Chapter 7 Decision analysis for screening tests for GDM: Case identification . 151
7.6 Populating the screening test decision tree for GDM
In the beginning of this chapter, the decision tree was outlined and shown to be constructed of decision and chance nodes pertaining to various screening and diagnostic methods based on various test strategies. Moreover, all the relevant evidence presented in previous sections was used to populate the decision tree for case identification. The relevant parameters were converted into probabilities and expressed as a number between zero and one. Probability can be calculated by dividing the desired outcome by a hundred or by the total number of outcomes. All probabilities can then be applied to the branches of the decision tree to represent the possible events patients may experience at any point in the tree. For example, disease status, the first chance node relates to whether or not a mother experiences disease. The probability of GDM prevalence is applied to the disease positive branch (D+), whereas, 1 minus the probability of GDM prevalence is applied to the disease negative branch (D-). Moving from left to right, all subsequent branches show the probability of sensitivity and specificity for all screening and diagnostic tests. This section presents pathway probabilities and the costs of case identification for GDM, with each strategy being summarised as four possible outcomes of case identification.
7.6.1 Expected case identifications
In the decision tree for GDM, the statistics of disease status and diagnostic outcomes indicate the probability along each of the pathways for prevalence of disease (D+) or without disease (D-), prevalence of risk factors (R+) or without risk factors (R-), test positive (T+) and test negative (T-). The combination of branches in the tree that represent screening for GDM outline a series of pathways along which the mother can pass through. The probabilities show the likelihood of a particular event occurring at branches throughout the GDM decision tree. The screening test strategies employed define pathways in the decision tree, for instance S1: 6 pathways, S2: 8 pathways, S3: 4 pathways, S4: 6 pathways and S5: 2 pathways. The expected outcomes are then
calculated by multiplying the pathway probabilities, which are joint probabilities. The probabilities for each strategy must total 1. For example, in strategy 2 (S2), there are four relevant probabilities, namely the probability of having a positive risk factor (R+), the probability of having GDM given the presence of risk factors P
( D+ R+)
, the probability of being test 1 positive given a positive disease state( T + D+)
1 and the probability of being test 2 positive given a positive disease state( T + D+)
2 , all of which have the values 0.381, 0.016, 0.781 and 1.000, respectively. The pathway probabilities are then multiplied along the pathway giving a result of 0.005.Expected case identifications for NDS
In the negative dominant strategy, a true positive result (cases detected) is taken into account for women who have positive results for both screening tests and diagnosis.
Consequently, probabilities in the decision tree pathways for each strategy only present one TP result each, as shown in Table 7.10. More than one FN and TN are likely to be found in an NDS. As a result, the probabilities for FN and TN each have to be presented as one probability by adding the individual values. For example, S1 (NDS) has two FN results, namely 0.000 and 0.013. By adding these FN results together the probability of FN in S1 (NDS) is 0.013. Similarly, two results for TN are found in S1 (NDS) giving a result of 0.965 when added together (0.193 + 0.772).
Combining the test results, assuming diagnostic tests have 100% sensitivity and specificity (gold standard), the probabilities for TN and FN are the same in each strategy, whereas, the probabilities of TP and FN outcomes vary depending on the sensitivity of the test employed. In NDS, S3 (NDS) presents higher case identifications than the other strategies. S3 (NDS) is a one-step approach, which involves screening all pregnancies by a diagnostic test with 100% sensitivity and specificity. Therefore, diagnostic tests with 100% accuracy detect GDM from pregnancy close to the actual prevalence in the population (3.5%).
Table 7.10 Expected case identifications for NDS
Expected case identifications for PDS
Table 7.11 presents the results for expected case identifications in the PDS. There is more than one TP result in each strategy. Therefore, to calculate case detection of each strategy, the probabilities of the TP results in each parthway were added up. For example, two results for PT are found in S1 (PDS) giving a result of 0.035 when added together (0.022+0.013). Patients that have an absence of disease but FP are more likely to be found in the PDS. For example, S1 (NDS) has two FP results, namely 0.193 and 0.000. By adding these FN results together the probability of FP in S1 (NDS) is 0.193.
Hence, the case identification rates in all PDS strategies are close to the prevalence in the population (3.5%).
Probabiltiy from decision tree pathways Probability for strategy
Disease state Probability Disease state Probability
S1 (NDS) TP 0.022 S1 (NDS) TP 0.022
FN 0.000 FN 0.013
FN 0.013 FP 0.000
FP 0.000 TN 0.965
TN 0.193
TN 0.772
1.000 1.000
S2 (NDS) TP 0.012 S2 (NDS) TP 0.012
FN 0.000 FN 0.022
FN 0.003 FP 0.000
FP 0.000 TN 0.965
TN 0.111
TN 0.254
FN 0.019
TN 0.600
1.000 1.000
S3 (NDS) TP 0.035 S3 (NDS) TP 0.035
FN 0.000 FN 0.000
FP 0.000 FP 0.000
TN 0.965 TN 0.965
1.000 1.000
S4 (NDS) TP 0.016 S4 (NDS) TP 0.016
FN 0.000 FN 0.019
FP 0.000 FP 0.000
TN 0.365 TN 0.965
FN 0.019
TN 0.600
1.000 1.000
In combination of the test results, assuming diagnostic tests have 100%
sensitivity and specificity (gold standard), the probability of TP outcomes in PDS is equal to the prevalence in the population. However, in PDS, the probabilities for TP and FN are the same in each strategy, whereas, the probabilities of FP and TN outcomes vary depending on the specificity of the test employed.
Table 7.11 Expected case identifications for PDS
7.6.2 Expected costs
Each pathway in the GDM tree has associated costs, including risk factor screening, screening and diagnostic tests, depending on the strategy. For example, in the first pathway of S2 (NDS), the significant costs are risk factor screening £9.50, screening tests £3.60 and diagnostic tests £18.76, totalling £31.86. The same principle is used for other pathways in the tree and it can be seen that for some pathways the total sum of the costs remain the same. The expected costs for each strategy can be calculated by
Probabiltiy from decision tree pathways Probability for strategy
Disease state Probability Disease state Probability
S1 (PDS) TP 0.022 S1 (PDS) TP 0.035
summing the values for the pathway costs weighted by the pathway probabilities. The total costs of risk factor screening, screening and diagnostic tests are shown as the expected value of each pathway. The pathway probabilities represent the sum of the different probabilities for each branch in the pathway. Of those, S2 (NDS) for example, has a pathway probability 0.012 and a pathway value of £31.86, a weighted value can be calculated to give the expected costs of this pathway, equaling 0.39, as shown in Table 7.12. The same principle is used for the other pathways in the tree to calculate expected costs. Adding up the expected costs along the pathways for each strategy can generate expected costs for the strategies. With the same example S2 (NDS), the expected cost is £13.19. Another way of working out the expected costs and consequences for a given option in a decision tree is by rolling back the tree. By doing so, the expected outcomes will be exactly the same as summing across all the pathways.