Reporting of Bayesian analysis in epidemiologic research should become more transparent.

OBJECTIVES: The objective of this systematic review is to investigate the use of Bayesian data analysis in epidemiology in the past decade and particularly to evaluate the quality of research papers reporting the results of these analyses. STUDY DESIGN AND SETTING: Complete volumes of five major epidemiological journals in the period 2005-2015 were searched via PubMed. In addition, we performed an extensive within-manuscript search using a specialized Java application. Details of reporting on Bayesian statistics were examined in the original research papers with primary Bayesian data analyses. RESULTS: The number of studies in which Bayesian techniques were used for primary data analysis remains constant over the years. Though many authors presented thorough descriptions of the analyses they performed and the results they obtained, several reports presented incomplete method sections and even some incomplete result sections. Especially, information on the process of prior elicitation, specification, and evaluation was often lacking. CONCLUSION: Though available guidance papers concerned with reporting of Bayesian analyses emphasize the importance of transparent prior specification, the results obtained in this systematic review show that these guidance papers are often not used. Additional efforts should be made to increase the awareness of the existence and importance of these checklists to overcome the controversy with respect to the use of Bayesian techniques. The reporting quality in epidemiological literature could be improved by updating existing guidelines on the reporting of frequentist analyses to address issues that are important for Bayesian data analyses.

Cost-effectiveness Analysis for Apixaban in the Acute Treatment and Prevention of Venous Thromboembolism in the Netherlands.

PURPOSE: Low-molecular weight heparin (LMWH) followed by vitamin K antagonists (VKAs) are the current standard treatment of acute venous thromboembolism (VTE) and prevention of recurrent VTE. The direct oral anticoagulant apixaban was recently found noninferior in efficacy and superior in preventing major bleeding compared with LMWH/VKAs in the AMPLIFY (Apixaban for the Initial Management of Pulmonary Embolism and Deep-Vein Thrombosis as First-Line Therapy) trial. The objective of this study was to calculate the cost-effectiveness of apixaban compared with LMWH/VKA in the treatment of acute VTE and prevention of recurrent VTE in the Netherlands. METHODS: A Markov model was designed to simulate a cohort of 1,000 VTE patients receiving either apixaban or LMWH/VKA. Transition probabilities, costs, and utilities were obtained from the AMPLIFY trial and other literature. The incremental cost-effectiveness ratio (ICER) was calculated from the societal perspective; therefore, the model included both direct (inside and outside the health care sector) and indirect costs. In the univariate and probabilistic sensitivity analyses (PSAs) the robustness of the results was tested, and various additional scenario analyses were conducted. FINDINGS: In the base-case analysis, apixaban saved €236 and 0.044 quality-adjusted life years (QALYs) and 0.039 LYs were gained compared with LMWH/VKA. In the univariate sensitivity analysis the model appeared to be robust. The results of 2,000 iterations in the PSA found that the probability of apixaban being cost-effective at a willingness-to-pay threshold of €20,000/QALY was 100% and cost-saving was 94%. The scenario of 18-month treatment duration was the only scenario not indicating cost-savings with an ICER of €425/QALY. IMPLICATIONS: In acute anticoagulation use apixaban was found to be cost-saving. A longer anticoagulation period (18 months) resulted in a higher difference in drug costs, indicating a higher ICER. The cost-effectiveness of long-term or life-long use should be examined in future research.

Diagnostic accuracy of conventional or age adjusted D-dimer cut-off values in older patients with suspected venous thromboembolism: systematic review and meta-analysis.

