Statistical Analysis of Patients’ Characteristics in Neonatal Intensive Care Units


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The staff in the neonatal intensive care units is
required to have highly specialized training and the using
equipment in this unit is so expensive. The random number
of arrivals, the rejections or transfers due to lack of capacity
and the random length of stays, make the advance
knowledge of the optimal staff; equipments and materials
requirement for levels of the unit behaves as a stochastic
process. In this paper, the number of arrivals, the rejections or
transfers due to lack of capacity and the random length of
stays in a neonatal intensive care unit of a university hospital
has been statistically analyzed.

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Statistical Analysis of Patients’ Characteristics in Neonatal Intensive Care Units

  1. 1. J Med SystDOI 10.1007/s10916-009-9259-8 ORIGINAL PAPERStatistical Analysis of Patients’ Characteristics in NeonatalIntensive Care UnitsAli Kokangul & Ayfer Ozkan & Serap Akcan &Kenan Ozcan & Mufide NarliReceived: 2 December 2008 / Accepted: 26 January 2009# Springer Science + Business Media, LLC 2009Abstract The staff in the neonatal intensive care units is Introductionrequired to have highly specialized training and the usingequipment in this unit is so expensive. The random number The child/baby mortality is one of the most important sub-of arrivals, the rejections or transfers due to lack of capacity indexes of national life standards, determined by Humanand the random length of stays, make the advance Developing Index [1]. A baby might require neonatalknowledge of the optimal staff; equipments and materials intensive care due to premature birth, low birth weight orrequirement for levels of the unit behaves as a stochastic a respiratory disorder. The staff and physicians in theprocess. In this paper, the number of arrivals, the rejections or neonatal intensive care units (NICU) are the most experi-transfers due to lack of capacity and the random length of enced and specialized, and they are required to have highlystays in a neonatal intensive care unit of a university hospital specialized training to work in the NICU.has been statistically analyzed. The arrival patients are The patients admitted to NICU are placed in one of fourclassified according to the levels based on the required nurse: levels based on the required nurse: patient ratio. This ratio ispatient ratio and gestation age. Important knowledge such as calculated by using patient level or dependency scales, whicharrivals, transfers, gender and length of stays are analyzed. operate on the assumption that the more critically ill the patient,Finally, distribution functions for patients’ arrivals, rejections the more nurse time is needed to care for the patient [2]. Mostand length of stays are obtained for each level in the unit. National Health Service hospital trusts in England began using the EURICU-1 level system, which calculates nurse:Keywords Newborn . Neonatal intensive care units . patient ratio [3, 4]. A nurse to patient ratio of 1:2 and 1:4 forPatients’ characteristics . Statistical analysis non-ventilation beds are maintained round the clock [5]. In this study, the NICU of a university hospital is considered. It is capable of invasive and non-invasiveA. Kokangul : A. Ozkan : S. Akcan (*) : M. Narli monitoring of the neonate’s cardio respiratory systems andDepartment of Industrial Engineering, can provide oxygen, and age appropriate thermoregulation.Faculty of Engineering and Architecture, Cukurova University, In addition, heart rate, respiratory rate, blood pressure and01330, Adana, Turkey oxygen saturation are monitored continuously. There aree-mail: three levels in the unit. The patients in these levels mayA. Kokangul become stabilized or worse and re-categorized into one ofe-mail: the other levels. The arrival patients are placed in one ofA. Ozkan three levels as described below.e-mail: ayferdursoy@yahoo.comM. Narli & Level I patients are those who require close observation,e-mail: but not necessarily the continuous presence of a nurse at the bedside.K. Ozcan & Level II patients are those who require close observa-Neonatal Intensive Care Unit, Cukurova University,01330, Adana, Turkey tion, but not necessarily the continuous presence of ae-mail: nurse at the bedside.
