4. Evaluation of the HSMR 2023 model

This chapter presents and evaluates the HSMR model results. Summary outcomes of the 158 logistic regressions are presented, with in-hospital mortality as the dependent variable and the variables mentioned in section 3.4 as explanatory variables. More detailed results are presented in the tables “Statistical significance of covariates HSMR 2023 model” and “Coefficients HSMR 2023”. These tables are published together with this report.

4.1 Target population and data set

All hospitals that register complete records of inpatient admissions and prolonged observations without overnight stay in the LBZ are included in the HSMR model. In 2020-2023 all general hospitals and university hospitals were included in the model, as well as three short-stay specialised hospitals (two cancer hospitals and an eye hospital). From 2022 onwards a fourth short-stay specialised (orthopaedic) hospital also participated in the LBZ and was included in the model as well. All of the hospitals had completely registered all admissions in the LBZ.

4.1.1 Admissions in HSMR 2023 model
	2020	2021	2022	2023	total
Excluded admissions not meeting the NZa criteria*	123,889	131,521	143,399	148,014	546,823
Excluded admissions of foreigners	6,231	5,993	7,973	8,707	28,904
Excluded admissions due to COVID-19**	40,430	60,228			100,658
Excluded admissions of healthy persons***	18,202	19,196	18,943	19,398	75,739
Total number of admissions included in model	1,395,545	1,407,749	1,481,648	1,489,868	5,774,810
Number of inpatient admissions	1,288,291	1,295,255	1,367,700	1,381,070	5,332,316
Number of observations	107,254	112,494	113,948	108,798	442,494
Number of deaths included in model	29,151	29,779	36,207	34,808	129,945
Crude mortality (in admissions in model)	2.1%	2.1%	2.4%	2.3%	2.3%
Admissions that do not meet the billing criteria of the Dutch Healthcare Authority (NZa) for inpatient admissions, and for prolonged observations, unplanned, without overnight stay. The number of these admissions in the LBZ varies over the years, due to different registration instructions of DHD. Admissions with COVID-19 as the main diagnosis (ICD-10 codes U07.1 (COVID-19, virus identified (lab confirmed)), U07.2 (COVID-19, virus not identified (clinically diagnosed)) and, from 2021 onwards, U10.9 (Multisystem inflammatory syndrome associated with COVID-19, unspecified)). ** Admissions of healthy persons are admissions of healthy newborns, healthy parents accompanying sick children, or other healthy boarders.

The total number of hospitals included in the HSMR model of 2020-2023 is 75 and includes 64 general hospitals, 7 university hospitals and 4 short stay specialised hospitals. These numbers are based on the number of hospital units in 2023, counting hospitals that merged in the period 2020-2023 as one unit for all years.

Table 4.1.1 lists some characteristics of the admissions included in the HSMR 2023 model per year. Admissions not meeting the criteria of the Dutch Healthcare Authority, admissions of foreigners and admissions of healthy persons were excluded. For the years 2020 and 2021, admissions with COVID-19 as the principal diagnosis were also excluded. The number of admissions included in 2023 (1,489,868) was comparable to the number of admissions in 2022 (1,481,648). The total number of admissions in the 2020-2023 model (5,774,810) however, is 2.2% lower than the total number of admissions in the previous model (2019-2022; 5,902,313). This decrease is due to the effect of the COVID-19 pandemic: the pre-pandemic year 2019, with substantially more admissions (1,617,371) than in the pandemic and post-pandemic years, was still included in the HSMR 2019-2022 model, but is excluded in the present 2020-2023 model.

Crude mortality of the admissions included in the HSMR model was increased in 2022 compared to mortality of previous years (partly due to the inclusion of COVID-19 admissions), but similar in 2023 (2.3%) compared to 2022 (2.4%).

4.2 Hospital exclusion

Hospitals were only provided with (H)SMR outcomes if the data fulfilled the criteria stated in paragraph 3.5. In order to qualify for a three-year report (2021-2023) hospitals had to fulfil these criteria for the three consecutive years.