OBJECTIVE: To review the diagnostic accuracy of D-dimer testing in older patients (>50 years) with suspected venous thromboembolism, using conventional or age adjusted D-dimer cut-off values. DESIGN: Systematic review and bivariate random effects meta-analysis. DATA SOURCES: We searched Medline and Embase for studies published before 21 June 2012 and we contacted the authors of primary studies. STUDY SELECTION: Primary studies that enrolled older patients with suspected venous thromboembolism in whom D-dimer testing, using both conventional (500 µg/L) and age adjusted (age × 10 µg/L) cut-off values, and reference testing were performed. For patients with a non-high clinical probability, 2 × 2 tables were reconstructed and stratified by age category and applied D-dimer cut-off level. RESULTS: 13 cohorts including 12,497 patients with a non-high clinical probability were included in the meta-analysis. The specificity of the conventional cut-off value decreased with increasing age, from 57.6% (95% confidence interval 51.4% to 63.6%) in patients aged 51-60 years to 39.4% (33.5% to 45.6%) in those aged 61-70, 24.5% (20.0% to 29.7% in those aged 71-80, and 14.7% (11.3% to 18.6%) in those aged >80. Age adjusted cut-off values revealed higher specificities over all age categories: 62.3% (56.2% to 68.0%), 49.5% (43.2% to 55.8%), 44.2% (38.0% to 50.5%), and 35.2% (29.4% to 41.5%), respectively. Sensitivities of the age adjusted cut-off remained above 97% in all age categories. CONCLUSIONS: The application of age adjusted cut-off values for D-dimer tests substantially increases specificity without modifying sensitivity, thereby improving the clinical utility of D-dimer testing in patients aged 50 or more with a non-high clinical probability.

Accuracy of symptoms, signs, and C-reactive protein for early chronic obstructive pulmonary disease.

BACKGROUND: Guidelines recommend detection of early chronic obstructive pulmonary disease (COPD), but evidence on the diagnostic work-up for COPD only concerns advanced and established COPD. AIM: To quantify the accuracy of symptoms and signs for early COPD, and the added value of C-reactive protein (CRP), in primary care patients presenting with cough. DESIGN AND SETTING: Cross-sectional diagnostic study of 73 primary care practices in the Netherlands. METHOD: Four hundred primary care patients (182 males, mean age 63 years) older than 50 years, presenting with persistent cough (>14 days) without established COPD participated, of whom 382 completed the study. They underwent a systematic diagnostic work-up of symptoms, signs, conventional laboratory CRP level, and hospital lung functions tests, including body plethysmography, and an expert panel decided whether COPD was present (reference test). The independent value of all items was estimated by multivariable logistic regression analysis. RESULTS: According to the expert panel, 118 patients had COPD (30%). Symptoms and signs with independent diagnostic value were age, sex, current smoking, smoking more than 20 pack-years, cardiovascular comorbidity, wheezing complaints, diminished breath sounds, and wheezing on auscultation. Combining these items resulted in an area under the receiver operating characteristic curve (ROC area) of 0.79 (95% confidence interval = 0.74 to 0.83) after internal validation. The proportion of subjects with elevated CRP was higher in those with early COPD, but CRP added no relevant diagnostic information above symptoms and signs. CONCLUSION: In subjects presenting with persistent cough, the CRP level has no added value for detection of early COPD.

Validation of two age dependent D-dimer cut-off values for exclusion of deep vein thrombosis in suspected elderly patients in primary care: retrospective, cross sectional, diagnostic analysis.

OBJECTIVE: To determine whether the use of age adapted D-dimer cut-off values can be translated to primary care patients who are suspected of deep vein thrombosis. DESIGN: Retrospective, cross sectional diagnostic study. SETTING: 110 primary care doctors affiliated with three hospitals in the Netherlands. PARTICIPANTS: 1374 consecutive patients (936 (68.1%) aged >50 years) with clinically suspected deep vein thrombosis. MAIN OUTCOME MEASURES: Proportion of patients with D-dimer values below two proposed age adapted cut-off levels (age in years × 10 µg/L in patients aged >50 years, or 750 µg/L in patients aged ≥ 60 years), in whom deep vein thrombosis could be excluded; and the number of false negative results. RESULTS: Using the Wells score, 647 patients had an unlikely clinical probability of deep vein thrombosis. In these patients (at all ages), deep vein thrombosis could be excluded in 309 (47.8%) using the age dependent cut-off value compared with 272 (42.0%) using the conventional cut-off value of 500 µg/L (increase 5.7%, 95% confidence interval 4.1% to 7.8%). This exclusion rate resulted in 0.5% and 0.3% false negative cases, respectively (increase 0.2%, 0.004% to 8.6%).The increase in exclusion rate by using the age dependent cut-off value was highest in the oldest patients. In patients older than 80 years, deep vein thrombosis could be safely excluded in 22 (35.5%) patients using the age dependent cut-off value compared with 13 (21.0%) using the conventional cut-off value (increase 14.5%, 6.8% to 25.8%). Compared with the age dependent cut-off value, the cut-off value of 750 µg/L had a similar exclusion rate (307 (47.4%) patients) and false negative rate (0.3%). CONCLUSIONS: Combined with a low clinical probability of deep vein thrombosis, use of the age dependent D-dimer cut-off value for patients older than 50 years or the cut-off value of 750 µg/L for patients aged 60 years and older resulted in a considerable increase in the proportion of patients in primary care in whom deep vein thrombosis could be safely excluded, compared with the conventional cut-off value of 500 µg/L.

