Description of data

Anonymised data were provided by Ian Frayling from the All Wales Medical Genetics Service, including details of predictive tests within 33 families with LS mutations. For each predictive test we were provided with the date when the family mutation was first reported, the date when the predictive test result was reported, the sex of the person receiving the predictive test and whether or not they were diagnosed as a LS carrier. In some cases the data also contained the kinship of the predictive test, i.e. whether the person was a FDR, SDR or more distant relation of the index case.

The data cover reports from October 2000 to November 2012 and include details of 109 predictive tests on members of 33 families. The mean time between diagnostic test and predictive test was 747 days (median 415 days, interquartile range 182–1206 days, range 0–3510 days).

Proportion of relatives who test positive

Of the 109 relatives who received predictive testing, 44 (40%, 95% CI 31% to 50%) tested positive for the family mutation. There is significant evidence to suggest that the true proportion who would test positive is < 0.5 (one-tailed binomial test, p = 0.027), and there are a number of factors which contribute to this, including non-paternity, de novo mutations, mortality bias and offering testing to those at < 50% genetic risk because it is not possible (e.g. owing to death or to testing being declined) or not appropriate to test intervening relatives.

Proportion of relatives who are male

Of the 109 relatives who received predictive testing, 39 (36%, 95% CI 27% to 46%) were male. There is significant evidence to suggest that the true proportion who would be male is not 0.5 (two-tailed binomial test, p = 0.004). Ian Frayling also analysed the sex of the index cases (those receiving diagnostic tests) and found that there were 17 female and 16 male index cases. It is his belief that men are less likely to take up predictive testing than women and we cannot identify any alternative explanations.

Independence of test result and sex

We tested whether or not the test result and sex of the relative were dependent variables by constructing a 2 × 2 table (Table 126) and using a Pearson’s chi-squared test. We found no evidence of dependency (chi-squared = 0.262, degrees of freedom = 1, p = 0.61).

TABLE 126

2 × 2 table of test result and sex

Kinship of relatives to proband

For 70 (64%) of the 109 tests, we were provided with the kinship of the relative being tested to the proband. These are summarised in Table 127, which shows that 47% of relatives tested are FDRs while 53% are more distantly related.

TABLE 127

Kinship of relatives to probands

Expected number of relatives tested per proband over time

The data provided clearly indicated that relatives are not tested immediately after a positive diagnostic test. It is important to know the expected number of relatives that would be tested for each proband over time as this has an effect on workload and the overall effectiveness of testing (if all relatives waited decades before being tested for the family mutation, most of the potential benefit of testing would have been forgone).

We analysed the number of relatives tested per proband by using a Kaplan–Meier-style estimator. We assumed that all families were censored at the date of the most recent database search (an effective ‘study end’ date of 1 November 2012).

If d_i is the number of predictive tests at time t_i and n_i is the number of families still being observed at time t_i, our estimator is

Results of applying this method are given in Tables 128 and 129 and Figure 126.

TABLE 128

Expected number of relatives tested over time

TABLE 129

Expected time since proband diagnostic test to test a specified number of relatives

FIGURE 126

Expected number of relatives tested per proband (ticks indicate when families are censored).

Adjustment for families without predictive tests

The data provided do not include families without any predictive tests. Ian Frayling has advised that the number of such families would be very low as the likelihood of identifying family members for testing is considered during genetic counselling, and, as a result, people without relatives would be less likely to be tested. Ian Frayling gave an estimate that 2% of probands, or fewer, would never identify relatives to be tested. To investigate the effect of this on our analysis, we added a family which would be observed throughout the experiment but would never lead to a predictive test. As there were originally 33 families, this meant that 1 out of 34 = 2.9% of probands would never identify relatives to be tested.

The results with the adjustment are given in Tables 130 and 131 and Figure 127. Figure 128 additionally shows a comparison plot of the estimator with and without the adjustment.

TABLE 130

Expected number of relatives tested over time after adjusting for probands never identifying relatives for testing

TABLE 131

Expected time since proband diagnostic test to test a specified number of relatives after adjusting for probands never identifying relatives for testing

FIGURE 127

Expected number of relatives tested per proband, accounting for the possibility of probands never identifying relatives for testing (ticks indicate when families are censored).

FIGURE 128

Effect of adjusting for probands never identifying relatives for testing.