In this study, all methods were performed in accordance with the relevant guidelines and regulations.
Data description and study design
A retrospective study design was carried out from September 2019-August 2021 in DTGH to conduct this study. Relevant information was extracted from the medical records of T1DM patients. The study population for this study was T1DM patients who were under the follow up of insulin medication at DTGH who start medication in September 2019 and followed up to August 2021. Here there were 604 T1DM patients in the study period. From these, only 210 patients were with relevant information. These 210 patients were followed until they got either the event or censored.
The response variable in the current investigation was fasting blood sugar level measured in mg/dl. The longitudinal outcome variable FBS (Fasting Blood Sugar) is measured approximately every 3 months irrespective of patient visits to the OPD section of chronic disease at DTGH. that is; at the start of the treatment, 0-, 3-, 6-, 9-, 12-, 15-, 18-, 21- and 24-month visits (that means ni= 9). The sample sizes at these 9-time points are (210, 210, 210, 210, 195, 178, 151, 116, 57) which show up to third follow up the sample sizes were constant but after the third follow up it shows a high degree of missing data over time due to patients attained the first recovery. Age, gender, place of residence, presence of comorbidity, family history of DM, creatinine, weight, visit time and hemoglobin were the potential explanatory considered in this study (Table 1).
Longitudinal data analysis
Figure 1 shows a flowchart of longitudinal data analysis in this retrospective study. The flow chart included 11 stages, and these stages described as follows. stage 1 A longitudinal data on T1DM patients in DTGH were collected based on our variable of interest in this study. stage 2 We have drawn the mean plot of fasting blood sugar level for T1DM patients at each follow up time (visit time). This plot helps to know the variability of fasting blood sugar level among T1DM patients in DTGH over visit time. In addition, this is also helpful to observe the mean of fasting blood sugar level for T1DM patients in DTGH over visit time, and to check the linearity assumption of the variable (fasting blood sugar level)14:15. stage 3 We used QQ plot to check the normality assumption of the variable (fasting blood sugar level). It is one of the requirements of the linear mixed model. We also constructed a 95% CI for the mean blood sugar level at each visit time. It is helpful to estimate the interval which holds the mean blood sugar level of TIDM patients in DTGH14:15. stage 4 We used the logarithm transformation to fulfill the normality assumption of the variable (fasting blood sugar level)14. stage 5 At this stage, different covariate structure (eg UN, CS, AR) was considered to analyze the data using linear mixed model framework. This procedure helps to fit model with more parsimonious structures by selecting appropriate variance–covariance structure of Σ16. stage 6 At this stage, we select model with appropriate variance–covariance structure of Σ16:17. stage 7 At this stage, we analyze data using the selected model in stage 6 by considering different random effects. This procedure helps to provide differed random effect models (eg Random intercept, Random slope, and Random intercept & slope)14,15,17. stage 8 We have selected one of the above suggested model in stage 7 using AIC/BIC criteria17. stage 9 We analyze the data using the two version of the above selected model in stage 8 (Null model or Full model)14,15,17. stage 10 We have selected the final model from the two version considered in stage 917. stage 11 Finally, we draw our conclusion based on the result of this final model (Fig. 1).
Weakness of the linear mixed model
Even though the model has several advantages in longitudinal data analysis, it has amiss. First, more assumptions on distribution should be made and then, approximations are used to estimate the parameters of this model. This implies that the result is highly dependent on more distributional assumptions. Consequently, if the assumptions are entirely not satisfied, it may lead to biased parameter estimates18.
Ethics approval and consent to participate
We have got a permission letter with Ref ≠ 2019-RCS-006 from the Ethical approval committee of statistics department in Assosa University, Ethiopia to conduct this study by use of this secondary data. When the data collected primarily, subjects were properly instructed, and they provided informed consent to participate by signing the appropriate consent form. It was assured by the Ethical approval committee and DTGH Managers.