Identifying KDIGO Trajectory Phenotypes Associated with Increased Inpatient Mortality

Abstract

Acute kidney injury (AKI) is a complex systemic syndrome associated with high morbidity and mortality and risk for the subsequent development of renal and non-renal complications. Nearly 50% of patients in the ICU experience AKI. AKI severity is a key metric for evaluating patients risk of hospital mortality. Current AKI stratification is based on absolute changes in Serum Creatinine (SCr) and the maximal increase relative to the patients baseline value. However, such measurement does not consider either the progression or duration of AKI, both of which are associated with adverse outcomes post-AKI. In this article, by leveraging a large volume of SCr temporal variabilities, we present a novel model called Trajectory of Acute Kidney Injury (TAKI) for the identification of AKI trajectory subtypes. Experimental results demonstrate that TAKI is better than the existing trajectory subtyping methods on both the inpatient mortality stratification and the post-7-day AKI progression estimation. With TAKI, it is found that the trend of KDIGO trajectory appears to be more highly associated with inpatient mortality rates than the maximum KDIGO score.

I. INTRODUCTION

Acute kidney injury (AKI) is a common and detrimental syndrome associated with a variety of poor outcomes [1]. More than 5 million patients are admitted to hospital intensive care units (ICUs) each year in the U.S., and approximately 50% of these patients suffer from AKI [2], [3]. In particular, AKI is associated with high morbidity [4], [5] and mortality [6], [7] and high risk for incident or progressive chronic kidney disease (CKD) [8]–[11]. Furthermore, about 30–40% of patients that suffer from severe AKI will develop CKD or end-stage renal disease (ESRD) [6], [12]. Therefore, AKI is a public health burden that markedly increases morbidity, mortality and health care costs [13], [14]. Existing risk-stratification tools for AKI have focused on and are validated for early AKI recognition [15], [16] and little is known about their utility to predict post-AKI outcomes.

Serum creatinine (SCr) is a marker of kidney function that is elevated during AKI and is widely available, inexpensive, and heavily utilized in routine clinical care [17]. In current practice, AKI is defined by a relative or absolute increase in SCr in reference to a baseline value or based on a decrease in urine output according to the Kidney Disease: Improving Global Outcomes (KDIGO) consensus [17]. However, the single interpretation of isolated changes in SCr may delay AKI detection and certainly lack information regarding the duration of AKI, multiple AKI hits or the degree of recovery from AKI [18]. Furthermore, SCr interpretation has several caveats in critically ill patients, in part due to the challenges related to the acute dilutional effect of severe fluid overload [19], [20], the decrease in creatinine production in sepsis [21], and the loss of muscle mass in patients with prolonged ICU stay [22].

In this context, computational tools have been developed to model AKI temporal developments (trajectories) under prespecified patients clinical characteristics, aiming to capture a broad range of AKI features, and to accurately predict adverse outcome post-AKI, particularly in critically ill patients. Guttterez et al [23] proposed a random intercept and slope model to describe the trajectory of SCr rise and its determinants after exposure to radiocontrast media. However, the tool cannot model trajectories with varying length. Bhatraju et al [24] utilized a RR regression to model the probability of death as a function of covariates using a generalized linear model with log-link binomial error distribution. However, their tool is limited to modeling simple SCr changing trends.

There is an urgent need to develop big data-oriented tools to identify AKI trajectory subtypes that are highly sensitive (prognostic value) and specific (treatment effect value) to provide accurate post-AKI risk-stratification and aid the implementation of cost-effective surveillance strategies and therapeutics that could promote AKI recovery, reduce the burden of CKD post-AKI, and ameliorate cardiovascular complications post-AKI [25]. The examination of AKI trajectory requires a detailed approach that incorporates clinical data such as baseline SCr, the presence of sepsis, the degree of fluid overload, body mass index and the utilization of renal replacement therapy (RRT). Note that this is not to suggest that the maximum KDIGO score shall be replaced by AKI trajectory subtypes, rather that there is additional critical information contained in the progression over time that has not been captured when only the maximum KDIGO score is considered.

AKI trajectory subtyping is a computationally challenging problem. First, patient record lengths are highly variable. Generally, there are a large number of patients with a relatively short duration in the ICU (~ 7 days), with progressively fewer patients as the duration is increased. Additionally, each patient may have multiple SCr records for each day, with the exact frequency of records still variable. For example, the distribution of the patients in the ICU at the University of Kentucky (UK) Albert B. Chandler Hospital (over 40,000 ICU patients, see Suppl Document) demonstrates that the SCr record length is highly variable and skewed to the left. Given a duration threshold, a traditional approach is to truncate records longer than the threshold and remove all patients with records shorter than the threshold. However, this may result in a significant loss of information. For example, if we choose patients with records in the ICU lasting no less than 7 days since admission, ~ 60% of patients in the UK data will be removed from the study cohort. Second, missing information in outpatient records makes it difficult to compute the baseline SCr value, which is essential for the calculated KDIGO scores to accurately reflect the degree of AKI. Third, it is generally unknown how many distinct AKI trajectory subtypes are present in AKI patients. All these complications, particularly the combination of variable record lengths and resolutions, coupled with missing information, pose a fundamental problem in AKI trajectory data analysis.

In this article, by leveraging a large volume of SCr variabilities over time, we present a novel machine learning model called Trajectory of Acute Kidney Injury (TAKI) for the identification of AKI trajectory subtypes. The workflow of TAKI is shown in Figure 1. Compared with the existing AKI models, TAKI is advantageous on the following aspects. First, TAKI includes a population-based approach to align and compare long and short KDIGO trajectories. Second, an AKI-specific distance function has been developed to compare AKI patients. Third, a clinical-oriented approach has been developed to determine the number of AKI trajectory subtypes. Finally, the subtypes of AKI trajectories identified by TAKI could lead to the characterization of critical AKI trajectory features, which are not commonly detectable by the conventional KDIGO definition or the recently proposed AKI trend models [24], for a more precise prediction of post-AKI outcomes.

Fig. 1.

Flowchart of TAKI, an AKI trajectory subtyping method. The general procedure is as follows: 1) SCr records for the ICU are extracted from hospital data, 2) following baseline determination, sequences are prepared by imputing missing SCr values and calculating corresponding KDIGO scores, 3) sequences are aligned using population-based DTW, 4) distance (or dissimilarity) computed between each pair of aligned sequences, 5) hierarchical clustering is applied with a dynamic merging process, and 6) final KDIGO trajectory subtypes are obtained.

