Handling missing predictor values when validating and applying a prediction model to new patients

The regulatory effect of zinc on the association between periodontitis and atherosclerotic cardiovascular disease: a cross-sectional study based on the National Health and Nutrition Examination Survey

BACKGROUND

Zinc has been proven to be effective against periodontitis, and also reported to reduce the risk of cardiovascular diseases (CVD). This study aims to explore the regulatory effect of zinc intake on the association between periodontitis and atherosclerotic cardiovascular disease (ASCVD).

METHODS

This was a cross-sectional study based on the National Health and Nutrition Examination Survey (NHANES). Logistic regression model was used to explore the association between zinc-RDA or periodontitis and 10-year ASCVD risk ≥ 20%, and results were shown as odds ratio (OR) and 95% confidence interval (95% CI). The regulatory effect of zinc intake on the association between periodontitis and 10-year ASCVD risk ≥ 20% was also assessed using logistic regression model. Subgroup analysis was performed based on age, gender, obesity, education level, lipid-lowering therapy, and dental floss.

RESULTS

6,075 patients were finally included for analysis. Zinc intake reaching the recommended level (OR = 0.82, 95%CI: 0.69-0.98) and periodontitis (OR = 2.47, 95%CI: 2.04-3.00) were found to be associated with 0.82-fold and 2.47-fold odds of 10-year ASCVD risk ≥ 20%, respectively. In addition, we found that the odds of 10-year ASCVD risk ≥ 20% was lower in patients with zinc intake reaching the recommended level than those without [OR (95%CI): 2.25 (1.81-2.80) vs. 2.72 (2.05-3.62)]. The similar regulatory effect was found in patients with age ≥ 60 years and < 60 years, in male and female, with or without obesity, in different education levels, with or without lipid lowering therapy, and with or without use of dental floss (all P < 0.05).

CONCLUSIONS

This study found the regulatory effect of adequate zinc intake on the association between periodontitis and ASCVD, providing guidance for periodontitis patients to decrease the risk of ASCVD.

Adaptive predictor-set linear model: An imputation-free method for linear regression prediction on data sets with missing values

Linear regression (LR) is vastly used in data analysis for continuous outcomes in biomedicine and epidemiology. Despite its popularity, LR is incompatible with missing data, which frequently occur in health sciences. For parameter estimation, this shortcoming is usually resolved by complete-case analysis or imputation. Both work-arounds, however, are inadequate for prediction, since they either fail to predict on incomplete records or ignore missingness-induced reduction in prediction accuracy and rely on (unrealistic) assumptions about the missing mechanism. Here, we derive adaptive predictor-set linear model (aps-lm), capable of making predictions for incomplete data without the need for imputation. It is derived by using a predictor-selection operation, the Moore-Penrose pseudoinverse, and the reduced QR decomposition. aps-lm is an LR generalization that inherently handles missing values. It is applied on a reference data set, where complete predictors and outcome are available, and yields a set of privacy-preserving parameters. In a second stage, these are shared for making predictions of the outcome on external data sets with missing entries for predictors without imputation. Moreover, aps-lm computes prediction errors that account for the pattern of missing values even under extreme missingness. We benchmark aps-lm in a simulation study. aps-lm showed greater prediction accuracy and reduced bias compared to popular imputation strategies under a wide range of scenarios including variation of sample size, goodness of fit, missing value type, and covariance structure. Finally, as a proof-of-principle, we apply aps-lm in the context of epigenetic aging clocks, linear models that predict a person's biological age from epigenetic data with promising clinical applications.

Prediction models for post-discharge mortality among under-five children with suspected sepsis in Uganda: A multicohort analysis

