key: cord-0022181-cpdqvbq1
authors: Camerlingo, Nunzio; Vettoretti, Martina; Sparacino, Giovanni; Facchinetti, Andrea; Mader, Julia K.; Choudhary, Pratik; Del Favero, Simone
title: Design of clinical trials to assess diabetes treatment: Minimum duration of continuous glucose monitoring data to estimate time‐in‐ranges with the desired precision
date: 2021-07-21
journal: Diabetes Obes Metab
DOI: 10.1111/dom.14483
sha: fa41e61066da488fdc5fb713b7a522f0910641cb
doc_id: 22181
cord_uid: cpdqvbq1

AIM: To compute the uncertainty of time‐in‐ranges, such as time in range (TIR), time in tight range (TITR), time below range (TBR) and time above range (TAR), to evaluate glucose control and to determine the minimum duration of a trial to achieve the desired precision. MATERIALS AND METHODS: Four formulas for the aforementioned time‐in‐ranges were obtained by estimating the equation's parameters on a training set extracted from study A (226 subjects, ~180 days, 5‐minute Dexcom G4 Platinum sensor). The formulas were then validated on the remaining data. We also illustrate how to adjust the parameters for sensors with different sampling rates. Finally, we used study B (45 subjects, ~365 days, 15‐minute Abbott Freestyle Libre sensor) to further validate our results. RESULTS: Our approach was effective in predicting the uncertainty when time‐in‐ranges are estimated using n days of continuous glucose monitoring (CGM), matching the variability observed in the data. As an example, monitoring a population with TIR = 70%, TITR = 50%, TBR = 5% and TAR = 25% for 30 days warrants a precision of ±3.50%, ±3.68%, ±1.33% and ±3.66%, respectively. CONCLUSIONS: The presented approach can be used to both compute the uncertainty of time‐in‐ranges and determine the minimum duration of a trial to achieve the desired precision. An online tool to facilitate its implementation is made freely available to the clinical investigator.

Continuous glucose monitoring (CGM) sensors are increasingly used in research and clinical practice. 1 A recent consensus panel 2 identified 'time-in-ranges' as key outcome metrics to assess glycaemic control based on CGM data. The identified time-in-ranges include: time in range (TIR), that is, the percentage of time spent within 70-180 mg/dL (3.9-10 mmol/L); time below range (TBR), that is, the percentage of time spent with CGM less than 70 mg/dL (<3.9 mmol/L); and time above range (TAR), that is, the percentage of time spent with CGM more than 180 mg/dL (>10 mmol/L). [3] [4] [5] Furthermore, the percentage of readings within 70-140 mg/dL (3.9-7.8 mmol/L) is referred to as time in tight range (TITR). 1 These time-in-ranges were used as final endpoints in several studies evaluating the effects of new treatments and/or drugs on glucose control. [6] [7] [8] [9] The duration of these trials, which varied from a single day to several months, strongly impacted the precision of the estimation of time-in-ranges in these studies: the longer the trial duration then the less uncertain/more precise the estimated time-in-ranges, 2, 10 and, in turn, the more reliable the clinical conclusions. For example, over a longer monitoring period, confounding factors such as meal times, meal composition and exercise/sports, which cause intra-day variability, but also other factors such as menstrual cycle, shiftwork, vacations, intercurrent illness and weekend lifestyle, which affect inter-day variability, average out. On the other hand, a long trial duration is associated with higher costs, 11, 12 increased recruitment difficulties, larger likelihood of withdrawal 13, 14 and a greater risk of protocol deviations. 15 Therefore, in the design of a clinical trial, a careful balance between these two opposing needs must be found. 16, 17 In particular, for trials with time-in-ranges as final endpoints, understanding the impact of trial duration on the precision of CGM-derived metrics would be particularly useful in power calculations. Similarly, in clinical practice, time-in-ranges are increasingly used to assess current glycaemic status and can influence decisions to change therapy or start new therapies. A 5% change in TIR is believed to be clinically significant, 18 but understanding the effect of assessing TIR over 14 days, 1 month or 3 months can affect clinical decision-making.