II. BACKGROUND

A. Sequence Alignment

Dynamic time-warping (DTW) is a computational method for aligning two temporal sequences of variable speed or length and has been used extensively in audio-visual applications, e.g. speech recognition [26]. The ultimate goal of DTW is to identify the optimal non-decreasing mapping between the elements in each sequence that minimizes the sum of a given local cost measure for the aligned sequences. For example, consider two sequences X := [x₁...x_N] and Y := [y₁...y_M] whose elements x_n, y_m belong to a feature space $\mathcal{F}$, and a local cost measure $c:\mathcal{F}\times \mathcal{F}\to {ℝ}_{\ge 0}$. Then DTW aims to find an optimal alignment such that the sum of the local cost measure is minimized.

Given the local cost measure c and an N × M warping path p, the total cost is given by

$$c_p(X,Y):={\Sigma }_{l=1}^{L}c\left(x_{n_l},y_{m_l}\right)$$ (1)

Finally, the objective function for DTW is

$$DTW(X,Y):=c_{p^{*}}(X,Y)={\min }_p\left\{c_p(X,Y)\right\}$$ (2)

where p* is an optimal warping path. Note that although there may be multiple minimal cost paths, the minimal cost itself is determinant.

Traditional DTW is designed to find a globally optimal alignment that minimizes the total cost given a local cost measure, typically defined as the sum of the absolute differences between sequence values. This alignment procedure effectively translates to stretching out portions of one sequence (or both) to align with the other. Each point in one sequence is mapped to a point (or multiple points) in the other sequence, with the sole goal of minimizing this cumulative cost (or distance). This, however, can be problematic if attempting to align KDIGO trajectories. Specifically, our problem has two distinct differences from that defined in the context of traditional DTW. First, the sequences being aligned do not truly reflect the same real-world event or entity. Instead, we are attempting to align sequences captured from different individuals at different times in the way that most accurately reflects clinically significant factors such as the duration and rate of AKI progression. Second, rather than values from a continuous domain, our sequences contain distinct values. These sequence values still lie along a specific scale (i.e. KDIGO 3 is worse than 2 which is worse than 1), however, the clinical meaning between KDIGO development from 1 to 2 and from 2 to 3 are dramatically different [6].

B. Distance Function for Aligned Sequences

The Bray-Curtis (BC) dissimilarity is a metric developed to quantify the compositional dissimilarity between two sequences. It is naturally scaled in the range of [0, 1], regardless of the length of the input, where dissimilarity of 0 indicates identical sequences and 1 indicates maximal dissimilarity. The BC dissimilarity was initially constructed for the purpose of comparing counts at different sites for different populations. In the context of trajectory comparison, the different ‘sites’ correspond to individual time-points in the sequences, and the ‘counts’ correspond to the KDIGO score at that time-point. Mathematically, given two sequences of non-negative values X and Y, each of length l, the Bray-Curtis dissimilarity is given by

$$\text{BC}(X,Y)=\frac{{\mathrm{\Sigma }}_{i=1}^l\left|X_i-Y_i\right|}{{\mathrm{\Sigma }}_{i=1}^l\left|X_i+Y_i\right|}$$ (3)

Other possible alternatives are normalized Euclidean or Cityblock distances. Since these metrics scale relative to the length of the sequences being compared, they must be normalized [27]. Given a scalar distance metric $d(\cdot ,\cdot ):\mathcal{F}\times \mathcal{F}\to ℝ$ and two sequences $X,Y\in \mathcal{F}$, both of length l, the corresponding normalized distance is given by

$$d_{norm}(X,Y)=\frac{d(X,Y)}{M_{\mathcal{F},l}}$$ (4)

where

$$\begin{gathered} M_{D,l}=\max (\{d\left(V_1,V_2\right):V_1,V_2\in \mathcal{F}\text{and} \\ len\left(V_1\right)=len\left(V_2\right)=l\}) \end{gathered}$$

In this context, X and Y correspond to sequences of KDIGO scores, where $\mathcal{F}$ is the set of possible scores.

Regardless of the selected dissimilarity/distance function, applying it on the integer values of the corresponding KDIGO scores ignores the relative difference in AKI severity attributed to the different scores. For example, 2−1 = 4−3, however, in reality, the difference in the clinical significance of the higher scores is greater than lower scores.

C. Hierarchical Clustering

Agglomerative hierarchical clustering (AHC) is a robust clustering model which seeks to build a hierarchy of clusters [28]. Initially, each point is assigned to its own singleton cluster, and then clusters are sequentially combined by considering the distance to all other clusters. Given clusters c_i and c_j, the distance d(c_i, c_j) can be considered as the minimum distance between the clusters (called single-linkage), the maximum distance (complete linkage), the corresponding increase in the variance of c_i (Ward’s method), or one of any other number of options.

Unlike other clustering methods such as K-means where the number of clusters need be pre-specified, AHC generates a dendrogram. Consequently, deciding where to cut a dendrogram to generate the corresponding clusters depends on the context of the problem and the distance distributions between the underlying groups.

One potential limitation is that to adequately separate the groups when applying the traditional cophenetic distance-based threshold for cluster separation, additional clusters may be identified other than those desired. In order to obtain a minimum number of meaningful clusters for practical application, this means that merging superficially separated clusters may be necessary.

III. METHODS

We propose a novel AKI trajectory subtyping model call TAKI. TAKI has four steps. First, the SCr records for the ICU are extracted from hospital data and are preprocessed (such as data cleaning, data imputation). For patients with missing information in outpatient records, a rule-based method is implemented to estimate their baseline SCr values. For every patient, given the SCr baseline and the SCr records over time, a KDIGO trajectory is composed. Second, for KDIGO trajectories with different length, a population-based DTW method is developed to align the KDIGO trajectories. Third, the pair-wise distance between any two aligned KDIGO trajectories is computed using a population-based distance function. Finally, hierarchical clustering is adopted with a dynamic merging process to determine the final KDIGO trajectory subtypes.