In many low-income countries, over five percent of hospitalized children die following hospital discharge. The lack of available tools to identify those at risk of post-discharge mortality has limited the ability to make progress towards improving outcomes. We aimed to develop algorithms designed to predict post-discharge mortality among children admitted with suspected sepsis. Four prospective cohort studies of children in two age groups (0-6 and 6-60 months) were conducted between 2012-2021 in six Ugandan hospitals. Prediction models were derived for six-months post-discharge mortality, based on candidate predictors collected at admission, each with a maximum of eight variables, and internally validated using 10-fold cross-validation. 8,810 children were enrolled: 470 (5.3%) died in hospital; 257 (7.7%) and 233 (4.8%) post-discharge deaths occurred in the 0-6-month and 6-60-month age groups, respectively. The primary models had an area under the receiver operating characteristic curve (AUROC) of 0.77 (95%CI 0.74-0.80) for 0-6-month-olds and 0.75 (95%CI 0.72-0.79) for 6-60-month-olds; mean AUROCs among the 10 cross-validation folds were 0.75 and 0.73, respectively. Calibration across risk strata was good: Brier scores were 0.07 and 0.04, respectively. The most important variables included anthropometry and oxygen saturation. Additional variables included: illness duration, jaundice-age interaction, and a bulging fontanelle among 0-6-month-olds; and prior admissions, coma score, temperature, age-respiratory rate interaction, and HIV status among 6-60-month-olds. Simple prediction models at admission with suspected sepsis can identify children at risk of post-discharge mortality. Further external validation is recommended for different contexts. Models can be digitally integrated into existing processes to improve peri-discharge care as children transition from the hospital to the community.

Predicting absolute risk for a person with missing risk factors

We compared methods to project absolute risk, the probability of experiencing the outcome of interest in a given projection interval accommodating competing risks, for a person from the target population with missing predictors. Without missing data, a perfectly calibrated model gives unbiased absolute risk estimates in a new target population, even if the predictor distribution differs from the training data. However, if predictors are missing in target population members, a reference dataset with complete data is needed to impute them and to estimate absolute risk, conditional only on the observed predictors. If the predictor distributions of the reference data and the target population differ, this approach yields biased estimates. We compared the bias and mean squared error of absolute risk predictions for seven methods that assume predictors are missing at random (MAR). Some methods imputed individual missing predictors, others imputed linear predictor combinations (risk scores). Simulations were based on real breast cancer predictor distributions and outcome data. We also analyzed a real breast cancer dataset. The largest bias for all methods resulted from different predictor distributions of the reference and target populations. No method was unbiased in this situation. Surprisingly, violating the MAR assumption did not induce severe biases. Most multiple imputation methods performed similarly and were less biased (but more variable) than a method that used a single expected risk score. Our work shows the importance of selecting predictor reference datasets similar to the target population to reduce bias of absolute risk predictions with missing risk factors.

Impact of missing values on the ability of the acute physiology and chronic health evaluation III and Japan risk of death models to predict mortality

PURPOSE

This study assessed model performance of the Acute Physiology and Chronic Health Evaluation (APACHE) III and Japan Risk of Death (JROD) when degraded by the number and category of missing variables. We also examined the impact of missing data on predicted mortality for facilities with missing physiological variables.

METHODS

We obtained data from the Japanese Intensive care PAtient Database (JIPAD). We calculated observed and predicted mortality rates using the APACHE III and JROD and the standardized mortality ratio (SMR) by the number and category of missing variables. Smoothed spline curves were calculated for the SMR to the missing proportion of the facility.

RESULTS

A total of 61,357 patients from 57 ICUs were included between April 2015 and March 2019. The APACHE III and JROD SMRs increased as the number of missing values increased. The SMR in the APACHE III model was elevated in facilities with a larger proportion of missing in each of the APS categories, arterial blood gas, albumin, glucose, and bilirubin. Facilities with a high proportion of missing albumin data preserved their SMRs in only the JROD model.

CONCLUSION

An increased number of missing physiological variables resulted in falsely low predicted mortality rates and high SMRs.

Lifestyle predictors of colorectal cancer in European populations: a systematic review

Background

Colorectal cancer (CRC) is the second most prevalent cancer in Europe, with one-fifth of cases attributable to unhealthy lifestyles. Risk prediction models for quantifying CRC risk and identifying high-risk groups have been developed or validated across European populations, some considering lifestyle as a predictor.

Purpose

To identify lifestyle predictors considered in existing risk prediction models applicable for European populations and characterise their corresponding parameter values for an improved understanding of their relative contribution to prediction across different models.

Methods

A systematic review was conducted in PubMed and Web of Science from January 2000 to August 2021. Risk prediction models were included if (1) developed and/or validated in an adult asymptomatic European population, (2) based on non-invasively measured predictors and (3) reported mean estimates and uncertainty for predictors included. To facilitate comparison, model-specific lifestyle predictors were visualised using forest plots.

