A comprehensive review and shiny application on the matching-adjusted indirect comparison.

Population-adjusted indirect comparison (PAIC) is an increasingly used technique for estimating the comparative effectiveness of different treatments for the health technology assessments when head-to-head trials are unavailable. Three commonly used PAIC methods include matching-adjusted indirect comparison (MAIC), simulated treatment comparison (STC), and multilevel network meta-regression (ML-NMR). MAIC enables researchers to achieve balanced covariate distribution across two independent trials when individual participant data are only available in one trial. In this article, we provide a comprehensive review of the MAIC methods, including their theoretical derivation, implicit assumptions, and connection to calibration estimation in survey sampling. We discuss the nuances between anchored and unanchored MAIC, as well as their required assumptions. Furthermore, we implement various MAIC methods in a user-friendly R Shiny application Shiny-MAIC. To our knowledge, it is the first Shiny application that implements various MAIC methods. The Shiny-MAIC application offers choice between anchored or unanchored MAIC, choice among different types of covariates and outcomes, and two variance estimators including bootstrap and robust standard errors. An example with simulated data is provided to demonstrate the utility of the Shiny-MAIC application, enabling a user-friendly approach conducting MAIC for healthcare decision-making. The Shiny-MAIC is freely available through the link: https://ziren.shinyapps.io/Shiny_MAIC/.

Origami plot: a novel multivariate data visualization tool that improves radar chart.

OBJECTIVES: We propose the origami plot, which maintains the original functionality of a radar chart and avoids potential misuse of its connected regions, with newly added features to better assist multicriteria decision-making. STUDY DESIGN AND SETTING: Built upon a radar chart, the origami plot adds additional auxiliary axes and points such that the area of the connected region of all dots is invariant to the ordering of axes. As such, it enables ranking different individuals by the overall performance for multicriteria decision-making while maintaining the intuitive visual appeal of the radar chart. We develop extensions of the origami plot, including the weighted origami plot, which allows reweighting of each attribute to define the overall performance, and the pairwise origami plot, which highlights comparisons between two individuals. RESULTS: We illustrate the different versions of origami plots using the hospital compare database developed by the Centers for Medicare & Medicaid Services (CMS). The plot shows individual hospital's performance on mortality, readmission, complication, and infection, as well as patient experience and timely and effective care, as well as their overall performance across these metrics. The weighted origami plot allows weighing the attributes differently when some are more important than others. We illustrate the potential use of the pairwise origami plot in electronic health records (EHR) system to monitor five clinical measures (body mass index [BMI]), fasting glucose level, blood pressure, triglycerides, and low-density lipoprotein ([LDL] cholesterol) of a patient across multiple hospital visits. CONCLUSION: The origami plot is a useful visualization tool to assist multicriteria decision making. It improves radar charts by avoiding potential misuse of the connected regions. It has several new features and allows flexible customization.

Longitudinal transition of body mass index status and its associated factors among Chinese middle-aged and older adults in Markov model.

Introduction: Body mass index (BMI) has a strong correlation with chronic diseases and all-cause mortality. However, few studies have previously reported the longitudinal transition of BMI status and its influential factors, especially among Chinese middle-aged and older adults. Methods: This population-based cohort study involved 6,507 participants derived from the China Health and Retirement Longitudinal Study from 2011 to 2015, including objectively measured BMI recorded in 26,028 person-year of all observations followed up. Multistate Markov model was performed to estimate the BMI state transition intensity and hazard ratios of each potential exposure risk. Results: The mean intensity of the population that shifted from normal to overweight was more than twice than shifted to underweight. Besides, a predicted probability was up to 16.16% that the population with overweight would suffer from obesity and more than half of the population with underweight would return to normal weight over a 6-year interval. The study also implied significant effects of baseline age, gender, marital status, education level, alcohol consumption, smoking, depression symptoms, and activities of daily living impairment on BMI status transition to varying degrees. Conclusions: Findings of this study indicated that the mean transition probability between different BMI statuses varied, specific exposure factors serving as barriers or motivators to future transitions based on current BMI status was clarified for the health promotion strategies.

Changes over Time in Racial/Ethnic Differences in Quality of Life for Nursing Home Residents: Patterns within and between Facilities.