A. Data Preprocessing

SCr Data Imputation

All valid SCr records from the first 7 days in the ICU are placed onto a uniform time-grid with 4 time-points per day (6 hours apart from each other), and any missing values within the time-grid are imputed using linear interpolation. For example, if a patient does not have a valid SCr record at noon, we will estimate it using the patient’s SCr records at 6 AM and 6 PM of the same day.

Baseline SCr Estimation

Baseline SCr value can be determined using a three-tier definition, similar to that in [29]. If a patient has any outpatient SCr records at least one day prior to indexed admission within the prior year, we use the latest value as a baseline. If the patient does not have any valid outpatient values but has at least one inpatient record within the prior year and at least seven days prior to indexed admission, we use the latest value as a baseline. Finally, if no valid inpatient or outpatient values are present within the prior year, the MDRD equation for GFR estimation is derived for baseline SCr assuming a GFR of 75 mL/min/1.73m² [30].

Computation of KDIGO Trajectory

Each SCr value is converted to a KDIGO score, where a higher KDIGO score indicates a higher degree of AKI severity. This results in a collection of KDIGO trajectories with the same time-resolution, but variable length. Mathematically, given a SCr value at time point t_i, denoted as s_i, and baseline s_b, the corresponding KDIGO score is 1 if 1.5 × s_b ≤ s_i < 2.0 × s_b or s_i – s_j ≥ 0.3mg/dl where t_i – t_j ≤ 48hours; KDIGO score is 2 if 2.0 × s_bs_i < 3.0 × s_b; and KDIGO score is 3 if s_i > 3.0 × s_b or s_i ≥ 4.0mg/dl. In our studies, the requirement of inpatient RRT was considered a separate severity category (KDIGO 3D). Additionally, all records in the 48 hours following termination of RRT are also designated KDIGO 3D to allow sufficient time for SCr levels to reach basal levels.

B. Population Based DTW

Given two sequences, DTW aligns them to identify the optimal non-decreasing mapping that minimizes the total alignment cost. It is natural to apply DTW on patients’ KDIGO trajectories to identify the best match. For a classical DTW, the mismatch penalty between two adjacent KDIGO scores is 1, no matter it is between KDIGO 1 and 2 or between 2 and 3. However, the difference between KDIGO scores reflects a certain degree of clinical significance that is strongly associated with AKI severity.

Our task is to identify an optimal alignment between the sequences while preserving the clinical significance of the shape and progression of each individual sequence, including the rate of progression and the duration of different stages of AKI. For example, the clinical significance of extending a segment of KDIGO 0 is marginal compared to that for KDIGO 3/3D. Hence, rather than using arbitrarily defined values or using the natural differences between integers, we developed a population-based DTW where the transition probabilities between any two adjacent KDIGO scores is determined by the data. Mathematically, given two adjacent KDIGO scores k_i, k_i+1 ∈ [0..4] (for simplicity, we rename KDIGO 3D to 4) the mismatch penalty between k_i and k_i+1 is defined using the transition weight:

$$T_w^{*}\left(k_i,k_{i+1}\right)=-log\left(\frac{\#\text{transitions}{k}_i\leftrightarrow k_{i+1}}{\text{total}\#\text{transitions}}\right)$$ (5)

Given two KDIGO trajectories X and Y with a different length, and a warping path p of length L, the cumulative mismatch penalty MM_p(X, Y) is given by:

$$M{M}_p(X,Y)={\mathrm{\Sigma }}_{l=1}^{L}M{M}_{p\left(X_{m_{\iota }},Y_{n_{\iota }}\right)}$$

where

$$M{M}_p\left(X_{m_{\iota }},Y_{n_{\iota }}\right)={\mathrm{\Sigma }}_{k=\min \left(X_{m_{\iota }},Y_{n_{\iota }}\right)}^{\max \left(X_{m_{\iota }},Y_{n_{\iota }}\right)-1}{T}_w(k,k+1)$$ (6)

Similarly, during sequence alignment, we consider a population-based cost of extending a KDIGO score to achieve the best match. The extension penalty is determined by the population derived transition weight and grows linearly with each subsequent repetition. mathematically, given a KDIGO trajectory X of length m and a M × N warping path p of length L, the cumulative extension penalty is given by

$$E_p(X)={\mathrm{\Sigma }}_{l=1}^L{E}_p\left(X_{m_{\iota }}\right)$$

where

$$E_p\left(x_{m_{\iota }}\right)=\{\begin{array}{ll}{T}_w\left(X_{m_{\iota }}-1,x_{m_{\iota }}\right)+E_p\left(x_{m_{\iota -1}}\right)\hfill & x_{m_{\iota }}=x_{m_{\iota -1}}\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$$ (7)

The objective function of the population based DTW is:

$$\begin{gathered} DTW(X,Y)= \\ argma{x}_p(M{M}_p(X,Y)+E_p(X)+E_p(Y)) \end{gathered}$$ (8)

With the new objective function, the mismatch penalties are scaled to the relative difference of the severity of each KDIGO score, as defined by the population transition probabilities. Similarly, the cost of extending higher KDIGO scores is greater than that for lower scores, scaled according to the same transition probabilities.

An example of the population-based DTW is shown in Figure 2. It highlights the effects of the population derived mismatch and extension penalties on the alignment of two example sequences of KDIGO scores. These examples are fairly short to conserve space, however, note that the observed differences are amplified for larger absolute differences in sequence length. First, note that the population mismatch has no effect by itself. This is because the traditional DTW algorithm seeks to minimize the absolute difference between aligned sequence values, regardless of what those values might be. This example particularly illustrates how traditional DTW can extend periods of high KDIGO in order to minimize the local cost, despite the fact that extending the KDIGO 0 in this example preserves more of the clinical significance of patient 1’s duration and severity of AKI. Incorporating the extension penalty causes the opposite to happen, exclusively extending the region of patient 1’s sequence with the lowest KDIGO scores. Although the local duration of patient 1’s sequence is preserved, in the context of comparing the trajectories of the two sequences, the extension penalty has arguably gone ‘too far’. When combined with the extension penalty, incorporating the population derived mismatch penalty effectively tampers the effect of the extension penalty, producing a happy medium of the extremes observed with traditional DTW vs. with the extension penalty alone.

Fig. 2.

Comparison of DTW alignment with and without population derived mismatch and extension penalties. First one is two original sequences of KDIGO scores with different lengths. Next is the result of sequence alignment using traditional DTW. The next two alignments correspond to the incorporation of the population mismatch penalty or the population extension penalty, respectively. Finally, the last alignment shows the results of population-based DTW.