Results

A total of 21 risk prediction models for CRC (reported in 16 studies) were eligible, of which 11 were validated in a European adult population but developed elsewhere, mostly USA. All models but two reported at least one lifestyle factor as predictor. Of the lifestyle factors, the most common predictors were body mass index (BMI) and smoking (each present in 13 models), followed by alcohol (11), and physical activity (7), while diet-related factors were less considered with the most commonly present meat (9), vegetables (5) or dairy (2). The independent predictive contribution was generally greater when they were collected with greater detail, although a noticeable variation in effect size estimates for BMI, smoking and alcohol.

Conclusions

Early identification of high-risk groups based on lifestyle data offers the potential to encourage participation in lifestyle change and screening programmes, hence reduce CRC burden. We propose the commonly shared lifestyle predictors to be further used in public health prediction modelling for improved uptake of the model.

Exploring the connection between caffeine intake and constipation: a cross-sectional study using national health and nutrition examination survey data

BACKGROUND

Caffeine has been reported to increase gastrointestinal motility and change intestinal microbiota. Constipation may be caused by colonic motor dysfunction and colonic microbiomeis disturbances. In this study, we aimed to explore the association between caffeine intake and constipation.

METHODS

This was a cross-sectional study based on the National Health and Nutrition Examination Survey (NHANES). Caffeine intake was assessed using 24-h dietary recall method, and constipation was defined based on stool consistency or stool frequency. Logistic regression analysis was used to assess the association between caffeine intake and constipation, and results were expressed as odds ratio (OR) with 95% confidence intervals (95%CI). Subgroup analysis was performed based on age.

RESULTS

A total of 13,816 participants were finally included for analysis. After adjusting potential confounders, high intake of caffeine was found to be associated with the low odds of constipation (Q3: OR = 0.60, 95%CI: 0.49-0.74; Q4: OR = 0.77, 95%CI: 0.59-0.99; Q5: OR = 0.72, 95%CI: 0.56-0.92). The similar association was found in young people and middle-age people (P < 0.05).

CONCLUSION

High caffeine intake was associated with the low odds of constipation. Our finding indicated that individuals should develop consciousness and habit of consuming caffeinated foods and drinks to prevent and relief the constipation.

Methodological issues of the electronic health records' use in the context of epidemiological investigations, in light of missing data: a review of the recent literature

BACKGROUND

Electronic health records (EHRs) are widely accepted to enhance the health care quality, patient monitoring, and early prevention of various diseases, even when there is incomplete or missing information in them.

AIM

The present review sought to investigate the impact of EHR implementation on healthcare quality and medical decision in the context of epidemiological investigations, considering missing or incomplete data.

METHODS

Google scholar, Medline (via PubMed) and Scopus databases were searched for studies investigating the impact of EHR implementation on healthcare quality and medical decision, as well as for studies investigating the way of dealing with missing data, and their impact on medical decision and the development process of prediction models. Electronic searches were carried out up to 2022.

RESULTS

EHRs were shown that they constitute an increasingly important tool for both physicians, decision makers and patients, which can improve national healthcare systems both for the convenience of patients and doctors, while they improve the quality of health care as well as they can also be used in order to save money. As far as the missing data handling techniques is concerned, several investigators have already tried to propose the best possible methodology, yet there is no wide consensus and acceptance in the scientific community, while there are also crucial gaps which should be addressed.

CONCLUSIONS

Through the present thorough investigation, the importance of the EHRs' implementation in clinical practice was established, while at the same time the gap of knowledge regarding the missing data handling techniques was also pointed out.

Machine learning algorithm improves the detection of NASH (NAS-based) and at-risk NASH: A development and validation study

BACKGROUND AND AIMS

Detecting NASH remains challenging, while at-risk NASH (steatohepatitis and F≥ 2) tends to progress and is of interest for drug development and clinical application. We developed prediction models by supervised machine learning techniques, with clinical data and biomarkers to stage and grade patients with NAFLD.

