Patient preferences, referral process, and access to specialized care. Is patient choice constrained?

Figures & data

Table 1. Descriptive statistics on patient characteristics and hospitals attributes.

	Mean	Std	Min	Max
Patients characteristics (n=33,101)
Distance to chosen hospital	26.36	29.85	0.09	159.89
Age	61.5	13.44	15	102
Geographical avail. of providers	18.76	25.79	1	95
Share of patients choosing their nearest provider	21.72%
Share of patients choosing a:
- Public hospital	1.06%
- Private for-profit hospital	58.8%
- Private not-for-profit hospital	40.14%
Hospital attributes (n=232)
Room rate	73.27	4.62	59.05	85.64
Share of hospital stay in oncology	43.11%	34.85	2.81%	100%
Bed occupancy rate	58.80%	30.43	18.19%	297.21%
Share of hospitals with accreditation level:
- A	42.67%
- B	40.09%
- C or D	17.24%
Share of hospitals of type:
- Public	1.30%
- Private for-profit	80.17%
- Private not-for-profit	18.53%

Standard deviation (std); Score relating how patients rated their room during their hospital stay from the “e-Satis” survey (Room rate); Geographical availability of providers (Geographical avail. of providers) corresponds to the number of providers within 50 kilometres. The accreditation level is separated into four levels: without recommendations (A), with recommendations (B), with reservations (C), and conditional accreditation (D).

Table 2. Parameter estimates from the mixed Logit model, and of the bound estimator.

	Mixed Logit		Bound estimator
	Coef.	Std coef.	Coef.	Std coef.
Nearest	0.8372***		−2.648
Distance	−0.0419***		−0.0886*
Age x Distance	−0.0006***		0.0001
Length of stay x Distance	−0.0012***		−0.0044***
Patient room rate	0.0318***		−0.1182***
Patient room rate x Geographical avail.	−0.0406***		−0.146***
Hospital accreditation level
- A	Ref		Ref
- B	0.4341***		−1.9594***
- C or D	0.3784***		0.3947***
Geographical avail. x Hospital accreditation level
- Geographical avail. x A	Ref		Ref
- Geographical avail. x B	−0.3717***		−1.3485***
- Geographical avail. x C or D	−0.1899***		−0.8613***
Type of hospital
- Public	Ref	Ref	Ref	Ref
- Private for-profit	0.2495***	6.3252***	0.8931***	1.1646**
- Private not-for-profit	0.6667***	−0.0888	0.5193***	0.2066***
Share of hospital stay in oncology	2.1956***	0.7319	4.2555**	−2.3541***
Bed occupancy rate	−0.0028***	−0.0075***	−0.0150***	−0.0212***
# patients	33,101		33,101
# observations	986,012		986,012
Log-Likelihood	−52,124,912		n.a.

Number of (#); modality in reference (Ref); significant at 1%, 5%, and 10% is indicated as ***, ** and * respectively; not applicable (n.a.); coefficient (coef.); standard deviation of coefficient (std coef.); geographical availability of providers (Geographical avail.).

Table 3. Expected distribution of hospital characteristics, based on the predicted probabilities of patient referral and predicted patient choice.

	Predicted patient referral	Predicted patient choice with complete information^a
Distance (kilometres) to chosen hospital	26.387	45.153
Share of patients choosing their nearest provider	20.93%	2.76%
Room rate (score)	74.319	71.9
Share of patients choosing a hospital with accreditation level
− A	43.02%	66.32%
− B	42.98%	13.58%
− C or D	14%	20.11%
Share of patients choosing a hospital of type:
− Public	1.07%	5.13%
- Private for-profit	58.62%	66.55%
- Private not-for-profit	40.30%	28.33%
Share of hospital stay in oncology	67.03%	70.65%
Bed occupancy rate	58.28%	57.55%
Parameters	Mixed Logit	Bound Estimator

Choice that patients would have made, based on their individual preferences only, if they had the opportunity to select their preferred provider directly from the full choice set (a); score relating how patients rated their room during their hospital stay from the ‘e-Satis’ survey (Room rate). The accreditation level is separated into four levels: without recommendations (A), with recommendations (B), with reservations (C), and conditional accreditation (D). We tested for statistical differences in the mean characteristics between the predicted patient referral and the predicted patient choice using Student’s t-test. We found significant differences at a level of 1% for all attributes. Foremost consideration should be given, however, to the magnitude of the statistically significant differences.

Figure B1. Distance patients – hospitals distribution fitted in the raw dataset, before restricting the sample to hospitals within 160 kilometres of the patients’ places of residence.

Table C1. Share of patients (%) having at least h hospitals available within a radius of k kilometres.

	h = 1	h = 2	h = 3	h = 4	h = 5
k = 10	60.7	46.8	34.9	27.6	23.1
k = 20	82.4	68.5	51.9	40.6	35.1
k = 30	93.4	84.3	69.2	55.4	47.4
k = 40	97.9	92.8	84.9	72.7	63
k = 50	99.3	97.2	93.9	86.9	78.7

Number of hospitals available (h); radius in kilometres (k).

