Time of Admittance and Mortality Rates
An Analysis of Patient Time of Admittance on InHospitalMortality Rates
Jay Lee
junghwan@princeton.edu
Woramanot Yomjinda
yomjinda@princeton.edu
Abstract
This paper explores the relationship between the admittance time and inhospitalmortality rates for critical care patients. Since upon ﬁrst glance patient mortalityrates vary signiﬁcantly by hour, this study aims to carefully analyze if these disparities still remain in the absence of confounding variables, and if so, why they occur.The problem is stated as one of causal inference, and propensity score matching isused to estimate the average eﬀect of a patient’s admittance time on their survival.
1. Introduction
Countless diﬀerent factors can aﬀect inhospital mortality rates for critical care patients. Many studies have been performed on how quality of medical care is aﬀectedby factors like race [6], socioeconomic status [4], and even the day of week the patient
was admitted [1], many of which produced interesting results.One perhaps bizarre but nonetheless interesting factor we would also like to exploreis if the patient’s admittance hour (time of day) has any signiﬁcant eﬀects on inhospital mortality rates. One might wonder if patients admitted during the nighthave higher mortality rates since doctors might be more tired or understaﬀed. Orperhaps patients admitted during daytime receive poorer care since there are morepatients during these hours. This paper aims to explore if such disparities in mortalityrate do occur across diﬀerent admittance hours, and if so, why they occur.
2. Related Work
One famous related phenomenon in this area is the socalled ”weekend eﬀect”, wherepatients admitted during the weekends showed higher overall inhospital mortalityrates [1]. Weekend admissions were highly correlated with increased mortality inCanada [3], Wales and England [9], and also overall across North America, South
America, Europe, Asia, and Oceania [7], even after controlling for patient age, codiseases, and other covariates.
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While diﬀerent patient diagnoses are aﬀected diﬀerently by the weekend eﬀect,one of the most signiﬁcantly impacted groups were emergency department intensivecare patients, where the riskadjusted increase in mortality for weekends was about9% [2].Furthermore, explanations on why the weekend eﬀect occurs can also vary bypatient diagnoses; for some patients, the generally lower staﬃng of hospitals duringweekends cause the problem, while for others, it may be the unavailability of certaintests and services [5].But while the admittance time of patients as in day of week have been studiedin detail, a less explored ﬁeld is the eﬀects of the patient admittance time as in thetime of day on mortality rates. So in the same spirit as the studies mentioned above,this paper will analyze how patient admittance hours can aﬀect diﬀerent patientsof varying diagnoses, and what underlying causes might be responsible for such aneﬀect.
3. Preliminary Analysis
3.1 Data and Prepossessing
We used data from the electronic health records in the MIMICIII critical caredatabase to test our methods. As a ﬁrst step in preprocessing, we removed patientswith missing chart and lab data from our sample. Another design choice made wasto remove from our data any patients that were admitted multiple times. For thesemultiple admittance patients, while we could have used their ﬁrst admittance time,their last admittance time, or even an average of all admittance times, we did notﬁnd any one option more convincing than the others, and decided to remove thementirely.Secondly, we computed the Charlson Comorbidity Index (CCI) value for each of the patients. A patient’s CCI value essentially takes in as input all of the diagnosesthe patient has received, and outputs an integer value that estimates the overallcondition of a patient’s longterm health aspects. We used a package in R to ﬁnd thecomorbidity index values for each of our patients in the MIMIC data set, and addedthese values into our data
1
.
3.2 Data Exploration
The ﬁrst step in our analysis was to see if a patient’s admittance hour had anycorrelation on mortality rate at all. Upon ﬁrst glance, in Figure 1, we do see aclear disparity between admittance hour and mortality rates (
n
= 38914). The mostobvious note is that while a large amount of patients are admitted within the seventhhour (7 AM), the relative number of mortalities is very low for that particular hour.
1. https://github.com/chvlyl/Comorbidity Index
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Time of Admittance and Mortality Rates
(a) Number of patients by admittance hour (b) Number of mortalities by admittance hour
Figure 1: Admittance hours range from 0 to 23, with 0 representing midnight and23 representing 11PM. Patients are grouped by hour of admission, without rounding.For example, a patient admitted at 2:45 AM will be grouped under hour 2. This willbe the case for all ﬁgures in the paper.Figure 2: Mean patient mortality rates by hourSimilarly, Figure 2 displays the mean inhospital mortality rates by admittancehour, along with their 95% conﬁdence intervals. We can see in this graph that overall,there does exist a statistically signiﬁcant correlation between admittance hour andmortality rates. Using this as our motivation, we will analyze throughout the restof the paper whether or not time is signiﬁcant in and of itself, or if this is simply aresult of confounding variables.
