Municipalities 46 the Reported Values in All Tables Are Averages of the 2012 and 2013 Values
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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 µ^j SE(^µj ) 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 Oslo 1.417 6.978 0.040 0.052 0.446 13 CO<CG>=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 <HPG>=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', µ^k 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 Aurskog- 31 (2) 15.0k 122 (57) 32 Høland 33 Eidsvoll (3) 21.8k 137 (112) 34 Enebakk (4) 10.5k 128 (53) 35 Fet (5) 10.7k 130 (46) Frogn (6) 15.2k 119 (53) 36 Gjerdrum (7) 6.2k 168 (12) 37 Grorud (8) 26.8k 133 (96) 38 Hurdal (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 Nesodden (13) 17.9k 137 (68) 44 Nittedal (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 Skedsmo (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 Ullensaker (23) 31.2k 130 (114) 53 Vestby (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% Nannestad (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.