Trial arm outcome variance difference after dropout as an indicator of missing-not-at-random bias in randomized controlled trials.

Randomized controlled trials (RCTs) are vulnerable to bias from missing data. When outcomes are missing not at random (MNAR), estimates from complete case analysis (CCA) and multiple imputation (MI) may be biased. There is no statistical test for distinguishing between outcomes missing at random (MAR) and MNAR. Current strategies rely on comparing dropout proportions and covariate distributions, and using auxiliary information to assess the likelihood of dropout being associated with the outcome. We propose using the observed variance difference across trial arms as a tool for assessing the risk of dropout being MNAR in RCTs with continuous outcomes. In an RCT, at randomization, the distributions of all covariates should be equal in the populations randomized to the intervention and control arms. Under the assumption of homogeneous treatment effects and homoskedastic outcome errors, the variance of the outcome will also be equal in the two populations over the course of follow-up. We show that under MAR dropout, the observed outcome variances, conditional on the variables included in the model, are equal across trial arms, whereas MNAR dropout may result in unequal variances. Consequently, unequal observed conditional trial arm variances are an indicator of MNAR dropout and possible bias of the estimated treatment effect. Heterogeneous treatment effects or heteroskedastic outcome errors are another potential cause of observing different outcome variances. We show that for longitudinal data, we can isolate the effect of MNAR outcome-dependent dropout by considering the variance difference at baseline in the same set of patients who are observed at final follow-up. We illustrate our method in simulation for CCA and MI, and in applications using individual-level data and summary data.

Neural Networks for Survival Prediction in Medicine Using Prognostic Factors: A Review and Critical Appraisal.

Survival analysis deals with the expected duration of time until one or more events of interest occur. Time to the event of interest may be unobserved, a phenomenon commonly known as right censoring, which renders the analysis of these data challenging. Over the years, machine learning algorithms have been developed and adapted to right-censored data. Neural networks have been repeatedly employed to build clinical prediction models in healthcare with a focus on cancer and cardiology. We present the first ever attempt at a large-scale review of survival neural networks (SNNs) with prognostic factors for clinical prediction in medicine. This work provides a comprehensive understanding of the literature (24 studies from 1990 to August 2021, global search in PubMed). Relevant manuscripts are classified as methodological/technical (novel methodology or new theoretical model; 13 studies) or applications (11 studies). We investigate how researchers have used neural networks to fit survival data for prediction. There are two methodological trends: either time is added as part of the input features and a single output node is specified, or multiple output nodes are defined for each time interval. A critical appraisal of model aspects that should be designed and reported more carefully is performed. We identify key characteristics of prediction models (i.e., number of patients/predictors, evaluation measures, calibration), and compare ANN's predictive performance to the Cox proportional hazards model. The median sample size is 920 patients, and the median number of predictors is 7. Major findings include poor reporting (e.g., regarding missing data, hyperparameters) as well as inaccurate model development/validation. Calibration is neglected in more than half of the studies. Cox models are not developed to their full potential and claims for the performance of SNNs are exaggerated. Light is shed on the current state of art of SNNs in medicine with prognostic factors. Recommendations are made for the reporting of clinical prediction models. Limitations are discussed, and future directions are proposed for researchers who seek to develop existing methodology.

Disease progression in osteosarcoma: a multistate model for the EURAMOS-1 (European and American Osteosarcoma Study) randomised clinical trial.

