Comparison of Rates of Type 2 Diabetes in Adults and Children Treated With Anticonvulsant Mood Stabilizers

This cohort study evaluates the association between anticonvulsant mood stabiliziers and rates of type 2 diabetes in adults and children using data from a nationwide sample of US commercially insured patients.


eMethods. Details on Estimating Inverse Probability Weights and Treatment Effects
We used inverse probability weights to adjust for confounding due to lack of baseline randomization, as well as selection bias due to loss to follow-up [ITT and PP] and treatment nonadherence [PP only]. [3][4][5] The analytic dataset was structured so that each patient had one record for each two-week interval of follow up. In the ITT analysis, follow up ended at the two-week interval of T2D incidence, loss to follow-up, or 5 years, whichever came first. In the PP analysis, we additionally censored patients in the first interval where patients reached the end of the grace period without refilling their initiated medication (treatment discontinuation) or switched treatments (the date a different anticonvulsant medication was dispensed). Therefore, follow up ended at the 2-week interval of T2D incidence, loss to follow up, 5 years, treatment discontinuation, or treatment switch, whichever came first.

Treatment Weights
In both the intention-to-treat and per-protocol analyses, we applied inverse probability of treatment weights (IPTW) to account for baseline confounding. 5 Specifically, we defined the numerator of the weight for a particular individual as the marginal probability of initiating treatment and the denominator of the weight as the probability of initiating that treatment conditional on that individual's levels of the measured baseline covariates. We used multinomial logistic regression to estimate these initiation probabilities. These weights were time-fixed, so each patient had the same IPTW for each 2-week interval of follow up. More details and SAS code for implementation available elsewhere. 5 Censoring Weights

Intention-to-Treat Analysis
In the intention-to-treat analysis, we applied inverse probability of censoring weights (IPCW) to account for potential selection bias due to loss to follow-up. 5 Probabilities needed for these weights were estimated separately for each treatment group. These weights varied for each individual over time. Therefore, the weight for an individual in a particular 2week interval of follow-up t, who was still uncensored by t, is a product, over all prior intervals k<t, of a ratio of probabilities indexed by interval k: the numerator was an estimate of the marginal probability of remaining uncensored by loss to followup through k and the denominator was an estimate of this probability conditional on that individual's level of measured baseline covariates. We used logistic regression to estimate these probabilities, with the censoring indicator as the dependent variable. Patients received a weight of zero once they were censored. Therefore, censored individuals contributed information to the probabilities used for the weight construction up until their censoring time. More details and SAS code for implementation available elsewhere. 5

Per-Protocol Analysis
In the per-protocol analysis, we applied IPCW to account for potential selection bias due to censoring by treatment discontinuation (C1 k ), treatment switching (C2 k ), or loss to follow-up (C3 k ) by a particular interval k. 5 The same approach above to constructing IPCW for the ITT analysis was used here with a few exceptions.
First, we constructed ICPW separately for each type of censoring (C1, C2, C3). The final IPCW at a particular time was defined as the product of these three weights at that time (C1 k *C2 k *C3 k ), for individuals still uncensored by that time. As in the ITT analysis, individuals receive a weight of zero at the time of censoring, but they still contribute information to the analysis up until their censoring time. Separate models were used for each censorship reason to allow better prediction of these different types of censorship events.
Second, the denominator of each of the three weights depended not only on baseline covariates (V), but also the history of time-varying covariates to account for potential time-varying confounding. To estimate the probability of remaining uncensored for a given reason in an interval k conditional on baseline and time-varying covariates, we additionally included the values of time-varying covariates corresponding to the current 2-week interval (L k ), the previous 2-week interval (L k-1 =lag[L k ]), and an interaction term between these measurements (L k *lag[L k ]). For time-varying covariates that were chronic conditions, the presence of a diagnosis code was carried forward for the remainder of the follow up period. For example, a patient diagnosed with depression during the 2 nd week of follow up was flagged as having depression for each subsequent 2-week interval over follow up. Because we defined treatment discontinuation using the grace period algorithm described in the main text, censoring by treatment discontinuation was only possible during time intervals where a patient's grace period (i.e., allowable gap between prescription fills) would expire if no medication refill were dispensed (G k =1). Therefore, the weights were not updated during these intervals (as the contribution to the product mentioned above was 1). This approach minimizes model misclassification by incorporating knowledge that this form of censoring was not possible during certain intervals for certain patients. The time k contribution to the denominator of the censoring weights can be summarized as follows: Third, the numerator of the weights further depended on a subset of the baseline covariates (Z) which were conditioned on in the weighted outcome regression model described below. This provided further weight stabilization at the expense of the assumption that this conditional outcome model was correctly specified. 4 The time k contribution to the numerator of the censoring weights can be summarized as follows: Pr(C2 k =0|Z) Loss to follow up: Pr(C3 k =0|Z)

