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1 Barra et al. Page 18 of 26 2 3 4 5 6 7 Appendix – Model selection 8 The LLOS-distribution resulting from log-transforming the dependent variable is shown in Figure1. 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Figure 1: The LLOS distribution; by sex. 26 27 28 The observations that the transformed LOS-data is more spread out, and that regression residuals 29 were better behaved on initial test-specifications suggested the choice of LLOS as the dependent 30 31 variable in the ensuing analyses. 32 Table7 contains the results from the full-factor, LOOCV routine, performed on the set of demo- 33 34 graphic and admission variables. Here, the specifications that achieved lowest AIC, BIC, and RMSE 35 on LOOCV, are presented. 36 Table1 contains the changes in AIC, BIC, and coefficient estimates from fitting the data to the 37 38 base model and one MCk at the time. 39 Table8 contains the results from the full-factor, LOOCV routine, performed on the base model, 40 41 with the four MC’s identified in the previous step (reported in Tables1&7). Again, the specifications 42 that achieved lowest AIC, BIC, and RMSE on LOOCV, are presented. 43 44 45 Appendix – Municipalities 46 The reported values in all tables are averages of the 2012 and 2013 values. See also Table2 for 47 complete description of these variables. 48 49 The next tables give an overview of the average values of the various MC’s in the municipalities 50 included in this study. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 19 of 26 2 3 4 5 6 7 Table 1: Results: adding MCk to the base specification. a 8 Variable ∆AIC ∆BIC µˆj SE(ˆµj ) p 9 MedInc 1.772 7.333 0.000 0.000 0.634 10 Pop 1.998 7.559 -0.002 0.043 0.961 11 Pop(67+)Share -0.780 4.781 -3.351 2.014 0.096 Fem(66−)Share -1.082 4.479 -6.629 3.784 0.080 12 1.417 6.978 0.040 0.052 0.446 13 CO/Cap 14 DTR 1.788 7.349 0.022 0.047 0.646 15 CAIN -1.873 3.688 -0.029 0.015 0.050 16 CAHO -0.227 5.334 0.481 0.323 0.137 17 ACEL 0.637 6.198 -0.058 0.050 0.244 18 /Cap 19 Nur -4.452 1.109 -0.094 0.037 0.011 20 GerNur -3.722 1.840 -0.455 0.190 0.017 21 SpNur 1.967 7.528 0.030 0.165 0.856 HFA 1.882 7.443 0.029 0.083 0.732 22 PMA 1.707 7.269 -0.008 0.014 0.590 23 HoPMA 1.987 7.548 0.003 0.023 0.908 24 HoSpPMA 1.768 7.329 -0.020 0.042 0.631 25 Notes: aSee Table2 for variable definitions; ∆AIC is the difference in AIC be- 26 tween the base model and the base model with the addtion of the indicated 27 MC. Similarly for ∆BIC’, µˆk is the coefficient estimate 28 29 30 Appendix – Sensitivity analyses 31 32 Sensitivity analyses 1–4 33 The regression results from the sensitivity analyses can be seen in Table 12. In Table 12, the 34 35 ‘All data’ model corresponds to sensitivity analysis 3. Here we observe that the effects of the two 36 retained MC’s appear orthogonal to the effects from the other regressors: coefficient estimates, and 37 their significance are quite comparable. The ‘−Oslo’ model corresponds to sensitivity analysis 1: 38 omitting data from the three Oslo boroughs; the ‘DoD’ and ‘AoD’ models correspond to sensitivity 39 40 analysis 4, to see if results are stable when only considering those that were discharged alive. In 41 particular, we see that when estimating the final specification to only in-hopital fatalities, none of 42 the coefficients have p-values > 0.1, except for stroke type intracerebral haemorrhage, consistent 43 with our hypotheses that municipal readiness to accept the transfer of care is a driver of LOS 44 45 variation. We have not included the estimates from sensitivity analysis 2 – omitting data from two 46 municipalities with more questionable municipal data. The effect on coefficients and goodness-of-fit 47 statistics was negligible. 48 49 50 Ad hoc sensitivity analyses 51 52 We also performed an additional ad hoc sensitivity analysis in which we fitted the same final 53 specification, but with (linear) LOS substituted for LLOS. The linear LOS fit, while clearly not 54 directly comparable, showed the same pattern of estimated coefficient signs and significance levels, 55 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 20 of 26 2 3 4 5 6 7 although most were substantially weakened. Both Nur/Cap and Fem(66−)Share remained significant 8 (p = 0.038 and p = 0.029; results not shown). 9 We also estimated standard errors that are robust for heteroskedasticity of the residuals for the final 10 11 model, using the sandwich-package.[44] Although our model selection criteria (AIC/BIC/RMSE) 12 are independent if estimated standard errors, we were please that there was only minor pertur- 13 bations to the model’s coefficents’ significances. Importantly, Nur/Cap and COCAIN/Cap were still 14 significant with, respectively, p = 0.028 and p = 0.006. 15 16 17 Figure Legends 18 19 Figure 1 20 The LLOS distribution; by sex. 21 22 23 Tables 24 25 26 Table 4: Municipalities 27 a Map d 28 Mun. c LLOS (n) Map of Catchment area ref. Pop. 29 (1) 47.9k 128 (201) 30 Alna - 31 (2) 15.0k 122 (57) 32 Høland 33 (3) 21.8k 137 (112) 34 (4) 10.5k 128 (53) 35 (5) 10.7k 130 (46) (6) 15.2k 119 (53) 36 (7) 6.2k 168 (12) 37 Grorud (8) 26.8k 133 (96) 38 (9) 2.7k 155 (8) 39 Lørenskog (10) 33.9k 119 (141) 40 Nannes- (11) 11.4k 178 (57) 41 tad 42 Nes (12) 19.6k 115 (62) 43 (13) 17.9k 137 (68) 44 (14) 21.6k 121 (65) 45 Oppeg˚ard (15) 25.6k 102 (100) 46 Rælingen (17) 16.2k 134 (57) 47 Rømskog (18) 0.7k 288 (1) 48 (19) 49.9k 142 (187) 49 Ski (20) 29.1k 140 (117) 50 Stovner (21) 30.6k 152 (119) 51 Sørum (22) 16.2k 127 (78) 52 (23) 31.2k 130 (114) 53 (24) 15.3k 165 (57) 54 As˚ (25) 17.4k 110 (61) 55 Continued on next page 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 21 of 26 2 3 4 5 6 Table 4 – continued from previous page

