Modelling the risk of failure to progress in labour

The QAMC web page allows a user to enter a description of a particular case[*]. The case can be described in terms of

• maternal age (in five year groups);
• number of children now living;
• maternal height (less or greater than 155cm);
• previous obstetrical history (previous Caesarian sections or neonatal deaths);
• current health state as represented by 30 different ICD-9 codes [12].

After entering a specific patient profile, a user can (after agreeing to a legal disclaimer) receive information about the observed and estimates incidence of failure to progress for a case with those characteristics. This information is presented in three parts.

Prior probability of failure to progress

Before we know any information about a specific case, we can express our degree of prior belief that a labour will fail to progress. This prior can be formed in a variety of ways but it is most convenient for us to give the rate of incidence of failure to progress observed in the SMR2 data from 1980-88 (9.61%).

Observed rate of incidence

Given a specific patient profile, we can report the number of cases in the SMR2 data that exactly match that description, and also the number of matching cases in which an adverse outcome occurred. If we were to ignore our prior belief, we could use the ratio of these numbers to estimate the probability of adverse outcome associated with the patient profile. The variance of this maximum likelihood estimate depends on the total number of cases matching the specified profile: the more cases, the lower the variance.

Note that this section of the web page reports the cases that exactly match the description provided. This can come as a surprise to uses who expect the page to report cases that match any of the specified characteristics. For example, the results of a query regarding a 20-24 year old mother, who has 2 children, is taller than 155cm and is obese (ICD-9 code 2780) will report all cases in the SMR2 data with those and only those characteristics. The query will not cause a report which aggregates the number of cases with the specified characteristics and any other conditions.

Different aspects of this section of the web page are best demonstrated using four test cases.

1. Age 20-24, 0 children, taller than 155cm, no previous obstetric history or ICD-9 codes.
   This is the modal patient profile in the SMR2 data. Note the observed incidence of failure to progress is about 5% higher than the incidence across the entire database.

2. Age 15-19, 4+ children, taller than 155cm, no previous obstetric history or ICD-9 codes.
   ISD Scotland has asked that we suppress precise details of profiles for which there are fewer than 10 cases. The observed incidence of failure to progress is rounded to the nearest 5%.

3. Age 15-19, 4+ children, taller than 155cm, no previous obstetric history, obese (ICD-9 code 2780).
   No instances of this profile are recorded in the SMR2 data. Recall that we are searching for and exact match of all details, including the presence of ICD-9 code 2780 and the absence of all other codes.

4. Age 25-29, 0 children, shorter than 155cm, no previous obstetric history, poor fetal growth (ICD-9 code 6565) AND excessive fetal growth (ICD-9 code 6566).
   This case suggests the presence of inconsistent information in the SMR2 data - it is very unlikely for both poor and excessive fetal growth to occur. A quality audit of 651 SMR2 records (presented in [6]) showed that ICD-9 codes of maternal condition were particularly prone to error. These errors can cause incongruities in prediction systems derived from the data [6].

Estimated rates of incidence

This section of the web page shows the predicted risk of adverse outcome according to three different risk models: logistic regression [3], an ensemble of neural networks [1,10] and a look-up table smoothed with a Dirichlet[*] prior [8]. Details of these models and how they were trained are given in [6,7].

These models estimate the probability of adverse outcome associated with ( i.e. , conditional upon) a specific patient profile. They do not provide information about the joint probability of patient characteristics, that is to say, they cannot directly estimate whether a given profile is common or unusual. Some degree of novelty detection is possible by looking at how well these prediction models agree. If the mean absolute deviation of the three predictions is greater than 5% (as in case 4 above), a warning message is printed with the predictions.