Leitthema Z Rheumatol 2015 · 74:113–118 DOI 10.1007/s00393-014-1451-7 Published online: 24. März 2015 © Springer-Verlag Berlin Heidelberg 2015

Redaktion

A. Zink, Berlin J. Sieper, Berlin

Although easier to perform than randomized clinical trials and very common in rheumatology, ­observational studies are associated with numerous pitfalls relating to bias and confounding. In the current article, I use examples from my own experience to make readers aware of the vital interaction between appropriate expert statistical treatment of observational study data and the considered evaluation and interpretation of these data by the epidemiologically experienced clinician. Observational studies are clinical studies that follow—for a certain period of time— the fate of a group of patients having certain selection criteria in common. This provisional definition unveils at least two important aspects of observational studies: F selection (of patients) and F duration (of follow-up). Selection criteria may be strict and exclusive, or broad and inclusive; with implications for the homogeneity of the study population and the likelihood of selection bias. Follow-up in observational studies may imply regular interval visits to measure outcomes of interest (e.g., a Disease Activity Score, DAS, assessment every 3 months), or may be undetermined and without preplanned visits, waiting for one unequivocal outcome (e.g., myocardial infarction, death). Observational studies (or registries) are generally considered inappropriate for answering questions regarding drug (treatment) efficacy. Such

R.B.M. Landewé1, 2 1 Amsterdam Rheumatology Center (ARC), Amsterdam 2 Atrium Medical Center, Heerlen, The Netherlands

New analysis tools for observational studies questions are considered to belong to the domain of randomized controlled trials (RCTs). While I am in principle sympathetic to this opinion, it should be clear that observational studies may allow the analysis of particular aspects of “effectiveness”, either directly or indirectly. Vice versa, the importance of an RCT is often largely overstated: RCTs may have many flaws too and randomization alone does not automatically lead to “level 1 evidence”. In addition, observational studies could very well serve to investigate particular relationships between variables, irrespective of—or adjusted for—treatment. An important and trendy subtype of observational studies in rheumatology nowadays is the registry. A registry includes patients that start a new (biological) treatment. These patients are then followed-up indefinitely, but always with regular (e.g., annual) investigations and assessments. The viability of registers in modern rheumatology has been boosted by the competition inherent to market access of many new drugs with rather uncertain toxicity profiles at the time of market approval. This is combined with a healthy dose of regulatory pressure, forcing manufacturers to accept their responsibilities and fund these registries. Beyond reasonable doubt, the best-organized registries have greatly contributed to our understanding of the (long-term) toxicity of modern treatments, which is commendable. Unfortunately, smaller local registries—designed and performed with less methodological rigor, less funding and less robust conclusions—have occasionally raised confusion due to con-

tradictory results and too much emphasis on efficacy rather than toxicity. Fortunately, methodological initiatives focusing on how to run registries, how to deal with databases, and how to analyze data appropriately have, in parallel, led to very valuable additions to guidelines such as STROBE (“STrengthening the Reporting of OBservational studies in Epidemiology”) and will further homogenize registries all over the world. This article considers the analysis of an observational study as the starting point. Such a starting point suggests that the analysis is the crucial factor in the entire project; however, this is not true. The STROBE guidelines spell out which factors are of critical importance for researchers planning and conducting an observational study. Issues such as a relevant and feasible study question, appropriate patient selection for the particular study question, completeness of followup, and strategies for handling missing data are likely of greater importance than the choice of appropriate analysis, but will not be discussed in detail here. In this article I offer my umbrella view on how to address certain analytical questions in an observational study. I will not discuss specific models in detail (they are only “tools”), but rather provide some insights into key considerations that allow the investigator to “frame” the analysis. In order to clarify certain issues, I will use examples from my own experience where possible.

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The general analytical approach in observational research Study questions requiring a longitudinal approach Ideally, a research question should frame the design of a study. Biologics registries are good examples of this. Realistically, a research question often follows a particular study design: many researchers start to collect data without a pertinent question or with only a vague idea about the aim of their study, the optimal duration, sample size etc. Very often, though, interesting and valid observations are made using data from convenient (and available) databases, rather than as a logical consequence of a preplanned research question. A few years ago, we became interested in the longitudinal relationship between disease activity and syndesmophyte formation in ankylosing spondylitis (AS). At that point in time, this relationship was still uncertain, although critically relevant to the clinical community because it was thought that biologics could prevent syndesmophyte formation and “bamboo spine”. A question like this calls for a prospective cohort study, with AS patients selected at some point in time and subsequently followed-up for many, many years (because radiographic progression is an extremely slow process). Conducting such a study solely on the basis of this question was considered unfeasible and we thus decided to make use of the existing OASIS (“Outcome in Ankylosing Spondylitis International Study”) cohort for this purpose. This cohort was started in 1996, in order to validate the core set of outcome measures in AS. Subsequent extensions of data collection have finally resulted in a study in which patients were followed for up to 12 years with biannual assessments, so repeated measures were available for almost all patients. This is an important prerequisite for addressing a longitudinal study question, because it allows an interval approach. In fact, this setup has enabled us to investigate the relationship between disease activity at the start of the interval and radiographic progression during that interval; whereby we could repeat this up