7 a Map d Mun. c LOS (n) Map of Catchment area 8 ref. Pop. 9 Notes: aThe three Oslo bouroughs Alna, Grorud, and Stovner are included in Ahus’ catchment area. 10 bColour on map represents number of SU admissions per person. cPop. contains popoulation in 1000 11 inhabitants. d LOS contains mean LOS (in hours) for patients from the municipality (no. of admissions) 12 13 14 15 16 17 18 Table 9: Municipal income and demographic characteristicsa 19 20 Municipality Map ref. Pop MedInc Pop(67+) Fem(66−) Share Share 21 Alna (1) 47.9k 423.0k 11.03% 49.34% 22 Aurskog-Høland (2) 15.0k 478.1k 14.34% 48.60% 23 Eidsvoll (3) 21.8k 497.4k 11.87% 48.62% 24 Enebakk (4) 10.5k 565.7k 9.45% 48.68% 25 Fet (5) 10.7k 579.3k 12.02% 48.47% Frogn (6) 15.2k 569.2k 13.50% 50.28% 26 Gjerdrum (7) 6.2k 598.0k 10.31% 47.11% 27 Grorud (8) 26.8k 407.3k 11.72% 49.94% 28 Hurdal (9) 2.7k 462.8k 16.61% 48.10% 29 Lørenskog (10) 33.9k 535.5k 11.38% 49.03% (11) 11.4k 522.6k 10.70% 48.30% 30 Nes (12) 19.6k 524.9k 12.22% 48.64% 31 Nesodden (13) 17.9k 560.8k 11.00% 50.54% 32 Nittedal (14) 21.6k 593.2k 10.79% 49.42% 33 Oppeg˚ard (15) 25.6k 609.0k 13.26% 49.96% Rælingen (17) 16.2k 542.6k 10.59% 49.34% 34 Rømskog (18) 0.7k 482.0k 20.27% 45.87% 35 Skedsmo (19) 49.9k 513.0k 12.26% 48.95% 36 Ski (20) 29.1k 580.0k 12.00% 49.24% 37 Stovner (21) 30.6k 447.6k 12.10% 48.91% Sørum (22) 16.2k 573.6k 10.72% 48.69% 38 Ullensaker (23) 31.2k 522.0k 10.15% 49.08% 39 Vestby (24) 15.3k 564.4k 11.03% 49.56% 40 As˚ (25) 17.4k 521.4k 11.71% 48.49% 41 Notes: Map ref.: see Table4. bSee Table2 for details and definitions 42 on the variables. 43 44 45 46 47 48 Table 10: Municipal cost/resource characteristicsa 49 Municipality Map ref. DTR CAIN CAHO ACEL 50 Alna (1) 0.51k 9.60k 0.00k 1.68k 51 Aurskog-Høland (2) 1.50k 8.17k 0.10k 0.32k Eidsvoll (3) 1.94k 5.87k 0.03k 0.83k 52 Enebakk (4) 1.84k 4.47k 0.16k 0.31k 53 Fet (5) 1.54k 5.04k 0.17k 1.00k 54 Continued on next page. . . 55 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 22 of 26 2 3 4 5 6 Table 10 – continued from previous page 7 Municipality Map ref. DTR CAIN CAHO ACEL Frogn (6) 1.54k 5.40k 0.02k 1.12k 8 Gjerdrum (7) 1.23k 6.96k 0.21k 0.75k 9 Grorud (8) 0.59k 9.02k 0.00k 1.13k 10 Hurdal (9) 1.91k 10.56k 0.29k 2.18k 11 Lørenskog (10) 1.66k 6.56k 0.02k 0.52k Nannestad (11) 1.91k 6.38k 0.14k 0.44k 12 Nes (12) 1.35k 7.93k 0.03k 0.53k 13 Nesodden (13) 1.27k 5.79k 0.02k 0.38k 14 Nittedal (14) 1.36k 5.25k 0.02k 1.27k 15 Oppeg˚ard (15) 1.33k 7.04k 0.02k 1.38k Rælingen (17) 1.29k 5.67k 0.01k 0.90k 16 Rømskog (18) 4.76k 21.88k 1.89k 0.18k 17 Skedsmo (19) 1.78k 6.45k 0.02k 0.49k 18 Ski (20) 1.54k 6.68k 0.02k 1.11k 19 Stovner (21) 0.77k 5.87k 0.00k 1.11k Sørum (22) 1.30k 6.52k 0.02k 0.28k 20 Ullensaker (23) 1.54k 5.88k 0.02k 0.61k 21 Vestby (24) 1.00k 4.96k 0.12k 0.74k 22 As˚ (25) 1.32k 7.94k 0.09k 0.85k a 23 Notes: Map ref.: See Table4 See Table2 for details and definitions 24 on the variables. Column headers are cost groups 25 26 27 28 29 30 Table 11: Municipal care staff FTE characteristicsa 31 Municipality Map ref. GerNur SpNur Nur HFA PMA 32 Alna (1) 0.12 0.24 3.01 0.82 3.89 33 Aurskog-Høland (2) 0.16 0.35 4.92 0.51 7.69 Eidsvoll (3) 0.24 0.17 2.56 0.95 7.93 34 Enebakk (4) 0.10 0.62 2.54 0.75 3.13 35 Fet (5) 0.05 0.30 2.59 0.64 5.56 36 Frogn (6) 0.18 0.28 2.67 0.85 5.12 37 Gjerdrum (7) 0.16 0.69 2.02 0.60 5.12 Grorud (8) 0.12 0.24 3.01 0.82 3.89 38 Hurdal (9) 0.38 0.34 3.07 1.15 12.13 39 Lørenskog (10) 0.13 0.44 3.18 1.02 4.80 40 Nannestad (11) 0.15 0.18 3.15 0.38 