APPROACH AND RESULTS

Learning data were collected in the Liver Investigation: Testing Marker Utility in Steatohepatitis metacohort (966 biopsy-proven NAFLD adults), staged and graded according to NASH CRN. Conditions of interest were the clinical trial definition of NASH (NAS ≥ 4;53%), at-risk NASH (NASH with F ≥ 2;35%), significant (F ≥ 2;47%), and advanced fibrosis (F ≥ 3;28%). Thirty-five predictors were included. Missing data were handled by multiple imputations. Data were randomly split into training/validation (75/25) sets. A gradient boosting machine was applied to develop 2 models for each condition: clinical versus extended (clinical and biomarkers). Two variants of the NASH and at-risk NASH models were constructed: direct and composite models.Clinical gradient boosting machine models for steatosis/inflammation/ballooning had AUCs of 0.94/0.79/0.72. There were no improvements when biomarkers were included. The direct NASH model produced AUCs (clinical/extended) of 0.61/0.65. The composite NASH model performed significantly better (0.71) for both variants. The composite at-risk NASH model had an AUC of 0.83 (clinical and extended), an improvement over the direct model. Significant fibrosis models had AUCs (clinical/extended) of 0.76/0.78. The extended advanced fibrosis model (0.86) performed significantly better than the clinical version (0.82).

CONCLUSIONS

Detection of NASH and at-risk NASH can be improved by constructing independent machine learning models for each component, using only clinical predictors. Adding biomarkers only improved the accuracy of fibrosis.

Prospective multicenter external validation of postoperative mortality prediction tools in patients undergoing emergency laparotomy

BACKGROUND

Accurate preoperative risk assessment in emergency laparotomy (EL) is valuable for informed decision making and rational use of resources. Available risk prediction tools have not been validated adequately across diverse health care settings. Herein, we report a comparative external validation of four widely cited prognostic models.

METHODS

A multicenter cohort was prospectively composed of consecutive patients undergoing EL in 11 Greek hospitals from January 2020 to May 2021 using the National Emergency Laparotomy Audit (NELA) inclusion criteria. Thirty-day mortality risk predictions were calculated using the American College of Surgeons National Surgical Quality Improvement Program (ACS-NSQIP), NELA, Portsmouth Physiological and Operative Severity Score for the Enumeration of Mortality and Morbidity (P-POSSUM), and Predictive Optimal Trees in Emergency Surgery Risk tools. Surgeons' assessment of postoperative mortality using predefined cutoffs was recorded, and a surgeon-adjusted ACS-NSQIP prediction was calculated when the original model's prediction was relatively low. Predictive performances were compared using scaled Brier scores, discrimination and calibration measures and plots, and decision curve analysis. Heterogeneity across hospitals was assessed by random-effects meta-analysis.

RESULTS

A total of 631 patients were included, and 30-day mortality was 16.3%. The ACS-NSQIP and its surgeon-adjusted version had the highest scaled Brier scores. All models presented high discriminative ability, with concordance statistics ranging from 0.79 for P-POSSUM to 0.85 for NELA. However, except the surgeon-adjusted ACS-NSQIP (Hosmer-Lemeshow test, p = 0.742), all other models were poorly calibrated ( p < 0.001). Decision curve analysis revealed superior clinical utility of the ACS-NSQIP. Following recalibrations, predictive accuracy improved for all models, but ACS-NSQIP retained the lead. Between-hospital heterogeneity was minimum for the ACS-NSQIP model and maximum for P-POSSUM.

CONCLUSION

The ACS-NSQIP tool was most accurate for mortality predictions after EL in a broad external validation cohort, demonstrating utility for facilitating preoperative risk management in the Greek health care system. Subjective surgeon assessments of patient prognosis may optimize ACS-NSQIP predictions.

LEVEL OF EVIDENCE

Diagnostic Test/Criteria; Level II.

Graphical and numerical diagnostic tools to assess multiple imputation models by posterior predictive checking

Problem

The congenial of the imputation model is crucial for valid statistical inferences. Hence, it is important to develop methodologies for diagnosing imputation models.

Aim

We propose and evaluate a new diagnostic method based on posterior predictive checking to diagnose the congeniality of fully conditional imputation models. Our method applies to multiple imputation by chained equations, which is widely used in statistical software.

Methods

The proposed method compares the observed data with their replicates generated under the corresponding posterior predictive distributions to diagnose the performance of imputation models. The method applies to various imputation models, including parametric and semi-parametric approaches and continuous and discrete incomplete variables. We studied the validity of the method through simulation and application.