Objectives: To investigate trends in racial/ethnic differences in nursing home (NH) residents' quality of life (QoL) and assess these patterns within and between facilities. Method: Data include resident-reported QoL surveys (n = 60,093), the Minimum Data Set, and facility-level characteristics (n = 376 facilities) for Minnesota. Hierarchical linear models were estimated to identify differences in QoL by resident race/ethnicity and facility racial/ethnic minority composition for 2011-2015. Results: White residents in low-proportion racial/ethnic minority facilities reported higher QoL than both minority and white residents in high-proportion minority facilities. While the year-to-year differences were not statistically significant, the point estimates for white-minority disparity widened over time. Discussion: Racial/ethnic differences in QoL are persistent and may be widening over time. The QoL disparity reported by minority residents and all residents in high-proportion minority facilities underscores the importance of examining NH structural characteristics and practices to ultimately achieve the goal of optimal, person-centered care in NHs.

Inverse probability of treatment-weighted competing risks analysis: an application on long-term risk of urinary adverse events after prostate cancer treatments.

BACKGROUND: To illustrate the 10-year risks of urinary adverse events (UAEs) among men diagnosed with prostate cancer and treated with different types of therapy, accounting for the competing risk of death. METHODS: Prostate cancer is the second most common malignancy among adult males in the United States. Few studies have reported the long-term post-treatment risk of UAEs and those that have, have not appropriately accounted for competing deaths. This paper conducts an inverse probability of treatment (IPT) weighted competing risks analysis to estimate the effects of different prostate cancer treatments on the risk of UAE, using a matched-cohort of prostate cancer/non-cancer control patients from the Surveillance, Epidemiology and End Results (SEER) Medicare database. RESULTS: Study dataset included men age 66 years or older that are 83% white and had a median follow-up time of 4.14 years. Patients that underwent combination radical prostatectomy and external beam radiotherapy experienced the highest risk of UAE (IPT-weighted competing risks: HR 3.65 with 95% CI (3.28, 4.07); 10-yr. cumulative incidence = 36.5%). CONCLUSIONS: Findings suggest that IPT-weighted competing risks analysis provides an accurate estimator of the cumulative incidence of UAE taking into account the competing deaths as well as measured confounding bias.

A two-part mixed effects model for cigarette purchase task data.

The Cigarette Purchase Task is a behavioral economic assessment tool designed to measure the relative reinforcing efficacy of cigarette smoking across different prices. An exponential demand equation has become a standard model for analyzing purchase task data, but its utility is compromised by its inability to accommodate values of zero consumption. We propose a two-part mixed effects model that keeps the same exponential demand equation for modeling nonzero consumption values, while providing a logistic regression for the binary outcome of zero versus nonzero consumption. Therefore, the proposed model can accommodate zero consumption values and retain the features of the exponential demand equation at the same time. As a byproduct, the logistic regression component of the proposed model provides a new demand index, the "derived breakpoint", for the price above which a subject is more likely to be abstinent than to be smoking. We apply the proposed model to data collected at baseline from college students (N = 1,217) enrolled in a randomized clinical trial utilizing financial incentives to motivate tobacco cessation. Monte Carlo simulations showed that the proposed model provides better fits than an existing model. We note that the proposed methodology is applicable to other purchase task data, for example, drugs of abuse.

Propensity-Weighted Comparison of Long-Term Risk of Urinary Adverse Events in Elderly Women Treated For Cervical Cancer.

PURPOSE: Cervical cancer treatment is associated with a risk of urinary adverse events (UAEs) such as ureteral stricture and vesicovaginal fistula. We sought to measure the long-term UAE risk after surgery and radiation therapy (RT), with confounding controlled through propensity-weighted models. METHODS AND MATERIALS: From the Surveillance, Epidemiology, and End Results (SEER)-Medicare database, we identified women ≥66 years old with nonmetastatic cervical cancer treated with simple surgery (SS), radical hysterectomy (RH), external beam RT plus brachytherapy (EBRT+BT), or RT+surgery. We matched them to noncancer controls 1:3. Differences in demographic and cancer characteristics were balanced by propensity weighting. Grade 3 to 4 UAEs were identified by diagnosis codes plus treatment codes. Cumulative incidence was measured using Kaplan-Meier methods. The hazard associated with different cancer treatments was compared using Cox models. RESULTS: UAEs occurred in 272 of 1808 cases (17%) and 222 of 5424 (4%) controls; most (62%) were ureteral strictures. The raw cumulative incidence of UAEs was highest in advanced cancers. UAEs occurred in 31% of patients after EBRT+BT, 25% of patients after RT+surgery, and 15% of patients after RH; however, after propensity weighting, the incidence was similar. In adjusted Cox models (reference = controls), the UAE risk was highest after RT+surgery (hazard ratio [HR], 5.07; 95% confidence interval [CI], 2.32-11.07), followed by EBRT+BT (HR, 3.33; 95% CI, 1.45-7.65), RH (HR, 3.65; 95% CI, 1.41-9.46) and SS (HR, 0.99; 95% CI, 0.32-3.01). The higher risk after RT+surgery versus EBRT+BT was statistically significant, whereas, EBRT+BT and RH were not significantly different from each other. CONCLUSIONS: UAEs are common after cervical cancer treatment, particularly in patients with advanced cancers. UAEs are more common after RT, but these women tend to have the advanced cancers. After propensity weighting, the risk after RT was similar to that after surgery.