A simple adaptation method improved the interpretability of prediction models for composite end points.

OBJECTIVE: The pros and cons of composite end points in prognostic research are discussed, and an adaptation method, designed to accurately adjust absolute risks for a composite end point to risks for the individual component outcomes, is presented. STUDY DESIGN AND SETTING: An example prediction model for recurrent cardiovascular events (composite end point) was used to evaluate the performance regarding the individual component outcomes (cardiovascular death, myocardial infarction, and stroke) before and after the adaptation method. RESULTS: Discrimination for the individual component outcomes (concordance index for myocardial infarction, 0.68; concordance index for stroke, 0.70) was very similar to discrimination for the original composite end point (concordance index, 0.70). For cardiovascular death, it even increased substantially (concordance index, 0.78). After adaptation, calibration plots for the component outcomes also improved, with visible convergence of the predicted risks and the observed incidences. CONCLUSION: In sum, these findings show that the adaptation method is useful when validating or applying a composite end point prediction model to the individual component outcomes. Following from this, recommendations concerning reporting of composite end points in future research are also included. Without the need for extra data, composite end point prediction models can easily be directly expanded to allow for the estimation of risk for each individual component outcome, improving the interpretability for clinicians and patients.

Adjusting for partial verification or workup bias in meta-analyses of diagnostic accuracy studies.

A key requirement in the design of diagnostic accuracy studies is that all study participants receive both the test under evaluation and the reference standard test. For a variety of practical and ethical reasons, sometimes only a proportion of patients receive the reference standard, which can bias the accuracy estimates. Numerous methods have been described for correcting this partial verification bias or workup bias in individual studies. In this article, the authors describe a Bayesian method for obtaining adjusted results from a diagnostic meta-analysis when partial verification or workup bias is present in a subset of the primary studies. The method corrects for verification bias without having to exclude primary studies with verification bias, thus preserving the main advantages of a meta-analysis: increased precision and better generalizability. The results of this method are compared with the existing methods for dealing with verification bias in diagnostic meta-analyses. For illustration, the authors use empirical data from a systematic review of studies of the accuracy of the immunohistochemistry test for diagnosis of human epidermal growth factor receptor 2 status in breast cancer patients.

Development and validation of clinical prediction models: marginal differences between logistic regression, penalized maximum likelihood estimation, and genetic programming.

OBJECTIVE: Many prediction models are developed by multivariable logistic regression. However, there are several alternative methods to develop prediction models. We compared the accuracy of a model that predicts the presence of deep venous thrombosis (DVT) when developed by four different methods. STUDY DESIGN AND SETTING: We used the data of 2,086 primary care patients suspected of DVT, which included 21 candidate predictors. The cohort was split into a derivation set (1,668 patients, 329 with DVT) and a validation set (418 patients, 86 with DVT). Also, 100 cross-validations were conducted in the full cohort. The models were developed by logistic regression, logistic regression with shrinkage by bootstrapping techniques, logistic regression with shrinkage by penalized maximum likelihood estimation, and genetic programming. The accuracy of the models was tested by assessing discrimination and calibration. RESULTS: There were only marginal differences in the discrimination and calibration of the models in the validation set and cross-validations. CONCLUSION: The accuracy measures of the models developed by the four different methods were only slightly different, and the 95% confidence intervals were mostly overlapped. We have shown that models with good predictive accuracy are most likely developed by sensible modeling strategies rather than by complex development methods.

Prediction model with metabolic syndrome to predict recurrent vascular events in patients with clinically manifest vascular diseases.