Of the 75 hospitals included in the model, all had registered (valid) data over 2023. The four short stay specialised hospitals and one general hospital had not been asked to grant authorization for providing HSMR numbers because their case mix was very different from that of the other hospitals. In fact, all of these hospitals had participated in the LBZ but the data of these hospitals did not meet one or more of the previously stated criteria, such as a minimum number of 60 registered deaths or on average a minimum number of 1.5 comorbidities per admission. All of the other 70 hospitals that had granted authorization fulfilled the criteria and were provided with a HSMR figure for 2023. For these 70 hospitals the data of 2021 and 2022 was additionally investigated in order to determine if a three-year report could be provided. The data of all 70 hospitals met the criteria in all years considered and so all hospitals were also provided with three-year HSMR figures.

4.3 Impact of the covariates on mortality and HSMR

The table “Statistical significance of covariates HSMR 2023 model” published together with this report shows which covariates have a statistically significant (95 percent confidence) impact on in-hospital mortality for each of the 158 diagnosis groups: “1” indicates (statistical) significance, and “0” non-significance, while a dash (-) means that the covariate has been dropped as the number of admissions is smaller than 50 (or as there are no deaths) for all but one category of a covariate; see section 3.6.2.

The last row of the table “Statistical significance of covariates HSMR 2023 model” published together with this report gives the numbers of significant results across the diagnosis groups for each covariate. These values are presented again in table 4.3.1, as a summary, but ordered by the number of times a covariate is significant. Age, urgency of the admission, and severity of the main diagnosis are significant for a large majority of the diagnosis groups. This is also true for several of the comorbidity groups, especially for group 2 (Congestive heart failure and cardiomyopathy). Comorbidity 15 (HIV) is only rarely registered as a comorbidity; most diagnosis groups had fewer than 50 admissions with HIV comorbidity. In only one of the models comorbidity 15 is statistically significant. The number of times month of admission is significant varies over the years (CBS, 2017, 2018, 2019, 2020, 2021, 2022): it increased from 27 in 2017 to 43 in 2018 and decreased steadily since 2019 to 28 in 2022. In 2023 it increases slightly to 32. The number of times year of discharge is significant was 22 in the HSMR models of 2019, 2020 and 2021, increased substantially to 32 in 2022 (CBS 2020, 2021, 2022, 2023), and drops again to 26 in 2023. Compared to the HSMR 2022 model, other large changes were observed for the covariate comorbidity 3 (Peripheral vascular disease): it was significant in 95 models in 2021, increased to 103 in 2022, and decreases again to 91 models in 2023. The changes are smaller for the other covariates. The total number of significant covariates decreased from 1,613 in 2022 to 1,586 in 2023.

4.3.1 Statistical significance of the covariates for the 158 logistic regressions (summary), HSMR 2023 model
var	No. of significant results
Age	141
Urgency	127
Comorbidity 2	126
Severity main diagnosis	114
Comorbidity 13	106
Comorbidity 16	104
Comorbidity 9	94
Source of admission	94
Comorbidity 3	91
Comorbidity 6	82
Comorbidity 14	64
Comorbidity 4	61
Comorbidity 5	57
Comorbidity 17	45
Comorbidity 1	41
Sex	39
Month of admission	32
Comorbidity 10	29
Comorbidity 12	27
Comorbidity 7	27
Comorbidity 11	26
Year of discharge	26
SES	21
Comorbidity 8	11
Comorbidity 15	1
Comorbidity groups: 1 Myocardial infarction, 2 Congestive heart failure and cardiomyopathy, 3 Peripheral vascular disease, 4 Cerebrovascular disease , 5 Dementia, 6 Pulmonary disease, 7 Connective tissue disorder, 8 Peptic ulcer, 9 Liver disease, 10 Diabetes, 11 Diabetes complications, 12 Hemiplegia or paraplegia, 13 Renal disease, 14 Cancer, 15 HIV, 16 Metastatic cancer, 17 Severe liver disease.