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to six times in every “complete” patient (six intervals of 2 years). It is easy to understand that such an analysis provides a lot of “analytical power”, although the researcher has to take certain precautions. He should, for example, realize that repeated measures within a patient can no longer be considered as independent observations and apply appropriate intrapatient adjustments. Nowadays, there are many statistical models that can easily accomplish this. We could, however, have taken a different, much easier approach, i.e., the conventional prediction model. Such a conventional model determines the association between one value of disease activity per patient (e.g., measured at baseline or, alternatively, as mean disease activity over 12 years) and one value of radiographic progression (between baseline and 12 years of follow-up). In fact, such classic analyses are very often pursued in medicine and rheumatology, and are erroneously called “longitudinal analysis”. I have deemed such approaches “pseudolongitudinal”, because the data are not truly longitudinal but “cross-sectionalized”. Such an approach is valid, but at the cost of a tremendous loss of valuable longitudinal information. As expected, a pseudolongitudinal approach often falls short because of a “lack of statistical power” (regression coefficients do suggest some correlation, but with confidence intervals that are far too wide), leaving investigators and readers with residual uncertainty. I am certainly not claiming that conventional prediction models should not be used anymore. The choice of the analytical strategy is entirely dependent on the research question of interest. If one is interested in which factors independently predict 12-year outcome, for example in order to build a prediction algorithm for clinical usage, then conventional prediction models (based on linear or logistic regression analysis) that have the insurmountable advantage of “common understanding” are preferred. In summary, assuming that it is unfeasible to perform a new long-term observational study to address every new study question, most researchers will have to tailor-fit their study question to an available

database. There are, however, a number of no-goes: performing longitudinal analyses in databases without at least three repeated measurements are meaningless. Furthermore, prediction analysis should not be confused with longitudinal analysis and should not be called as such, even though the character of the study implies follow-up of patients.

Study questions with a censored outcome When the research question points to the occurrence of an “event” (e.g., mortality, drug discontinuation, myocardial infarction, malignancy), the variable of interest becomes the “time-to-event”. This parameter aggregates the occurrence (yes or no) of an event as well as the time elapsed between inclusion and the said event. Many researchers are familiar with survival analysis and proportional hazard regression analysis (Cox). These models build on the epidemiological principle that participants in the cohort are “at risk” for some event that may occur sooner or later (e.g., death) or maybe never (e.g., adverse drug event). Since the participants in the cohort cannot be followed infinitely (participants “at risk” but still without the event have to be censored at some point in time) and the start of the “at risk” period can often not be synchronized for all participants, the time elapsed between the start of the “at risk” period and the event (or the data of censoring) is crucial. Databases not providing exact information about the time-to-event (e.g., start and stop dates) are useless for this type of analysis. Extensions of classic survival analyses, such as Cox regression with time-changing covariates, are far less well known: let’s assume we would like to investigate whether disease activity is a determinant of mortality in the OASIS cohort. Obviously, disease activity changes over a period of 12 years and the allowance of changing levels of disease activity over time may give better justice to the model than (timefixed) disease activity at baseline alone.

Abstract · Zusammenfassung

Subgroup analysis in observational research Fixed factors With the exception of those that are solely interested in longitudinal relationships (e.g., “does the rate of radiographic progression in a patient increase if disease activity increases?”), by far the most researchers analyzing observational databases have questions that refer to relevant subgroups of patients. The most classic example is gender diversity: most investigators want to know if the outcome of interest is different in females than in males. Obviously, this gender variable can be assessed at baseline and is constant; in statistical terms we speak of fixed factors. By far the most frequent application is the classic prediction model: a logistic regression analysis with a dichotomous outcome and a set of fixed baseline factors (including gender), which allows independent determination of the contribution of each factor to the occurrence of the outcome. It is important to realize that in a longitudinal model describing the course of repeated measures over time, the determination of the effect in subgroups requires a model with an interaction term, as well as an appropriate statistical test for the significance of the interaction. In OASIS, we have recently described the 12-year course of radiographic damage over time in patients with AS, making use of all available spinal radiographs (close to 1000 time points) obtained in 185 patients. Assuming a linear course of Modified Stoke Ankylosing Spondylitis Spinal Score (mSASSS) over time, the regression equation can be written as follows:

in which (t) is time at follow-up and mSASSS (bl) is the mSASSS at baseline. The parameter estimate (regression coefficient) a1 was determined using generalized estimating equations, a technique that appropriately accounts for the effect of statistical dependence of repeated measurements within the same patient and reflects the rate of progression (here 1.0 mSASSS unit per year).

