Prediction Models for Disease: The Effect of Associations between Markers on Calculating the Risk for Disease by Likelihood Ratio Products

BACKGROUND:
Prediction models using a combination of features can calculate risk for disease. Likelihood Ratios (LR) can be used to estimate the risk for disease. When multiple features are present, it is often assumed that the LR of the combined features can be calculated by multiplying individual LRs. However, in reality the features are often not independent.
PURPOSE:
To evaluate the effect of dependency of markers on the calculation of risks for disease in real life datasets and in a partly modeled dataset.
METHODS:
Population I consist of 144 consecutive rheumatoid arthritis (RA) and 629 non-RA patients. Rheumatoid factor, anti-citrullinated protein/peptide antibodies and the HLA-shared epitope were determined. Scenario 1 estimates the risks based on LR products and scenario 2 based on observed LRs. Population II consists of 847 patients with definite ankylosing spondylitis (AS). Six variables (psoriasis, inflammatory bowel disease, uveitis, HLA-B27 status and latest available CRP) were evaluated. Scenario 1 estimates the risk for AS based on LR products, scenario 2a assumes independency in controls while association is present in cases and scenario 2b assumes equal association in cases and controls. In this partly modeled dataset specificities of the features were derived from literature.
RESULTS:
When two features are similarly associated in cases and controls, the risk for disease will be overestimated by the LR product method. This is the case for RF and ACPA as shown in table 1 for the diagnosis of RA. In case of association in cases and independency in controls, the risk for disease will be underestimated as is the case for RF and SE in RA. Table 2 shows the results for combinations of six variables for the diagnosis of AS. Different scenarios on associations in cases and controls are assumed. Similar results are observed and confirm the observations from the first dataset.
CONCLUSIONS:
If features are dependent, the use of the LR products is not an exact method to estimate risks for disease. The strength of the association between the features in cases opposed to controls determines the direction and magnitude of the error.
Table 1: Risk for disease (RA) given positivity for the different tests by LR product and exact risk

Table 1: Risk for disease (RA) given positivity for the different tests by LR product and exact risk

double positivity for	LR test1	LR test 2	LR product (scen1)	Exact LR (scen2)	OR between tests in RA	OR between tests in non-RA	Risk for disease calculated by LR products (scen 1)	Exact risk for disease (scen 2)
RF and SE	7.0	1.5	10.4	14.0	3.1	0.7	70%	76%
RF and ACPA	7.0	32.8	228.0	58.9	11.1	9.7	98%	93%
ACPA and SE	32.8	1.5	48.9	25.9	4.2	4.6	92%	86%
RF, SE and ACPA			339.7	47.5			99%	92%

Table 2: Likelihood ratios and risks for disease (AS) in function of different scenarios

Table 2: Likelihood ratios and risks for disease (AS) in function of different scenarios

variable1	variable2	LR var1	LR var2	OR in AS	Estimated LR for double positivity			Risk for disease in case of double positivity and an a priori risk of 14%
					scen 1	scen 2a	scen 2b	scen 1	scen 2a	scen 2b
HLA B27+	Raised CRP	8.3	1.8	1.4	15.3	16.0	12.8	71%	72%	68%
HLA B27+	Anterior uveïtis	8.3	9.1	2.2	75.7	86.7	26.3	92%	93%	81%
Enthesitis	Arthritis	4.5	5.8	2.4	26.3	30.9	16.6	81%	83%	73%
Enthesitis	Raised CRP	4.5	1.8	1.3	8.4	9.1	7.5	58%	60%	55%
Psoriasis	Arthritis	2.7	5.8	2.1	15.7	20.0	11.1	72%	77%	64%
Anterior uveïtis	Arthritis	9.1	5.8	1.9	52.9	63.3	37.3	90%	91%	86%

 R. Wittoek, None; F. De Keyser, None; A. Boonen, None; K. De Vlam, None; N. Vastesaeger, None; H. Mielants, None; G. Verbruggen, None; B. Vander Cruyssen, None.