John L. Moran

In the literature, the propriety of the meta-analytic treatment-effect produced by combining randomized controlled trials (RCT) and non-randomized studies (NRS) is questioned, given the inherent confounding in NRS that may bias the meta-analysis. The current study compared an implicitly principled pooled Bayesian meta-analytic treatment-effect with that of frequentist pooling of RCT and NRS to determine how well each approach handled the NRS bias. Binary outcome Critical-Care meta-analyses, reflecting the importance of such outcomes in Critical-Care practice, combining RCT and NRS were identified electronically. Bayesian pooled treatment-effect and 95% credible-intervals (BCrI), posterior model probabilities indicating model plausibility and Bayes-factors (BF) were estimated using an informative heavy-tailed heterogeneity prior (half-Cauchy). Preference for pooling of RCT and NRS was indicated for Bayes-factors > 3 or < 0.333 for the converse. All pooled frequentist treatment-effects and 95% confidence intervals (FCI) were re-estimated using the popular DerSimonian-Laird (DSL) random effects model. Fifty meta-analyses were identified (2009–2021), reporting pooled estimates in 44; 29 were pharmaceutical-therapeutic and 21 were non-pharmaceutical therapeutic. Re-computed pooled DSL FCI excluded the null (OR or RR = 1) in 86% (43/50). In 18 meta-analyses there was an agreement between FCI and BCrI in excluding the null. In 23 meta-analyses where FCI excluded the null, BCrI embraced the null. BF supported a pooled model in 27 meta-analyses and separate models in 4. The highest density of the posterior model probabilities for 0.333 < Bayes factor < 1 was 0.8. In the current meta-analytic cohort, an integrated and multifaceted Bayesian approach gave support to including NRS in a pooled-estimate model. Conversely, caution should attend the reporting of naïve frequentist pooled, RCT and NRS, meta-analytic treatment effects.

Background: Intensive care unit (ICU) length of stay (LOS) and the risk adjusted equivalent (RALOS) have been used as quality metrics. The latter measures entail either ratio or difference formulations or ICU random effects (RE), which have not been previously compared. Methods: From calendar year 2016 data of an adult ICU registry-database (Australia & New Zealand Intensive Care Society (ANZICS) CORE), LOS predictive models were established using linear (LMM) and generalised linear (GLMM) mixed models. Model fixed effects quality-metric formulations were estimated as RALOSR for LMM (geometric mean derived from log(ICU LOS)) and GLMM (day) and observed minus expected ICU LOS (OMELOS from GLMM). Metric confidence intervals (95%CI) were estimated by bootstrapping; random effects (RE) were predicted for LMM and GLMM. Forest-plot displays of ranked quality-metric point-estimates (95%CI) were generated for ICU hospital classifications (metropolitan, private, rural/regional, and tertiary). Robust rank confidence sets (point estimate and 95%CI), both marginal (pertaining to a singular ICU) and simultaneous (pertaining to all ICU differences), were established. Results: The ICU cohort was of 94,361 patients from 125 ICUs (metropolitan 16.9%, private 32.8%, rural/regional 6.4%, tertiary 43.8%). Age (mean, SD) was 61.7 (17.5) years; 58.3% were male; APACHE III severity-of-illness score 54.6 (25.7); ICU annual patient volume 1192 (702) and ICU LOS 3.2 (4.9). There was no concordance of ICU ranked model predictions, GLMM versus LMM, nor for the quality metrics used, RALOSR, OMELOS and site-specific RE for each of the ICU hospital classifications. Furthermore, there was no concordance between ICU ranking confidence sets, marginal and simultaneous for models or quality metrics. Conclusions: Inference regarding adjusted ICU LOS was dependent upon the statistical estimator and the quality index used to quantify any LOS differences across ICUs. That is, there was no “one best model”; thus, ICU “performance” is determined by model choice and any rankings thereupon should be circumspect.

Meta-analyses typically consider multiple outcomes and report univariate effect sizes considered as independent. Multivariate meta-analysis (MVMA) incorporates outcome correlation and synthesises direct evidence and related outcome estimates within a single analysis. In a series of meta-analyses from the critically ill literature, the current study contrasts multiple univariate effect estimates and their precision with those derived from MVMA. A previous meta-epidemiological study was used to identify meta-analyses with either one or two secondary outcomes providing sufficient detail to structure bivariate or tri-variate MVMA, with mortality as primary outcome. Analysis was performed using a random effects model for both odds ratio (OR) and risk ratio (RR); borrowing of strength (BoS) between multivariate outcome estimates was reported. Estimate comparisons, β coefficients, standard errors (SE) and confidence interval (CI) width, univariate versus multivariate, were performed using Lin’s concordance correlation coefficient (CCC). In bivariate meta-analyses, for OR (n = 49) and RR (n = 48), there was substantial concordance (≥ 0.69) between estimates; but this was less so for tri-variate meta-analyses for both OR (n = 25; ≥ 0.38) and RR (≥ -0.10; n = 22). A variable change in the multivariate precision of primary mortality outcome estimates compared with univariate was present for both bivariate and tri-variate meta-analyses and for metrics. For second outcomes, precision tended to decrease and CI width increase for bivariate meta-analyses, but was variable in the tri-variate. For third outcomes, precision increased and CI width decreased. In bivariate meta-analyses, OR coefficient significance reversal, univariate versus MVMA, occurred once for mortality and 6 cases for second outcomes. RR coefficient significance reversal occurred in 4 cases; 2 were discordant with OR. For tri-variate OR meta-analyses reversal of coefficient estimate significance occurred in two cases for mortality, nine cases for second and 7 cases for third outcomes. In RR meta-analyses significance reversals occurred for mortality in 2 cases, 6 cases for second and 3 cases for third; there were 7 discordances with OR. BoS was greater in trivariate MVMAs compared with bivariate and for OR versus RR. MVMA would appear to be the preferred solution to multiple univariate analyses; parameter significance changes may occur. Analytic metric appears to be a determinant.

