Sequence symmetry analysis graphic adjustment for prescribing trends

Abstract

Background: Sequence symmetry analysis (SSA) is a signal detection method that can be used to assist with adverse drug event detection. It provides both a risk estimate and a data visualisation. Published methods provide results in the form of an adjusted sequence ratio, which adjusts for underlying market trends of medicine use, however no method for adjusting the visualisation is available. We aimed to develop and evaluate another method of adjustment for prescribing trends and apply it to the SSA visualisation.

Methods: The SSA method relies on incident prescriptions for pairs of medicines of interest. Smoothing curves were fitted to the frequency distributions of incident medicine use. When divided and normalised, these curves yielded a set of proportions related to differences in prescribing trends over follow-up. These were then used to adjust the unit counts for incident prescriptions in the SAA visualisation and to calculate the sequence ratio. Curve fitting was also used to identify the proportional relationship between sequences over time for SSA and is presented as a supplementary visualisation to the SSA. We compared the sensitivity and specificity of our method with that from the SSA method of Tsiropolous et al. RESULTS: Curve-fit adjusted SSA visualisations yielded adjusted sequence ratios very close to those of Tsiropolous, with a p-value of 0.999 for the two sample Kolmogorov-Smirnov test. Results for sensitivity and specificity derived from adjusted sequence ratios were also practically the same. The curve-fit method graphically indicates the proportionality of the sequence and provides a useful supplement of net differences between the two sides of the SSA visualisation. Additionally, we found that incident prescriptions for patients common to both distributions are best precluded from adjustment calculations, leaving only incident prescriptions for patients unique to one or other distribution. This improved the accuracy of SSA in some atypical instances with negligible affect on accuracy elsewhere.

Conclusions: Our curve-fit method is equivalent to current methods in the literature for adjusting prescribing trends in SAA, with the advantage of providing adjustment incorporated in the SAA visualisation.

Keywords: Curve fitting; Prescribing trend; Rate ratio (RR); Sequence symmetry analysis (SSA); Waiting time distribution (WTD).

Fig. 1

Waiting time distributions for a: amlodipine and b: frusemide over 10.5 years. The first year includes prevalent users, hence it is precluded from follow-up

Fig. 2

Unadjusted SSA visualisation for amlodipine and frusemide. The crude RR, 1.58, is the ratio of counts for first dispensings of frusemide occurring after amlodipine (RHS) to counts for first dispensings of frusemide occurring before amlodipine (LHS). The Tsiropolous adjusted RR is 1.62

Fig. 3

a: Curve fitted WTD over a 9.5-year follow-up for amlodipine (suspected cause medicine). b: Corresponding curve fitted WTD for frusemide (suspected effect medicine)

Fig. 4

Supply lag 101 for frusemide (medicine b) after amlodipine (medicine a) across WTDs. There are nine supply lags with 101 days between each medicine of a pair. Many pairs of first supply days are unique to a patient but others can be the same for two or more patients, such as pairs 2 and 3. (Note: interleaving earlier pairs can be resolved by observing paired numbers)

Fig. 5

a: Effect as a proportion of cause due to prescribing trends. On average, 1.816 times more patients started frusemide than started amlodipine. b: Effect as a normalised proportion of cause due to prescribing trends. Dividing by the average (1.816) excludes the frequency difference but retains the proportional difference in shape over the WTD period

Fig. 6

The lower curves of Figures a and b show the prescribing trend for exclusive components—true trend—and the upper curves show the prescribing trend for all components. In this example, using all components resulted in a differential change in shape between respective WTDs owing to the change in shape of the distribution at Figure a. For little or no change in shape between WTDs, both curves should run close to parallel within each WTD. (The two-year gap at the beginning of the WTDs indicates that fist supply times took extra time to settle down to where they could be used for reliable follow-up)

Fig. 7

The curve-fit adjusted RR for amlodipine and frusemide is 1.61, which effectively agrees with the Tsiropoulos adjusted RR of 1.62. The proportion of patients prescribed both medicines is 3.2%

Fig. 8

a: The curve-fit adjusted RR for risperidone and frusemide is 1.26, which effectively agrees with the Tsiropoulos adjusted RR of 1.27. The proportion of patients prescribed both medicines is 1.82%. b: The curve fitted difference where counts for after-prescribed frusemide generally exceed those for before-prescribed frusemide is greatest around week 5 and extends to week 37. After that, the counts for after-prescribed frusemide are generally less than those for before-prescribed frusemide. A sufficiently large positive effect denotes an adverse effect, a sufficiently large negative effect denotes a protective effect, and zero is the locus for no effect

Fig. 9

The Kolmogorov-Smirnov statistic represents distance between two samples; here adjusted RRs derived from exclusive WTD components over 9.5 years. Of 124 corresponding pairs of RRs for Tsiropoulos and Curve-fit, only a handful did not effectively coincide (four or five, depending on how an outlier is defined), and these were for grossly deficient numbers of medicine pairs, typically in single digits. The exact p-value for the 124 pairs of RRs was 0.994

Fig. 10

The lower curve shows the prescribing trend for exclusive components—true trend—for meloxicam and the upper curve shows the prescribing trend for all components. Again, using all components resulted in a differential change in shape between respective WTDs owing to the change in shape mainly of the meloxicam distribution