and Valsecchi.[2]

  26. Standard deviations are usually computed applying the Greenwood formula. Note that the confidence intervals are obtained by neglecting the dependence between survival estimates at different times. For this reason, the band that connects the limits of the confidence intervals is not a proper confidence band for the whole curve. The R library km.ci implements several methods for computing pointwise confidence intervals as well as a ‘simultaneous’ confidence band.

  27. In probabilistic terms, this translates into the remark that C1(t) is not a cumulative distribution function; see, for example, Kalbfleisch and Prentice,[43] Chapter 8, and Marubini and Valsecchi,[2] Chapter 10.

  28. The Gray test and the Fine and Gray regression model work best under the assumption of the proportionality of a mathematical quantity called the ‘sub-distribution hazard’, which unfortunately has no clinical meaning. This makes it difficult to determine when this hypothesis of proportionality may not occur; see for example Scheike and Zhang.[45]

  29. An analysis of both CSH is efficaciously combined in a multi-state framework.

  30. The ‘traditional’ separation of GVHD into acute and chronic based on a time threshold (100 days) is currently being replaced on a clinical basis, and as soon as data collection rises above this rigid definition, the statistical analysis will necessarily switch entirely to the competing risks setting. To date, acute GVHD was most often analysed as described in this section, while chronic GVHD as a competing risks endpoint was left-truncated (Section 2.1.4) at 100 days, thus restricting to survivors at 100 days.

  31. The timing of engraftment, for example, would be described as the median among the cases who had engraftment.

  32. For an event without competing risks the methods proposed in Klein et al.[13] and Logan et al.[14] may be used to compare the overall rates of events at time x even with censored cases.

  33. Indicate with E1 the event of interest and with E2 the competing event. The corresponding probabilities of occurrence are π1 and π2; 1−π1−π2 represents the probability of being alive and failure-free (no event) at the time of assessment. Correspondingly, define:

    To compare two exposure groups, A and B, it is possible to implement regression models, where the effect of A vs B is estimated in terms of the ratios:

  34. It was already remarked that censoring observations when the patients go off-protocol is erroneous (Section 2.1.1), and it is suggested in this case to define combined endpoints to account for interruptions or violations of the prescribed treatment, considering them as types of failure (Section 2.1.3).

  35. We refer here to explanatory variables. Cases with a missing value for the main endpoints are usually excluded from the study, although the investigators should always be concerned with generalisation and bias (Section 2.3) and undertake the necessary investigations. A few missing values in secondary outcomes may be tolerated, but the reduction of the sample for that particular analysis must be documented in the publication, together with some discussion on whether the restricted population is still representative of the whole sample and whether there is any possible relationship between missing data and the value of the endpoint. The reasons are explained in the text.

  36. In clinical trials, the presence of missing values for relevant variables is particularly problematic (for issues related to the ITT principle, see Section 2.3). The strategy used to manage missing values should always be indicated in the protocol of any type of prospective study. Avoiding missing values as much as possible should be planned for during any data collection or prospective study. Usually, it is necessary to restrict data collection to the main items needed, implement a good method of data entry, perform monitoring to avoid errors and so on.

  37. This holds for X categorical covariates; if X is continuous, the best approach is to categorise it (in some texts, it is suggested instead to replace the missing value with a fixed value such as the mean or median of the known values of X, and add a dummy variable to indicate missing data (1 if missing, 0 if known) in the models (dummy variables are illustrated in Section 4.2.3).

  38. The overall significance is tested using the Likelihood Ratio test. The Score test and the Wald test are based on approximations and generally lead to the same conclusions (if not, refer to the Likelihood Ratio test).

  39. AIC=−2·Log-likelihood+kp, where p is the number of (relevant) parameters in the model, and k is a constant, usually 2. This quantity decreases as p begins to increase, up to the point where unnecessary variables are included. For its application in the framework of the Cox regression, see for example Klein and Moeschberger,17, par. 8.7.

  40. The ‘forward’ approach adds the variables one after another, choosing the most significant at each step, until no variable adds significant information. The ‘backward’ procedure starts with all variables and removes the least significant variable at each step, until the loss of information becomes significant (between these two, the latter approach is preferred, unless the initial set is very large). Some software programs also implement combinations of forward and backward methods, or other methods (for example, ‘best subset’).