OBJECTIVES: Investigating the effect of prognostic factors in a multistate framework on survival in a large population of patients with osteosarcoma. Of interest is how prognostic factors affect different disease stages after surgery, with stages of local recurrence (LR), new metastatic disease (NM), LR+NM, secondary malignancy, a second NM, and death. DESIGN: An open-label, international, phase 3 randomised controlled trial. SETTING: 325 sites in 17 countries. PARTICIPANTS: The subset of 1631 metastases-free patients from 1965 patients with high-grade resectable osteosarcoma, from the European and American Osteosarcoma Study. MAIN OUTCOME MEASURES: The effect of prognostic factors on different disease stages, expressed as HRs; predictions of disease progression on an individual patient basis, according to patient-specific characteristics and history of intermediate events. RESULTS: Of 1631 patients, 526 experienced an intermediate event, and 305 died by the end of follow-up. An axial tumour site substantially increased the risk of LR after surgery (HR=10.84, 95% CI 8.46 to 13.86) and death after LR (HR=11.54, 95% CI 6.11 to 21.8). A poor histological increased the risk of NM (HR=5.81, 95% CI 5.31 to 6.36), which sharply declined after 3 years since surgery. Young patients (<12 years) had a lower intermediate event risk (eg, for LR: HR=0.66, 95% CI 0.51 to 0.86), when compared with adolescents (12-18 years), but had an increased risk of subsequent death, while patients aged >18 had a decreased risk of death after event (eg, for death after LR: HR=2.40, 95% CI 1.52 to 3.90; HR=0.35, 95% CI 0.21 to 0.56, respectively). CONCLUSIONS: Our findings suggest that patients with axial tumours should be monitored for LR and patients with poor histological response for NM, and that for young patients (<12) with an LR additional treatment options should be investigated. TRIAL REGISTRATION NUMBER: NCT00134030.

Sensitivity to missing not at random dropout in clinical trials: Use and interpretation of the trimmed means estimator.

Outcome values in randomized controlled trials (RCTs) may be missing not at random (MNAR), if patients with extreme outcome values are more likely to drop out (eg, due to perceived ineffectiveness of treatment, or adverse effects). In such scenarios, estimates from complete case analysis (CCA) and multiple imputation (MI) will be biased. We investigate the use of the trimmed means (TM) estimator for the case of univariable missingness in one continuous outcome. The TM estimator operates by setting missing values to the most extreme value, and then "trimming" away equal fractions of both groups, estimating the treatment effect using the remaining data. The TM estimator relies on two assumptions, which we term the "strong MNAR" and "location shift" assumptions. We derive formulae for the TM estimator bias resulting from the violation of these assumptions for normally distributed outcomes. We propose an adjusted TM estimator, which relaxes the location shift assumption and detail how our bias formulae can be used to establish the direction of bias of CCA and TM estimates, to inform sensitivity analyses. The TM approach is illustrated in a sensitivity analysis of the CoBalT RCT of cognitive behavioral therapy (CBT) in 469 individuals with 46 months follow-up. Results were consistent with a beneficial CBT treatment effect, with MI estimates closer to the null and TM estimates further from the null than the CCA estimate. We propose using the TM estimator as a sensitivity analysis for data where extreme outcome value dropout is plausible.

Mendelian randomization analysis of the causal impact of body mass index and waist-hip ratio on rates of hospital admission.

We analyze how measures of adiposity - body mass index (BMI) and waist hip ratio (WHR) - causally influence rates of hospital admission. Conventional analyses of this relationship are susceptible to omitted variable bias from variables that jointly influence both hospital admission and adipose status. We implement a novel quasi-Poisson instrumental variable model in a Mendelian randomization framework, identifying causal effects from random perturbations to germline genetic variation. We estimate the individual and joint effects of BMI, WHR, and WHR adjusted for BMI. We also implement multivariable instrumental variable methods in which the causal effect of one exposure is estimated conditionally on the causal effect of another exposure. Data on 310,471 participants and over 550,000 inpatient admissions in the UK Biobank were used to perform one-sample and two-sample Mendelian randomization analyses. The results supported a causal role of adiposity on hospital admissions, with consistency across all estimates and sensitivity analyses. Point estimates were generally larger than estimates from comparable observational specifications. We observed an attenuation of the BMI effect when adjusting for WHR in the multivariable Mendelian randomization analyses, suggesting that an adverse fat distribution, rather than a higher BMI itself, may drive the relationship between adiposity and risk of hospital admission.