Association of Net Ultrafiltration Rate With Mortality Among Critically Ill Adults With Acute Kidney Injury Receiving Continuous Venovenous Hemodiafiltration

Key Points Question Is the net ultrafiltration (ie, fluid removal) rate associated with survival among critically ill patients with acute kidney injury? Findings In this secondary analysis of a randomized clinical trial involving 1434 critically ill patients treated with continuous venovenous hemodiafiltration, a net ultrafiltration rate greater than 1.75 mL/kg/h compared with a net ultrafiltration rate less than 1.01 mL/kg/h was significantly associated with lower 90-day risk-adjusted survival. Meaning Among critically ill patients with acute kidney injury being treated with continuous venovenous hemodiafiltration, net ultrafiltration rates greater than 1.75 mL/kg/h were associated with increased mortality.


Values and Estimated Glomerular Filtration Rate
Premorbid renal function as determined by serum creatinine and estimated glomerular filtration rate (eGFR) is a strong predictor of mortality. However, premorbid serum creatinine is frequently unavailable in acute kidney injury studies due to missing data. Generally, there are three different patterns of missing data. 3,4 First, data may be missing completely at random when the probability of missing values does not depend on any observed or unobserved variables. Second, data may be missing not completely at random if the probability of missing values depends on observed variables. Third, data may be missing non-random when the probability of missing values depends unobserved variables. Because the decision to measure premorbid serum creatinine is usually based on some existing clinical information, missing premorbid creatinine data are generally considered missing not completely at random. 5,6 Multiple imputation is a widely used approach to estimate premorbid creatinine values when data are missing at random. 5 We used the multivariable imputation by chained equation (MICE) method 7 to impute the creatinine values using age, sex, and weight as predictors among 637 subjects (44.4%) with missing premorbid serum creatinine values. By leveraging known patient characteristics and accounting for uncertainty in the multiple estimations of missing values, multiple imputation preserves sample size and reduces bias while examining association between variables. 4 For each multiple imputation strategy, values of premorbid serum creatinine were imputed using linear regression. Serum creatinine was imputed 20 times using MICE 7 and values were averaged to obtain the final estimate.
We subsequently used the Modification of Diet in Renal Disease (MDRD) equation to estimate the premorbid glomerular filtration rate using the imputed and unimputed creatinine. 8 eFigure 1 shows the distribution of imputed and unimputed premorbid serum creatinine and eGFR. The distributions were compared using the Kolmogorov-Smirnov Two-Sample test, which is a nonparametric test of the equality of continuous, one-dimensional probability distributions that can be used to compare two samples. We found no difference in distribution of imputed and unimputed premorbid creatinine values (P=0.29) and corresponding premorbid eGFR (P=0.13; eFigure 1).

Regression Model for Time to Mortality
There are well known risk factors for death after fluid overload in critically ill patients such as age, premorbid renal function, shock, severity of illness or cumulative fluid overload. The impact of these factors on mortality change overtime. For instance, an elderly patient in shock is initially at greater risk of death from shock than from premorbid renal function or cumulative fluid overload. Should she survive shock, premorbid renal function and cumulative fluid overload will become important determinants of late survival. 9,10 This observation could be important when using survival models to estimate differences in outcomes between different groups (e.g., NUF rate).
Survival models analyze time-to-event data to identify predictors of outcome. The most common approach, described by Cox, 11 assumes constant hazard ratios throughout a subject's time course. By assuming constant hazard ratios for all risk factors, Cox models assume the relative contribution of each risk factor to mortality is constant over time. This assumption is known as the "proportional hazards" and does not hold true in patients with fluid overload, 9 nor in other acute illness diseases (e.g., sepsis). 12 Considering again our example, the hazard ratio for shock at presentation will likely decrease over time because, if the subject survives the initial shock, the fact that shock was present will become less and less important as time passes. Consequently, traditional survival models, which depend on proportional hazards such as the Cox model, do not adequately describe survival after fluid overload in critically ill patients. 9,10 Gray's piecewise-constant time-varying coefficients survival model [13][14][15][16] is an approach that directly estimates how the hazards from individual risk factors change over time and therefore is better suited for modeling survival after fluid overload. 9 We fitted Gray's model for three reasons: First, NUF variable violated proportionality assumption (eFigure 3). 11 Second, the Gray's model does not assume time-invariant effects of the exposure. 15 This is important because the association between NUF rate and mortality is likely to vary over time. 9,10 Third, the Gray's model accounts for differences in exposure time, which is important because patients with low rate of NUF and positive fluid balance will have shorter survival time within each time interval. 10 The advantage of Gray's model is that it does not rely on the proportional hazards assumption, does not require arbitrary decisions regarding time intervals as it assigns the duration of these time intervals automatically, based on the actual data themselves, and provides a richer description of risk of death over-time. 15 Another advantage of the Gray's model is that it provides coefficients that can be interpreted in the same way as those obtained from a traditional Cox model and provides a statistical method sensitive to clinical nuance. For example, the model demonstrated that the association between NUF rate >1.75 mL/kg/hr compared with <1.01 mL/kg/hr and mortality was variable: there was no association between NUF rate >1.75 mL/kg/hr and mortality until day 6, however the risk increased from day 7 to 26 and then stayed constant from day 27 to day 90 ( Figure A in the manuscript).