  41. Interactions among more than two variables (typically three) can in principle be considered, but they hardly correspond to real biological phenomena. They are in any case very difficult to interpret, and thus are rarely seen.

  42. To assess the presence of an interaction term X1*X2, the model must be ‘hierarchical’, that is, it must include both main effects X1 and X2.

  43. Because it is a model of a hazard function, it can also be used to model the cause-specific hazard of an event with competing risks (Section 2.2.2).

  44. In R this manipulation is necessary. Some libraries provide functions to do it, for example mstate or Epi. Continuous X(t) can be computed using the command survSplit from the in-built survival library.

  45. Frailty models are extensions of the Cox regression to include random effects, represent unobserved heterogeneity or create dependence among observations from the same cluster, such as multiple endpoints for the same patient, or more simply observations from patients grouped according to the centre (to account for the centre effect). The latter situation can also be addressed with a ‘marginal’ approach that corrects the variance and covariance matrix (in R, see the options ‘frailty’ and ‘cluster’ within the coxph procedure, respectively).

  46. This is also the context where adjusted survival curves[42] can be used, see note 8.

  47. This idea is theoretically supported by work initiated by Rosenbaum and Rubin,[46] which shows that: (1) given the PS, the distribution of the covariates is the same in treated and not-treated groups, (2) under a condition called ‘strong ignorability’ (which corresponds to the assumption that there is no unmeasured confounder and that given the covariates there is no certainty regarding which treatment the patient will receive) and given a fixed PS, the difference of outcomes in treated and not-treated groups yields an unbiased estimate of the treatment effect.

  48. For example, the standardised difference of two averages is: , where sj2 for j=0, 1 is the variance in group j.

  49. The website provides the R software, general manuals, and other useful material or links. Additional programs for specific methods are available from local websites (R Cran). The programs (all documented with help files and a manual in pdf format) can be easily and quickly installed online or downloaded as archive files and then installed.

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Acknowledgements

L. de Wreede contributed to the final version. All members of the EBMT Statistical Committee reviewed the Guidelines and agreed with the final version. SI has received grant support through her research position at the Tor Vergata University of Rome.

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  1. European Group for Blood and Marrow Transplantation & Università di Roma Tor Vergata, Italy

    Simona Iacobelli

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Statistical Committee: Myriam Labopin (Chair), Ariane Boumendil, Ronald Brand, Ulrike Poetschger, Antonella Santucci, Stefan Suciu, Richard Szydlo, Liesbeth de Wreede.

Sponsorship Statement: This supplement is sponsored by the European Group for Blood and Marrow Transplantation (EBMT).

Appendix

Appendix

Procedures/commands in R, SAS and SPSS

For the purpose of helping new users perform their analyses, we provide here a list of procedures and instructions for the methods indicated in the previous chapters that are available in the statistical software packages R, SAS and SPSS. These three software programs are very commonly used in clinical analysis, but other reliable programs may provide good tools for survival and event-history analysis, for example STATA.

R is a reliable software package that is distributed freely on the web (http://www.r-project.org).Footnote 49 Although it may appear difficult to use, we encourage investing some time and patience in learning how to use it, especially if the user is willing to apply more than the usual standard methods of survival analysis. Consider also that the majority of basic statistical procedures can be applied through a menu-based interface (R Commander, for which you will need to install the library Rcmdr), and that there is abundant material available to facilitate the use of this program.,

Table 7 Procedures in R, SAS and SPSS for the description of categorical and continuous variables
Full size table
Table 8 Proceduresin R, SAS and SPSS for the description of the occurrence of events
Full size table

This list is not an exhaustive companion for statistical analysis; it is only intended to help new users quickly find material to start their search in the Help pages of the software.

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Iacobelli, S., On behalf of the EBMT Statistical Committee. Suggestions on the use of statistical methodologies in studies of the European Group for Blood and Marrow Transplantation. Bone Marrow Transplant 48 (Suppl 1), S1–S37 (2013). https://doi.org/10.1038/bmt.2012.282

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