  2. 2. J Med Syst Materials and methods It is crucial that the staff or equipment requirement should be appropriate to the dependency of the patients in the unit. To present the statistical analysis we consider the patients flow in the NICU. Patients come from outside to one of the levels in the NICU. When the patients arrive to the NICU: If there is unoccupied staff and equipments they will be admitted and accepted, if there is not any unoccupied staff or equipment in the level, they will be rejected or transmitted to elsewhere. The patients in the levels may become stabilized or worse and re-categorized into one ofFig. 1 Yearly amount of unclassified patient admissions the other levels or they may die during the shift. Patients come from a level to another level have higher priority then patient come from outside the NICU. When a patient transmitting from a level to another one, if there is no& Level III patients are those who require a nurse at the unoccupied staff and equipments the transmitting patient bedside continuously for 24 h/day. will stay in the same level for any unoccupied staff and The number of arrivals, transmitting rate among levels equipments.and length of stays (LOS) are random and this randomness The considered NICU is able to serve patients withmake the number of patients in each level behave as a different level of medical treatment. The NICU observedstochastic process. In practice, the variance of the differ- through this study has dedicated equipments to serve atence of the arrival and departure rates can deplete patients three different levels of medical treatments. The distribu-in the levels causing unoccupied staff and equipment or fill tions of the equipments with respect to the levels of the unitthe unit causing rejection or transfer. Naturally, the are listed as follows: Level I: two open beds; level II: threemanagement of the unit tries to avoid these problems. open beds and eight incubators; level III: three open beds, Several methods such as ratio based method [6–8], discrete ten incubators and ten ventilators. To perform the statisticalevent simulation [9, 10], stochastic simulation and queuing analysis of the NICU the patients flow in the unit ismodels [11, 12], a combination of simulation, queuing theory observed for 5 years (2000–2004), then for each level andand statistical analysis [13, 14] and integrated methodologies gestation age obtain distributions for the following param-that combined stochastic and deterministic approaches [15– eters: Daily arrivals, LOS and rejected or transmitted17] have been suggested to solve the equipment planning arrivals. In addition; the gestation age, gender, birth weight,problem of hospital in the literature. diagnosis, arrival date, leave date and leave reasons data of All of these methods are based on the statistical analysis of 3,330 patients treated in 2000–2004 period is collected.patients’ arrivals and LOS. In most of these studies, the This study aims to investigate the characteristics of thevariation of requested admissions over time has not been taken patients and to form basis for other studies. For thisinto account. The variations in demand of staff, equipments or proposes, the registration data of the patients were analyzedmaterials arise due to unpredictable nature of NICU admission and interpreted statistically and graphically.rates and LOS. Using the average number of patients expectedin a year, average LOS and target occupancy level to calculatethe capacity needed is mathematically incorrect because ofnon-linearity and variability in the factors that control LOS[18]. Also, the level of the economic use of any units’capacity may be changed from a unit to another unit in thesame hospital. Therefore, the statistical analysis for each unitin the hospital is useful in practice. In this study, the probability distributions for accepted,transferred or rejected arrivals and LOS are determined foreach gestation age and level in the NICU. Also, arrivalsources, transfer reasons, gender of arrivals and transmittingrate among levels are statistically analyzed. To the best of theauthors’ knowledge these kinds of statistical analysis havenot been performed for a NICU of a university hospital. Fig. 2 Gender based distribution of accepted patients
  3. 3. J Med SystTable 1 Patient sourceSource Year Total % patients 2000 2001 2002 2003 2004 The number of % The number of % The number of % The number of % The number of % patients patients patients patients patientsConsidered 379 61 461 69 452 70 536 75 453 73 2281 70 HospitalOther 119 19 100 15 114 18 101 14 84 14 518 16 hospitalsOther 126 20 108 16 83 13 75 11 82 13 474 14 provinces Statistical analysis was done in two different cases. In arrivals are in agreement with the Poisson distribution.the first case, no special features of the patients were taken Cochran and Bharti [15] performed statistical analysisinto consideration and no classifying has been done. In the related to arrival, stay distributions, and unit usage rate ofsecond case, patients are classified according to the gestation patients that covers the whole units in the hospital.age and levels of the unit. In both cases the analyses were In this study, patients applying to NICU were statisti-done considering patients’ arrivals frequency, LOS and cally investigated without classifying. As seen in Fig. 1,discharge probability at monthly and yearly basis. Further- 3,330 admitted patients are considered and more than 600more, to obtain the LOS and rejection rate, patients were patients have been accepted per year. It is also observed thatclassified in terms of the level base. the highest admission occurred in the year 2003. To analyze