The consensus panel of Battelino et al. 2 recommends assessing 14 days of CGM, as the most recent 14 days of CGM data provide a good approximation of time-in-ranges collected over a 3-month period. 10, 19 However, this indication is empirical, 20, 21 and the literature lacks a description of how the precision in the estimation of time-in-ranges improves as the trial duration increases.

In a recent work, 22 

Equation (1) involves three parameters, k, p r and α.

1. The first parameter, k, is the number of CGM samples produced in 1 day when no measurement is missed (e.., k ¼ 288 for a CGM sensor providing measurements every 5 minutes, k ¼ 96 for CGM measurements collected every 15 minutes).

2. The second parameter, p r , represents the expected average TBR in the population.

3. The third parameter, α, depends on the CGM sensor sampling period (but also on the glycaemic range considered, as will be illustrated in the following).

Moreover, in 22 we provided a single set of parameters able to predict the uncertainty of TBR estimates of a whole population of heterogeneous subjects.

Notably, the mathematical machinery used to derive Equation (1) also holds for any other time-in-range, provided that the parameters (in particular, the parameter α) are changed accordingly.

In the current paper, we first provide suitable values of the for a generic population. These values were estimated using the procedure proposed in 22 on the population of study A. As such, they should be used with a 5-minute CGM sensor. If a sensor with a different sampling rate is used then these parameters can be easily adjusted. Specifically, the α T value to be used for a sensor providing one measurement every T minutes can be linked to α 5 , the parameter α used for a 5-minute CGM sensor, by

As an example, for 10-and 15-minute CGM sensors, α 5 can be adjusted to α 10 ¼ α 2 5 , and α 15 ¼ α 3 5 , respectively. 3. Lastly, the parameter k in Equation (1), representing the number of CGM samples provided in one day, remains independent of the glycaemic range.

Suitable values of the parameters p r and α for the four considered glycaemic ranges are obtained using study A. Specifically, patients in study A are randomly split into training (70%) and test (30%) sets. The training set is used to estimate the parameters and the test set is then used to validate the resulting formulas.

The estimated values of p r are: 64.5% for TIR, 40.0% for TITR, 3.10% for TBR and 33.0% for TAR. The values of α are: 0.961 for TIR, 0.958 for TBR, 0.940 for TBR and 0.968 for TAR (also reported in the third column of Table 1 ).

In Table 1 we summarize the formulas with p r as the only parameter (α is fixed to the values above) for the four time-in-ranges under analysis and a sensor with a 5-minute sampling rate. In this table, to improve readability, the term α kn of Equation (1) is neglected because it is close to zero.

To validate the equations of Table 1 

where M p is the number of different windows available for each patient p, obtained by considering different starting points (with a window shift of 1 day), as proposed in. 21 Repeating this procedure for all the patients, we obtained a total of M values of the estimation error committed using windows of duration n in the whole population.

Finally, for each window duration n, the standard deviation of the estimation error was computed, that is:

Notation: to distinguish the standard deviation provided by the proposed formula from the standard deviation computed by data, from now on we will denote the first as theoretical standard deviation,

, and the second as sample standard deviation, SD S e n ð Þ ½ .

Remark: when dealing with extremely long datasets, the ground- adjusting the values of α by means of Equation (2).

In addition, to show that the parameters reported in Table 1 can be used, with limited approximation, for different populations, we also validated the formulas on the whole of study B. Because the CGM used in study B provides one sample every 15 minutes, the values of Table 1 were adjusted according to Equation (2).

These analyses investigate the generalizability of the parameters proposed.

All the analyses were performed in Matlab 2020b (MathWorks, Natick, MA, USA). All the scripts for implementing the methodology in Matlab are publicly available at https://github.com/NunzioCamer/ AnalyticalTBRestimation.

In Figure 1A -D, the sample and theoretical standard deviations of the estimation error (SD S and SD T , respectively) are compared considering different window durations n, from 1 to n max ¼ 30 days, and for the time-in-ranges under study: TIR (A), TITR (B), TBR (C) and TAR (D). In particular, SD S , reported as a solid red curve, was computed on a test set extracted from study A, as in Equation (3), while SD T , reported as a dashed blue curve, was obtained by substituting the values of the parameters p r and α estimated by the training set data of study A into Equation (1).