Results

The proposed diagnostic method based on posterior predictive checking demonstrates its validity in assessing the performance of imputation models. The method can diagnose the consistency of imputation models with the substantive model and can be applied to a broad range of research contexts.

Conclusion

The diagnostic method based on posterior predictive checking provides a valuable tool for researchers who use fully conditional specification to handle missing data. By assessing the performance of imputation models, our method can help researchers improve the accuracy and reliability of their analyzes. Furthermore, our method applies to different imputation models. Hence, it is a versatile and valuable tool for researchers identifying plausible imputation models.

Prediction models for cardiovascular disease risk among people living with HIV: A systematic review and meta-analysis

Background

HIV continues to be a major global health issue. The relative risk of cardiovascular disease (CVD) among people living with HIV (PLWH) was 2.16 compared to non-HIV-infections. The prediction of CVD is becoming an important issue in current HIV management. However, there is no consensus on optional CVD risk models for PLWH. Therefore, we aimed to systematically summarize and compare prediction models for CVD risk among PLWH.

Methods

Longitudinal studies that developed or validated prediction models for CVD risk among PLWH were systematically searched. Five databases were searched up to January 2022. The quality of the included articles was evaluated by using the Prediction model Risk Of Bias ASsessment Tool (PROBAST). We applied meta-analysis to pool the logit-transformed C-statistics for discrimination performance.

Results

Thirteen articles describing 17 models were included. All the included studies had a high risk of bias. In the meta-analysis, the pooled estimated C-statistic was 0.76 (95% CI: 0.72-0.81, I ² = 84.8%) for the Data collection on Adverse Effects of Anti-HIV Drugs Study risk equation (D:A:D) (2010), 0.75 (95% CI: 0.70-0.79, I ² = 82.4%) for the D:A:D (2010) 10-year risk version, 0.77 (95% CI: 0.74-0.80, I ² = 82.2%) for the full D:A:D (2016) model, 0.74 (95% CI: 0.68-0.79, I ² = 86.2%) for the reduced D:A:D (2016) model, 0.71 (95% CI: 0.61-0.79, I ² = 87.9%) for the Framingham Risk Score (FRS) for coronary heart disease (CHD) (1998), 0.74 (95% CI: 0.70-0.78, I ² = 87.8%) for the FRS CVD model (2008), 0.72 (95% CI: 0.67-0.76, I ² = 75.0%) for the pooled cohort equations of the American Heart Society/ American score (PCE), and 0.67 (95% CI: 0.56-0.77, I ² = 51.3%) for the Systematic COronary Risk Evaluation (SCORE). In the subgroup analysis, the discrimination of PCE was significantly better in the group aged ≤40 years than in the group aged 40-45 years (P = 0.024) and the group aged ≥45 years (P = 0.010). No models were developed or validated in Sub-Saharan Africa and the Asia region.

Conclusions

The full D:A:D (2016) model performed the best in terms of discrimination, followed by the D:A:D (2010) and PCE. However, there were no significant differences between any of the model pairings. Specific CVD risk models for older PLWH and for PLWH in Sub-Saharan Africa and the Asia region should be established.Systematic Review Registration: PROSPERO CRD42022322024.

External Validation of the Individualized Prediction of Breast Cancer Survival (IPBS) Model for Estimating Survival after Surgery for Patients with Breast Cancer in Northern Thailand

The individualized prediction of breast cancer survival (IPBS) model was recently developed. Although the model showed acceptable performance during derivation, its external performance remained unknown. This study aimed to validate the IPBS model using the data of breast cancer patients in Northern Thailand. An external validation study was conducted based on female patients with breast cancer who underwent surgery at Maharaj Nakorn Chiang Mai hospital from 2005 to 2015. Data on IPBS predictors were collected. The endpoints were 5-year overall survival (OS) and disease-free survival (DFS). The model performance was evaluated in terms of discrimination and calibration. Missing data were handled with multiple imputation. Of all 3581 eligible patients, 1868 were included. The 5-year OS and DFS were 85.2% and 81.9%. The IPBS model showed acceptable discrimination: C-statistics 0.706 to 0.728 for OS and 0.675 to 0.689 for DFS at 5 years. However, the IPBS model minimally overestimated both OS and DFS predictions. These overestimations were corrected after model recalibration. In this external validation study, the IPBS model exhibited good discriminative ability. Although it may provide minimal overestimation, recalibrating the model to the local context is a practical solution to improve the model calibration.