Propensity-weighted long-term risk of urinary adverse events after prostate cancer surgery, radiation, or both.

BACKGROUND: Prostate cancer is the second most common cancer in men and has high survivorship, yet little is known about the long-term risk of urinary adverse events (UAEs) after treatment. OBJECTIVE: To compare the long-term UAE incidence across treatment and control groups. DESIGN, SETTING, AND PARTICIPANTS: Using a matched-cohort design, we identified elderly men treated with external-beam radiotherapy (EBRT; n=44 318), brachytherapy (BT; n=14 259), EBRT+BT (n=11 835), radical prostatectomy (RP; n=26 970), RP+EBRT (n=1557), or cryotherapy (n=2115) for non-metastatic prostate cancer and 144 816 non-cancer control individuals from the population-based Surveillance, Epidemiology, and End Results-Medicare linked data from 1992-2007 with follow-up through 2009. OUTCOME MEASURES AND STATISTICAL ANALYSIS: The incidence of treated UAEs and time from cancer treatment to first UAE were analyzed in terms of propensity-weighted survival. RESULTS: Median follow-up was 4.14 yr. At 10 yr, all treatment groups experienced higher propensity-weighted cumulative UAE incidence than the control group (16.1%; hazard risk [HR] 1.0), with the highest incidence for RP+EBRT (37.8%; HR 3.19, 95% confidence interval [CI] 2.79-3.66), followed by BT+EBRT (28.4%; HR 1.97, CI 1.85-2.10), RP (26.6%; HR 2.44, CI 2.34-2.55), cryotherapy (23.4%; HR 1.56, CI 1.30-1.87), BT (19.8%; HR 1.43, CI 1.33-1.53), and EBRT (19.7%; HR 1.11, CI 1.07-1.16). Bladder outlet obstruction was the most common event. CONCLUSIONS: Men undergoing RP, RP+EBRT, and BT+EBRT experienced the highest UAE risk at 10 yr, although UAEs accrued differently over extended follow-up. The significant background UAE rate among non-cancer control individuals yields a risk attributable to prostate cancer treatment that is 17% lower than prior estimates. PATIENT SUMMARY: We show that treatment for prostate cancer, especially combinations of two treatments such as radiation and surgery, carries a significant risk of urinary adverse events such as urethral stricture. This risk increases with time since treatment, emphasizing that treatments have long-term effects.

Analysis of cigarette purchase task instrument data with a left-censored mixed effects model.

The drug purchase task is a frequently used instrument for measuring the relative reinforcing efficacy (RRE) of a substance, a central concept in psychopharmacological research. Although a purchase task instrument, such as the cigarette purchase task (CPT), provides a comprehensive and inexpensive way to assess various aspects of a drug's RRE, the application of conventional statistical methods to data generated from such an instrument may not be adequate by simply ignoring or replacing the extra zeros or missing values in the data with arbitrary small consumption values, for example, 0.001. We applied the left-censored mixed effects model to CPT data from a smoking cessation study of college students and demonstrated its superiority over the existing methods with simulation studies. Theoretical implications of the findings, limitations of the proposed method, and future directions of research are also discussed.

Network meta-analysis of margin threshold for women with ductal carcinoma in situ.