BACKGROUND: Although the overall average 10-year cardiovascular risk for patients with manifest atherosclerosis is considered to be more than 20%, actual risk for individual patients ranges from much lower to much higher. We investigated whether information on metabolic syndrome (MetS) or its individual components improves cardiovascular risk stratification in these patients. DESIGN AND METHODS: We conducted a prospective cohort study in 3679 patients with clinical manifest atherosclerosis from the Secondary Manifestations of ARTerial disease (SMART) study. Primary outcome was defined as any cardiovascular event (cardiovascular death, ischemic stroke or myocardial infarction). Three pre-specified prediction models were derived, all including information on established MetS components. The association between outcome and predictors was quantified using a Cox proportional hazard analysis. Model performance was assessed using global goodness-of-fit fit (χ(2)), discrimination (C-index) and ability to improve risk stratification. RESULTS: A total of 417 cardiovascular events occurred among 3679 patients with 15,102 person-years of follow-up (median follow-up 3.7 years, range 1.6-6.4 years). Compared to a model with age and gender only, all MetS-based models performed slightly better in terms of global model fit (χ(2)) but not C-index. The Net Reclassification Index associated with the addition of MetS (yes/no), the dichotomous MetS-components or the continuous MetS-components on top of age and gender was 2.1% (p = 0.29), 2.3% (p = 0.31) and 7.5% (p = 0.01), respectively. CONCLUSIONS: Prediction models incorporating age, gender and MetS can discriminate between patients with clinical manifest atherosclerosis at the highest vascular risk and those at lower risk. The addition of MetS components to a model with age and gender correctly reclassifies only a small proportion of patients into higher- and lower-risk categories. The clinical utility of a prediction model with MetS is therefore limited.

Incorporation of historical data in the analysis of randomized therapeutic trials.

Historical studies provide a valuable source of information for the motivation and design of later trials. Bayesian techniques offer possibilities for the quantitative inclusion of prior knowledge within the analysis of current trial data. Combining information from previous studies into an informative prior distribution is, however, a delicate case. The power prior distribution is a tool to estimate the effect of an intervention in a current study sample, while accounting for the information provided by previous research. In this study we evaluate the use of the power prior distribution, illustrated with data from a large randomized clinical trial on the effect of ST-wave analysis in intrapartum fetal monitoring. We advocate the use of a power prior distribution with pre-specified fixed study weights based on differences in study characteristics. We propose obtaining a ranking of the historical studies via expert elicitation, based on relevance for the current study, and specify study weights accordingly.

A model for preconceptional prediction of recurrent early-onset preeclampsia: derivation and internal validation.

OBJECTIVE: To develop a model to identify women at very low risk of recurrent early-onset preeclampsia. METHODS: We enrolled 407 women who had experienced early-onset preeclampsia in their first pregnancy, resulting in a delivery before 34 weeks' gestation. Preeclampsia was defined as hypertension (systolic blood pressure ≥140 mm Hg and/or diastolic blood pressure ≥90 mm Hg) after 20 weeks' gestation with de novo proteinuria (≥300 mg urinary protein excretion/day). Based on the previous published evidence and expert opinion, 5 predictors (gestational age at previous birth, prior small-for-gestational-age newborn, fasting blood glucose, body mass index, and hypertension) were entered in a logistic regression model. Discrimination and calibration were evaluated after adjusting for overfitting by bootstrapping techniques. RESULTS: Early-onset disease recurred in 28 (6.9%) of 407 women. The area under the receiver operating characteristic (ROC) curve of the model was 0.65 (95% CI: 0.56-0.74). Calibration was good, indicated by a nonsignificant Hosmer-Lemeshow test (P = .11). Using a predicted absolute risk threshold of, for example, 4.6% (ie, women identified with an estimated risk either above or below 4.6%), the sensitivity was 100%, with a specificity of 26%. In such a strategy, no women who developed preeclampsia were missed, while 98 of the 407 women would be regarded as low risk of recurrent early-onset preeclampsia, not necessarily requiring intensified antenatal care. CONCLUSION: Our model may be helpful in the identification of women at very low risk of recurrent early-onset preeclampsia. Before widespread application, our model should be validated in other populations.

Adjusting for differential-verification bias in diagnostic-accuracy studies: a Bayesian approach.

In studies of diagnostic accuracy, the performance of an index test is assessed by verifying its results against those of a reference standard. If verification of index-test results by the preferred reference standard can be performed only in a subset of subjects, an alternative reference test could be given to the remainder. The drawback of this so-called differential-verification design is that the second reference test is often of lesser quality, or defines the target condition in a different way. Incorrectly treating results of the 2 reference standards as equivalent will lead to differential-verification bias. The Bayesian methods presented in this paper use a single model to (1) acknowledge the different nature of the 2 reference standards and (2) make simultaneous inferences about the population prevalence and the sensitivity, specificity, and predictive values of the index test with respect to both reference tests, in relation to latent disease status. We illustrate this approach using data from a study on the accuracy of the elbow extension test for diagnosis of elbow fractures in patients with elbow injury, using either radiography or follow-up as reference standards.

