Targeted Maximum Likelihood Based Estimation for Longitudinal Mediation Analysis

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex longitudinal data structure with time-varying confounders, competing risks, and informative censoring, there exists a general desire to combine machine learning techniques and semiparametric theory. In this manuscript, we focus on targeted maximum likelihood estimation (TMLE) of longitudinal natural direct and indirect effects defined with random interventions. The proposed estimators are multiply robust, locally efficient, and directly estimate and update the conditional densities that factorize data likelihoods. We utilize the highly adaptive lasso (HAL) and projection representations to derive new estimators (HAL-EIC) of the efficient influence curves of longitudinal mediation problems and propose a fast one-step TMLE algorithm using HAL-EIC while preserving the asymptotic properties. The proposed method can be generalized for other longitudinal causal parameters that are smooth functions of data likelihoods, and thereby provides a novel and flexible statistical toolbox

Applying the causal roadmap to longitudinal national Danish registry data: a case study of second-line diabetes medication and dementia

The causal roadmap is a formal framework for causal and statistical inference that supports clear specification of the causal question, interpretable and transparent statement of required causal assumptions, robust inference, and optimal precision. The roadmap is thus particularly well-suited to evaluating longitudinal causal effects using large scale registries; however, application of the roadmap to registry data also introduces particular challenges. In this paper we provide a detailed case study of the longitudinal causal roadmap applied to the Danish National Registry to evaluate the comparative effectiveness of second-line diabetes drugs on dementia risk. Specifically, we evaluate the difference in counterfactual five-year cumulative risk of dementia if a target population of adults with type 2 diabetes had initiated and remained on GLP-1 receptor agonists (a second-line diabetes drug) compared to a range of active comparator protocols. Time-dependent confounding is accounted for through use of the iterated conditional expectation representation of the longitudinal g-formula as a statistical estimand. Statistical estimation uses longitudinal targeted maximum likelihood, incorporating machine learning. We provide practical guidance on the implementation of the roadmap using registry data, and highlight how rare exposures and outcomes over long-term follow up can raise challenges for flexible and robust estimators, even in the context of the large sample sizes provided by the registry. We demonstrate how simulations can be used to help address these challenges by supporting careful estimator pre-specification. We find a protective effect of GLP-1RAs compared to some but not all other second-line treatments

Treatment with glucagon-like peptide-1 receptor agonists and incidence of dementia:Data from pooled double-blind randomized controlled trials and nationwide disease and prescription registers

INTRODUCTION: People with type 2 diabetes have increased risk of dementia. Glucagon‐like peptide‐1 (GLP‐1) receptor agonists (RAs) are among the promising therapies for repurposing as a treatment for Alzheimer's disease; a key unanswered question is whether they reduce dementia incidence in people with type 2 diabetes. METHODS: We assessed exposure to GLP‐1 RAs in patients with type 2 diabetes and subsequent diagnosis of dementia in two large data sources with long‐term follow‐up: pooled data from three randomized double‐blind placebo‐controlled cardiovascular outcome trials (15,820 patients) and a nationwide Danish registry‐based cohort (120,054 patients). RESULTS: Dementia rate was lower both in patients randomized to GLP‐1 RAs versus placebo (hazard ratio [HR]: 0.47 (95% confidence interval [CI]: 0.25–0.86) and in the nationwide cohort (HR: 0.89; 95% CI: 0.86–0.93 with yearly increased exposure to GLP‐1 RAs). DISCUSSION: Treatment with GLP‐1 RAs may provide a new opportunity to reduce the incidence of dementia in patients with type 2 diabetes

Day-to-day fasting glycaemic variability in DEVOTE: associations with severe hypoglycaemia and cardiovascular outcomes (DEVOTE 2)

AIMS/HYPOTHESIS: The Trial Comparing Cardiovascular Safety of Insulin Degludec vs Insulin Glargine in Patients with Type 2 Diabetes at High Risk of Cardiovascular Events (DEVOTE) was a double-blind, randomised, event-driven, treat-to-target prospective trial comparing the cardiovascular safety of insulin degludec with that of insulin glargine U100 (100 units/ml) in patients with type 2 diabetes at high risk of cardiovascular events. This paper reports a secondary analysis investigating associations of day-to-day fasting glycaemic variability (pre-breakfast self-measured blood glucose [SMBG]) with severe hypoglycaemia and cardiovascular outcomes. METHODS: In DEVOTE, patients with type 2 diabetes were randomised to receive insulin degludec or insulin glargine U100 once daily. The primary outcome was the first occurrence of an adjudicated major adverse cardiovascular event (MACE). Adjudicated severe hypoglycaemia was the pre-specified secondary outcome. In this article, day-to-day fasting glycaemic variability was based on the standard deviation of the pre-breakfast SMBG measurements. The variability measure was calculated as follows. Each month, only the three pre-breakfast SMBG measurements recorded before contact with the site were used to determine a day-to-day fasting glycaemic variability measure for each patient. For each patient, the variance of the three log-transformed pre-breakfast SMBG measurements each month was determined. The standard deviation was determined as the square root of the mean of these monthly variances and was defined as day-to-day fasting glycaemic variability. The associations between day-to-day fasting glycaemic variability and severe hypoglycaemia, MACE and all-cause mortality were analysed for the pooled trial population with Cox proportional hazards models. Several sensitivity analyses were conducted, including adjustments for baseline characteristics and most recent HbA1c. RESULTS: Day-to-day fasting glycaemic variability was significantly associated with severe hypoglycaemia (HR 4.11, 95% CI 3.15, 5.35), MACE (HR 1.36, 95% CI 1.12, 1.65) and all-cause mortality (HR 1.58, 95% CI 1.23, 2.03) before adjustments. The increased risks of severe hypoglycaemia, MACE and all-cause mortality translate into 2.7-, 1.2- and 1.4-fold risk, respectively, when a patient's day-to-day fasting glycaemic variability measure is doubled. The significant relationships of day-to-day fasting glycaemic variability with severe hypoglycaemia and all-cause mortality were maintained after adjustments. However, the significant association with MACE was not maintained following adjustment for baseline characteristics with either baseline HbA1c (HR 1.19, 95% CI 0.96, 1.47) or the most recent HbA1c measurement throughout the trial (HR 1.21, 95% CI 0.98, 1.49). CONCLUSIONS/INTERPRETATION: Higher day-to-day fasting glycaemic variability is associated with increased risks of severe hypoglycaemia and all-cause mortality. TRIAL REGISTRATION: ClinicalTrials.gov NCT01959529