C. Population Based Coordinates

Regardless of the chosen distance metric, the natural encoding of KDIGO scores to their corresponding integer values ignores the relative severity discussed above. By embedding the scores into a coordinate system that reflects the relative severity, the distance function can capture these same effects.

Thus, the population Based coordinate for a KDIGO score k is

$$PC(k)=\{\begin{array}{ll}{\sum }_{j=1}^k{T}_w(j-1,j)\hfill & k\ge 1\hfill \\ 0\hfill & k=0\hfill \end{array}$$ (9)

where T_w is the transition weight defined in Equation 5. Note that replacing the raw KDIGO scores in the original sequences by the corresponding population coordinates reflects the relative severity of each state, informed by how often that state is visited.

Using the population-based coordinates and a pre-selected distance function, a distance matrix for all the KDIGO trajectories can be obtained.

D. KDIGO Trajectory Subtyping

Given a distance matrix of KDIGO trajectories, hierarchical clustering can be applied to obtain a dendrogram, which provides a hierarchical relationship between all patients. By specifying the maximum cophenetic intra-cluster distance, which is represented in the dendrogram as the branching point, KDIGO trajectories can be separated into groups. While the representation of hierarchical relationships within the data provides a framework for identifying distinct clusters, there is no universal algorithm to extract an optimal set of clusters. The most direct approach to extract corresponding clusters is to define a universal distance threshold, such that the maximum intra-cluster cophenetic distance for all clusters is less than the given threshold. However, depending on the data distribution, setting a threshold low enough to generate meaningful clusters for one partition of the data may produce additional, unintended separations elsewhere. Consequently, deciding where to cut a dendrogram to generate the corresponding clusters depends on the context of the problem and the distance distributions between the underlying groups.

In this article, we instead present an alternative approach to proactively determining the number of clusters in two steps. First, we set a uniform low distance threshold to generate more clusters than desired. Second, based on domain knowledge, we compare clusters pair-wisely to determine which clusters (if any) to merge. Specifically, each cluster is categorized according to the following two criteria, by considering the cluster as a whole: 1) the maximum KDIGO score: 1, 2, 3, or 3D, and 2) the trend of KDIGO trajectory: improving, stable, or worsening. This provides a total of 9 possible categorizations. Each pair of clusters in the same category are then sorted by the averaged distance between each cluster and their lowest common ancestor in the dendrogram. The pair of clusters with the smallest distance is then merged, and the new clusters maximum cophenetic intra-cluster distance is considered equal to that of the previous lowest common ancestor, and this procedure repeats until a prespecified stopping criterium is met.

IV. EXPERIMENTAL RESULTS

In this experiment, we applied TAKI on the records of the patients in the ICU at the University of Kentucky Albert B. Chandler Hospital. We also compared TAKI with existing trajectory subtype identification methods using two evaluation criteria.

A. Cohort Definition and Data Preprocessing

We collected patient records from 37,095 patients at the University of Kentucky Nephrology Clinic who were admitted to the ICU from January 2009 to January 2017, with the exclusion criteria listed below:

• Less than two records in ICU, or spanning less than six hours

• Baseline S_Cr <4.0 mg/dL or eGFR >15 mL/min/1.73m²

• Missing DOB or Age <18yrs

• ESRD status at/before indexed admission

• Kidney transplant

• Died in first 48 hours of ICU admission

Finally, we exclusively considered those patients who experienced AKI as defined by a maximum KDIGO score ≥ 1 during the first seven days of ICU admission, resulting in a total of 6,816 patients (called UK data). In Table I, the patient cohort statistics indicates that the selected patients are balanced between gender but are biased towards white and old patients. In the table, “mortality” refers to the patients who died in the hospital, “>7d in ICU” is the number and percentage of patients who remained in the ICU for more than 7 days, and “>7d Progression” is the number and percentage of the patients who were in the ICU for >7 days who ultimately progressed to a higher KDIGO score than in the first 7 days. “Male” is the number and percentage of the male patients. “Age” is the mean and standard deviation of the patient ages. “Days in ICU” is the median, IQ1, and IQ3 of the days in the ICU for all the selected patients.

TABLE I.

Patient cohort statistics, grouped by maximum KDIGO score.

	All	KDIGO 1	KDIGO 2	KDIGO 3/3D
Patients count	6816	3131	1670	2015
Mortality	1605 (23.5)	497 (15.9)	381 (22.8)	727 (36.1)
>7d in ICU	2491 (36.5)	1073 (34.3)	561 (33.6)	857 (42.53)
>7d Progression	319 (12.8)	165 (15.4)	89 (15.9)	65 (17.9)
Male	3821 (56.1)	1815 (58.0)	890 (53.3)	1116 (55.4)
White	6361 (93.3)	2927 (93.5)	1554 (93.1)	1880 (93.3)
Age	60.6 (16.1)	61.4 (16.3)	62.2 (15.7)	57.9 (15.6)
Days in ICU	5.0 (2.0–11.0)	5.0 (2.0–10.0)	5.0 (2.0–10.0)	6.0 (3.0–12.0)

The patient cohort statistics also indicate that the cohort is biased towards KDIGO 1. More than 50% of the patients are KDIGO 1 patients. KDIGO 1 patients could have much sparser AKI trajectories compared with that of high AKI patients indicating KDIGO 1 patients are relatively easier to recover from kidney injury than high KDIGO patients. As shown in the UK data, 66% of values in all the KDIGO 1 trajectories are 0. In order to obtain KDIGO 1 trajectory subtypes, we divided patients into two subpopulations, i.e., patients with a maximum KDIGO score of 1 and the others with a higher KDIGO score, and the ran TAKI on the two datasets separately to obtain desired trajectory subtypes.

Following the establishment of the final cohort, we preprocessed the SCr data using the following steps: data imputation, SCr baseline computation, and KDIGO score computation (see Section III–A), and transition probability estimation (see Section III–B). The transition probabilities between adjacent KDIGO categories are calculated according to Equation 4 and are shown in Table II, where k₁ and k₂ indicate two adjacent KDIGO scores, and all the weights T_w(k₁, k₂) are scaled ≥ 1. With the transition weights determined, we defined the population-based pair-wise mismatch penalty which was computed using Equation 5, as shown in Table III. In the table, each value in a cell indicates the population-based mismatch penalty between two KDIGO scores.