Accommodating heterogeneous missing data patterns for prostate cancer risk prediction

BACKGROUND

We compared six commonly used logistic regression methods for accommodating missing risk factor data from multiple heterogeneous cohorts, in which some cohorts do not collect some risk factors at all, and developed an online risk prediction tool that accommodates missing risk factors from the end-user.

METHODS

Ten North American and European cohorts from the Prostate Biopsy Collaborative Group (PBCG) were used for fitting a risk prediction tool for clinically significant prostate cancer, defined as Gleason grade group ≥ 2 on standard TRUS prostate biopsy. One large European PBCG cohort was withheld for external validation, where calibration-in-the-large (CIL), calibration curves, and area-underneath-the-receiver-operating characteristic curve (AUC) were evaluated. Ten-fold leave-one-cohort-internal validation further validated the optimal missing data approach.

RESULTS

Among 12,703 biopsies from 10 training cohorts, 3,597 (28%) had clinically significant prostate cancer, compared to 1,757 of 5,540 (32%) in the external validation cohort. In external validation, the available cases method that pooled individual patient data containing all risk factors input by an end-user had best CIL, under-predicting risks as percentages by 2.9% on average, and obtained an AUC of 75.7%. Imputation had the worst CIL (-13.3%). The available cases method was further validated as optimal in internal cross-validation and thus used for development of an online risk tool. For end-users of the risk tool, two risk factors were mandatory: serum prostate-specific antigen (PSA) and age, and ten were optional: digital rectal exam, prostate volume, prior negative biopsy, 5-alpha-reductase-inhibitor use, prior PSA screen, African ancestry, Hispanic ethnicity, first-degree prostate-, breast-, and second-degree prostate-cancer family history.

CONCLUSION

Developers of clinical risk prediction tools should optimize use of available data and sources even in the presence of high amounts of missing data and offer options for users with missing risk factors.

Development and validation of prediction model for incident overactive bladder: The Nagahama study

Objectives

We aimed to develop models to predict new‐onset overactive bladder in 5 years using a large prospective cohort of the general population.

Methods

This is a secondary analysis of a longitudinal cohort study in Japan. The baseline characteristics were measured between 2008 and 2010, with follow‐ups every 5 years. We included subjects without overactive bladder at baseline and with follow‐up data 5 years later. Overactive bladder was assessed using the overactive bladder symptom score. Baseline characteristics (demographics, health behaviors, comorbidities, and overactive bladder symptom scores) and blood test data were included as predictors. We developed two competing prediction models for each sex based on logistic regression with penalized likelihood (LASSO). We chose the best model separately for men and women after evaluating models' performance in terms of discrimination and calibration using an internal validation via 200 bootstrap resamples and a temporal validation.

Results

We analyzed 7218 participants (male: 2238, female: 4980). The median age was 60 and 55 years, and the number of new‐onset overactive bladder was 223 (10.0%) and 288 (5.8%) per 5 years in males and females, respectively. The in‐sample estimates for C‐statistic, calibration intercept, and slope for the best performing models were 0.77 (95% confidence interval 0.74–0.80), 0.28 and 1.15 for males, and 0.77 (95% confidence interval 0.74–0.80), 0.20 and 1.08 for females. Internal and temporal validation gave broadly similar estimates of performance, indicating low optimism.

Conclusion

We developed risk prediction models for new‐onset overactive bladder among men and women with good predictive ability.

Validation and recalibration of OxMIV in predicting violent behaviour in patients with schizophrenia spectrum disorders

Oxford Mental Illness and Violence (OxMIV) addresses the need in mental health services for a scalable, transparent and valid tool to predict violent behaviour in patients with severe mental illness. However, external validations are lacking. Therefore, we have used a Dutch sample of general psychiatric patients with schizophrenia spectrum disorders (N = 637) to evaluate the performance of OxMIV in predicting interpersonal violence over 3 years. The predictors and outcome were measured with standardized instruments and multiple sources of information. Patients were mostly male (n = 493, 77%) and, on average, 27 (SD = 7) years old. The outcome rate was 9% (n = 59). Discrimination, as measured by the area under the curve, was moderate at 0.67 (95% confidence interval 0.61–0.73). Calibration-in-the-large was adequate, with a ratio between predicted and observed events of 1.2 and a Brier score of 0.09. At the individual level, risks were systematically underestimated in the original model, which was remedied by recalibrating the intercept and slope of the model. Probability scores generated by the recalibrated model can be used as an adjunct to clinical decision-making in Dutch mental health services.

