Response to "Response to 'Characteristics of nursing homes associated with COVID-19 outbreaks and mortality among residents in Victoria, Australia'".

We refute the contention of Lange that the stated findings in our recent article are not supported by the statistical analysis and rebut his claim that our conclusions ought to be altered.

First, the p values highlighted by Lange were reported in our subgroup analyses (Tables S1–S3). These are separate to our primary analyses. The appropriate and correct p values should have been computed from Tables 1, 2, 3. The associations between variables with p < 0.05 are correctly annotated in those tables.

TABLE 1

Nursing homes by intrusion

Variable	Intrusion	No intrusion	χ 2	p
Number of residents
1–50	6	246
51‐–100	38	280
101 and greater	30	166	24.37	<0.001*
Maximum room occupancy
Single only	44	444
Double or more	30	243	0.78	0.38
Number of facilities
1	13	153
2–10	22	287
11 or more	39	252	7.59	0.02*
Ownership
Private	44	283
Not‐for‐profit	29	251
Public	1	158	20.41	<0.001*
Board of governance
Yes	62	614
No	32	78	35.65	<0.001*
CEO clinical
Yes	23	268
No	51	424	1.66	0.20
Compliance
Non‐compliant	19	105
Compliant	55	587	5.43	0.02*
MMM remoteness
1	69	404
2–4	4	161
5–7	1	127	34.62	<0.001*
SES category
1–3	13	175
4–6	19	214
7–10	42	303	4.73	0.09
Proximity to high‐risk industry
Within 10 km	29	203
10–25 km	36	273
>25 km	9	213	11.50	0.003*
Proximity to a public hospital
Within 10 km	59	435
10–25 km	11	86
>25 km	4	168	13.82	<0.001*
Size of closest hospital
1–100	9	130
101–500	28	348
>500	37	213	11.28	0.004*

*p < 0.05.

TABLE 2

Nursing homes by size of outbreak

Variable	Small	Large	χ 2	p
Number of residents
1–90	12	23
91 and greater	12	27	0.10	0.75
Maximum room occupancy
Single only	17	27
Double or more	7	23	1.91	0.17
Number of facilities
1–10	13	22
11 or more	11	28	0.67	0.41
Ownership
Private	10	34
Not‐for‐profit	13	16
Public	1	0	†	0.04*
Board of governance
Yes	22	40
No	2	10	†	0.32
CEO clinical
Yes	9	14
No	15	36	0.68	0.41
Compliance
Non‐compliant	8	11
Compliant	16	39	1.09	0.30
MMM remoteness
1	19	50
2–7	5	0	†	0.003*
SES category
1–3	5	8
4–6	3	16
7–10	16	26	†	0.21
Proximity to high‐risk industry
Within 10 km	7	22
>10 km	17	28	1.50	0.22
Proximity to a public hospital
Within 10 km	20	39
>10 km	4	11	0.29	0.59
Size of closest hospital
1–500	11	26
>500	13	24	0.25	0.62

*p < 0.05, †Fisher's exact test due to low cell counts

TABLE 3

Nursing homes by CFR

Variable	Low CFR	Medium CFR	High CFR	χ 2	p
Number of residents
1–90	13	8	14
91 and greater	14	9	16	0.01	0.99
Maximum room occupancy
Single only	18	9	17
Double or more	9	8	13	0.98	0.61
Number of facilities
1–10	14	11	10
11 or more	13	6	20	4.64	0.10
Ownership
Private	16	13	15
Not‐for‐profit	10	4	15
Public	1	0	0	†	0.23
Board of governance
Yes	23	12	27
No	4	5	3	†	0.22
CEO clinical
Yes	9	5	9
No	18	12	21	0.10	0.95
Compliance
Non‐compliant	6	4	9
Compliant	21	13	21	†	0.79
MMM remoteness
1	23	16	30
2–7	4	1	0	†	0.07
SES category
1–3	6	3	4
4–6	4	6	9
7–10	17	8	17	†	0.50
Proximity to high‐risk industry
Within 10 km	9	5	15
>10 km	18	12	15	2.54	0.28
Proximity to a public hospital
Within 10 km	20	15	24
>10 km	7	2	6	†	0.62
Size of closest hospital
1–500	11	9	17
>500	16	8	13	1.52	0.47

*p < 0.05, †Fisher's exact test due to low cell counts.

Second, Lange's statistical interpretation is fundamentally flawed. The foundations of interpreting empirical research are frequently noted as differentiating what is statistically significant, what is real and what is clinically important, (p119) and of appreciating the assumptions of statistical tests and the implications when these are violated.  The Pearson χ 2 test and associated p values assume that the finite data are sampled from an (effectively infinite) population. (p308) This is to be distinguished from our research study, which did not sample but rather included the entire population of nursing homes in Victoria.

The p values may be of interest in approximately quantifying the effect size relative to the population size but have no meaningful statistical interpretation when there is no sampling. We accordingly omitted numerical p values from Tables 1, 2, 3 for economy of space. We did not make any claims about χ 2 statistics, p values or statistical significance in the discussion of our primary results.

Our descriptive results are correctly stated for an entire study population. For example, it is true that the proportion of not‐for‐profit operators was highest among homes with a high case‐fatality rate (50.0%) than those with medium (23.5%) or low (37.0%) case‐fatality rates. This cannot be rendered untrue by a calculated p value (0.3) that is interpreted as being ‘not statistically significant’.

We acknowledged our research is subject to other types of measurement error beyond the scope of significance testing; for example database incompleteness. We reviewed these limitations at length, and our conclusion is appropriately cautious. The descriptive results are presented accurately without embellishment, international studies are presented for comparison and associations are described without necessarily implying causation.

CONFLICTS OF INTEREST

No conflicts of interest declared.

Table S1‐S4

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