TABLE II.

Transition weights for adjacent KDIGO scores determined using the UK data.

(k1, k2)	Tw (k1, k2)
(0, 1)	1.00
(1, 2)	2.73
(2, 3)	4.36
(3, 3D)	6.74

TABLE III.

Pair-wise population based mismatch penalties for each KDIGO score, using the transition weights in table II.

	0	1	2	3	3D
0	0	1.00	3.73	8.09	14.83
1	-	0	2.73	7.09	13.83
2	-	-	0	4.36	11.10
3	-	-	-	0	6.74
3D	-	-	-	-	0

Next, each pair of sequences were aligned using population-based DTW, and the distances were calculated with the population coordinates as defined in Equation 9. After obtaining the full distance matrix, all the 3,131 patients with a maximum KDIGO score 1 were first separated from the remaining 3,685 patients with higher KDIGO scores. The clusters are then extracted from each subpopulation separately. For the UK data, we obtained 5 clusters for the patients with max KDIGO 1 and 13 clusters for the remaining patients with higher KDIGO. Finally, given all the 18 clusters, the merging procedure described in section III–D was performed, resulting in the final 13 KDIGO trajectory subtypes.

The final results indicate that TAKI captures not only the maximum KDIGO score but also the duration and rate of progression over time, reflected in the corresponding mortality rates. Figure 3 shows the mean daily maximum KDIGO scores for each trajectory subtype. The subtypes are grouped according to their maximum KDIGO scores indicating mild AKI (KDIGO 1), moderate AKI (KDIGO 2), and severe AKI (KDIGO 3/3D), with a clear trend of increasing mortality, as has previously been shown in the literature. Additionally, the subtypes are grouped according to their general trend for the entire 7 days of improving, stationary, or worsening. The corresponding association of these three trends with inpatient mortality is striking, providing a significantly more meaningful stratification of patients than when only considering the maximum KDIGO score alone. Even within the same category, trajectory subtypes reflecting a distinct progression of AKI can provide critical information relevant to the risk of inpatient mortality.

Fig. 3.

Aligned Daily KDIGO Scores for AKI Trajectory Subtypes with associated rates of inpatient mortality. Subtypes are grouped according to maximum KDIGO score, as well as the general trend of improving, stationary, or worsening.

It is worth noting that the trend of KDIGO trajectory progression appears to be more highly associated with inpatient mortality rates than the maximum KDIGO score. Two of the identified subtypes that particularly demonstrate this phenomenon are clusters “2Ws” and “3Im”. Using only the maximum KDIGO scores as the indicator of AKI severity, one would generally assume that the mortality rate for 3Im would be higher than 2Ws, however, in reality, the mortality rate for 2Ws is six times higher than 3Im. Considering the daily trajectories in Figure 3, these mortality rates clearly reflect the trends in the corresponding trajectories. Despite having a lower maximum score, 2Im primarily consists of patients who gradually decline over time, whereas 3Im corresponds to patients who arrive in the ICU with a high score, but rapidly recover, as indicated by the mean KDIGO score of 0 by day 3. Consequently, despite the patients in 3Im having an indication of Severe AKI, their rapid recovery renders this group that with the lowest mortality out of all of the trajectory subtypes.

One of the most notable discoveries in the experimental data was that the shape of the trajectories has a stronger association with the rate of inpatient mortality than the maximum score, even when comparing patients with mild vs. severe AKI. This emphasizes that the rate of progression and duration of AKI are critical components in assessing those patient’s risk for inpatient mortality. This may allow early identification of patients that may have previously been considered low risk based on their maximum score alone. However, more work is required to explicitly identify key trajectory features that may further describe the differences in mortality rates from a clinical perspective. In future work, a machine learning framework will learn these key features and evaluate their predictive performance for predicting inpatient mortality with and without additional clinical characteristics such as those included in the SOFA and APACHE II scores, established clinical scores for estimating the risk of inpatient mortality based on multiple laboratory values and clinical vitals, such as mean arterial pressure [31], [32].

B. Evaluation Metrics

We consider two kinds of external data, i.e. inpatient mortality and AKI progression, for performance evaluation for AKI trajectory subtyping.

The primary consideration for cluster evaluation was the association of the resulting groups with inpatient mortality. In particular, for clusters with the same maximum KDIGO score in the first 7 days, we consider the difference in mortality between the groups identified. Quantitatively, given clusters c₁, … , c_n with corresponding inpatient mortality rates mort₁, … , mort_n, we define

$$MaxMortDiff=\max \left(mor{t}_i–mor{t}_j\right)$$

$$MinMortDiff=\min \left(mor{t}_i–mor{t}_j\right)$$

$$RelMortDiff=\frac{MaxMortDiff}{(100\%-MinMortDiff)}$$

Here, MaxMortDiff measures how well the most dissimilar clusters are separated in terms of mortality, MinMortDiff indicates how well the most similar clusters are separated, and RelMortDiff provides a single scaled combination of the two.

In addition to inpatient mortality rates, we consider the association of the clusters with the patient’s likelihood to progress to a higher KDIGO score after 7 days. To evaluate the rate of post 7-day KDIGO progression for each cluster, we consider only those patients with ≥ 7 days of records in the ICU and then determine the percentage of those patients who reached a higher KDIGO score after 7 days than they did in the first 7 days. Given clusters c₁, … , c_n, with corresponding post 7-day KDIGO progression rates prog₁, … , prog_n, we define

$$MaxProgDiff=\max \left(pro{g}_i–pro{g}_j\right)$$

$$MinProgDiff=\min \left(pro{g}_i–pro{g}_j\right)$$

$$RelMortDiff=\frac{MaxMortDiff}{(100\%-MinMortDiff)}$$

Here, MaxProgDiff measures how well the most dissimilar clusters are separated in terms of post-7-day KDIGO progression, MinProgDiff indicates how well the most similar clusters are separated, and RelProgDiff provides a single scaled combination of the two.