The significance only partially reflects the effect of the covariates on mortality. This is better measured using the Wald statistic. Table 4.3.2 presents the total of all Wald statistics summed over the diagnosis groups with the respective sum of the degrees of freedom, for each of the covariates ordered by value. It shows that severity of the main diagnosis has the highest explanatory power. Age and urgency of admission are also important variables. Of the comorbidities in the model, comorbidity groups 2, 16, and 13 are the groups with the most impact on mortality. Compared to the outcome of the 2022 model (CBS, 2023), the order of the covariates with regard to explanatory power is almost identical. Note that the values of the Wald statistics themselves cannot be compared directly between years as these values depend on the number of admissions used in the models.

4.3.2 Wald chi-square statistics for the 158 logistic regressions, HSMR 2023 model
Covariate	Sum of Wald statistics	Sum of df
Severity main diagnosis	39,017	408
Age	30,489	2,000
Urgency	16,082	156
Comorbidity 2	9,285	147
Comorbidity 16	4,082	139
Comorbidity 13	3,485	151
Source admission	2,929	281
Comorbidity 3	2,415	147
Comorbidity 6	1,979	152
Month of admission	1,653	788
Comorbidity 9	1,601	123
Comorbidity 17	1,496	66
Comorbidity 4	1,249	122
Comorbidity 14	1,225	144
Comorbidity 5	1,221	119
SES	1,013	706
Year of discharge	913	468
Sex	837	150
Comorbidity 12	791	99
Comorbidity 1	641	149
Comorbidity 10	395	152
Comorbidity 7	308	129
Comorbidity 11	282	114
Comorbidity 8	137	32
Comorbidity 15	14	11
Comorbidity groups: 1 Myocardial infarction, 2 Congestive heart failure and cardiomyopathy, 3 Peripheral vascular disease, 4 Cerebrovascular disease , 5 Dementia, 6 Pulmonary disease, 7 Connective tissue disorder, 8 Peptic ulcer, 9 Liver disease, 10 Diabetes, 11 Diabetes complications, 12 Hemiplegia or paraplegia, 13 Renal disease, 14 Cancer, 15 HIV, 16 Metastatic cancer, 17 Severe liver disease.

The explanatory power of year of discharge increases since the HSMR 2021 model, with the largest increase in 2022 (13%) and a further small increase of 3.2% in this year’s HSMR 2023 model. This implies that the differences in mortality between the years in the model (corrected for differences in patient characteristics) has slightly increased. The impact of comorbidity 1 (myocardial infarction) has stabilized after having decreased for seven years.

In addition, the impact of comorbidity 14 (cancer) has decreased by 33% since the 2016 model. A decreased impact of a comorbidity could reflect a decreased effect of the comorbidity (e.g. the likelihood of dying in hospital when having this condition as comorbidity has decreased), and/or a decreased number of patients with this comorbidity resulting in less accurate estimates of the effect of this comorbidity (which also decreases the Wald statistic). The opposite applies in the case of an increased impact of a variable.

The impact of month of admission has increased considerably in the 2022 (12%) and 2023 models (8%). The increase in 2022 is probably caused by the inclusion of COVID-19 in the 2022 model for which month of admission is an important predictor. In 2023 the increase of the impact of month of admission is mostly caused by diagnoses other than COVID-19, such as pneumonia. As was mentioned in section 3.6.2, when the hospitals differ little on a covariate, the effect of this covariate on the HSMR can still be small even if this covariate is a strong predictor for mortality. Table 4.3.3 shows the impact of each covariate on the HSMR, as measured by the formula in paragraph 3.6.2, for the hospitals for which HSMRs are calculated. The comorbidities, which are considered here as one group (17 comorbidities together), have the largest effect on the HSMR. This is caused by differences in case mixes between hospitals, but possibly also by differences in coding practices (see Van der Laan, 2013). The effect of comorbidities has increased somewhat (from 4.25 to 5.05) compared to the 2022 HSMR model. Deleting sex as a covariate hardly has an impact on the HSMRs, whereas SES has a reasonable impact on the HSMR. This is probably because hospitals differ more in terms of SES categories of the postal areas in their vicinity than in terms of the sex distribution of their patients. In general, the magnitudes of the effect on the HSMR of the covariates shown in table 4.3.3 are about the same as in the previous model.