Z Rheumatol 2015 · 74:113–118  DOI 10.1007/s00393-014-1451-7 © Springer-Verlag Berlin Heidelberg 2015 R.B.M. Landewé

New analysis tools for observational studies Abstract Observational studies, which are very common in rheumatology, usually follow a selected group of patients for a predetermined period of time, or infinitely, with regard to a certain outcome. Such an outcome could be a “score” reflecting an important aspect of the disease (e.g., a disease activity score), or an “event” (e.g., myocardial infarction). Rather than investigating the efficacy of a particular treatment, observational studies serve to investigate clinical associations between different (outcome) variables. Confounding, which may spuriously inflate or reduce the magnitude of a particular association, is an inherent risk in observational studies. The modern analytical approach of an observational study depends on the study question, the study de-

sign, and on how the outcome of interest has been assessed. The current article discusses several aspects of the analytical approach and requirements of the database. The focus is on longitudinal analysis, subgroup analysis, and adjustment for confounding. It is concluded that the appropriate analysis of an observational study should be a close collaboration between the clinical researcher with sufficient epidemiological knowledge and the expert statistician with sufficient interest in clinical questions. Keywords Bias · Confounding · Longitudinal analysis · Outcome variable · Subgroup analysis

Neue Analyseinstrumente für Beobachtungsstudien Zusammenfassung Beobachtungsstudien sind sehr häufig in der Rheumatologie und dokumentieren gewöhnlich den Verlauf einer ausgewählten Patientengruppe über eine vorher fest­gelegte Zeitdauer oder unbegrenzt im Hinblick auf ein bestimmtes Ergebnis. Ein sol­ches ­Ergebnis könnte ein „Score“ sein, der einen bedeutenden Aspekt der Erkrankung widerspiegelt (z. B. ein Krankheitsaktivitäts­score), oder ein „Ereignis“ (z. B. ein Herz­infarkt). Beobachtungsstudien dienen eher der Untersu­chung klinischer Zusammenhänge ­zwischen verschiedenen (Ergebnis-)Variablen als der Untersuchung der Wirksamkeit ­einer speziellen Behandlung. Konfundierung ist ein ­inhärentes Risiko bei ­Beobachtungsstudien, das fälschlicherweise die Größenordnung eines speziellen Zusammenhangs vergrößern oder verkleinern kann. Der moderne analytische Ansatz einer Beobachtungsstudie ist

While it is informative to know about the course of progression (linear, quadratic, exponential, etc.) and its rate, we were, obviously, more interested in whether this progression was different in males than in females, and in fact it was: we pursued the following regression equation with a so called interaction term including gender:

abhängig von der Fragestellung der ­Studie sowie vom Studiendesign und davon, wie das interessierende Ergebnis ermittelt worden ist. Im vorliegenden Beitrag werden verschiedene Aspekte des analytischen ­Ansatzes und Erfordernisse der Datenbank ­diskutiert. Der Schwerpunkt liegt auf Längsschnittanalyse, Subgruppenanalyse und Adjustie­ rung in Hinblick auf Konfundierung. ­Fazit ist, dass für eine angemessene Auswertung ­einer Beobachtungsstudie eine enge Zusammenarbeit zwischen dem ­klinischen Wissen­schaftler mit ausreichenden epidemiologischen Kenntnissen und dem Statistikexperten mit ausreichendem Interesse an klinischen Fragestellungen erfolgen sollte. Schlüsselwörter Bias · Konfundierung · Längsschnittanalyse · Ergebnisvariable · Subgruppenanalyse

in which b1, b2 and b3 are parameter estimates (regression coefficients). The main (and only) interest here is in the parameter estimate b3 of the interaction term (t*gender). If it can be proven beyond statistical uncertainty that this estimate is not zero (i.e., that the interaction term is relevant), this implies that the course of mSASSS over time is significantly different in males than in females and progression should be analyzed in these prognostically relevant subgroups. Zeitschrift für Rheumatologie 2 · 2015 

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Leitthema In our analyses, it turned out that the parameter estimate b3 was statistically significantly different from zero. Substituting male =1 and female =0 into equation 2 yields:

and

A closer look at these equations teaches us that with increasing t and positive values for b2 and b3, mSASSS will increase in males and in females—but at different rates and dependent on the sign of b2 and b3. Interaction analysis, which is often of secondary importance in classic linear or logistic analysis, is pivotal in longitudinal analysis, in order to disentangle courses over time in relevant subgroups.