C. Performance Comparison

For performance comparison, we implemented six trajectory subtyping methods. These methods can be categorized by 1) how the trajectories are aligned and 2) how the pair-wise distance between two trajectories are computed. To align trajectories, the simplest method is to truncate trajectories which are longer than a duration threshold and to extend short trajectories using zero-padding until the trajectories are of the desired length. Alternatively, sequence alignment method (such as DTW) can be adopted to stretch/contract segments of trajectories of different lengths such that the aligned trajectories are the same length. To compute the pair-wise distance between any two trajectories, three distance functions, i.e., the Bray-Curtis distance, the Euclidean distance, and the Cityblock distances, were adopted. Finally, hierarchical clustering was used to obtain all of the trajectory subtypes. All these methods were named after the methods for alignment and for distance measurement. For example, ZB means zero-padding and Bray-Curtis, whereas DC means DTW and Cityblock.

Figure 4A shows the performance of TAKI and all the six methods-to-compare using the inpatient mortality rate based evaluation metrics introduced in Section IV–B. See details in Table VII. TAKI clearly outperforms all the other methods for KDIGO 2 and KDIGO 3/3D (Note: for population methods that compute the distance using population coordinates, a shift of 0 is assumed unless otherwise indicated), while the performance for KDIGO 1 is comparable. Additionally, for both zero-padding and DTW based trajectory alignment, the Bray-Curtis distance outperformed the other distance functions.

Fig. 4.

Performance Evaluation on the inpatient mortality stratification (A) and the post 7 day AKI progression estimation (B).

TABLE VII.

Performance comparison of different methods for each maximum KDIGO based AKI severity classification. Alignment: Z - zero-padding, D - DTW. Distance function: B - Bray-Curtis, E - Euclidean, C - Cityblock. TAKI is the proposed method.

	MinMortDiff			MaxMortDiff			RelMortdiff			MinProgDiff			MaxProgDiff			RelProgDiff
Method	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D
ZB	0.47	0.71	1.71	13.94	30.86	29.36	0.14	0.31	0.30	1.41	0.00	7.03	9.78	18.55	18.79	0.10	0.19	0.20
ZE	0.09	0.36	0.35	6.81	9.23	29.28	0.07	0.09	0.29	0.08	0.78	1.60	11.96	7.26	20.47	0.12	0.07	0.21
ZC	1.14	0.55	0.14	7.45	27.91	39.71	0.08	0.28	0.40	0.97	0.01	0.00	14.98	7.85	16.88	0.15	0.08	0.17
DB	0.04	1.03	4.35	15.13	45.81	53.67	0.15	0.46	0.56	1.75	0.10	0.00	31.77	23.88	25.00	0.32	0.24	0.25
DE	0.06	1.12	2.52	14.31	34.69	47.63	0.14	0.35	0.49	0.42	0.13	0.00	35.08	29.92	28.38	0.35	0.30	0.28
DC	0.23	0.61	0.69	13.71	34.23	47.03	0.14	0.34	0.47	0.07	0.55	0.00	34.51	24.30	26.25	0.35	0.24	0.26
TAKI	0.43	1.17	7.42	14.07	54.78	69.50	0.14	0.55	0.75	1.43	0.70	0.00	17.98	43.10	35.71	0.18	0.43	0.36

Figure 4B shows the performance of TAKI and all the six methods-to-compare using the post seven day AKI progression based evaluation metrics introduced in Section IV–B. See details in Table VII. TAKI receives the best performance for KDIGO 2 patients while its performance on KDIGO 1 is not as good as traditional DTW based method.

V. DISCUSSION

AKI is a complex systemic syndrome associated with high morbidity and mortality and risk for the subsequent development of renal and non-renal complications. Current AKI severity measure is based on the maximal increase in SCr relative to the patients baseline value without considering the progression or duration of AKI, both of which are associated with adverse outcomes post-AKI.

In this article, we present TAKI for the identification of AKI trajectory subtypes from a large volume of SCr temporal variabilities. With TAKI, we are able to further stratify patients in a way that preserves the clinical characteristics relevant to a risk of inpatient mortality and post 7-day KDIGO progression. Furthermore, our population-based approach utilizes big datadriven approach to define mismatch and extension penalties for sequence alignment and subsequent distance calculation. Notably, our extension penalty considers local effects of extending regions within a single sequence, in addition to the corresponding mismatch penalty between the sequences being aligned. This ultimately preserves trajectory features corresponding to the rate of progression and duration of AKI, as demonstrated by the superior performance for risk stratification. In conclusion, the AKI trajectory subtypes identified by TAKI demonstrate generally superior performance compared to all the compared methods in terms of their associations with both inpatient mortality and the further progression of AKI beyond 7 days in the ICU.

Since there are two key steps in TAKI, i.e. trajectory alignment and distance computation, both of which rely on the population-based transition weights, we tested the effectiveness of each component using the leave-one-out approach. Figure 5 shows the results for the two key components of TAKI separately, as well as combined. For patients with a maximum KDIGO score of 2, the population DTW with normal distance performed better than traditional DTW with population derived coordinate distances. However, this trend was reversed for the other groups. See details in Table VIII. In general, TAKI with both the population derived DTW and population coordinates for distance performed better than each component by itself, with the exception of post-7-day progression for patients with a maximum KDIGO score of 1.

Fig. 5.

Evaluating the components of TAKI on the inpatient mortality stratification (A) and the post 7 day AKI progression estimation (B). TAKI V1 corresponds to traditional DTW with the population coordinates for distance. TAKI V2 corresponds to population based DTW with the classical BC distance using the KDIGO scores. TAKI is the combination of both.

TABLE VIII.

Independent evaluation of components of TAKI. TAKI V1 represents classic DTW with the population derived Bray-Curtis distance. TAKI V2 represents population DTW with the classic Bray-Curtis distance.

	MinMortDiff			MaxMortDiff			RelMortdiff			MinProgDiff			MaxProgDiff			RelProgDiff
Method	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D	K1	K2	K3/3D
TAKI V1	0.22	0.34	1.30	13.87	41.96	50.73	0.14	0.42	0.51	2.03	1.68	0.00	27.52	22.42	26.55	0.28	0.23	0.27
TAKI V2	0.65	0.75	9.91	13.57	51.05	45.66	0.14	0.51	0.51	1.18	0.00	1.80	15.86	30.53	16.67	0.16	0.31	0.17
TAKI	0.43	1.17	7.42	14.07	54.78	69.50	0.14	0.55	0.75	1.43	0.70	0.00	17.98	43.10	35.71	0.18	0.43	0.36

In conclusion, TAKI is an effective tool for the identification of AKI trajectory subtypes. In the future, we will test whether the model can be applied to data collected from multiple medical centers.

