Lu, Z. Lu, R. Lu, M. Bagheri, R.. Yan, X. Wang, L. Lu, Ling Zhang, A. Harrison, M. Bagheri, R. Medical Imaging: Computer-Aided Diagnosis R19, Chi-Tung Cheng, et al. Kim, E. Turkbey, B. Sahiner, N. Cheng, H. Roth, N. Lay, Le Lu, B. Turkbey, W. Gander, E. McCreedy, P. Choyke, R.
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In this analysis, they demonstrated that the methods used in the analysis of cluster randomized trials could give varying results, with standard logistic regression ignoring clustering being the least conservative. Cheng et al. The results were robust to various statistical models, but showed more variability in the presence of a larger cluster effect higher within-patient correlation.
A trial evaluated the effects of lansoprazole on gastro-esophageal reflux disease in children from 19 clinics with asthma. The primary analysis was based on GEE to determine the effect of lansoprazole in reducing asthma symptoms. Subsequently they performed a sensitivity analysis by including the study site as a covariate. Their finding that lansoprazole did not significantly improve symptoms was robust to this sensitivity analysis [ 50 ].
In addition to comparing the performance of different methods to estimate treatment effects on a continuous outcome in simulated multicenter randomized controlled trials [ 12 ], the authors used data from the Computerization of Medical Practices for the Enhancement of Therapeutic Effectiveness COMPETE II [ 51 ] to assess the robustness of the primary results based on GEE to adjust for clustering by provider of care under different methods of adjusting for clustering.
The results, which showed that a shared electronic decision support system improved care and outcomes in diabetic patients, were robust under different methods of analysis.
A competing risk event happens in situations where multiple events are likely to occur in a way that the occurrence of one event may prevent other events from being observed [ 48 ]. For example, in a trial using a composite of death, myocardial infarction or stroke, if someone dies, they cannot experience a subsequent event, or stroke or myocardial infarction—death can be a competing risk event.
Similarly, death can be a competing risk in trials of patients with malignant diseases where thrombotic events are important. Therefore, the best approach to assessing the influence of a competing risk would be to plan for sensitivity analysis that adjusts for the competing risk event.
A previously-reported trial compared low molecular weight heparin LMWH with oral anticoagulant therapy for the prevention of recurrent venous thromboembolism VTE in patients with advanced cancer, and a subsequent study presented sensitivity analyses comparing the results from standard survival analysis Kaplan-Meier method with those from competing risk methods—namely, the cumulative incidence function CIF and Gray's test [ 52 ].
The results using both methods were similar. For patients at increased risk of end stage renal disease ESRD but also of premature death not related to ESRD, such as patients with diabetes or with vascular disease, analyses considering the two events as different outcomes may be misleading if the possibility of dying before the development of ESRD is not taken into account [ 49 ].
Different studies performing sensitivity analyses demonstrated that the results on predictors of ESRD and death for any cause were dependent on whether the competing risks were taken into account or not [ 53 , 54 ], and on which competing risk method was used [ 55 ]. These studies further highlight the need for a sensitivity analysis of competing risks when they are present in trials. In RCTs, randomization is used to balance the expected distribution of the baseline or prognostic characteristics of the patients in all treatment arms.
Therefore the primary analysis is typically based on ITT approach unadjusted for baseline characteristics. However, some residual imbalance can still occur by chance. One can perform a sensitivity analysis by using a multivariable analysis to adjust for hypothesized residual baseline imbalances to assess their impact on effect estimates. A paper presented a simulation study where the risk of the outcome, effect of the treatment, power and prevalence of the prognostic factors, and sample size were all varied to evaluate their effects on the treatment estimates.
Logistic regression models were compared with and without adjustment for the prognostic factors. The study concluded that the probability of prognostic imbalance in small trials could be substantial. Also, covariate adjustment improved estimation accuracy and statistical power [ 56 ]. In a trial testing the effectiveness of enhanced communication therapy for aphasia and dysarthria after stroke, the authors conducted a sensitivity analysis to adjust for baseline imbalances.
Both primary and sensitivity analysis showed that enhanced communication therapy had no additional benefit [ 57 ]. Most statistical analyses rely on distributional assumptions for observed data e. Normal distribution for continuous outcomes, Poisson distribution for count data, or binomial distribution for binary outcome data. It is important not only to test for goodness-of-fit for these distributions, but to also plan for sensitivity analyses using other suitable distributions.
For example, for continuous data, one can redo the analysis assuming a Student-T distribution—which is symmetric, bell-shaped distribution like the Normal distribution, but with thicker tails; for count data, once can use the Negative-binomial distribution—which would be useful to assess the robustness of the results if over-dispersion is accounted for [ 52 ].
Bayesian analyses routinely include sensitivity analyses to assess the robustness of findings under different models for the data and prior distributions [ 58 ]. Analyses based on parametric methods—which often rely on strong distributional assumptions—may also need to be evaluated for robustness using non-parametric methods. The latter often make less stringent distributional assumptions.
However, it is essential to note that in general non-parametric methods are less efficient i. The similarities in the results after using the different methods confirmed the results of the primary analysis: the CHAT intervention was not superior to usual care [ 10 ].
A negative binomial regression model was used [ 52 ] to analyze discrete outcome data from a clinical trial designed to evaluate the effectiveness of a pre-habilitation program in preventing functional decline among physically frail, community-living older persons. The negative binomial model provided an improved fit to the data than the Poisson regression model.
The negative binomial model provides an alternative approach for analyzing discrete data where over-dispersion is a problem [ 59 ]. A: No. Sensitivity analysis is typically a re-analysis of either the same outcome using different approaches, or different definitions of the outcome—with the primary goal of assessing how these changes impact the conclusions. Essentially everything else including the criterion for statistical significance needs to be kept constant so that we can assess whether any impact is attributable to underlying sensitivity analyses.