eAppendix 4. Joint Model
Longitudinal data and time-to-event data can be modelled separately using linear mixed effects model and Cox proportional hazards model. However, these separate models fail to account for correlation between the longitudinal data and the time-to-event data that may result in biased estimates of treatment effect. A Joint model accounts for this correlation by simultaneously modelling the time-to-event and longitudinal data in a single unified model. 17,18 We conducted longitudinal analyses using Joint model to account for correlation between daily NUF rate and cardiovascular (CV) SOFA score over time and its association with survival. We chose Joint modelling because it allowed us to simultaneously model associations between NUF rate, changes in NUF rate and CV SOFA score over time, NUF rate and CV SOFA before death and risk of time-to-death in a single unified model. The effect on the hazard of a longitudinally measured covariate is accomplished by assuming that the hazard is a function of the "true" but latent trajectory that defines the longitudinal profile.
This approach is similar to the time dependent model in that it uses the current value of the time dependent covariate as the major driving force affecting time-to-death, but the use of a linear model for the longitudinal portion allows a more precise estimate of the NUF rate and CV SOFA score before death. The parameter estimates(β) for the baseline NUF rate and the change in NUF rate immediately prior to death adjusting for daily CV SOFA score can be used to estimate the effect of these variables on risk of death. If we transform the parameter estimate as 100*(exp(β*K)-1), this will give the percent increase or decrease in the hazard per K unit increase in NUF rate. However, the association estimates derived for rate of change in NUF rate over time cannot be transformed in the same manner to the magnitude of the hazard.
Using Joint modelling, we fitted daily NUF rates and CV SOFA score as longitudinal variables and other baseline covariates in the Cox model. We adjusted for age; sex; eGFR; duration from ICU admission to study enrollment; APACHE-III score; baseline total SOFA score; organ edema, sepsis and use of mechanical ventilation; cumulative daily fluid balance; duration of CVVHDF; source of admission including whether the patient was transferred to the ICU from an emergency department, hospital ward, operating room after elective or emergency surgery, another hospital or ICU; hospital type; and hospital region. The association parameter was 0.056 and the P value was significant at <0.001. A parameter value of <0 implies that increases in the longitudinal NUF rate after adjusting for CV SOFA score and other baseline covariates decreases time-to-death (or increased hazard of death). Table below shows the interpretation of the coefficients from a Joint model and its relationship to time-to-event.

Value of Longitudinal Variables
Time-to-Death Hazard Less than 0 Increase Increase Decrease Greater than 0 Increase Decrease Increase

eAppendix 5. Statistical Methods for Propensity Score Estimation and Matching
We generated a propensity score (logit) using logistic regression and then matched 405 patients out of the possible 478 patients who received NUF rate >1.75 mL/kg/hr on a 1:1 basis with 405 patients of the 956 patients who received NUF rate 1.75 mL/kg/hr, on a random seed, nearest neighbour, without replacement and a caliper distance of 0.05 (approximately 5% of the standard deviation of the logits) (eFigure 4; eTable 3).
The starting model included all available patient characteristics to maximize patient similarity across the two groups. Variables were removed from the model if their standard errors were greater than 0.1 to ensure that the model was not over-fit. Model calibration and discrimination were not calculated because the goal was to match the patients as closely as possible with the NUF rate >1.75 mL/kg/hr group instead of predicting NUF rate >1.75 mL/kg/hr group. An odds ratio for 90 day mortality was generated for NUF rate >1.75 mL/kg/hr group using an unadjusted logistic regression model restricted to 405 propensity-matched subjects (total N=810). Propensity score generation and matching were run using SAS 9.4 (SAS Institute, Cary, NC, USA).

eAppendix 6. Multivariable Logistic Regression Model
Univariable and multivariable modelling of the association between NUF rate and 90day mortality was performed using logistic regression adjusted for covariates with robust standard errors and mixed effects to account for nonindependence of cases across ICUs. Binary covariates were modelled as indicator covariates and continuous variables included as linear covariates after assessing for nonlinear relationships. Variance Inflation Factor (VIF) were generated to confirm that there was no collinearity among the independent variables. Specifically, the VIF for the NUF variable was 1.