3.3 Problem Formulation
We will formulate our problem as one of causal inference. In order to do this, we willﬁrst divide the admittance hours into two groups: a test (or treatment) group anda control group. In order to divide the patients, we clustered the patients into twogroups based on mortality rates (see Figure 3) . The test group will be the patients
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who were admitted during the lower mortality hours (hours 511 and 13, which willsometimes be referred to as ”the good hours”), and the control group will be thosewho were admitted during the remaining hours (hours 04, 12, and 1423).Since the goal of the our study is to test whether admittance time itself has asigniﬁcant eﬀect on mortality rates, we will control for the confounding variables inboth groups and then estimate the ’treatment’ eﬀect gained from being placed in thetest group. We discuss this methodology in detail in the next section.Figure 3: Kmeans clustering of patients into two clusters by mortality rate
4. Methods
4.1 Feature Selection
In order to test the true signiﬁcance of admittance time, we must ﬁrst select a setof features to control for. To do this, we ﬁrst studied the various diﬀerent patientdemographic information and time series data found in the MIMIC data set, andused Recursive Feature Elimination to determine the set of features that were thebest predictors of a patient’s admittance time. This was done because we believedthat many of the features that were essential to predicting the admittance time werealso potential underlying confounders for mortality.We ﬁrst started out with 40 possible features from our dataset, and ﬁt it on alogistic regression model to predict whether a patient was in the test group or not(i.e. given these features, which time group do we believe the patient was admitted?).Then, as per the recursive elimination process, we removed the least signiﬁcant featureand ﬁt the model again. This process was repeated twenty times until we ended upwith 20 features from our srcinal set of 40.
4.2 Causal Inference
One of the most important confounders to control for is the overall severity of thepatient’s condition. Thus, dividing and grouping the patients by their diagnoses was
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Time of Admittance and Mortality Rates
a natural choice to make. We studied ﬁve diﬀerent diagnoses in particular: congestiveheart failure, cardiac arrest, acute respiratory failure, severe sepsis, and pneumonia.Since this is an observational study, we cannot perform a real randomized controltrial to gauge the eﬀects of the treatment (i.e. being admitted during the ”goodhours”). In order to best simulate the eﬀects of such a trial, we use a statisticalmatching technique called propensity score matching.Matching is a technique used to estimate the causal eﬀect of receiving a treatment.In an ideal matching scenario, we would compare pairs of individuals who are identicalin all aspects except for whether they received the treatment or not. This way, theeﬀect of the treatment on the outcome (in our case, mortality rate) would be assessedin absence of confounding variables.However, since these ideal matching scenarios can be extremely diﬃcult to obtain(for instance, ﬁnding two patients that have the same 20 features but only diﬀeringin admittance time is hard to ﬁnd), we resort to propensity score matching. Givena patient’s feature vector
x
and a patient being in the test group as
T
= 1, thepropensity score
p
can be expressed as
p
(
x
)
def
=Pr(
T
= 1

X
=
x
)or simply put, the propensity score
p
(
x
) measures the probability of a patientbeing in the test group given a set of features
x
. These scores are usually constructedusing logistic regression, and balanced amongst the test and control groups. Lastly,in the matching process, instead of using individual features to match patients withother similar patients, we use this propensity score.
4.2.1 Average Treatment Effect
Our ultimate goal is to ﬁnd the average treatment eﬀect (ATE) of being in the treatment group. By simulating randomized controlled trials and put propensity scorematching into practice, we can utilize the Rubin Causal Model framework to calculate the ATE of the treatment in question [8].The model framework considers two possible scenarios for a given outcome
Y
i
(inour case, outcome is the patient’s mortality rate):
Y
i
(1) if individual i undergoestreatment
T
and
Y
i
(0) otherwise; these are not random. Because
T
i
is an indicatorof treatment status, the treatment eﬀect for i is
τ
i
=
Y
i
(1)
−
Y
i
(0), and thus
Y
i
=(1
−
T
i
)
Y
i
(0)+
T
i
Y
i
(1) =
Y
i
(0)+
T
i
τ
i
. It is important that
τ
i
varies across individualswith a distribution in the population despite being ﬁxed for each individual.The fundamental problem of causal inference is that since we only observe either
Y
i
(0) or
Y
i
(1), and not both simultaneously, we cannot estimate
τ
i
directly. At itscore, causal inference is a missing data problem.And before discussing the speciﬁcs of the model, the Rubin Causal Model makesthe Stable Unit Treatment Value Assumption (SUTVA), which states that a patient’san individual’s outcome is unaﬀected by whether other individuals receive the treatment or not. We therefore also make this assumption in our study.
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