the patient characteristics statistically, hypoth- Gender based distribution of accepted patients witheses were developed and tested with a statistical software respect to years is shown in Fig. 2. It can be concludedpackage such as Statistica 6.0 [19] and MatLab 7.0 [20]. that newborn boy babies need more treatment compared to girl babies. Although the total number of accepted patients may change, mostly the distribution of the patients at theResearch and finding gender base remains unaltered. The arrival characteristics for 57 admitted patients couldThe analysis of non-classified patients not be collected. Therefore, arrival characteristics of 3,273 patients are considered. To determine the arrival character-Gronescu et al. [21] investigated all patients’ arrivals to the istics of the patients, their admission data are classified intogeriatric unit in terms of the arrival frequencies, LOS and three groups. These are the patients that come from therejection rate to determine the bed fill rate and cost. other units of the same, the patients that come from theGroothius et al. [22] did not classify the patients applied other hospitals that are located in the same province, andto the cardiology units. They performed the statistical patients who come from other provinces.analyses to determine the demands and the characteristics It can be seen in Table 1, that 70% of patients have comeof patients. Analysis results showed that the patients’ from the considered, 16% of patients have come from theTable 2 Departure reasons of patients per yearReasons Year Total % Patients 2000 2001 2002 2003 2004 The number of % The number of % The number of % The number of % The number of % patients patients patients patients patientsGetting Well 508 85 497 75 510 79 623 88 348 77 2486 80,9Transmitting 28 4,7 58 9 67 10 13 1,8 11 2 177 5,8Death 60 10 111 17 71 11 73 10 95 21 410 13,3
  4. 4. J Med SystFig. 3 Monthly patients’arrivalsother hospitals that are in the same province and 14% of H1 = Patients’ arrivals are not in agreement with thepatients have come from the other provinces. The number of Poisson distributionpatients originated from other hospitals and provinces Hypotheses were analyzed with chi-square test, which isdecreased during 5 years period. Transmitting a sick baby used to determine the differences between the variables andfrom a hospital to another one may increase the mortality operates with the frequency distributions. Statistical soft-rate; therefore, most of patients preferred the closed hospital. ware analyzed the patients’ arrivals using the chi-square test Patients are accepted to be departure from the hospital in with 95% confidence. The test parameters, namely, the chi-the event of getting well, death, or when they are sent to square test statistics and the level of significance (p) wereanother hospital while the illness is continued. The departure found to be 3.57 and 0.46 respectively. As the obtained chi-characteristics for 257 admitted patients could not be square test statistic is lower than the chi-square table value,collected. Therefore, during this study the departure character- the difference between the expected and the real values areistics of 3,073 patients are considered. As it can be seen from not significantly low.the Table 2, while 80.9% of the patients are departure from As the test, significance level (p) is larger than of 0.05;the NICU due to recovery of health, 13.3% departure due to H0 hypothesis cannot be rejected [24]. Thus, the patients’death and 5.8% sent to another hospital or another unit. arrival per year found to be in agreement with the Poisson When the number of patients’ arrivals is investigated at distribution. Similarly chi-square test was applied for thethe month basis, it can be seen in Fig. 3 that, there exist an other 4 years and the patients’ arrivals and distributionincrease by January, which is decreased around April and parameters were obtained as seen in Table around June. The same hypotheses test was applied on the monthly patients’ arrivals and they also found to be in agreementArrival distribution for the non-classified patients with the Poisson distribution.To introduce the demand on the NICU and inspect thearrived patients’ profile, the number of patients applied in a5 years period has been obtained. The distribution of dailypatients’ arrivals in 2000 is given in Fig. 4 as an example.Although there were no arrivals for 73 days either due to thelack of capacity in the equipments used for the treatment ordue to the existence of no application, the number of arrivalsin some days increased up to six patients. In most of studies, the arrival pattern of patients isconsidered as Poisson process [21–23]. It can be concludedfrom Fig. 4 that the patients’ arrivals are in agreement withPoisson process. To check the suitability with the Poissonprocess a zero and an alternative hypothesis were formed.In that respect, H0 = Patients’ arrivals are in agreement with the Poissondistribution Fig. 4 Patients’ arrival distribution in 2000
