Statistical analyses

a. Estimation of the acute effects of SH on subsequent SH

We estimated the RRs of SH (index SH) on subsequent SH in three subsequent time windows after the index SH corresponding to approximate months 1-3, 4-6, and 7-9 after index SH, respectively. It should be noted that the above defined windows would not be the exact durations as the months 1-3, 4-6 and 7-9 after the index SH because the period between the time when the index SH occurred and the time when next quarterly visit was conducted would not be captured by this definition (Figure 3). However, we used months to describe the timeline after index SH in the following sections for simplicity.

We used log-linear multivariable models to estimate RRs and their 95% confidence intervals (CI). We controlled for confounding by a set of priori specified covariates (Table 2) based on directed acyclic graph (DAG) [38] (Figure 6). We defined all time-dependent covariates using the most recent value before the occurrence of the index SH to avoid the

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value to be in the intermediate pathway between the exposure and outcome. Since each patient could contribute multiple observations, we used GEE by specifying working

correlation structure as “exchangeable” to allow for the dependence of observations within a person [28, 29]. When the log-linear models did not converge, we used Poisson models to approximate RRs as previously described [39].

We also estimated transition probabilities as the risk of subsequent SH episodes in the three subsequent observation windows using the estimation models. We assigned the following values for the covariates in the estimation models including the intercept term and to produce predictive values as the corresponding transition probabilities (except for the index SH, we fixed all covariates with the following referent values in corresponding models): occurrence of index SH (yes or no), gender (female), baseline age (>29 years), duration of disease ( >10 years) and history of SH (no), most recent SH (no) and incidence rates of SH episodes (less or equal to the 90th percentiles of the rates in corresponding treatment groups up to the index SH), expected A1C (6-6.9%), actual A1C (6-6.9%), alcohol use (no use), exercise activities (moderate), meal plan (adherence) and insulin adherence (adherence), use of SMBG (often done), blood glucose variability (population mean 3.89) and the follow- up time (24 months). I did not include any occurrences of SH in three subsequent time windows following index SH as the covariates in the models to obtain transition probabilities. For instance, we did not include occurrences of SH in the first 3-month observation window as the covariates in the models when estimating the transition probabilities for subsequent SH episodes in the 4-6 and 7-9 month observation windows after the index SH because the occurrences of SH in the first 3-month were treated as the intermediated effects of the index SH on the 4-6 and 7-9 month observation windows. If log-linear models could not converge, we used logistic regression to estimate transition probabilities.

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Figure 6: Directed acyclic graph for the effect of occurrence of SH (index SH) on subsequent

SH episodes in observation windows following index SH.

b. Estimation of the effects of SH on subsequent weight gain over various periods

We used linear multivariable models to estimate the effects of SH (index SH), which occurred in a quarterly interval, on weight change/actual weight in various periods with

Index SH (exposure) Subsequent SH (outcome)

Gender

Age at DCCT baseline Duration of type 1 diabetes at DCCT baseline

blood glucose variability prior to index SH

Use of SMBG prior to index SH

insulin use adherence prior to index SH meal plan adherence prior to index SH

physical activities prior to index SH

alcohol use prior to index SH

actual A1C prior to index SH expected A1C prior to index SH Recent SH prior to index SH

Rates of SH prior to index SH History of SH at DCCT baseline

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ranges approximately from 3 months to 36 months after index SH. We also looked at the effects of index SH on weight change in three subsequent fixed-term time windows at the 1st, 2nd and 3rd quarterly interval following index SH (the observation period for each time

window approximated a 3-month period in this analysis), and the outcome as the weight change in this analysis was the quarterly weight change for three fixed-term time windows, respectively. The corresponding comparison intervals were the intervals without occurrence of index SH.

We controlled for confounding by including a set of priori specified covariates in the models based on DAG (Figure 7). We tried several parameter specifications (original values, categories and splines) for continuous covariates in the models. Based on the precision of the estimates for the main exposure and model fit statistics, the most appropriate

specifications (formats) for continuous covariates were used in final models (Table 3). Since each patient could contribute multiple observations, similarly we used GEE by specifying working correlation structure as “exchangeable” to allow for the dependence of observations within a person [28, 29].