4.3.3 Average shift in HSMR 2023 by inclusion/deletion of covariates
Covariate	Average shift in HSMR
Comorbidity*	5.05
Age	3.68
Severity main diagnosis	2.25
Urgency	1.92
Source of admission	0.99
SES	0.96
Month of admission	0.13
Sex	0.12
*The comorbidities were deleted as one group and not separately.

4.4 Model evaluation for the 158 regression analyses

Table 4.4.1 presents numbers of admissions and deaths, and C-statistics for the 158 diagnosis groups. The C-statistic is explained in section 3.6.2. Overall the C-statistics have changed little compared to the previous model. Only three C-statistics show a moderate increase: an increase from 0.94 to 0.99 for “Cancer of testis and other male genital organs” (24), an increase from 0.88 to 0.92 for “Cystic fibrosis” (43) and an increase from 0.86 to 0.91 for “Complications of pregnancy, childbirth, and the puerperium; liveborn” (118). All other changes are smaller than 0.04, with most below 0.02. For 67 diagnosis groups the C-statistic did not change compared to last year.

Only two of the 158 diagnosis groups have a C-statistic below 0.70: “Congestive heart failure, nonhypertensive” (70), and “Aspiration pneumonitis; food/vomitus” (84). For the diagnosis groups with a C-statistic below 0.70, the model’s ability to explain patient mortality is less than ‘good’. This increases the risk that the model does not completely correct for population differences between the hospitals. For the highest scoring diagnosis groups (0.90 and above) the covariates strongly reduce the uncertainty in predicting patient mortality. In 2023, 65 diagnosis groups had a C-statistic above or equal to 0.90, compared to 64 diagnosis groups in 2022.

As mentioned in chapter 2 and section 3.4, it was decided not to change the model for COVID-19 compared to last year - except for adding year of discharge as we now have two years of data in the model (2022 and 2023). Only in case the model quality would deteriorate significantly (resulting in a C-statistic <0.7), we would consider changing the model. As the C-statistic has decreased only slightly from 0.75 to 0.74 (see table 4.4.1), we did not change the COVID-19 model. However, as we only use additive models (without interactions) in calculating the HSMR, the present two year’s COVID-19 model with month of admission and year of discharge does not capture all of the differences in the COVID-19 waves between 2022 and 2023 (the months at which they occurred differ and the COVID-19 variants differ; see section 3.4). As the C-statistic of the present two year’s model is almost the same as in the previous one year model, this had little effect on the model quality.