TABLE IV.

Clinical characteristics of trajectory subtypes with max KDIGO 1.

-	1Im	1St	1Ws
Count	914	1541	676
Inpatient Mortality - n (%)	104 (11.38)	221 (14.34)	172 (25.44)
Demographics
Age - mean(SD)	61.6 (16.4)	61.5 (16.2)	60.9 (16.6)
Gender - male n(%)	487 (53.3)	918 (59.6)	410 (60.7)
Ethnic group - white n(%)	856 (93.7)	1439 (93.4)	632 (93.5)
BMI - mean(SD)	30.2 (9.7)	30.1 (9.7)	29.5 (8.6)
Acuity of Critical Illness
SOFA score - median[IQ1 - IQ3]	8.0 (5.0– 10.0)	8.0 (6.0– 10.0)	8.0 (5.0– 9.0)
APACHE score - median[IQ1 - IQ3]	23.0 (19.0– 26.0)	23.0 (19.0– 27.0)	22.0 (19.0– 26.0)
AKI characteristics
ALL Baseline SCr - median[IQ1 - IQ3]	0.9 (0.8– 1.0)	1.0 (0.8– 1.0)	1.0 (0.8– 1.1)
ALL Baseline eGFR - median[IQ1 - IQ3]	62.5 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)
Measured Baselines - n (%)	266 (29.1)	416 (27.0)	174 (25.7)
Measured Baseline SCr - median[IQ1 - IQ3]	0.8 (0.7– 1.0)	1.0 (0.8– 1.3)	1.0 (0.8– 1.4)
Measured Baseline eGFR - median[IQ1 - IQ3]	72.1 (53.9– 91.1)	56.9 (40.4– 76.7)	53.1 (37.8– 74.1)
Imputed Baseline SCr - median[IQ1 - IQ3]	1.0 (0.8– 1.0)	1.0 (0.8– 1.0)	1.0 (0.8– 1.0)
Imputed Baseline eGFR - median[IQ1 - IQ3]	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)
Admit SCr - median[IQ1 - IQ3]	1.5 (1.3– 1.7)	1.1 (0.9– 1.4)	1.0 (0.8– 1.3)
Peak SCr - median[IQ1 - IQ3]	1.5 (1.3– 1.8)	1.5 (1.2– 1.8)	1.5 (1.2– 1.8)
Maximum KDIGO Stage - Whole ICU:
Stage 1 - n (%)	896 (30.2)	1447 (48.8)	623 (21.0)
Stage 2 - n (%)	7 (0.4)	49 (2.9)	27 (1.6)
Stage 3 - n (%)	4 (0.4)	19 (1.7)	7 (0.6)
Stage 3D - n (%)	7 (0.7)	26 (2.5)	19 (1.8)
Maximum KDIGO Stage – 7 Days:
Stage 1 - n (%)	914 (29.2)	1541 (49.2)	676 (21.6)
Stage 2 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 3 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 3D - n (%)	0 (0.0)	0 (0.0)	0 (0.0)
Urine output D0-D2 - median[IQ1 - IQ3]	1.5 (1.0– 2.4)	1.6 (1.0– 2.7)	1.6 (1.0– 2.5)
Urine flow D0-D2 - median[IQ1 - IQ3]	0.7 (0.4– 1.2)	0.8 (0.5– 1.3)	0.8 (0.5– 1.3)

TABLE V.

Clinical characteristics of trajectory subtypes with max KDIGO 2.

-	2Im	2St	2St-1	2Ws
Count	836	551	94	391
Inpatient Mortality - n (%)	98 (11.72)	151 (27.40)	7 (7.45)	177 (45.27)
Demographics
Age - mean(SD)	61.7 (15.9)	64.4 (16.0)	58.1 (15.4)	61.2 (14.7)
Gender - male n(%)	413 (49.4)	291 (52.8)	59 (62.8)	243 (62.1)
Ethnic group - white n(%)	780 (93.3)	513 (93.1)	90 (95.7)	359 (91.8)
BMI - mean(SD)	32.6 (11.4)	31.7 (11.8)	30.3 (7.9)	30.3 (10.5)
Acuity of Critical Illness
SOFA score - median[IQ1 - IQ3]	9.0 (6.0– 11.0)	9.0 (6.0– 11.0)	9.0 (6.0– 10.0)	9.0 (6.0– 10.0)
APACHE score - median[IQ1 - IQ3]	25.0 (21.0– 28.0)	25.0 (21.5– 29.0)	24.0 (21.0– 27.0)	25.0 (21.0– 28.0)
AKI characteristics
ALL Baseline SCr - median[IQ1 - IQ3]	0.9 (0.8– 1.0)	0.9 (0.8– 1.0)	0.9 (0.8– 1.0)	1.0 (0.8– 1.0)
ALL Baseline eGFR - median[IQ1 - IQ3]	68.8 (55.3– 74.6)	61.2 (55.3– 74.6)	61.9 (55.3– 74.6)	55.3 (55.3– 74.6)
Measured Baselines - n (%)	218 (26.1)	107 (19.4)	39 (41.5)	120 (30.7)
Measured Baseline SCr - median[IQ1 - IQ3]	0.8 (0.7– 1.1)	0.8 (0.7– 1.0)	0.8 (0.7– 1.0)	0.9 (0.7– 1.1)
Measured Baseline eGFR - median[IQ1 - IQ3]	69.3 (54.0– 88.2)	74.8 (55.3– 89.5)	71.7 (58.0– 87.6)	65.8 (48.9– 85.1)
Imputed Baseline SCr - median[IQ1 - IQ3]	0.9 (0.8– 1.0)	0.9 (0.8– 1.0)	1.0 (0.9– 1.0)	1.0 (0.8– 1.0)
Imputed Baseline eGFR - median[IQ1 - IQ3]	61.5 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)
Admit SCr - median[IQ1 - IQ3]	2.0 (1.6– 2.3)	1.9 (1.6– 2.4)	1.0 (0.8– 1.2)	1.2 (0.9– 1.5)
Peak SCr - median[IQ1 - IQ3]	2.1 (1.8– 2.5)	2.4 (2.1– 2.9)	2.1 (1.8– 2.5)	2.2 (1.9– 2.6)
Maximum KDIGO Stage - Whole ICU:
Stage 1 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 2 - n (%)	764 (45.9)	391 (23.5)	81 (4.9)	345 (20.7)
Stage 3 - n (%)	53 (4.7)	142 (12.6)	13 (1.2)	19 (1.7)
Stage 3D - n (%)	19 (1.8)	18 (1.7)	0 (0.0)	27 (2.5)
Maximum KDIGO Stage – 7 Days:
Stage 1 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 2 - n (%)	788 (47.2)	421 (25.2)	84 (5.0)	377 (22.6)
Stage 3 - n (%)	47 (4.2)	130 (11.6)	10 (0.9)	9 (0.8)
Stage 3D - n (%)	1 (0.1)	0 (0.0)	0 (0.0)	5 (0.6)
Urine output D0-D2 - median[IQ1 - IQ3]	1.7 (1.0– 2.6)	1.4 (0.8– 2.3)	1.5 (1.0– 2.6)	1.3 (0.8– 2.3)
Urine flow D0-D2 - median[IQ1 - IQ3]	0.8 (0.5– 1.3)	0.7 (0.4– 1.2)	0.7 (0.4– 1.4)	0.6 (0.4– 1.0)