6.02 41 Nes (12) 0.20 0.54 3.07 1.17 8.36 Nesodden (13) 0.00 0.31 2.54 1.13 2.53 42 Nittedal (14) 0.21 0.31 2.09 0.54 4.03 43 Oppeg˚ard (15) 0.54 0.57 3.96 0.84 4.84 44 Rælingen (17) 0.21 0.16 2.55 0.53 3.77 45 Rømskog (18) 0.00 0.00 9.24 0.70 12.67 Skedsmo (19) 0.23 0.40 3.13 0.73 5.06 46 Ski (20) 0.28 0.29 3.08 0.66 4.54 47 Stovner (21) 0.12 0.24 3.01 0.82 3.89 48 Sørum (22) 0.20 0.32 3.56 0.90 5.61 Ullensaker (23) 0.10 0.20 3.09 0.68 5.44 49 Vestby (24) 0.11 0.51 1.95 0.79 3.66 50 As˚ (25) 0.39 0.36 3.92 0.87 4.13 51 Notes: Map ref.: see Table4. aSee Table2 for details and definitions on the variables. 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 23 of 26 2 3 4 5 6 7 8 Table 2: Variables explored for model specifications 9 Cat. Abb. Var. Name Variable Definition Sourcea 10 LOS LOS the patient’s LOS in hours 11 nor-spot LLOS LLOS the patient’s log-LOS: log(LOS) nor-spot 12 13 Pat P1 Age The patient’s age, in years at admission nor-spot 14 Pat P2 Sex The patient’s sex nor-spot Pat P3 ΣPC The number of known previous conditions at admission nor-spot 15 Pat P4 STR A nominal variable with levels: nor-spot 16 INF (ref) ischemic INFarction (reference) nor-spot 17 TIA Transient Ischemic Attack nor-spot 18 ICH Intra Cerebral Haemorrhage nor-spot 19 MIMIC stroke MIMIC (i.e. other diagnoses) nor-spot Pat P5 AoD (Alive on Discharge) a dummy variable coded as 0 for nor-spot 20 in-hospital fatality 21 Adm A1 DayAdm (daytime arrival) – a dummy coded as 1 iff the patient nor-spot 22 arrived to the SU between 07:00 and 19:00 23 Adm A2 HolAdm (holiday arrival) – a dummy coded as 1 iff the patient nor-spot b 24 arrived to the hospital during one of the main Norwegian 25 holidays. Adm A3 Wkd (weekday of arrival) – a factor-variable coding for week- nor-spot 26 day of arrival to the SU 27 Adm A4 Mth (month of arrivall) – a factor-variable coding for month nor-spot 28 of arrival to the SU Adm A LOS LOS (in hours) at the emergency department. 29 5 ED nor-spot Dem MC1 MedInc The median income over all households, after tax, for the sn06944 30 municipality 31 Dem MC2 Pop The (total) population of the municipality sn05212 32 Dem MC3 Fem(66−)Share The share of inhabitants below the age of 67 years who sn05212 33 are female Dem MC4 Pop(67+)Share The share of inhabitants who are above the age of 67 sn05212 34 years 35 Definition of CO/Cap 36 Costc MC DTR Diagnosing, Treatment, and Rehabilitation 05065 37 5 sn Cost MC6 CAIN CAre provided in INstitutions sn05065 38 Cost MC7 CAHO CAre provided in patients’ HOmes sn05065 39 Cost MC8 ACEL ACtivity and services for Elderly sn05065 40 Definition of /Cap d 41 FTE MC9 Nur Nurses (with a bachelor) sn09934 42 FTE MC10 GerNur Geriatric nurses sn09934 43 FTE MC11 SpNur Special nurses (with a MSc/Specialisation) sn09934 FTE MC12 HFA Nurse’s assistants; a lower degree in health care sn09934 44 (‘HelseFagArbeider’) 45 FTE MC13 PMA Care staff without formal health care training sn09934 46 (‘PleieMedArbeider’) 47 FTE MC14 HoPMA Care staff at homes (‘HjemmePleieMedArbeider’) sn09934 FTE MC15 HoSpPMA Nurse’s assistants at