Multiple Linear Regression (MLR) Model
4.6. Study space Cardiac Inpatient Unit
4.7.3. Limitations of the pilot study and strategies for principal study
Specific limitations of the pilot study were that the duration of the study was around two months; as a result, a smaller sample size (40 patients) was possible to include in the model. To include a large number of samples, the duration of principal study was designed for one year to generate statistically more significant model with greater confidence level on the impact of daylight on patient LoS.
Another, limitation of pilot survey was that, the study population was restricted to the patients who had undergone heart surgery of different types (eight types) comprises of CABG, coarctation repair, valve replacement, ASD or patch closure. To build a stronger model for principal study, only CABG patients, who were the highest in number among heart surgery cases, were separated (as a more uniform sample group) for analysis at the beginning.
Under the limitation of actual prediction capacity of daylight intensity by available simulation software (Pechacek et al. 2008), FlucsDL of IES software package was used to calculate average daylight intensity of the in-patient rooms. Actual HEI measured by an outdoor data logger from site, was used to include the unpredictable nature of outdoor daylight intensity. As a result, the patients, who may have adjusted their blinds,
115 were not accounted in pilot study and the simulated data for average daylight inside the room represents a part of outdoor daylight due to the room location and geometry that a patient might experience without any internal obstruction to windows (e.g. blinds). Due to the lack of sufficient number of indoor data loggers and pyranometers to measure outdoor radiation data to do a raytracing simulation, the validation of the simulated daylight data generated during pilot survey was not possible. To overcome this limitation and to consider the outcome of internal blind operations, 31 indoor data loggers were installed above each bed of the cardiac unit of the hospital to measure the daylight that the patient actually experienced during their stay in inpatient rooms, during principal study periods.
4.8. Principal study
The principal study started on 21 July 2009 at 00:00 and ended on 31 July 2010 at 23.00. Illumination values above patient beds with respect to the patient LoS in cardiac surgery unit were obtained by the readings of indoor data loggers (Figure 3.5) as described in Section 3.4.2.
A total number of 1889 patients were admitted during principal study period in cardiac inpatient unit. Among them 339 were open heart surgery cases including 278 CABG patients. Operations were successful for the primary selected 278 CABG patients. Five patients were excluded from study, who stayed less than 48 hours in the Cardiac Unit after being transferred from CTICU. Three data loggers were stopped for some times during the principal study period on bed No. 1014A (from 17 April 2010 at 13:00 to 26 May 2010 at 10:00); bed No. 1017A (from 11 November 2009 at 11:00 to 26 May 2010 at 10:00) and bed No. 1007 (from 27 October 2009 at 16:00 to 26 May 2010 at 10:00). Once the malfunction of the data loggers were identified, necessary steps were taken (e.g. restarting and/or replacement of the batteries) to reinstall the data loggers. As a result, three CABG patients lighting data were missed and the patients were excluded from the study. Necessary clinical data was missing (e.g. heart rate and blood pressure) in patient record file for seven patients and they were not included in the sample. Finally, 263 patients were taken as sample for principal study who stayed at least 48 hours in the in-patient rooms and have the necessary data (clinical and environmental) for statistical analysis.
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4.8.1. Development of MLR model
For each observation, a total of 31 possible explanatory variables were considered at the beginning. Table 4.5 presents a sample summary statistics of the variables. Column one of Table 4.5 shows the list of provisional variables for the model. After Pearson Correlation and stepwise regression analysis, finally three environmental variables and three clinical variables were selected for MLR model. The final set of variables, their coefficients (B), standardized coefficients (Beta) t-statistics together with the p-values are shown in Table 4.6.
Table 4.5: A sample summary statistics of primary variables for principal study model.
Variables (unit/total no.) Min/No. Max/No. Mean Std. Deviation
Patient LoS (hour)- dependent variable 48.00 666.00 109.63 61.67 Systolic blood pressure (mm Hg) 87.00 158.28 113.16 10.00 Diastolic blood pressure (mm Hg) 52.00 86.72 72.55 4.84 Mean arterial pressure (mm Hg) 60.00 110.57 85.85 6.34
Heart rate (beats/ min) 72.00 120.00 91.03 7.79
Respiratory rate ( resp/min) 14.00 32.00 19.92 4.54
Body temperature (oF) 97.80 100.00 97.86 0.16
Saturation of peripheral oxygen (%) 91.00 98.13 96.06 1.25
Fasting blood sugar (mmol/l) 4.20 16.58 7.82 2.39
Fluid balance (ml) -2963.33 920.00 -575.47 396.71
Ejection fraction value (%) 23.00 73.00 54.96 8.13
Smoker (263) Y (90) N (173) - -
Hypertension (263) Y (189) N (74) - -
Dyslipidaemia (263) Y (115) N (148) - -
Diabetes mellitus (263) Y (107) N (156) - -
Myocardial infarction (263) Y (95) N (168) - -
Transient ischaemic attack (263) Y (1) N (262) - -
Bronchial asthma (263) Y (19) N (244) - -
Stroke (263) Y (0) N (263) - -
Cerebral vascular diseases (263) Y (1) N (262) - -
Chronic renal failure (263) Y (5) N (258) - -
Gender (263) M (235) F (28) - -
Age (year) 23.00 87.00 54.21 9.71
Weight (Kg) 39.00 93.00 63.44 9.22
Height (cm) 144.00 183.00 162.03 7.15
Body mass index 17.00 34.00 24.15 3.09
Room type (263) S (109) D (154) - -
Provision of outdoor view (263) Y (210) N (53) - -
Rent (Tk/day) 3500 17500 4655.89 1658.44
Room temperature (oC) 18.56 28.36 25.46 1.18
Relative humidity (%) 68.64 84.75 77.38 6.16
Daylight intensity at head point (lx) 5 549 185.41 106.59 * Y – Yes; N – No; M – Male; F – Female; S – Single; D – Double.