4.4.1 C-statistics for the logistic regressions of the 158 main diagnosis groups, HSMR 2023 model
Diag. group no.	Description of diagnosis group	Number of admis- sions	Number of deaths	C-statistic
1	Tuberculosis	1,469	48	0.87
2	Septicemia (except in labor)	11,348	3,312	0.72
3	Bacterial infection, unspecified site	10,059	664	0.80
4	Mycoses	2,674	329	0.78
5	HIV infection	725	23	0.83
6	Hepatitis, viral and other infections	23,166	299	0.93
7	Cancer of head and neck	14,475	239	0.90
8	Cancer of esophagus	9,516	584	0.78
9	Cancer of stomach	10,082	439	0.82
10	Cancer of colon	41,039	1,098	0.83
11	Cancer of rectum and anus	16,514	383	0.86
12	Cancer of liver and intrahepatic bile duct	7,354	466	0.82
13	Cancer of pancreas	16,006	899	0.81
14	Cancer of other GI organs, peritoneum	8,565	375	0.80
15	Cancer of bronchus, lung	44,395	4,074	0.80
16	Cancer, other respiratory and intrathoracic	2,061	140	0.82
17	Cancer of bone and connective tissue	8,034	94	0.92
18	Melanomas of skin and other non-epithelial cancer of skin	5,724	111	0.94
19	Cancer of breast	37,178	371	0.97
20	Cancer of uterus	9,049	126	0.94
21	Cancer of cervix and other female genital organs	10,015	87	0.93
22	Cancer of ovary	7,717	239	0.85
23	Cancer of prostate	24,785	326	0.94
24	Cancer of testis and other male genital organs	6,375	5	0.99
25	Cancer of bladder	53,078	431	0.93
26	Cancer of kidney, renal pelvis and other urinary organs	15,520	288	0.89
27	Cancer of brain and nervous system	11,590	234	0.78
28	Cancer of thyroid	6,060	51	0.98
29	Hodgkin`s disease	1,701	42	0.92
30	Non-Hodgkin`s lymphoma	22,872	961	0.83
31	Leukemias	21,318	1,201	0.80
32	Multiple myeloma	9,963	438	0.80
33	Cancer, other and unspec. primary, maintenance chemotherapy and radioth.	4,413	110	0.90
34	Secondary malignancies	77,034	4,179	0.77
35	Malignant neoplasm without specification of site	2,151	345	0.81
36	Neoplasms of unspecified nature or uncertain behavior	10,936	214	0.88
37	Other and unspecified benign neoplasm	61,439	117	0.85
38	Thyroid and other endocrine disorders	22,886	234	0.90
39	Diabetes mellitus without complication	12,486	137	0.87
40	Diabetes mellitus with complications	23,253	498	0.85
41	Nutritional deficiencies and other nutritional, endocrine, and metabolic disorders	53,923	492	0.94
42	Fluid and electrolyte disorders	31,935	923	0.84
43	Cystic fibrosis	1,460	7	0.92
44	Immunity and coagulation disorders, hemorrhagic disorders	10,393	182	0.88
45	Deficiency and other anemia	47,701	492	0.79
46	Diseases of white blood cells	8,986	256	0.77
47	Mental, affective, anxiety, somatoform, dissociative, and personality disorders	19,611	58	0.90
48	Senility and organic mental disorders	10,183	568	0.71
49	Schizophrenia, mental retardation, preadult disorders and other mental cond.	6,040	21	0.94
50	Other psychoses	2,526	21	0.88
51	Meningitis, encephalitis, and other central nervous system infections	9,537	567	0.88
52	Parkinson`s disease	4,915	96	0.84
53	Multiple sclerosis and other degenerative nervous system conditions	10,761	282	0.90
54	Paralysis and late effects of cerebrovascular disease	3,404	56	0.88
55	Epilepsy and convulsions	41,641	601	0.88
56	Coma, stupor, and brain damage	1,956	189	0.91
57	Headache and other disorders of the sense organs	55,486	43	0.92
58	Other nervous system disorders	43,877	395	0.93
59	Heart valve disorders	35,800	813	0.78
60	Peri-, endo-, myocarditis, and cardiomyopathy	21,043	630	0.87
61	Essential hypertension, hypertension with compl., and secondary hypertension	12,163	120	0.95
62	Acute myocardial infarction	135,542	3,404	0.85
63	Coronary atherosclerosis and other heart disease	94,141	720	0.84
64	Nonspecific chest pain	132,899	38	0.91
65	Pulmonary heart disease	30,495	1,056	0.79
66	Other and ill-defined heart disease	1,232	100	0.87
67	Conduction disorders (heart disease)	24,861	399	0.87
68	Cardiac dysrhythmias	165,244	741	0.90
69	Cardiac arrest and ventricular fibrillation	15,705	5,727	0.75
70	Congestive heart failure, nonhypertensive	127,317	10,160	0.66
71	Acute cerebrovascular disease	156,017	13,090	0.80
72	Transient cerebral ischemia, and other cerebrovascular disease	41,809	302	0.90
73	Peripheral and visceral atherosclerosis	46,722	1,970	0.90
74	Aortic and other artery aneurysms	26,933	2,448	0.89
75	Aortic and arterial embolism or thrombosis	10,350	425	0.85
76	Other circulatory disease	29,698	580	0.86
77	Phlebitis, varicose veins, and hemorrhoids	9,970	134	0.88