Optimisation of the diagnostic strategy for suspected deep-vein thrombosis in primary care.

Recently, a diagnostic score was developed to safely exclude deep-vein thrombosis (DVT) in primary care. A large prospective study, in which general practitioners used this diagnostic score to decide which patients needed referral, revealed that the number of referrals for ultrasound measurements was reduced by almost 50%, at the cost of an acceptably low risk (1.4%, 95% confidence interval [CI] 0.6% to 2.9%) of venous thromboembolic events in non-referred patients. However, simple adjustments to the diagnostic score (so-called updating) might further improve the accuracy; i.e. reduce the proportion of missed diagnoses (safety) or increase the proportion of patients who do not need to be referred (efficiency). We applied two updating methods to determine whether adjusting the weights of the predictors or adding new predictors could further improve the accuracy of the diagnostic score. The weights of the predictors did not need to be adjusted, but inclusion of 'history of DVT' and 'prolonged travelling' significantly added predictive value (p-values 0.014 and 0.023, respectively). However, adding these predictors to the diagnostic score did not improve the safety and efficiency: at equal safety (1.4% missed diagnoses among the non-referred patients), the efficiency was lower (43.5%, 95% CI 40.4% to 46.6% compared to 49.4%, 95% CI 46.3% to 52.5%). The diagnostic score for excluding DVT in primary care has good accuracy in its original form and could not be improved by including additional predictors. This suggests that the original diagnostic score can be used to safely exclude clinically suspected DVT in primary care.

Correcting for partial verification bias: a comparison of methods.

PURPOSE: A common problem in diagnostic research is that the reference standard has not been carried out in all patients. This partial verification may lead to biased accuracy measures of the test under study. The authors studied the performance of multiple imputation and the conventional correction method proposed by Begg and Greenes under a range of different situations of partial verification. METHODS: In a series of simulations, using a previously published deep venous thrombosis data set (n = 1292), the authors set the outcome of the reference standard to missing based on various underlying mechanisms and by varying the total number of missing values. They then compared the performance of the different correction methods. RESULTS: The results of the study show that when the mechanism of missing reference data is known, accuracy measures can easily be correctly adjusted using either the Begg and Greenes method, or multiple imputation. In situations where the mechanism of missing reference data is complex or unknown, we recommend using multiple imputation methods to correct. CONCLUSIONS: These methods can easily apply for both continuous and categorical variables, are readily available in statistical software and give reliable estimates of the missing reference data.

Diagnostic classification in patients with suspected deep venous thrombosis: physicians' judgement or a decision rule?

BACKGROUND: Clinical decision rules can aid in referral decisions for ultrasonography in patients suspected of having deep venous thrombosis (DVT), but physicians are not always convinced of their usefulness and rely on their own judgement. AIM: To compare the performance of a clinical decision rule with the probability of DVT presence as estimated by GPs. DESIGN OF STUDY: Cross-sectional survey. SETTING: Primary care practices in The Netherlands. METHOD: GPs (n = 300) estimated the probability of the presence of DVT (range 0-100%) and calculated the score for the clinical decision rule in 1028 consecutive patients with suspected DVT. The clinical decision rule uses a threshold of three points and so, for the GP estimates, thresholds were introduced at 10% and 20%. If scores were below these estimates, it was not considered necessary to refer patients for further examination. Differences between the clinical decision rule and the GP estimates were calculated; this is discrimination (c-statistic) and classification of patients. RESULTS: Data of 1002 patients were eligible for analysis. DVT was observed in 136 (14%) patients. Both the clinical decision rule and GP estimates had good discriminative power (c-statistic of 0.80 and 0.82 respectively). Fewer patients were referred when using the clinical decision rule compared with a referral decision based on GP estimates: 51% versus 79% and 65% (thresholds at 10% and 20% respectively). Both strategies missed a similar and low proportion of patients who did have DVT (range 1.4-2.0%). CONCLUSION: In patients suspected of DVT both GP estimates and a clinical decision rule can safely discriminate in patients with and without DVT. However, fewer patients are referred for ultrasonography when GPs rely on a clinical decision rule to guide their decision making.

