Statistical tests for latent class in censored data due to detection limit

Intensive Blood Pressure Lowering in Individuals With Low Diastolic Blood Pressure and Elevated Troponin Levels in SPRINT

BACKGROUND

Among individuals with hypertension and low diastolic blood pressure (DBP), the optimal BP target remains controversial due to concerns that BP lowering may reduce coronary perfusion. We determined the impact of intensive BP control among individuals with elevated systolic BP who have low DBP and elevated hs-cTnT (high-sensitivity cardiac troponin T) levels.

METHODS AND RESULTS

A total of 8828 participants in SPRINT (Systolic Blood Pressure Intervention Trial) were stratified by baseline DBP. Those with low DBP (<70 mm Hg) were further stratified by elevated hs-cTnT (≥14 ng/L) at baseline. The effects of intensive versus standard BP lowering on a cardiovascular disease composite end point, all-cause death, and 1-year change in hs-cTnT were determined. The combination of low DBP/high hs-cTnT was independently associated with a higher risk for cardiovascular disease and all-cause death, as well as greater 1-year increases in hs-cTnT, compared with DBP ≥70 mm Hg. However, randomization to intensive versus standard BP lowering led to similar reductions in cardiovascular disease risk among individuals with low DBP/high hs-cTnT (hazard ratio [HR], 0.82 [95% CI, 0.57-1.19]), low DBP/low hs-cTnT (HR, 0.48 [95% CI, 0.29-0.79]), and DBP ≥70 mm Hg (HR, 0.73 [95% CI, 0.60-0.89]; P for interaction=0.20). Intensive BP lowering also led to a reduction in all-cause death that was similar across groups (P for interaction=0.57).

CONCLUSIONS

In this nonprespecified subgroup analysis of SPRINT, individuals with low DBP and elevated hs-cTnT, low DBP and nonelevated hs-cTnT, and DBP ≥70 mm Hg derived similar cardiovascular disease and mortality benefits from intensive BP lowering. These findings warrant confirmation in other studies.

Joint modeling approaches for censored predictors due to detection limits with applications to metabolites data

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, exact measures cannot be obtained, and thus are left censored. The problem becomes more challenging when the censored data come from heterogeneous populations consisting of exposed and non-exposed subjects. If the censored data come from non-exposed subjects, their measures are always zero and hence censored, forming a latent class governed by a distinct censoring mechanism compared with the exposed subjects. The exposed group's censored measurements are always greater than zero, but less than the detection limit. It is very often that the exposed and non-exposed subjects may have different disease traits or different relationships with outcomes of interest, so we need to disentangle the two different populations for valid inference. In this article, we aim to fill the methodological gaps in the literature by developing a novel joint modeling approach to not only address the censoring issue in predictors, but also untangle different relationships of exposed and non-exposed subjects with the outcome. Simulation studies are performed to assess the numerical performance of our proposed approach when the sample size is small to moderate. The joint modeling approach is also applied to examine associations between plasma metabolites and blood pressure in Bogalusa Heart Study, and identify new metabolites that are highly associated with blood pressure.

Censoring in the time trade-off valuation of worse-than-dead EQ-5D-5L health states: can a time-based willingness-to-accept question be the solution?

PURPOSE

The left censoring of values at -1 by design of the composite time trade-off (cTTO) tasks leads to excessive amount of -1 values in some EQ-5D-5L valuation studies. This study aimed to investigate whether a time-based willingness-to-accept (tWTA) question can be used to elicit values lower than -1 and improve the estimation of EQ-5D-5L values.

METHODS

At the end of each cTTO task in the Taiwanese EQ-5D-5L valuation study, if the value of the health state was indicated to be lower than -1, a tWTA question eliciting the indifference point between a hypothetical life (i.e. x number of years in full health followed by 10 years in the health state) and immediate death was used to estimate its uncensored value. We compared the statistical characteristics of the censored and uncensored data.

RESULTS

Four hundred and twenty-nine of 1,000 respondents were offered the tWTA question in a total of 1,071 cTTO tasks. In 79.55% of those tasks, indifference was not reached. Spearman's correlation with level summary score was -0.41 and -0.40 for negative uncensored and censored data, respectively. The logical inconsistency rates of the uncensored and censored data were 0.88% vs. 0.29%, respectively. Modelling of the uncensored data resulted in coefficients with greater uncertainty and much lower predictions.

CONCLUSIONS

The elicitation of values lower than -1 using a tWTA question that grants more time for trading seems not a promising solution to the value censoring of the cTTO tasks. Other strategies for valuation of very poor health states should be explored.

Kidney tubule health, mineral metabolism and adverse events in persons with CKD in SPRINT

BACKGROUND

Measures of kidney tubule health are risk markers for acute kidney injury (AKI) in persons with chronic kidney disease (CKD) during hypertension treatment, but their associations with other adverse events (AEs) are unknown.