Confounding by indication in observational research Observational studies in patients with chronic diseases, such as in rheumatology, usually pertain to patients that receive some kind of treatment. Firstly, patients may receive treatment at the time they are selected for entering the observational study. Secondly, patients may receive treatment during the observational study or may change treatment during the course of the study. Very often, some outcome related to treatment is the subject of research. A good example is the analysis of the occurrence of a particular adverse event (event A) following the start of a particular treatment (treatment B) in comparison to another treatment (treatment C). Unlike the situation in an RCT, where treatments B and C (at baseline and during the RCT) are determined by randomization and protocol, patients with treatment B or C in an observational study have not usually received these treatments based on a certain protocol. In fact, patients followed in an observational study receive their treatment from the treating physician, which implies that the choice

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of (the intensity of) that treatment is determined on the basis of a consensus between patient and physician, and not (solely) by protocol rules. The aforementioned fact has important consequences; particularly in diseases such as rheumatoid arthritis (RA) for which multiple treatment options are available, all with different characteristics, expectations, intensities, toxicity profiles etc. For example, the patient and physician may base the selection of treatment B (which may be considered a more intensive treatment, but with a higher likelihood of toxicity) on different aspects of the patient: the patient may have more active disease and worse prognostic factors present, but at the same time may also be willing to accept the worse toxicity. Another patient could decide to choose treatment C, perhaps because this patient is older and less willing to accept toxicity, while perceiving disease activity to be only moderate. Such situations are very common in observational studies and may become an epidemiological problem if the following sequence is present (read the arrows below as “may lead to”): 1. treatment (B vs. C) -> event A (yes vs. no) 2. disease activity (high vs. low) -> event A (yes vs. no) 3. disease activity (high vs. low) -> ­treatment (B vs. C) In this situation, confounding by indication is possible: it is not only the treatment (B or C) that determines the occurrence of event A (1), but also the disease activity (high vs. low; 2), because disease activity independently determines the choice of the treatment (3). It is important to realize that confounding by indication may be present at baseline, but may also occur during follow-up of the patients, as patients with more severe disease may change from treatment C (on which they entered the study) to treatment B during follow-up. During the last decade, tremendous progress has been made with adjusting for this type of confounding.

Baseline adjustment for confounding by indication Basically, this type of adjustment is rather simple, because it involves classic multivariate regression analysis—in which event A is the dependent variable, treatment (B vs. C) at baseline the independent factor, and disease activity the covariate. However, over the years we have realized that the ultimate choice of treatment B or treatment C is actually determined not only by disease activity, but by a far more complex process involving many variables including disease activity. These variables are definitely not always known, measured, or measurable; but in theory they determine the likelihood (or the propensity) that a certain patient characterized by a certain combination of these variables will indeed be treated with treatment B rather than treatment C. In an observational study with a sufficient number of measured variables, it is often possible to approximate this likelihood by creating a propensity score per patient. Obtaining a propensity score is simple and can be achieved by performing classic logistic regression analysis on the choice of treatment (B vs. C), using all available variables that could have determined that choice, and asking the software to calculate an estimated likelihood (a figure between zero and one) per patient. In addition, the association that has been found for the relationship of primary interest, i.e., 1. treatment (B vs. C) -> event A could be adjusted by the propensity score in order to find out if the primary relationship is maintained, disappears, or changes in magnitude. The theory underlying propensity scores has a few important requirements that are sometimes ignored. The first requirement, which makes intuitive sense, is that the distribution of propensity scores in the database is sufficiently wide, including patients with a propensity close to zero and patients with a propensity close to one, as well as everything in between. In light of the principle of confounding, the second requirement also makes