BACKGROUND: Negative margins are associated with reduced risk of ipsilateral breast tumor recurrence (IBTR) for women with ductal carcinoma in situ (DCIS) treated with breast-conserving surgery (BCS). However, there is no consensus about the best minimum margin width. METHODS: We searched the PubMed database for studies of DCIS published in English between January 1970 and July 2010 and examined the relationship between IBTR and margin status after BCS for DCIS. Women with DCIS were stratified into two groups, BCS with or without radiotherapy. We used frequentist and Bayesian approaches to estimate the odds ratios (OR) of IBTR for groups with negative margins and positive margins. We further examined specific margin thresholds using mixed treatment comparisons and meta-regression techniques. All statistical tests were two-sided. RESULTS: We identified 21 studies published in 24 articles. A total of 1066 IBTR events occurred in 7564 patients, including BCS alone (565 IBTR events in 3098 patients) and BCS with radiotherapy (501 IBTR events in 4466 patients). Compared with positive margins, negative margins were associated with reduced risk of IBTR in patients with radiotherapy (OR = 0.46, 95% credible interval [CrI] = 0.35 to 0.59), and in patients without radiotherapy (OR = 0.34, 95% CrI = 0.24 to 0.47). Compared with patients with positive margins, the risk of IBTR for patients with negative margins was smaller (negative margin >0 mm, OR = 0.45, 95% CrI = 0.38 to 0.53; >2 mm, OR = 0.38, 95% CrI = 0.28 to 0.51; >5 mm, OR = 0.55, 95% CrI = 0.15 to 1.30; and >10 mm, OR = 0.17, 95% CrI = 0.12 to 0.24). Compared with a negative margin greater than 2 mm, a negative margin of at least 10 mm was associated with a lower risk of IBTR (OR = 0.46, 95% CrI = 0.29 to 0.69). We found a probability of .96 that a negative margin threshold greater than 10 mm is the best option compared with other margin thresholds. CONCLUSIONS: Negative surgical margins should be obtained for DCIS patients after BCS regardless of radiotherapy. Within cosmetic constraint, surgeons should attempt to achieve negative margins as wide as possible in their first attempt. More studies are needed to understand whether margin thresholds greater than 10 mm are warranted.

Bayesian posterior distributions without Markov chains.

Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.

Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits.

The analysis of data subject to detection limits is becoming increasingly necessary in many environmental and laboratory studies. Covariates subject to detection limits are often left censored because of a measurement device having a minimal lower limit of detection. In this paper, we propose a Monte Carlo version of the expectation-maximization algorithm to handle large number of covariates subject to detection limits in generalized linear models. We model the covariate distribution via a sequence of one-dimensional conditional distributions, and sample the covariate values using an adaptive rejection metropolis algorithm. Parameter estimation is obtained by maximization via the Monte Carlo M-step. This procedure is applied to a real dataset from the National Health and Nutrition Examination Survey, in which values of urinary heavy metals are subject to a limit of detection. Through simulation studies, we show that the proposed approach can lead to a significant reduction in variance for parameter estimates in these models, improving the power of such studies.

Relative excess risk due to interaction: resampling-based confidence intervals.

Relative excess risk due to interaction (RERI) has been used to quantify the joint effects of 2 exposures in epidemiology. However, the construction of confidence intervals (CIs) for RERI is complicated by sparse cells. Assuming that the data contain no zero cells, here we propose constructing CIs for RERI using nonparametric and parametric bootstrap methods with a continuity correction, and compare these proposed methods to existing methods using 3 empirical examples and Monte Carlo simulations. Our results show that, when cell counts are not sparse, CIs resulting from the explored bootstrap methods are generally acceptable in terms of CI coverage and length, although computationally more demanding than existing methods. However, when cell counts are sparse, the proposed bootstrap methods using a continuity correction outperform existing methods and continue to provide acceptable CIs. The continuity correction is needed for the explored bootstrap methods to provide acceptable CIs because resampled data sets may contain zero cells even when the observed data do not.

Linear regression with an independent variable subject to a detection limit.

BACKGROUND: Linear regression with a left-censored independent variable X due to limit of detection (LOD) was recently considered by 2 groups of researchers: Richardson and Ciampi (Am J Epidemiol. 2003;157:355-363), and Schisterman et al (Am J Epidemiol. 2006;163:374-383). METHODS: Both groups obtained consistent estimators for the regression slopes by replacing left-censored X with a constant, that is, the expectation of X given X below LOD E(X|X

Illustrating bias due to conditioning on a collider.

That conditioning on a common effect of exposure and outcome may cause selection, or collider-stratification, bias is not intuitive. We provide two hypothetical examples to convey concepts underlying bias due to conditioning on a collider. In the first example, fever is a common effect of influenza and consumption of a tainted egg-salad sandwich. In the second example, case-status is a common effect of a genotype and an environmental factor. In both examples, conditioning on the common effect imparts an association between two otherwise independent variables; we call this selection bias.

