COS 597C Final Report

COS 597C Final Report
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  Time of Admittance and Mortality Rates An Analysis of Patient Time of Admittance on In-HospitalMortality Rates Jay Lee Woramanot Yomjinda Abstract This paper explores the relationship between the admittance time and in-hospitalmortality rates for critical care patients. Since upon first glance patient mortalityrates vary significantly by hour, this study aims to carefully analyze if these dispar-ities 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 in-hospital mortality rates for critical care pa-tients. 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 in-hospital 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 so-called ”weekend effect”, wherepatients admitted during the weekends showed higher overall in-hospital 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, codis-eases, and other covariates. 1  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 risk-adjusted 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 MIMIC-III 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 long-term 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. Index 2  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 in-hospital 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 3  who were admitted during the lower mortality hours (hours 5-11 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 0-4, 12, and 14-23).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: K-means 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 4  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 treat-ment group. By simulating randomized controlled trials and put propensity scorematching into practice, we can utilize the Rubin Causal Model framework to calcu-late 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 treat-ment or not. We therefore also make this assumption in our study. 5
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