Figure C1. Cumulative density of patient geographical availabilities of providers.

Figure C2. Histogram of patient geographical availability of providers.

Table C2. Share of patients (%) choosing the i^th nearest hospital.

	Hospital’s rank in distance
	i=1	i=2	i=3	i=4	i=5	i=6	i=7	i=8	i=9	i=10+
Age (p < 0.001)
− Q1	22.77	16.93	11.64	7.24	5.25	4.46	2.98	2.35	1.92	24.46
− Q2	24.36	18.50	11.60	6.87	5.29	4.10	2.90	2.27	2.15	21.94
− Q3	26.00	19.42	12.14	6.88	5.10	4.07	2.62	2.50	1.92	19.35
− Q4	30.51	20.80	12.16	6.84	4.51	3.89	2.76	2.14	1.56	14.82
Geographical availability of providers (p < 0.001)
− Q1	35.48	21.82	10.21	3.21	2.12	3.02	2.28	2.48	1.54	17.83
− Q2	30.24	22.50	15.30	7.76	4.76	3.22	2.05	1.16	0.68	12.32
− Q3	20.87	18.97	13.80	8.95	8.23	6.33	3.49	3.06	2.53	13.76
− Q4	19.03	13.09	7.46	7.22	4.44	3.80	3.32	2.67	2.81	36.15
Length of stay (p < 0.001)
− Q1	22.33	16.97	11.68	7.53	6.05	5.11	2.85	2.56	2.11	22.81
− Q2	28.12	19.22	11.76	7.17	4.57	4.26	2.77	2.10	1.78	18.25
− Q3	26.19	28.33	11.57	6.83	4.42	3.47	3.10	2.36	1.93	21.80
− Q4	28.13	20.86	12.31	6.49	4.73	3.67	2.62	2.17	1.71	17.31
Total	26.05	18.97	11.90	6.96	5.02	4.12	2.81	2.31	1.88	19.98

First, second, third and fourth quartile are respectively indicated as Q1, Q2, Q3 and Q4. Chi Square test of independence are performed for each patients characteristics. The total is computed for our sample of 31,101 patients.

Figure C3. Histogram of the lower bound (i.e. hospitals chosen by other patients living within a radius of 15 kilometres) of the patient choice set size in our identification strategy.

Figure C4. Share of patients excluded from the lower bound according to the radius chosen for the lower bound.

Table C3. Average size of the lower bound choice set according to the radius chosen.

Radius (kilometres)	Number of providers included in $C{S}^{sub}$
	Median	Mean	Std
5	3	4.23	4.47
10	4	5.93	6.69
15	5	7.45	8.45
20	6	8.74	9.80
25	7	9.82	10.69
30	8	10.83	11.32
35	9	11.74	11.82
40	9	12.60	12.16
45	10	13.45	12.44
50	11	14.29	12.68
55	12	15.07	12.91
60	12	15.80	13.12
65	13	16.57	13.40
70	14	17.31	13.67

Standard deviation (Std); lower bound choice set ($C{S}^{sub}$).

Table D1. Descriptive statistics on hospital attributes in the full sample without missing data (i.e. excluding the parameters for the patients’ room rate) and in the restricted sample.

	Restricted sample (232 hospitals)	Full sample (511 hospitals)	Difference
Share of hospital stay in oncology	43.11	35.73	p = 0.016
Bed occupancy rate	58.81	53.25	p = 0.009
Hospital accreditation level
− A	42.67	13.41	p < 0.001
− B	40.08	45.93	p = 0.198
− C or D	17.24	40.65	p < 0.001
Type of hospital
− Public	1.29	78.45	p < 0.001
- Private for-profit	80.17	18.69	p < 0.001
- Private not-for-profit	18.53	2.84	p < 0.001

The accreditation level is separated into four levels: without recommendations (A), with recommendations (B), with reservations (C), and conditional accreditation (D).

Figure E1. Distribution of patients-hospitals distances.

Table F1. Parameter estimates from the mixed Logit model in the full sample without missing data, thus excluding the parameters on patients’ room rate.

	Mixed Logit
	Coef.	std coef.
Nearest	0.6747***
Distance	−0.0459***
Age x Distance	−0.0005***
Length of stay x Distance	−0.0004***
Hospital accreditation level
− A	Ref
− B	0.1955***
− C or D	0.0027
Geographical avail. x Hospital accreditation level
− Geographical avail. x A	Ref
− Geographical avail. x B	−0.0169
− Geographical avail. x C or D	−0.2829***
Type of hospital
− Public	Ref	Ref
- Private for-profit	0.2387***	−2.8933***
- Private not-for-profit	0.3117***	5.8149***
Share of hospital stay in oncology	2.0512***	−0.6056***
Bed occupancy rate	−0.0026***	−0.0023***
# patients	57,151
# observations	3,860,303
Log-Likelihood	−117,631.29

Number of (#); modality in reference (Ref); significant at 1%, 5%, and 10% is indicated as ***, ** and * respectively; coefficient (coef.); standard deviation of coefficient (std coef.); geographical availability of providers (Geographical avail.).