Missing data is poorly handled and reported in prediction model studies using machine learning: a literature review

OBJECTIVES

Missing data is a common problem during the development, evaluation, and implementation of prediction models. Although machine learning (ML) methods are often said to be capable of circumventing missing data, it is unclear how these methods are used in medical research. We aim to find out if and how well prediction model studies using machine learning report on their handling of missing data.

STUDY DESIGN AND SETTING

We systematically searched the literature on published papers between 2018 and 2019 about primary studies developing and/or validating clinical prediction models using any supervised ML methodology across medical fields. From the retrieved studies information about the amount and nature (e.g. missing completely at random, potential reasons for missingness) of missing data and the way they were handled were extracted.

RESULTS

We identified 152 machine learning-based clinical prediction model studies. A substantial amount of these 152 papers did not report anything on missing data (n = 56/152). A majority (n = 96/152) reported details on the handling of missing data (e.g., methods used), though many of these (n = 46/96) did not report the amount of the missingness in the data. In these 96 papers the authors only sometimes reported possible reasons for missingness (n = 7/96) and information about missing data mechanisms (n = 8/96). The most common approach for handling missing data was deletion (n = 65/96), mostly via complete-case analysis (CCA) (n = 43/96). Very few studies used multiple imputation (n = 8/96) or built-in mechanisms such as surrogate splits (n = 7/96) that directly address missing data during the development, validation, or implementation of the prediction model.

CONCLUSION

Though missing values are highly common in any type of medical research and certainly in the research based on routine healthcare data, a majority of the prediction model studies using machine learning does not report sufficient information on the presence and handling of missing data. Strategies in which patient data are simply omitted are unfortunately the most often used methods, even though it is generally advised against and well known that it likely causes bias and loss of analytical power in prediction model development and in the predictive accuracy estimates. Prediction model researchers should be much more aware of alternative methodologies to address missing data.

Missing data was handled inconsistently in UK prediction models: a review of method used

OBJECTIVES

No clear guidance exists on handling missing data at each stage of developing, validating and implementing a clinical prediction model (CPM). We aimed to review the approaches to handling missing data that underly the CPMs currently recommended for use in UK healthcare.

STUDY DESIGN AND SETTING

A descriptive cross-sectional meta-epidemiological study aiming to identify CPMs recommended by the National Institute for Health and Care Excellence (NICE), which summarized how missing data is handled across their pipelines.

RESULTS

A total of 23 CPMs were included through "sampling strategy." Six missing data strategies were identified: complete case analysis (CCA), multiple imputation, imputation of mean values, k-nearest neighbours imputation, using an additional category for missingness, considering missing values as risk-factor-absent. 52% of the development articles and 48% of the validation articles did not report how missing data were handled. CCA was the most common approach used for development (40%) and validation (44%). At implementation, 57% of the CPMs required complete data entry, whilst 43% allowed missing values. Three CPMs had consistent paths in their pipelines.

CONCLUSION

A broad variety of methods for handling missing data underly the CPMs currently recommended for use in UK healthcare. Missing data handling strategies were generally inconsistent. Better quality assurance of CPMs needs greater clarity and consistency in handling of missing data.

Evaluation of predictive model performance of an existing model in the presence of missing data

In medical research, the Brier score (BS) and the area under the receiver operating characteristic (ROC) curves (AUC) are two common metrics used to evaluate prediction models of a binary outcome, such as using biomarkers to predict the risk of developing a disease in the future. The assessment of an existing prediction models using data with missing covariate values is challenging. In this article, we propose inverse probability weighted (IPW) and augmented inverse probability weighted (AIPW) estimates of AUC and BS to handle the missing data. An alternative approach uses multiple imputation (MI), which requires a model for the distribution of the missing variable. We evaluated the performance of IPW and AIPW in comparison with MI in simulation studies under missing completely at random, missing at random, and missing not at random scenarios. When there are missing observations in the data, MI and IPW can be used to obtain unbiased estimates of BS and AUC if the imputation model for the missing variable or the model for the missingness is correctly specified. MI is more efficient than IPW. Our simulation results suggest that AIPW can be more efficient than IPW, and also achieves double robustness from miss-specification of either the missingness model or the imputation model. The outcome variable should be included in the model for the missing variable under all scenarios, while it only needs to be included in missingness model if the missingness depends on the outcome. We illustrate these methods using an example from prostate cancer.