Refined multiscale entropy using fuzzy metrics : validation and application to nociception assessment

The refined multiscale entropy (RMSE) approach is commonly applied to assess complexity as a function of the time scale. RMSE is normally based on the computation of sample entropy (SampEn) estimating complexity as conditional entropy. However, SampEn is dependent on the length and standard deviation of the data. Recently, fuzzy entropy (FuzEn) has been proposed, including several refinements, as an alternative to counteract these limitations. In this work, FuzEn, translated FuzEn (TFuzEn), translated-reflected FuzEn (TRFuzEn), inherent FuzEn (IFuzEn), and inherent translated FuzEn (ITFuzEn) were exploited as entropy-based measures in the computation of RMSE and their performance was compared to that of SampEn. FuzEn metrics were applied to synthetic time series of different lengths to evaluate the consistency of the different approaches. In addition, electroencephalograms of patients under sedation-analgesia procedure were analyzed based on the patient's response after the application of painful stimulation, such as nail bed compression or endoscopy tube insertion. Significant differences in FuzEn metrics were observed over simulations and real data as a function of the data length and the pain responses. Findings indicated that FuzEn, when exploited in RMSE applications, showed similar behavior to SampEn in long series, but its consistency was better than that of SampEn in short series both over simulations and real data. Conversely, its variants should be utilized with more caution, especially whether processes exhibit an important deterministic component and/or in nociception prediction at long scales

DEVOTE 3: temporal relationships between severe hypoglycaemia, cardiovascular outcomes and mortality

AIMS/HYPOTHESIS: The double-blind Trial Comparing Cardiovascular Safety of Insulin Degludec vs Insulin Glargine in Patients with Type 2 Diabetes at High Risk of Cardiovascular Events (DEVOTE) assessed the cardiovascular safety of insulin degludec. The incidence and rates of adjudicated severe hypoglycaemia, and all-cause mortality were also determined. This paper reports a secondary analysis investigating associations of severe hypoglycaemia with cardiovascular outcomes and mortality. METHODS: In DEVOTE, patients with type 2 diabetes were randomised to receive either insulin degludec or insulin glargine U100 (100 units/ml) once daily (between dinner and bedtime) in an event-driven, double-blind, treat-to-target cardiovascular outcomes trial. The primary outcome was the first occurrence of an adjudicated major adverse cardiovascular event (MACE; cardiovascular death, non-fatal myocardial infarction or non-fatal stroke). Adjudicated severe hypoglycaemia was the pre-specified secondary outcome. In the present analysis, the associations of severe hypoglycaemia with both MACE and all-cause mortality was evaluated in the pooled trial population using time-to-event analyses, with severe hypoglycaemia as a time-dependent variable and randomised treatment as a fixed factor. An investigation with interaction terms indicated that the effect of severe hypoglycaemia on the risk of MACE and all-cause mortality were the same for both treatment arms, and so the temporal association for severe hypoglycaemia with subsequent MACE and all-cause mortality is reported for the pooled population. RESULTS: There was a non-significant difference in the risk of MACE for individuals who had vs those who had not experienced severe hypoglycaemia during the trial (HR 1.38, 95% CI 0.96, 1.96; p = 0.080) and therefore there was no temporal relationship between severe hypoglycaemia and MACE. There was a significantly higher risk of all-cause mortality for patients who had vs those who had not experienced severe hypoglycaemia during the trial (HR 2.51, 95% CI 1.79, 3.50; p < 0.001). There was a higher risk of all-cause mortality 15, 30, 60, 90, 180 and 365 days after experiencing severe hypoglycaemia compared with not experiencing severe hypoglycaemia in the same time interval. The association between severe hypoglycaemia and all-cause mortality was maintained after adjustment for the following baseline characteristics: age, sex, HbA1c, BMI, diabetes duration, insulin regimen, hepatic impairment, renal status and cardiovascular risk group. CONCLUSIONS/INTERPRETATION: The results from these analyses demonstrate an association between severe hypoglycaemia and all-cause mortality. Furthermore, they indicate that patients who experienced severe hypoglycaemia were particularly at greater risk of death in the short term after the hypoglycaemic episode. These findings indicate that severe hypoglycaemia is associated with higher subsequent mortality; however, they cannot answer the question as to whether severe hypoglycaemia serves as a risk marker for adverse outcomes or whether there is a direct causal effect. TRIAL REGISTRATION: ClinicalTrials.gov NCT01959529