  5. 5. J Med SystTable 3 The statistical distributions of the admitted patientsYear Chi-Square Significance (p) Distribution Parameter2000 3,57 0,46 Poisson λ=1,66122001 2,03 0,72 Poisson λ=1,835622002 4,34 0,36 Poisson λ=1,802742003 3,65 0,6 Poisson λ=1,947952004 4,32 0,36 Poisson λ=1,74590Analyses of the classified patientsStudies performed on the basis of whole hospital and on thebasis of different units’ show that the classifying of patients Fig. 5 Gender distribution of groups (%)varies with respect to the units. Ridge et al. [25] and Utleyet al. [26] classify the patients into two groups after thestudies carried at the intensive care units, as urgent patientsand patients with appointments. Darzi et al. [27] and high probability of premature birth and they need treatmentNavarro et al. [28] classified the patients in geriatrics unit after birth. On the year based examination, however, it hasin to three groups with respect to the treatment period as been found that while the numbers of group IV patientsshort term, mid-term and long term treated. Utley et al. [29] were decreasing, numbers of group II patients wereon the other hand, classified the patients’ arrivals and LOS acute and non-acute. In this study the arrival patients are It can be seen from the Fig. 5 that the number of boyclassified according to the gestation age and treatment babies applied to newborn care units are higher than thelevel. number of girl babies. Group IV has the highest ratio of boy babies with 59.9%.Patient analysis with respect to gestation age Table 5 presents the departure reasons of the patients based on their gestation age’s groups. Group 0 patients haveIn a study carried by the Turkish Neonatology Association relatively low probability of survival and group III patientsin 2003 [30], patients were classified with respect to the have relatively high probability of survival. It can begestation period while analyzing the death ratio of newborn depicted that patients of the last four groups (Group II,infants. In this study, similarly, patients were classified Group III, Group IV and Group V) have higher probabilityaccording to their gestation period in to six groups. of getting well compared to the patients of the first two Classification with respect to gestation age is given in groups.Table 4. When the distribution of the patients applied to the The collected data for the group 0 is not sufficient forNICU is investigated, it can be seen that while the majority statistical analysis. Therefore, group based patients’ arrivalsof the patients belong to group III, minority belong to group distributions are analyzed for the last five groups. The0. Thus, it can be concluded that the group III patients has a group-based patients’ arrivals distributions, done with chi- square test statistical analysis, are in an agreement with the Poisson and Geometrical distributions as seen in Table 6.Table 4 The number of admitted patients with respect to gestation Patients’ analysis with respect to treatment levelageGroup Gestation Year The Total of Patients are directed by the doctors to the levels (Level I, age (week) Groups Level II and Level III) according to the necessary 2000 2001 2002 2003 2004 equipment and medical staff needed for their treatments.0 21–25 7 9 8 9 10 43 The LOS of the emergency patients and planned patients1 26–28 52 60 46 60 57 275 were described using either the negative exponential curve2 29–32 122 116 129 136 167 670 or a Weibull curve fitting routine [31]. Tu et al. [32] have3 33–37 161 220 200 246 209 1036 used discriminate analysis for post-operative prediction of4 38–42 236 178 122 120 56 712 LOS. A monogram is described for predicting the LOS of5 43– 38 73 140 139 119 509 neonatal patients [33]. Utley et al. [29] assumed that theTotal 616 656 645 710 618 3245 time a patient stays in a particular pool of beds before either
  6. 6. J Med SystTable 5 Departure reasons of the patients based on their gestation ageReasons Group (Gestation Age (week)) 0 (21–25) 1 (26–28) 2 (29–32) 3 (33–37) 4 (38–42) 5 (43– ) The number of % The number of % The number of % The number of % The number of % The number of % patients patients patients patients patients patientsGetting well 10 24 139 54 480 79 847 88 570 82 371 79Transmitting 0 0 14 6 41 7 60 6,2 48 7 42 9Death 32 76 103 40 84 14 56 5,8 74 11 58 12Table 6 Group based patient arrivals and statistical distribution parametersGroup Gestation Chi-Square Significance Distribution Parameter age (week) (p)0 21–25 - - - -1 26–28 0,05 0,81 Geometric p=0,869592 29–32 5,24 0,07 Poisson λ=0,363443 33–37 3,8 0,15 Poisson λ=0,561034 38–42 3,7 0,054 Geometric p=0,723855 43– 1,62 0,44 Poisson λ=0,27805Table 7 Level based patient arrivals’ and LOS distributions and parameters Arrival LOS Distribution Test Distribution TestLevel I Poisson (λ=0,24725) K-S (0.0144 < 0.56) Lognormal (μ=1.670 σ=0.998) K-S ( 0.073 < 0.074)Level II Poisson (λ=0,76438) K-S ( 0.0068 <0.56) Lognormal (μ=2.16 σ=0.689) K-S ( 0.087 < 0.098)Level III Poisson (λ=0,63288) K-S ( 0.012 < 0.56) Lognormal (μ=1.54 σ=1.139) Chi-Square (9.01 < 14.06)Table 8 Level based rejected patients’ distributions and parametersRejected patients Arrival Distribution TestLevel I Poisson (λ=0,87097) K-S (0.0422 < 0.565)Level II Poisson (λ=0,97561) K-S (0.0175 < 0.624)Level III Poisson (λ=0,96078) K-S (0.04926 < 0.624)
  7. 7. J Med Systdischarge or transfer to the other pool can be treated as distributions will make possible applying methods such asidentically and independently distributed. Each level of the simulation, queuing models, and integrated methodologiesNICU required different specialized equipments and qual- that combined stochastic and deterministic approaches toified staff. This requirement level varies from a level to determine the optimal necessary staff or equipments for anyanother level in the unit. All of these equipment and staff levels of a NICU. This study can further be enriched byrequirement for each level based on the patients’ arrivals adding the population-increasing rate.and LOS of the levels. Therefore, in this section thepatients’ arrivals and LOS for each level have beenobtained by employing the chi-square and kolmogorov- Referencessimirnov (K-S) tests. Considering the levels of the unit, as seen in Table 7 the 1. 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