sense, but is quite often neglected: increased propensity should be reflected by increased likelihood of the event of interest (here event A), a prerequisite for confounding to be present. A propensity score that is not associated with the outcome of interest cannot be expected to adjust for confounding by indication. Usually, this check is performed by subdividing the cohort of patients into quintiles by their propensity score and then calculating the incidence of event A per quintile. Ideally there is a “dose-response”: the higher the propensity score, the higher the incidence of event A. The third requirement is more paradoxical and open to argumentation: the variation in propensity scores (the propensity score distribution) should only partially explain the choice of treatment (B vs. C). In statistical terms: the R-square of the logistic model with which the propensity score is determined should not be too close to one. In fact, an R-square of 0.5 is probably most informative, because this means that there is significant misclassification: patients with a high likelihood of being treated with treatment B are nevertheless treated with treatment C! At first glance, this principle is difficult to comprehend, until one realizes what the “optimal propensity score” (with R-square of one) actually implies: such a score is “so good a prediction of the truth” that the prediction becomes the truth, and adjustment of the relationship 1. treatment (B vs. C) -> event A by the propensity of treatment (B vs. C) yields a meaningless solution. In fact, this problem is analogous to the problem of collinearity in ordinary regression analysis. Intuitively, it means that we may be able to exactly predict the use of treatment (B vs. C), but that we need many variables, which themselves are not very meaningful in the context of the outcome of interest (event A). In such circumstances (a perfect fit of the propensity model), the association between propensity score and event A (our second requirement) could be poor or even absent. Propensity modelling is not an exact science. The propensity score is an approximation of the truth and serves to

“challenge” the relationship of interest (here the association between treatment, i.e., B vs. C and event A). If that association does not change at all after adjustment, in a situation where the propensity score fulfils the abovementioned requirements, one may state that confounding of indication is an unlikely explanation of the observed association, which gives more credit to the finding per se. If the strength of that association is significantly reduced, one may state that confounding by indication has certainly contributed to the observed result; although to what extent is impossible to determine. As such, I tend to see propensity score adjustment as a kind of sensitivity analysis, not necessarily as a primary analysis. In my opinion, the appropriate use of propensity adjustment in an observational study adds to the credibility of the authors—in that they have realized the shortcomings of observational studies and the inherent problem of confounding by indication—rather than to the credibility of the reported result.

Longitudinal adjustment for confounding by indication Once a researcher is aware of the problem of confounding by indication, it is a relatively small step to extend the theory to longitudinal interpretations of observational studies. Often, this makes most sense if the outcome of interest is a variable that is collected longitudinally. This means that the presence of a particular event A (e.g., clinical remission) is measured repeatedly in the same patient. Indeed, the propensity to commence or— better—to continue a particular treatment may change over time during the period of observation, when the (perceived) severity of the disease changes. The latter may occur under the influence of therapy, changing insights, perceived toxicity, and so forth. In general, there are roughly two means of making adjustments for changing propensities over time: (1) introducing treatment (e.g., type of treatment or dose of a particular treatment) as a longitudinal variable; and (2) introducing propensity score as a longitudinal variable. Both techniques require the availability

of detailed information about treatment and variables determining treatment over time. The techniques themselves are not particularly complicated if one is used to proportional hazard regression analysis (in case of one censored event) with timechanging covariates or longitudinal data analysis, and the database is optimally prepared; however, the interpretation is somewhat more cumbersome. In fact, longitudinal analysis results, either with treatment over time as a longitudinal variable or propensity score over time, are best interpreted as a sensitivity analysis to test the robustness of the primary association of interest: if the primary analysis suggests an association between treatment (B vs. C) and event A, the sensitivity analysis serves to challenge this association and find out whether the association of interest persists independently of the confounding cointerventions.

Concluding remarks Observational studies are relatively easy to conduct compared to RCTs. However, analyzing them is more tricky, because numerous pitfalls related to epidemiological bias and confounding may show up to jeopardize the interpretation of the study results. To some extent, these pitfalls can be accounted for; at the very least, current analytical techniques allow these pitfalls to be made more visible, such that the research article reader may better understand the limitations of observational research. Obviously, clinical investigators not only need the skills to perform these rather sophisticated techniques, but they also need to be able to interpret them in the appropriate context. While statisticians may be of tremendous practical assistance, and may design and run the models, in my opinion it should be the investigator that is responsible for the correct interpretations and the appropriate wording. That implies a close collaboration between the consulting expert statistician and the wellinformed clinical researcher, who should not blindly trust the opinion of the statistician, but rather be a sparring partner!

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Fachnachrichten

Compliance with ethical guidelines Conflict of interest. R.B.M. Landewé states that there are no conflicts of interest. The accompanying manuscript does not include studies on humans or animals.

Corresponding address R.B.M. Landewé Professor of rheumatology Department of Rheumatology and Clinical Immunology (KIR) Amsterdam Rheumatology Center (ARC) Meibergdreef 9, 1100 DD Amsterdam The Netherlands [email protected]

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New analysis tools for observational studies.

Observational studies, which are very common in rheumatology, usually follow a selected group of patients for a predetermined period of time, or infin...
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