Estimating Treatment Effects
We estimated the absolute risks of type 2 diabetes for each treatment group using weighted pooled logistic regression models. The weight for each 2-week person-time record in the data was defined as the product of a time-fixed IPTW (i.e., weight remains the same for each person) and time-updated IPCW (i.e., weight changes for each 2-week interval of follow up). The weights were truncated at the 1 st and 99 th percentiles to prevent outliers from influencing the analysis. 6 The dependent variable in this pooled over interval model was T2D and the independent variables were indicators for which treatment the patient initiated and a function of time (modelled flexibly as linear and quadratic terms, as well as interactions terms with treatment to minimize misclassification of the baseline hazard). In the PP analysis, the independent variables also included subset of the baseline covariates Z that were included in the numerator of the censoring weights described above.
From these models, we predicted the hazard of T2D under each treatment strategy for each 2-week interval of follow up, which can be used to estimate the cumulative survival under initiation of or adherence to each treatment strategy. 7 We generated adjusted survival curves for the probability of remaining free of type 2 diabetes over follow up. In the per-protocol analysis, these survival curves were standardized by the subset of baseline covariates Z that were used to estimate the numerator of the censoring weights. 8 We estimated 95% confidence intervals for the 2-year and 5-year risk (complement of survival) differences using nonparametric bootstrapping of 400 samples. The desired interpretation of our estimates relied on the assumptions that our weight models were correctly specified, the hazard models were a correctly specified function of time (and Z), and that measured baseline and time-varying covariates were sufficient to control confounding due to lack of baseline randomization and selection bias due to loss to follow-up. Additional details on these analyses and how to implement them are available elsewhere Adjusted estimates were weighted by the inverse probability of treatment and the inverse probability or censoring. Subgroup analyses were not conducted in the pediatric trial emulation due to lack of power.

A. Adult Trial Emulation B. Pediatric Trial Emulation
Under the assumptions of the E-value, to nullify the adjusted estimate for valproate in the adult or pediatric trial emulation, an unmeasured confounder would need to be associated with both the choice of mood stabilizer treatment and the onset of T2D by a magnitude of at least 1.6-fold, above and beyond the measured confounders.
Sensitivity analysis was conducted on the adjusted hazard ratio comparing valproate treatment to lamotrigine treatment, where the strongest magnitude of association was observed. The plots illustrate the magnitude of confounding needed to explain away the observed association. The x-axis reflects the range of risk ratios for the association between an unmeasured confounder and the choice of mood stabilizer treatment (exposure). The y-axis reflects the range of risk ratios for the association between an unmeasured confounder and type 2 diabetes (outcome). The E-value is the minimum strength of association (on the risk ratio scale) that an unmeasured confounder would need to have on both the choice of mood stabilizer treatment and the onset of type 2 diabetes (conditional on measured covariates) to fully explain away the observed association in the intention-to-treat analysis. While the E-value was originally proposed for the risk ratio, the same formula can be applied to hazard ratios with a rare outcome. 9 Results were generated using the online E-value calculator. 10 eTable 11. Sensitivity Analysis Evaluating the Potential Impact of Truncating Inverse Probability Weights One of the censorship events in the per-protocol analysis was treatment discontinuation. In the primary analysis, we allowed a gap between the end of supply and the next prescription filled that was equal to the days supplied of the current dispensing (e.g., for a 30-day dispensing, we allowed an additional 30 days between the end of supply and the next prescription filled; "100% grace period"). Treatment episodes were considered discontinued if the next prescription was not filled by the end of this allowable gap. In a sensitivity analysis, we allowed a gap that was equal to twice the days supplied of the current dispensing (e.g., for a 30-day dispensing, we allowed an additional 60 days between the end of supply and the next prescription filled; "200% grace period"). Inverse probability weights were truncated at the 1 st and 99 th percentiles.
In the sensitivity analysis, the mean (SD)/range of the inverse probability weights were 0.96 (0.63)/0.18 to 4.27 in the adult trial emulation and 0.93 (0.66)/0.10 to 4.15 in the pediatric trial emulation.