Background: Mortality modelling in the critical care paradigm traditionally uses logistic regression, despite the availability of estimators commonly used in alternate disciplines. Little attention has been paid to covariate endogeneity and the status of non-randomized treatment assignment. Using a large registry database, various binary outcome modelling strategies and methods to account for covariate endogeneity were explored.Methods: Patient mortality data was sourced from the Australian & New Zealand Intensive Society Adult Patient Database for 2016. Hospital mortality was modelled using logistic, probit and linear probability (LPM) models with intensive care (ICU) providers as fixed (FE) and random (RE) effects. Model comparison entailed indices of discrimination and calibration, information criteria (AIC and BIC) and binned residual analysis. Suspect covariate and ventilation treatment assignment endogeneity was identified by correlation between predictor variable and hospital mortality error terms, using the Stata™ “eprobit” estimator. Marginal effects were used to demonstrate effect estimate differences between probit and “eprobit” models.Results: The cohort comprised 92,693 patients from 124 intensive care units (ICU) in calendar year 2016. Patients mean age was 61.8 (SD 17.5) years, 41.6% were female and APACHE III severity of illness score 54.5(25.6); 43.7% were ventilated. Of the models considered in predicting hospital mortality, logistic regression (with or without ICU FE) and RE logistic regression dominated, more so the latter using information criteria indices. The LPM suffered from many predictions outside the unit [0,1] interval and both poor discrimination and calibration. Error terms of hospital length of stay, an independent risk of death score and ventilation status were correlated with the mortality error term. Marked differences in the ventilation mortality marginal effect was demonstrated between the probit and the "eprobit" models which were scenario dependent. Endogeneity was not demonstrated for the APACHE III score.Conclusions: Logistic regression accounting for provider effects was the preferred estimator for hospital mortality modelling. Endogeneity of covariates and treatment variables may be identified using appropriate modelling, but failure to do so yields problematic effect estimates.

Background: The efficacy of prone positioning (PP) as therapy of the acute respiratory distress syndrome (ARDS) has varied in recent meta-analyses. The efficacy question was reviewed using a cohesive multivariate meta-analysis model incorporating all available common time-point data. Methods: Data from a core group of 8 randomized controlled trials (2001-2013) utilized in 8 current meta-analyses (2014-2017) was extracted for common time points. Multivariate meta-analysis and meta-regression models for prone-hours per day, mechanical ventilation tidal-volume and baseline patient PaO₂/FiO₂, considered as continuous and categorical predictors, determined the pooled relative risk (RR) of mortality for prone versus supine positioning. Results: Mortality RR at 28-30 days, 2-3 months and 6-months was not significant overall ( P > 0.05). Meta-regression of categorical predictors indicated significant mortality reduction ( P ≤ 0.001) for ≥ 12 prone-hours (versus < 12), lung protective ventilation (versus none) and moderate-severe ARDS (versus all ARDS). Meta-regressions of continuous predictors were also significant ( P ≤ 0.021) and yielded treatment inflection points of efficacious therapy for ≥ 12 prone-hours per day, ≤ 8.5 mL/kg tidal volume and ≤ PaO₂/FiO₂ ratio of 130. Conclusions: The mortality treatment effect of PP in ARDS, was not demonstrated in the unadjusted meta-analysis model. Moderator effects indicated consistent significant benefit of prone positioning. In the absence of individual patient data, multivariate models provide more decisive conclusions than individual time point analyses.

There has been renewed interest in lactate as a risk biomarker in sepsis and septic shock. However, the ability of the odds ratio (OR) and change in the area under the receiver operator characteristic curve (AUC-ROC) to assess biomarker added-value has been questioned. A sepsis cohort was identified from the ICU database of an Australian tertiary referral hospital using APACHE III diagnostic codes. Demographic information, APACHE III scores, 24-hour post-admission patient lactate levels, and hospital mortality were accessed. Hospital mortality was modelled using a base predictive logistic regression model and sequential addition of admission lactate, lactate clearance ([lactate^admission—lactate^final]/lactate^admission), and area under the lactate-time curve (LTC). Added-value was assessed using lactate index OR; AUC-ROC difference (base-model versus lactate index addition); net (mortality) reclassification index (NRI; range -2 to +2); and net benefit (NB), the number of true positives per patient adjusted for the number of false positives. The data set comprised 717 patients with mean(SD) age and APACHE III score 61.1(16.5) years and 68.3(28.2) respectively; 59.2% were male. Admission lactate was 2.3(2.5) mmol/l; with lactate of ≥ 4 mmol/L (37% hospital mortality) in 17% and patients with lactate < 4 mmol/L having 18% hospital mortality. The admission base-model had an AUC-ROC = 0.81 with admission lactate OR = 1.127 (95%CI: 1.038, 1.224), AUC-ROC difference of 0.0032 (-0.0037, 0.01615; P = 0.61), and NRI 0.240(0.030, 0.464). The over-time model had an AUC-ROC = 0.86 with (i) clearance OR = 0.771, 95%CI: 0.578, 1.030; P = 0.08; AUC-ROC difference 0.001 (-0.003, 0.014; P = 0.78), and NRI 0.109(-0.193, 0.425) and (ii) LTC OR = 0.997, 95%CI: 0.989, 1.005, P = 0.49; AUC-ROC difference 0.004 (-0.002, 0.004; P = 0.34), and NRI 0.111(-0.222, 0.403). NB was not incremented by any lactate index. Lactate added-value assessment is dependent upon the performance of the underlying predictive model and should incorporate risk reclassification and net benefit measures.