The curves describing SD S and SD T overlap well (the relative discrepancy between the two curves is smaller than 10% for all the glycaemic ranges for most of the durations considered). Therefore, we conclude that the proposed formulas are able to effectively describe the uncertainty of all time-in-ranges estimates for the overall population of study A.

In addition, in each part of Figure 1 , the boxplot of the estimation error e n, j ð Þ is also reported.

3.2 | Generalization of the results for different sampling rates (using study A data)

In Figure 1E -H, we investigate the adjustment of α proposed in Equation (2). Specifically, we report SD S computed on the test set extracted from study A, modified to emulate a 15-minute sensor.

This SD S is compared with SD T , which is obtained by Equation (1) using the values of α corrected as in Equation (2). Also in this case, SD S and SD T overlap well (the relative discrepancy between the two curves is smaller than 10% for most of the durations considered), thus proving the efficacy of Equation (1) combined with Equation (2).

Similar results are also obtained when emulating a 10-minute sensor (see Section S1).

A comparison between 5-, 10-and 15-minute CGM sensors in terms of the predicted decrease in the uncertainty of time-in-ranges is reported in Figure S2 .

In Figure 1I -L, we stress the generalizability of the formulas on a different dataset. In this case, for each time-in-range, SD S was computed using the whole study B, while SD T was obtained by substituting the values of the parameters p r and α estimated by the training set data of study A into Equation (1), and adjusting α as in Equation (2) (i. e., α 15 ¼ α 3 5 Þ: Despite the approximations introduced, the SD S curve overlaps well with the curve of SD T , for TIR, TITR and TAR. For these ranges, the relative discrepancy between the curves is below 13% for most of the durations considered. As expected, the agreement between the two curves achieved in this case is smaller compared with that observed in Figure 1A -H. The impact of the introduced approximation is larger for TBR, mainly as a result of a large difference in the incidence of hypoglycaemia in the two studies: the average TBR in the training set extracted by study A is TBR A ¼ 3:10%, while in study B it reaches TBR B ¼ 5:15% (~40% larger).

In Section S2, we show that a better estimate of the incidence of hypoglycaemia in the population of study B can significantly improve the agreement between the curves for TBR too.

T A B L E 1 Proposed formulas for the uncertainty around time-in-ranges estimates, for four different time-in-ranges: time in range (TIR), time in tight range (TITR), time below range (TBR) and time above range (TAR), for sensors with 5-min sampling rate Nonetheless, in the case of clinical studies focused on a specific subpopulation (e.g. children or the elderly), one may also consider optimizing the formula's parameters for the specific subpopulation being studied. This can be carried out by re-running the parameters' estimation procedure described in 22 on data collected in populations with similar characteristics.

To facilitate the use of these formulas, we implemented an online, freely accessible calculator, available at http://computecgmduration. dei.unipd.it. The tool requires the user to insert some information about the ongoing experiment then computes the parameters of the formulas. Next, the user can decide either to compute the uncertainty around time-in-ranges estimated in previous clinical trials, or to compute the optimal number of days necessary to achieve the desired uncertainty around the selected time-in-range.

The resulting number of days refers to days with no missing CGM data. To deal with the common issue of gaps in CGM data, a practical approach is to consider the total amount of available data (e.g. a 30-day study with four gaps of 6 hours could be considered as a 29-day study). Therefore, in the design of a clinical trial, if we expect 80% sensor usage (i.e. data loss of 20%), we suggest setting the study duration to 20% longer than the one provided by the proposed formula. In Section S5, we show that this is a conservative approach, as sporadic missing samples have no practical impact on the precision of the estimated time-in-ranges. 10, 19 However, it was recently shown in 20,21 that this approach 10,19 may produce inconsistent results in different datasets. The approach proposed in this work offers an alternative way to overcome this limitation.