78	Pneumonia	106,470	9,005	0.75
79	Influenza	17,964	790	0.80
80	Tonsillitis and upper respiratory infections	43,513	68	0.92
81	Acute bronchitis	28,885	89	0.94
82	Chronic obstructive pulmonary disease and bronchiectasis	97,218	6,261	0.70
83	Asthma	22,981	92	0.91
84	Aspiration pneumonitis, food/vomitus	7,936	1,671	0.64
85	Pleurisy, pneumothorax, pulmonary collapse	21,468	620	0.82
86	Respiratory failure, insufficiency, arrest	4,983	1,533	0.73
87	Lung disease due to external agents	1,738	165	0.76
88	Other lower respiratory disease	24,590	1,017	0.88
89	Other upper respiratory disease	43,770	292	0.89
90	Intestinal infection	43,128	518	0.88
91	Disorders of mouth, teeth, and jaw	19,880	53	0.96
92	Esophageal disorders	11,550	133	0.89
93	Gastroduodenal ulcer	5,124	225	0.91
94	Gastritis, duodenitis, and other disorders of stomach and duodenum	7,230	90	0.87
95	Appendicitis and other appendiceal conditions	69,811	79	0.96
96	Peritonitis and intestinal abscess	5,103	376	0.81
97	Abdominal hernia	42,280	505	0.90
98	Regional enteritis and ulcerative colitis	16,929	62	0.95
99	Intestinal obstruction without hernia	32,890	1,556	0.82
100	Diverticulosis and diverticulitis	35,201	531	0.91
101	Anal and rectal conditions	21,025	55	0.94
102	Biliary tract disease	106,813	1,043	0.89
103	Liver disease, alcohol-related	7,404	934	0.72
104	Other liver diseases	18,231	1,109	0.81
105	Pancreatic disorders (not diabetes)	36,807	888	0.83
106	Gastrointestinal hemorrhage	35,841	1,047	0.80
107	Noninfectious gastroenteritis	10,431	234	0.80
108	Other gastrointestinal disorders	32,423	783	0.94
109	Nephritis, nephrosis, renal sclerosis	14,317	117	0.90
110	Acute and unspecified renal failure	14,545	1,015	0.77
111	Chronic kidney disease	12,972	431	0.87
112	Urinary tract infections	95,678	2,853	0.77
113	Calculus and other diseases of urinary tract	76,682	186	0.92
114	Genitourinary symptoms and ill-defined conditions	25,702	148	0.87
115	Hyperplasia of prostate and other male genital disorders	41,866	59	0.94
116	Non-neoplastic breast conditions	11,115	3	0.99
117	Prolapse and other female genital disorders	58,892	39	0.99
118	Complications of pregnancy, childbirth, and the puerperium, liveborn	541,603	15	0.91
119	Skin and subcutaneous tissue infections	54,104	847	0.89
120	Other skin disorders, chronic ulcer of skin	16,191	224	0.92
121	Infective arthritis and osteomyelitis	13,930	327	0.90
122	Osteoarthritis, rheumatoid arthritis, and other musculoskeletal deformities	228,065	173	0.94
123	Other non-traumatic joint disorders	9,770	32	0.93
124	Spondylosis, back problems, and osteoporosis	79,768	190	0.96
125	Pathological fracture	4,798	80	0.83
126	Other connective tissue disease	28,254	307	0.96
127	Cardiac and circulatory congenital anomalies	8,839	153	0.89
128	Noncardiac congenital anomalies	25,422	167	0.94
129	Short gestation, low birth weight, and fetal growth retardation	77,344	493	0.86
130	Intrauterine hypoxia, perinatal asphyxia, and jaundice	61,431	226	0.95
131	Other perinatal conditions	228,985	227	0.95
132	Joint disorders and dislocations, trauma-related, sprains and strains	18,146	32	0.97
133	Fracture of neck of femur (hip)	89,111	2,811	0.80
134	Skull and face fractures, spinal cord injury	11,095	224	0.90
135	Fracture of upper limb	40,440	137	0.95
136	Fracture of lower limb	49,375	306	0.94
137	Other fractures	43,975	1,088	0.85
138	Intracranial injury	39,809	2,851	0.76
139	Crushing injury or internal injury	20,146	422	0.91
140	Open wounds of head, neck, and trunk	5,471	57	0.87
141	Open wounds of extremities	4,948	36	0.93
142	Complication of device, implant or graft	96,912	1,370	0.87
143	Complications of surgical procedures or medical care	98,727	912	0.85
144	Superficial injury, contusion	56,502	489	0.92
145	Burns	3,657	80	0.92
146	Poisoning by psychotropic agents, drugs, or other medications	35,827	355	0.86
147	Other injuries and conditions due to external causes	13,653	727	0.89
148	Syncope	40,937	129	0.85
149	Fever of other and unknown origin	17,374	86	0.82
150	Lymphadenitis and gangrene	3,735	20	0.96
151	Shock	1,315	507	0.74
152	Nausea and vomiting	10,956	58	0.87
153	Abdominal pain	34,503	95	0.94
154	Malaise and fatigue	8,482	150	0.79
155	Allergic reactions	10,270	34	0.95
156	Rehabilitation and other aftercare, medical examination/evaluation/screening	69,654	227	0.84
157	Residual codes, unclassified	28,159	165	0.95
158	COVID-19	44,440	4,124	0.74