Real-time imputation of missing predictor values improved the application of prediction models in daily practice

OBJECTIVES

In clinical practice, many prediction models cannot be used when predictor values are missing. We, therefore, propose and evaluate methods for real-time imputation.

STUDY DESIGN AND SETTING

We describe (i) mean imputation (where missing values are replaced by the sample mean), (ii) joint modeling imputation (JMI, where we use a multivariate normal approximation to generate patient-specific imputations), and (iii) conditional modeling imputation (CMI, where a multivariable imputation model is derived for each predictor from a population). We compared these methods in a case study evaluating the root mean squared error (RMSE) and coverage of the 95% confidence intervals (i.e., the proportion of confidence intervals that contain the true predictor value) of imputed predictor values.

RESULTS

-RMSE was lowest when adopting JMI or CMI, although imputation of individual predictors did not always lead to substantial improvements as compared to mean imputation. JMI and CMI appeared particularly useful when the values of multiple predictors of the model were missing. Coverage reached the nominal level (i.e., 95%) for both CMI and JMI.

CONCLUSION

Multiple imputations using either CMI or JMI is recommended when dealing with missing predictor values in real-time settings.

Real-time imputation of missing predictor values in clinical practice

Aims

Use of prediction models is widely recommended by clinical guidelines, but usually requires complete information on all predictors, which is not always available in daily practice. We aim to describe two methods for real-time handling of missing predictor values when using prediction models in practice.

Methods and results

We compare the widely used method of mean imputation (M-imp) to a method that personalizes the imputations by taking advantage of the observed patient characteristics. These characteristics may include both prediction model variables and other characteristics (auxiliary variables). The method was implemented using imputation from a joint multivariate normal model of the patient characteristics (joint modelling imputation; JMI). Data from two different cardiovascular cohorts with cardiovascular predictors and outcome were used to evaluate the real-time imputation methods. We quantified the prediction model's overall performance [mean squared error (MSE) of linear predictor], discrimination (c-index), calibration (intercept and slope), and net benefit (decision curve analysis). When compared with mean imputation, JMI substantially improved the MSE (0.10 vs. 0.13), c-index (0.70 vs. 0.68), and calibration (calibration-in-the-large: 0.04 vs. 0.06; calibration slope: 1.01 vs. 0.92), especially when incorporating auxiliary variables. When the imputation method was based on an external cohort, calibration deteriorated, but discrimination remained similar.

Conclusions

We recommend JMI with auxiliary variables for real-time imputation of missing values, and to update imputation models when implementing them in new settings or (sub)populations.

Handling missing predictor values when validating and applying a prediction model to new patients

Missing data present challenges for development and real‐world application of clinical prediction models. While these challenges have received considerable attention in the development setting, there is only sparse research on the handling of missing data in applied settings. The main unique feature of handling missing data in these settings is that missing data methods have to be performed for a single new individual, precluding direct application of mainstay methods used during model development. Correspondingly, we propose that it is desirable to perform model validation using missing data methods that transfer to practice in single new patients. This article compares existing and new methods to account for missing data for a new individual in the context of prediction. These methods are based on (i) submodels based on observed data only, (ii) marginalization over the missing variables, or (iii) imputation based on fully conditional specification (also known as chained equations). They were compared in an internal validation setting to highlight the use of missing data methods that transfer to practice while validating a model. As a reference, they were compared to the use of multiple imputation by chained equations in a set of test patients, because this has been used in validation studies in the past. The methods were evaluated in a simulation study where performance was measured by means of optimism corrected C‐statistic and mean squared prediction error. Furthermore, they were applied in data from a large Dutch cohort of prophylactic implantable cardioverter defibrillator patients.