METHODS

Among 2377 Systolic Blood Pressure Intervention Trial (SPRINT) participants with CKD, we measured at baseline eight urine biomarkers of kidney tubule health and two serum biomarkers of mineral metabolism pathways that act on the kidney tubules. Cox proportional hazards models were used to evaluate biomarker associations with risk of a composite of pre-specified serious AEs (hypotension, syncope, electrolyte abnormalities, AKI, bradycardia and injurious falls) and outpatient AEs (hyperkalemia and hypokalemia).

RESULTS

At baseline, the mean age was 73 ± 9 years and mean estimated glomerular filtration rate (eGFR) was 46 ± 11 mL/min/1.73 m2. During a median follow-up of 3.8 years, 716 (30%) participants experienced the composite AE. Higher urine interleukin-18, kidney injury molecule-1, neutrophil gelatinase-associated lipocalin (NGAL) and monocyte chemoattractant protein-1 (MCP-1), lower urine uromodulin (UMOD) and higher serum fibroblast growth factor-23 were individually associated with higher risk of the composite AE outcome in multivariable-adjusted models including eGFR and albuminuria. When modeling biomarkers in combination, higher NGAL [hazard ratio (HR) = 1.08 per 2-fold higher biomarker level, 95% confidence interval (CI) 1.03-1.13], higher MCP-1 (HR = 1.11, 95% CI 1.03-1.19) and lower UMOD (HR = 0.91, 95% CI 0.85-0.97) were each associated with higher composite AE risk. Biomarker associations did not vary by intervention arm (P > 0.10 for all interactions).

CONCLUSIONS

Among persons with CKD, several kidney tubule biomarkers are associated with higher risk of AEs during hypertension treatment, independent of eGFR and albuminuria.

Associations of High-Sensitivity Troponin and Natriuretic Peptide Levels With Serious Adverse Events in SPRINT

Background

Assessing the risk of serious adverse events (SAEs) during hypertension treatment is important for understanding the benefit‐harm trade‐offs of lower blood pressure goals. It is unknown whether high‐sensitivity cardiac troponin T (hs‐cTnT) and N‐terminal pro‐B‐type natriuretic peptide (NT‐proBNP) provide information about SAEs.

Methods and Results

In SPRINT (Systolic Blood Pressure Intervention Trial), hs‐cTnT and NT‐proBNP were measured at baseline in 8828 (94.3%) and 8836 (94.4%) participants, respectively. Multivariable Cox proportional hazards models were used to evaluate hs‐cTnT and NT‐proBNP associations with a composite of SPRINT’s SAEs of interest: hypotension, syncope, bradycardia, acute kidney injury, electrolyte abnormalities, and injurious falls. Elevations in hs‐cTnT and NT‐proBNP were associated with increased composite SAE risk (hazard ratio [HR] per 2‐fold higher hs‐cTnT: 1.15; 95% CI, 1.06‒1.25; HR per 2‐fold higher NT‐proBNP: 1.09; 95% CI, 1.05‒1.14). Compared with both hs‐cTnT and NT‐proBNP in the lower tertiles, both biomarkers in the highest tertile was associated with increased composite SAE risk (HR, 1.56; 95% CI, 1.32‒1.84). Composite SAE risk was higher in the intensive‐treatment group than in the standard‐treatment group for participants with both biomarkers in the lower tertiles, but similar between treatment groups for participants with both biomarkers in the highest tertile (P for interaction=0.008).

Conclusions

Elevations in hs‐cTnT and NT‐proBNP individually and in combination are associated with higher composite SAE risk in SPRINT. The differential impact of blood pressure treatment on SAE risk across combined biomarker categories may have implications for identifying individuals with more favorable benefit‐harm profiles for intensive blood pressure lowering.

A new statistical test for latent class in censored data due to detection limit

Biomarkers of interest in urine, serum, or other biological matrices often have an assay limit of detection. When concentration levels of the biomarkers for some subjects fall below the limit, the measures for those subjects are censored. Censored data due to detection limits are very common in public health and medical research. If censored data from a single exposure group follow a normal distribution or follow a normal distribution after some transformations, Tobit regression models can be applied. Given a Tobit regression model and a detection limit, the proportion of censored data can be determined. However, in practice, it is common that the data can exhibit excessive censored observations beyond what would be expected under a Tobit regression model. One common cause is heterogeneity of the study population, that is, there exists a subpopulation who lack such biomarkers and their values are always under the detection limit, and hence are censored. In this article, we develop a new test for testing such latent class under a Tobit regression model by directly comparing the amount of observed censored data with what would be expected under the Tobit regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Simulation studies are conducted to investigate the performance of the new test and compare the new one with the existing ones including the Wald test, likelihood ratio test, and score test. Two real data examples are also included for illustrative purpose.