homes (‘PleieMedArbeider’) sn09934 48 Notes: a The source of the data: nor-spot refers to own data; snxyz refer to Statistics table no. 49 xyz; b The main hollidays are: Easter (April 2nd—11th 2012), summer (July 9th—27th 2012), and Christmas 50 (December 23rd 2012—January 2nd 2013). An arrival was counted as a holiday arrival if the patient arrived at 51 the SU between 3 days prior to the holiday’s start and 3 days prior to the holiday’s end. c Costs are represented as 1000NOK per inhabitant; = cost group. d FTE’s are represented as FTE’s per 1000 inhabitants; 52 = health personel group. 53 54 55 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 24 of 26 2 3 4 5 6 7 Table 3: Descriptive statistics for the continuous variables. 8 Variable Median (IQR) Mean (SD) N 9 10 LOS 109.9 (47.8—177.49) 132.3 (117.58) 1922 11 LLOS 4.70 (3.87—5.18) 4.49 (1.00) 1922 12 Age 72 (61—82) 70.54 (14.93) 1922 13 ΣPC 1 (0—2) 1.48 (1.56) 1922 14 LOSED 2.8 (1.51—4.51) 5.75 (23.29) 1922 Notes: In the subsequent analyses, LLOS is the dependent variable. IQR = In- 15 terquartile range; SD = Sample deviation. 16 17 18 Table 5: Regression and ANOVA results – Base specification 19 Dependent variable: LLOS 20 Full model Base model Base + MFE 21 22 Var Coeff. p Coeff. p Coeff. p 23 Age 0.0004 0.814 Sex −0.019 0.666 24 a b b b 25 STR – 0.000 – 0.000 – 0.000 ICH −0.138 0.131 −0.158 0.082 −0.142 0.117 26 TIA −0.699 0.000 −0.708 0.000 −0.707 0.000 27 MIMIC −0.660 0.000 −0.657 0.000 −0.661 0.000 28 AoD 0.388 0.0002 0.377 0.0002 0.376 0.0003 ΣPC 0.070 0.065 0.027 0.065 0.027 0.060 29 2 30 ΣPC −0.009 0.236 LOSED 0.002 0.070 0.002 0.042 0.002 0.032 31 DayAdm 0.164 0.0003 0.158 0.0004 0.153 0.001 32 HolAdm 0.165 0.103 0.190 0.021 0.178 0.032 33 Wkd – 0.253b Mth – 0.034b 34 b 35 MFE – 0.010 36 Stat. Full model Base model Base + MFE 37 AIC 5 229.077 5 219.777 5 223.600 BIC 5 395.911 5 275.389 5 407.117 38 N 1 922 1 922 1 922 39 R2 0.143 0.129 0.148 40 Adj. R2 0.130 0.125 0.134 41 Res. SE 0.936 (df = 1 893) 0.938 (df = 1 913) 0.933 (df = 1 890) F Stat. 11.256 (df = 28; 1 893) 35.394 (df = 8; 1 913) 10.577 (df = 31; 1 890) 42 Notes: Intercepts not shown; See Table2 for variable definitions; aReference category for STR 43 is ischemic stroke; bp-value from ANOVA F-statistic. All p-values based on unadjusted standard 44 errors. 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 25 of 26 2 3 4 5 6 7 Table 6: Regression and ANOVA results – Final specification 8 9 Dependent variable: LLOS 10 Var Est. eEst. − 1 (se) t p 11 STRa – – – – 0.000b 12 ICH −0.163 −0.151 (0.090) −1.805 0.071 13 TIA −0.706 −0.507 (0.063) −11.186 0.000 14 MIMIC −0.656 −0.481 (0.052) −12.626 0.000 AoD 0.389 0.475 (0.101) 3.858 0.000 15 ΣPC 0.028 0.029 (0.014) 1.964 0.050 16 LOSED 0.002 0.002 (0.001) 2.131 0.033 17 DayAdm 0.155 0.168 (0.044) 3.506 0.000 HolAdm 0.193 0.213 (0.082) 2.349 0.019 18 Fem(66−)Share −8.5706 −0.082c (0.3836) −2.234 0.026 19 Nur/Cap −0.109 −0.103 (0.038) −2.890 0.004 20 N 1 922 21 AIC 5 212.312 22 BIC 5 279.045 2 23 R 0.134 Adj. R2 0.130 24 Res. SE 0.936 (df = 1911) 25 F Stat. 29.598 (df = 10; 1911) 26 Notes: Intercepts not shown; See Table2 for variable definitions; aReference category for STR is 27 ischemic stroke; bp-value from ANOVA F-statistic. c The tabulated value for Fem(66−)Share is 28 eEst./100 − 1. All p-values based on unadjusted standard errors. 