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4.8.2. Model interpretation
One of the interests of principal study was to check the results of pilot study (as the pilot study was done under several limitations) and build a stronger model. The analysis of principal study data (Table 4.6) showed that four variables decreased patient LoS inside in-patient unit and two variables were responsible for increasing the stay time (rent of the rooms and DM). Four variables were highly significant (rent, MAP, HR and DM), daylight was significant at a level of two percent and POV at a level of four percent in the MLR model. The column of un-standardised coefficients (B) provides the values for explanatory variables for final MLR equation.
Table 4.6: MLR Model for patient LoS in cardiac unit based on principal study data .
Explanatory variable Un- standardized coefficients (B) Standardized coefficients (Beta) t- statistics p- values Constant 289.891 - 5.953 <0.001
Daylight intensity at head point -0.073 -0.127 -2.425 0.016 Provision of outdoor view -17.437 -0.114 -2.100 0.037
Rent of the rooms 0.015 0.397 8.398 <0.001
Mean arterial pressure -1.703 -0.175 -3.960 <0.001
Heart rate -1.162 -0.147 -3.363 0.001
Diabetes mellitus 73.313 0.587 13.402 <0.001
* Dependent Variable: Patient LoS in hour; R square =0.516; Adjusted R square =0.505; F =45.473 (Sig. < 0.001).
Therapeutic and intuitive judgement confirmed the validity and practicality of mathematical signs in the model (Table 4.6). In a developing country, i.e. Bangladesh with per capita income around $418 a year (BBS, 2010), the government does not have the sufficient funds to address the adequate healthcare needs of the people. The government provides free health services to rural areas and the health system has not been designed to serve densely populated cities such as Dhaka, where the patient need is greatest. Due to the government‟s inadequacy in the health sector, only 30% of population use the free health services (Chaudhuri, 2003) and rest of the people need to pay for health services. According to the World Bank‟s estimation, more than 60% of Bangladeshis, about 80m people, have no access to modern health services (Mehovic and Blum, 2004) which are too expensive for average income group of people. Mainly the private hospitals meet the healthcare needs of the capital city with costly services.
118 The rent of the hospital in-patient rooms with modern facilities are usually high in private hospitals, and contribute to the major expenses of the treatment of the patients during hospital stay periods. Luxury rooms are only affordable to very rich people to whom cost of treatment matter little and they tend to stay longer in hospital till their complete satisfaction to recovery. On the other hand, patients who preferred a shared room to reduce the treatment cost tend to leave the hospital earlier with a reasonable recovery status of their health with doctors‟ consent. The impact of the rent of the room which reflects patients‟ economic capabilities, therefore, have a strong influence on LoS in hospital rooms. It is logical that in a modern and expensive hospital, such as Square Hospital, patients with better economic conditions are more intend to stay longer in luxury rooms with higher rents than the patients with less affording capabilities who choose a room with cheaper rent to reduce treatment cost (t=8.398, p value<0.001).
A view to the outdoor may help to reduce the stay time of patients (t=-2.1, p value=0.037), and reduction of patient stay time with the increase of daylight (t=-2.425, p value=0.016) agreed with the findings of pilot survey at a higher significance level. It is evident from principal study model that daylight is more significant between two environmental variables daylight and POV. The coefficient estimates show that while holding the other explanatory variables constant, the POV reduces patient LoS by, on average, 17.4 hours and stay time by 7.3 hours per 100 lx increase of daylight intensity (multiplying B with 100 lx) near a point above patient heads.
According to Equation 3.2, the elasticity (
y ) of patient stay time with respect todaylight intensity, near a point above patient head, is - 0.12 (Equation 4.2), implying that, if daylight intensity were increased by 1% at a point above patients‟ head, patient stay time would decrease by 0.12%.
0.12 63 . 109 41 . 185 * ) 073 . 0 ( y (4.2)
Medical judgements also confirmed the validity and practicality of the mathematical signs of clinical variables such as blood pressure (t=-3.96, p value<0.001), heart rate (t=-3.363, p value=0.001) and diabetes (t=13.402, p value < 0.001). Mathematical signs of the common explanatory variables also agreed with the findings of pilot survey.
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