The proposed formulas can be used for multiple applications. In the following, we will focus on two of them and illustrate four clinical cases. Furthermore, we will discuss the analogy of the proposed formula with tools for power calculation. In Table 2 we summarize the number of days needed to achieve the desired precision in the estimation for the four main time-inranges. Precision is expressed both in absolute terms (2.0%, 1.5%, 1.0% or 0.5%) and in relative terms (20%, 15%, 10% or 5%). The first option is preferable for TBR, while the latter option is preferable for the other ranges. Uncommon options are shaded, as they result in extremely demanding precisions and thus in very long trials. The p r values used for each time-in-range were extracted from the consensus of Battelino et al. 2 and are also reported in the table. Table 2 suggests that reaching a tight confidence interval for TBR requires more monitoring days than for the other time-in-ranges. To further assess this consideration, in Section S3 we compared the curves of absolute uncertainty and relative uncertainty for the four timein-ranges under study.

To better illustrate the main message of the current paper, it is useful to discuss the analogy between our formula and the power calculation tools commonly used by clinical practitioners to answer the question: How many participants should be recruited? These tools are based on a mathematical formula that returns the minimum number of subjects to be monitored, providing the desired study power and thus avoiding a type II error (i.e. the chance of declaring the findings non-significant, while instead the treatment has an effect). 26 The Finally, both approaches are based on simplified mathematical assumptions. For example, in power calculation tools, the study outcome is assumed to be normally distributed, while for the tool proposed in this work, we hypothesize mono-exponential autocorrelation in CGM-based outcome metric samples. 22 A schematic comparison between power calculation tools and the proposed formula is reported in Table 3 .

With increased use of CGM data and, in particular, time-in-ranges metrics for making therapeutic decisions and assessing differences T A B L E 2 Possible applications of the proposed formulas We tested the validity of the formula on patient data and showed its ability to generalize to different CGM sampling rates and populations.

We believe this formula can help the diabetes community in a number of different scenarios. First, when assessing time-in-ranges obtained in published studies, we can determine the precision around the estimated values, based on how long the CGM values were collected over. Some studies using 3 or 7 days of CGM data will have wide confidence intervals, while others using longer durations offer better precision. We believe that this analysis will also be valuable in clinical consultations. Clinicians receive reports on time-in-ranges through software linked to CGM devices, but the proposed formula can help provide an estimate of the confidence intervals (i.e. the precision) of those values.

Second, we believe this formula can be used by academic or industry clinical trial teams, to help them determine a suitable duration of the study. Furthermore, the value of the standard deviation provided by the formula could also be used in power calculations, for example, to determine the number of participants needed in a trial. This will help with designing better studies, providing more accurate results. To support academic colleagues around the world, we have developed an online calculator that we have made freely available and which facilitates the use of the formulas in performing the tasks mentioned above.

In conclusion, together with standard power calculation tools, this formula allows optimization of the cost-benefit ratio of a clinical trial: trials with too many subjects monitored for too long expose the subjects to unnecessary risks. Trials with too few subjects monitored for too short a duration do not permit collection of conclusive scientific evidence and thus waste patients' time and risk exposure. Statistical tools for an effective cost-benefit balance in clinical trials are important for all subjects, but they become essential when recruiting a minority of underprivileged patients.

Future developments include exploring relaxed mathematical assumptions under which the formula is derived, as well as further validation on datasets collected in wider and more heterogeneous populations. We also plan to explore the possibility of optimizing the formula's parameters for specific populations (e.g. type 2 diabetes, pregnant and paediatric) and for different co-variates (e.g.

HbA1c, diabetes duration, body weight, CGM sensor model and insulin therapy).

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Supporting Information section at the end of this article. How to cite this article

Design of clinical trials to assess diabetes treatment: Minimum duration of continuous glucose monitoring data to estimate time-in-ranges with the desired precision

The peer review history for this article is available at https://publons. com/publon/10.1111/dom.14483.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

https://orcid.org/0000-0003-3222-2479Julia K. Mader https://orcid.org/0000-0001-7854-4233Simone Del Favero https://orcid.org/0000-0002-8214-2752