TABLE VI.

Clinical characteristics for trajectory subtypes with max KDIGO 3/3D.

-	3Im	3Im-1	3St	3DSt	3Ws	3DWs
Count	133	163	586	752	61	118
Inpatient Mortality - n (%)	9 (6.77)	28 (17.18)	176 (30.03)	330 (43.88)	42 (68.85)	90 (76.27)
Demographics
Age - mean(SD)	55.0 (12.5)	61.4 (16.4)	60.1 (16.0)	55.1 (14.7)	59.1 (15.4)	55.2 (16.0)
Gender - male n(%)	67 (50.4)	79 (48.5)	308 (52.6)	427 (56.8)	40 (65.6)	79 (66.9)
Ethnic group - white n(%)	119 (89.5)	149 (91.4)	543 (92.7)	713 (94.8)	57 (93.4)	111 (94.1)
BMI - mean(SD)	32.2 (10.7)	31.7 (9.3)	32.4 (12.8)	34.1 (12.2)	29.6 (7.9)	29.8 (10.3)
Acuity of Critical Illness
SOFA score - median[IQ1 - IQ3]	9.0 (7.0– 12.0)	10.0 (8.0– 12.5)	10.0 (8.0– 12.0)	12.0 (10.0– 14.0)	9.0 (7.0– 11.0)	11.0 (9.0– 13.0)
APACHE score - median[IQ1 - IQ3]	25.0 (22.0– 29.0)	27.0 (24.0– 30.0)	26.0 (22.0– 30.0)	29.0 (25.0– 32.0)	25.0 (22.0– 30.0)	27.5 (23.0– 31.0)
AKI characteristics
ALL Baseline SCr - median[IQ1 - IQ3]	0.9 (0.8– 1.0)	0.9 (0.8– 1.0)	0.9 (0.8– 1.0)	1.0 (0.8– 1.1)	1.0 (0.8– 1.0)	1.0 (0.9– 1.1)
ALL Baseline eGFR - median[IQ1 - IQ3]	74.5 (55.3– 74.6)	74.6 (55.3– 74.6)	65.1 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.5)
Measured Baselines - n (%)	33 (24.8)	34 (20.9)	135 (23.0)	185 (24.6)	12 (19.7)	39 (33.1)
Measured Baseline SCr - median[IQ1 - IQ3]	0.8 (0.6– 1.0)	0.7 (0.6– 0.9)	0.8 (0.7– 1.0)	1.0 (0.8– 1.4)	0.8 (0.7– 0.9)	1.2 (0.9– 1.5)
Measured Baseline eGFR - median[IQ1 - IQ3]	77.7 (64.3– 97.4)	83.3 (59.5– 105.0)	73.7 (57.3– 90.7)	56.0 (36.7– 76.2)	74.4 (59.8– 81.7)	48.8 (35.7– 71.3)
Imputed Baseline SCr - median[IQ1 - IQ3]	1.0 (0.8– 1.0)	0.9 (0.8– 1.0)	1.0 (0.8– 1.0)	1.0 (0.8– 1.0)	1.0 (0.8– 1.0)	1.0 (0.9– 1.1)
Imputed Baseline eGFR - median[IQ1 - IQ3]	55.3 (55.3– 74.6)	61.5 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)	55.3 (55.3– 74.6)
Admit SCr - median[IQ1 - IQ3]	3.4 (2.8– 4.4)	3.3 (2.6– 4.3)	2.7 (1.9– 3.9)	3.1 (1.9– 4.6)	1.2 (0.8– 1.6)	1.4 (1.2– 1.9)
Peak SCr - median[IQ1 - IQ3]	3.5 (2.8– 4.5)	3.6 (2.9– 4.4)	4.2 (3.4– 5.5)	4.6 (3.3– 6.3)	3.9 (3.2– 5.0)	3.1 (2.4– 4.5)
Maximum KDIGO Stage - Whole ICU:
Stage 1 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 2 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 3 - n (%)	132 (11.7)	158 (14.0)	530 (47.1)	0 (0.0)	49 (4.4)	0 (0.0)
Stage 3D - n (%)	1 (0.1)	5 (0.5)	56 (5.3)	752 (70.9)	12 (1.1)	118 (11.1)
Maximum KDIGO Stage – 7 Days:
Stage 1 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 2 - n (%)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)
Stage 3 - n (%)	133 (11.9)	161 (14.4)	570 (51.0)	0 (0.0)	57 (5.1)	0 (0.0)
Stage 3D - n (%)	0 (0.0)	2 (0.2)	16 (1.8)	752 (83.7)	4 (0.4)	118 (13.1)
Urine output D0-D2 - median[IQ1 - IQ3]	2.2 (1.6– 3.6)	1.7 (1.0– 2.9)	1.2 (0.6– 2.1)	0.4 (0.1– 1.1)	1.3 (1.0– 2.8)	0.8 (0.3– 1.7)
Urine flow D0-D2 - median[IQ1 - IQ3]	1.0 (0.7– 1.9)	0.8 (0.5– 1.6)	0.5 (0.3– 1.1)	0.2 (0.1– 0.5)	0.5 (0.4– 1.0)	0.3 (0.1– 0.7)