Diagnostic accuracy and user-friendliness of 5 point-of-care D-dimer tests for the exclusion of deep vein thrombosis.

BACKGROUND: Point-of-care D-dimer tests have recently been introduced to enable rapid exclusion of deep venous thrombosis (DVT) without the need to refer a patient for conventional laboratory-based D-dimer testing. Before implementation in practice, however, the diagnostic accuracy of each test should be validated. METHODS: We analyzed data of 577 prospectively identified consecutive primary care patients suspected to have DVT, who underwent 5 point-of-care D-dimer tests-4 quantitative (Vidas®, Pathfast™, Cardiac®, and Triage®) and 1 qualitative (Clearview Simplify®)-and ultrasonography as the reference method. We evaluated the tests for the accuracy of their measurements and submitted a questionnaire to 20 users to assess the user-friendliness of each test. RESULTS: All D-dimer tests showed negative predictive values higher than 98%. Sensitivity was high for all point-of-care tests, with a range of 0.91 (Clearview Simplify) to 0.99 (Vidas). Specificity varied between 0.39 (Pathfast) and 0.64 (Clearview Simplify). The quantitative point-of-care tests showed similar and high discriminative power for DVT, according to calculated areas under the ROC curves (range 0.88-0.89). The quantitative Vidas and Pathfast devices showed limited user-friendliness for primary care, owing to a laborious calibration process and long analyzer warm-up time compared to the Cardiac and Triage. For the qualitative Clearview Simplify assay, no analyzer or calibration was needed, but interpretation of a test result was sometimes difficult because of poor color contrast. CONCLUSIONS: Point-of-care D-dimer assays show good and similar diagnostic accuracy. The quantitative Cardiac and Triage and the qualitative Clearview Simplify D-dimer seem most user-friendly for excluding DVT in the doctor's office.

Unpredictable bias when using the missing indicator method or complete case analysis for missing confounder values: an empirical example.

OBJECTIVE: Missing indicator method (MIM) and complete case analysis (CC) are frequently used to handle missing confounder data. Using empirical data, we demonstrated the degree and direction of bias in the effect estimate when using these methods compared with multiple imputation (MI). STUDY DESIGN AND SETTING: From a cohort study, we selected an exposure (marital status), outcome (depression), and confounders (age, sex, and income). Missing values in "income" were created according to different patterns of missingness: missing values were created completely at random and depending on exposure and outcome values. Percentages of missing values ranged from 2.5% to 30%. RESULTS: When missing values were completely random, MIM gave an overestimation of the odds ratio, whereas CC and MI gave unbiased results. MIM and CC gave under- or overestimations when missing values depended on observed values. Magnitude and direction of bias depended on how the missing values were related to exposure and outcome. Bias increased with increasing percentage of missing values. CONCLUSION: MIM should not be used in handling missing confounder data because it gives unpredictable bias of the odds ratio even with small percentages of missing values. CC can be used when missing values are completely random, but it gives loss of statistical power.

Missing covariate data in medical research: to impute is better than to ignore.

OBJECTIVE: We compared popular methods to handle missing data with multiple imputation (a more sophisticated method that preserves data). STUDY DESIGN AND SETTING: We used data of 804 patients with a suspicion of deep venous thrombosis (DVT). We studied three covariates to predict the presence of DVT: d-dimer level, difference in calf circumference, and history of leg trauma. We introduced missing values (missing at random) ranging from 10% to 90%. The risk of DVT was modeled with logistic regression for the three methods, that is, complete case analysis, exclusion of d-dimer level from the model, and multiple imputation. RESULTS: Multiple imputation showed less bias in the regression coefficients of the three variables and more accurate coverage of the corresponding 90% confidence intervals than complete case analysis and dropping d-dimer level from the analysis. Multiple imputation showed unbiased estimates of the area under the receiver operating characteristic curve (0.88) compared with complete case analysis (0.77) and when the variable with missing values was dropped (0.65). CONCLUSION: As this study shows that simple methods to deal with missing data can lead to seriously misleading results, we advise to consider multiple imputation. The purpose of multiple imputation is not to create data, but to prevent the exclusion of observed data.