A: Yes, especially if the results are different or lead to different a conclusion from the original results—whose sensitivity was being assessed. However, if the results remain robust i. A: It is desirable to document all planned analyses including sensitivity analyses in the protocol a priori. Sometimes, one cannot anticipate all the challenges that can occur during the conduct of a study that may require additional sensitivity analyses.
In that case, one needs to incorporate the anticipated sensitivity analyses in the statistical analysis plan SAP , which needs to be completed before analyzing the data. Clear rationale is needed for every sensitivity analysis. This may also occur posthoc. Q: How do I choose between the results of different sensitivity analyses?
Rather, the aim is to assess the robustness or consistency of the results under different methods, subgroups, definitions, assumptions and so on. The assessment of robustness is often based on the magnitude, direction or statistical significance of the estimates. You cannot use the sensitivity analysis to choose an alternate conclusion to your study. Rather, you can state the conclusion based on your primary analysis, and present your sensitivity analysis as an example of how confident you are that it represents the truth.
If the sensitivity analysis suggests that the primary analysis is not robust, it may point to the need for future research that might address the source of the inconsistency. Your study cannot answer the question which results are best? To answer the question of which method is best and under what conditions, simulation studies comparing the different approaches on the basis of bias, precision, coverage or efficiency may be necessary. A: The default position should be to plan for sensitivity analysis in every clinical trial.
Thus, all studies need to include some sensitivity analysis to check the robustness of the primary findings. All statistical methods used to analyze data from clinical trials rely on assumptions—which need to either be tested whenever possible, with the results assessed for robustness through some sensitivity analyses.
Similarly, missing data or protocol deviations are common occurrences in many trials and their impact on inferences needs to be assessed. A: The number is not an important factor in determining what sensitivity analyses to perform. The most important factor is the rationale for doing any sensitivity analysis.
Understanding the nature of the data, and having some content expertise are useful in determining which and how many sensitivity analyses to perform. Likewise, understanding the distribution of certain variables can help to determine which cut points would be relevant. Typically, it is advisable to limit sensitivity analyses to the primary outcome. Conducting multiple sensitivity analysis on all outcomes is often neither practical, nor necessary. A: Ideally, one can study the impact of all key elements using a factorial design—which would allow the assessment of the impact of individual and joint factors.
Alternatively, one can vary one factor at a time to be able to assess whether the factor is responsible for the resulting impact if any. For example, in a sensitivity analysis to assess the impact of the Normality assumption analysis assuming Normality e. T-test vs. Based on a sign test and outlier analysis with and without outlier , this can be achieved through 2x2 factorial design.
A: Secondary analyses are typically analyses of secondary outcomes. Like primary analyses which deal with primary outcome s , such analyses need to be documented in the protocol or SAP.
In most studies such analyses are exploratory—because most studies are not powered for secondary outcomes. They serve to provide support that the effects reported in the primary outcome are consistent with underlying biology.
They are different from sensitivity analyses as described above. A: Subgroup analyses are intended to assess whether the effect is similar across specified groups of patients or modified by certain patient characteristics [ 60 ]. If the primary results are statistically significant, subgroup analyses are intended to assess whether the observed effect is consistent across the underlying patient subgroups—which may be viewed as some form of sensitivity analysis.
Typically subgroup analyses require specification of the subgroup hypothesis and rationale, and performed through inclusion of an interaction term i. They may also require adjustment for alpha—the overall level of significance. Furthermore, most studies are not usually powered for subgroup analyses.
There has been considerable attention paid to enhancing the transparency of reporting of clinical trials. Not one of these guidelines specifically addresses how sensitivity analyses need to be reported. On the other hand, there is some guidance on how sensitivity analyses need to be reported in economic analyses [ 62 ]—which may partly explain the differential rates of reporting of sensitivity analyses shown in Table 1. We strongly encourage some modifications of all reporting guidelines to include items on sensitivity analyses—as a way to enhance their use and reporting.
The proposed reporting changes can be as follows:. In Methods Section: Report the planned or posthoc sensitivity analyses and rationale for each. In Results Section: Report whether or not the results of the sensitivity analyses or conclusions are similar to those based on primary analysis.
If similar, just state that the results or conclusions remain robust. If different, report the results of the sensitivity analyses along with the primary results.
In Discussion Section: Discuss the key limitations and implications of the results of the sensitivity analyses on the conclusions or findings. This can be done by describing what changes the sensitivity analyses bring to the interpretation of the data, and whether the sensitivity analyses are more stringent or more relaxed than the primary analysis.
Sensitivity analyses play an important role is checking the robustness of the conclusions from clinical trials. They are important in interpreting or establishing the credibility of the findings. If the results remain robust under different assumptions, methods or scenarios, this can strengthen their credibility.
The results of our brief survey of January editions of major medical and health economics journals that show that their use is very low. We recommend that some sensitivity analysis should be the default plan in statistical or economic analyses of any clinical trial. Investigators need to identify any key assumptions, variations, or methods that may impact or influence the findings, and plan to conduct some sensitivity analyses as part of their analytic strategy. The final report must include the documentation of the planned or posthoc sensitivity analyses, rationale, corresponding results and a discussion of their consequences or repercussions on the overall findings.
Schneeweiss S: Sensitivity analysis and external adjustment for unmeasured confounders in epidemiologic database studies of therapeutics. Pharmacoepidemiol Drug Saf. Article PubMed Google Scholar. Stat Med. Google Scholar. Guideline E9. We never send published papers to clients nor do we publish the papers after sending them to our clients.
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