29 30 31 32 Table 7: Base model selection statistics. 33 Value 34 Criteria AIC BIC RMSE Included variables (k) 35 AICmin 5219.75 5336.53 0.941 LOSED, STR, AoD, ΣPC, DayAdm, HolAdm, Mth (7) 36 BICmin 5226.307 5265.235 0.943 STR, AoD, DayAdm (3) 37 RMSEmin 5219.78 5275.39 0.941 LOSED, STR, AoD, ΣPC, DayAdm, HolAdm (6) 38 Notes: Results from implemented model selection search. Each row contains the model with best performance as judged 39 by the fit statistic named in the row header (under Criteria.) The fit statistics’ values are found in the AIC, BIC and RMSE 40 columns, Included variables list the variables, and (k) contains the number of retained variabels. 41 42 43 Table 8: Final model selection statistics. 44 45 Value 46 Criteria AIC BIC RMSE Included variables (k) 47 AICmin 5212.31 5279.05 0.939 LOSED, STR, AoD, ΣPC, DayAdm, HolAdm, (8) 48 Fem(66−)Share, Nur/Cap 49 BICmin 5226.31 5265.24 0.943 STR, AoD, DayAdm (3) 50 RMSEmin 5212.31 5279.05 0.939 LOSED, STR, AoD, ΣPC, DayAdm, HolAdm, (8) Fem(66−)Share, Nur/Cap 51 Notes: Results from implemented model selection search. Each row contains the model with best performance as judged 52 by the fit statistic named in the row header (under Criteria.) The fit statistics’ values are found in the AIC, BIC and RMSE 53 columns, Included variables list the variables, and (k) contains the number of retained variabels. 54 55 56 57 58 59 60 61 62 63 64 65 1 Barra et al. Page 26 of 26 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Table 12: Sensitivity analyses 18 19 Dependent variable: LLOS All data −Oslo DoD AoD Full Model 20 a 21 STR ICH −0.162 −0.883 0.059 −0.163 22 0.113 0.001 0.553 0.072 23 TIA −0.689 0.329 −0.704 −0.706 24 0.000 0.769 0.000 0.000 25 MIMIC −0.654 0.244 −0.668 −0.656 0.000 0.468 0.000 0.000 26 AoD 0.305 0.389 27 0.008 0.000 28 ΣPC 0.037 0.062 0.028 0.028 29 0.025 0.380 0.058 0.050 LOSED 0.002 0.004 0.002 0.002 30 0.040 0.451 0.104 0.034 31 DayAdm 0.142 0.106 0.149 0.155 32 0.005 0.663 0.001 0.001 33 HolAdm 0.187 0.390 0.186 0.193 0.049 0.517 0.023 0.019 34 Fem(66−)Share −8.398 −7.817 −13.914 −7.039 −8.570 35 0.040 0.062 0.554 0.068 0.026 36 Nur/Cap −0.107 −0.107 −0.308 −0.094 −0.109 37 0.008 0.005 0.186 0.013 0.004 38 n 1 922 1 506 99 1 823 1 922 R2 0.005 0.131 0.207 0.148 0.134 39 Adj. R2 0.004 0.125 0.127 0.144 0.130 40 Notes: Coefficient estimates with p-values below; Intercepts not shown; See Table2 for 41 variable definitions; aReference category for STR is ischemic stroke; The columns corresponds 42 to: All data = model fitted to all data, but with final MCs only; −Oslo = model fitted to only 43 non-Oslo municipalities; DoD = model fitted only to patients that were Dead on Discharge; AoD = model fitted only to patients that were Alive on Discharge. 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65