4.5 Regression coefficients

The file “coefficients HSMR 2023.xls” contains the estimated regression coefficients (columns “Estimate”), also called “log-odds”, for each of the 158 logistic regressions, as well as their standard errors (columns “Std. Err.”). The estimated regression coefficients are the elements of the estimate of vector 𝛽_d in the formula for p̂_dhi (see section 3.6.1), for each diagnosis d. Notice that a β-coefficient has to be interpreted as the difference in log-odds between the category in question and the reference category (first category of the same covariate). For the sake of clarity, the reference categories are given in the first row of the corresponding covariates and these have by definition a zero coefficient for each regression.

In many cases categories are collapsed (see section 3.6.2). This results in equal coefficients for the collapsed categories. If all categories were collapsed into one category for a certain variable and for a certain diagnosis group (i.e. if there was only one category with ≥50 admissions and ≥1 death), the variable was dropped from the model and all associated coefficients were set to zero. Therefore, the coefficients in the file “coefficients HSMR 2023” can be used directly to calculate mortality probabilities, with the exception of two of the Charlson comorbidities (Comorbidity 17 and Comorbidity 11). If Charlson comorbidity 17 (Severe liver disease) contains <50 admissions or no mortality, it is collapsed with Charlson comorbidity 9 (Liver disease). In this case the coefficient of Comorbidity 17 is set to zero. When a patient has both comorbidities, it counts as only one comorbidity. Therefore, when the coefficient of Comorbidity 17 is zero in the coefficients file, one should first recode all Charlson 17 comorbidities to Comorbidity 9 and use the coefficient of Comorbidity 9. The same holds for Charlson 11 (Diabetes complications) when it is collapsed with Charlson 10 (Diabetes).