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Figure 7: Directed acyclic graph for the effect of occurrence of SH (index SH) on

subsequent weight change/weight in various periods following index SH.

c. Estimation of the effects of SH on substantial weight gain, overweight, and obesity We used Cox proportional hazard models to estimate the HRs of SH on the substantial weight gain (defined as the 5, 10, 15 and 20% weight gain from the DCCT baseline, respectively), on becoming overweight (BMI≥25.0), or on becoming obese

(BMI≥30.0) comparing patients after they had their first SH episode with all patients who did

Index SH (exposure) _{Subsequent weight change/weight (outcome)}

Gender

Age at DCCT baseline Duration of type 1 diabetes at DCCT baseline

Daily insulin dose prior to index SH

insulin use adherence prior to index SH

meal plan adherence prior to index SH physical activities prior to index SH

BMI prior to index SH Recent SH prior to index SH

Rates of SH prior to index SH History of SH at DCCT baseline

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not experienced any SH episode at the same time during follow-up (they could have a SH episode later during follow-up) [30]. Hence, the exposure in the Cox models was a time- dependent variable: 1) the patient was defined as unexposed prior to the 1st SH episode; 2) after the 1st SH episode, the patient was defined as always exposed. We checked the proportional hazards assumption for main exposure by adding an interaction term between the exposure and the follow-up time. We controlled for confounding by including a set of priori specified covariates (Table 4) in the models based on the DAG (Figure 8).

Figure 8: Directed acyclic graph for the effect of occurrence of SH on developing

substantial weight gain, overweight or obesity during the follow-up.

Occurrence of SH (exposure) Substantial weight gain/overweight/obesity (outcome)

Gender

Age at DCCT baseline Duration of type 1 diabetes at DCCT baseline

Average meal plan adherence

Average physical activities Average daily insulin dose History of SH at DCCT baseline

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Average daily insulin dose may be seen as a time-dependent confounder affected by prior SH (Figure 9). Under this assumption the Cox model controlling for average daily insulin dose as well as a model not controlling for it would be biased [40]. Furthermore, as an ancillary analysis, we therefore used marginal structural models (MSM) that allow us to control for average daily insulin dose that may be affected by exposure. I used weighted pooled logistic regression models to approximate the parameters of the MSM [13]. Fitting the weighted estimation of the parameters involved three sets of models: 1) a pooled logistic model estimating the time-varying exposure propensity (the probabilities to have the first SH episode during the follow-up), 2) a pooled logistic model estimating the probability of

censoring, and 3) the final model weighting exposed and unexposed by the weights obtained in steps 1) and 2) to obtain the estimates for the main exposure with robust standard errors for the confidence intervals. We used a restricted spline with 3 knots for all continuous variables in all sets of models as recommended [41]. To estimate the time- dependent intercept for all three models in the MSM, we produced a restricted cubic spline for the follow-up time (the numbers of months since start of the trial) with SAS macro RCSPLNE [42]. We also examined the distribution of the estimated weights to check whether the weights were well constructed (the well-constructed weights should have a mean around 1 and narrow ranges for the estimated weights) [41].

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Figure 9: Conceptual directed acyclic graph to show that covariate average daily

insulin dose may be an intermediate and time-dependent confounder for the

association between the occurrence of severe hypoglycemia (exposure) and time to

substantial weight gain, time to becoming overweight or time to becoming obese

during follow-up.

d. Estimation of the effects of SH on insulin dosing changes

As a supplementary analysis, we used linear multivariable models to estimate the effects of SH occurring in the first composed quarterly interval in an analytic unit on the continuous outcome (the difference of daily insulin doses between the end and beginning of the analytic unit) and used log-linear multivariable models on the dichotomized outcome (≥ 10% dose reduction) in each analytic unit. Each analytic unit consisted of two consecutive quarterly visits to account for temporality of change of insulin dose following occurrence of SH (Figure 5). We used generalized GEE to account for multiple-observations per patient and to control relevant factors with working correlation structure “exchangeable”.

Furthermore, for continuous outcome (the difference of daily insulin doses), we also used mixed models as a sensitivity analysis. However, negative variance components were

Substantial weight gain /overweight/obesity (outcome) Exposure status

at time K

Exposure status at time K+1 Average insulin dose

up to time K

Average insulin dose up to time K+1

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reported when we used a random effect for the intercept for each subject by covariance structure as either variance component or unstructured in the mixed models. After serial diagnostic tests, we omitted the random effect for the intercept, but correlation within the random effect was modeled by including covariance parameter in the residual variance matrix R with a toeplitz structure and toep (5) appeared a best fit.