Estimating the odds ratio when exposure has a limit of detection.

BACKGROUND: In epidemiologic research, little emphasis has been placed on methods to account for left-hand censoring of 'exposures' due to a limit of detection (LOD). METHODS: We calculate the odds of anti-HIV therapy naiveté in 45 HIV-infected men as a function of measured log(10) plasma HIV RNA viral load using five approaches including ad hoc methods as well as a maximum likelihood estimate (MLE). We also generated simulations of a binary outcome with 10% incidence and a 1.5-fold increased odds per log increase in a log-normally distributed exposure with 25, 50 and 75% of exposure data below LOD. Simulated data were analysed using the same five methods, as well as the full data. RESULTS: In the example, the estimated odds ratio (OR) varied by 1.22-fold across methods, from 1.45 to 1.77 per log(10) copies of viral load and the standard error for the log OR varied by 1.52-fold across methods, from 0.31 to 0.47. In the simulations, use of full data or the MLE was unbiased with appropriate confidence interval (CI) coverage. However, as the proportion of exposure below LOD increased, substituting LOD, LOD/ radical 2 or LOD/2 was increasingly biased with increasingly inappropriate CI coverage. Finally, exclusion of values below LOD was unbiased but imprecise. CONCLUSIONS: In this example and the settings explored by simulation, and among methods readily available to investigators (i.e. sans full data), the MLE provided an unbiased and appropriately precise estimate of the exposure-outcome OR.

A Bayesian approach estimating treatment effects on biomarkers containing zeros with detection limits.

Often in randomized clinical trials and observational studies in occupational and environmental health, a non-negative continuously distributed response variable denoting some metabolites of environmental toxicants is measured in treatment and control groups. When observations occur in both unexposed and exposed subjects, the biomarker measurement can be bimodally distributed with an extra spike at zero reflecting those unexposed. In the presence of left censoring due to values falling below biomarker assay detection limits, those unexposed with true zeros are indistinguishable from those exposed with left-censored values. Since interventions usually do not enhance or eliminate exposure, they do not have any impact on those unexposed. Thus, only the subset of individuals who are exposed should be used to make comparisons to estimate the effect of interventions. In this article, we present Bayesian approaches using non-standard mixture distributions to account for true zeros. The performance of the proposed Bayesian methods is compared with the maximum likelihood methods presented in Chu et al. (Stat. Med. 2005; 24:2053-2067) through simulation studies and a randomized chemoprevention trial conducted in Qidong, People's Republic of China.

Confidence intervals for biomarker-based human immunodeficiency virus incidence estimates and differences using prevalent data.

Prevalent biologic specimens can be used to estimate human immunodeficiency virus (HIV) incidence using a two-stage immunologic testing algorithm that hinges on the average time, T, between testing HIV-positive on highly sensitive enzyme immunoassays and testing HIV-positive on less sensitive enzyme immunoassays. Common approaches to confidence interval (CI) estimation for this incidence measure have included 1) ignoring the random error in T or 2) employing a Bonferroni adjustment of the box method. The authors present alternative Monte Carlo-based CIs for this incidence measure, as well as CIs for the biomarker-based incidence difference; standard approaches to CIs are typically appropriate for the incidence ratio. Using American Red Cross blood donor data as an example, the authors found that ignoring the random error in T provides a 95% CI for incidence as much as 0.26 times the width of the Monte Carlo CI, while the Bonferroni-box method provides a 95% CI as much as 1.57 times the width of the Monte Carlo CI. Further research is needed to understand under what circumstances the proposed Monte Carlo methods fail to provide valid CIs. The Monte Carlo-based CI may be preferable to competing methods because of the ease of extension to the incidence difference or to exploration of departures from assumptions.

A general approach for sample size and statistical power calculations assessing of interventions using a mixture model in the presence of detection limits.

A zero-inflated log-normal mixture model (which assumes that the data has a probability mass at zero and a continuous response for values greater than zero) with left censoring due to assay measurements falling below detection limits has been applied to compare treatment groups in randomized clinical trials and observational cohort studies. The sample size calculation (for a given type I error rate and a desired statistical power) has not been studied for this type of data under the assumption of equal proportions of true zeros in the treatment and control groups. In this article, we derive the sample sizes based on the expected differences between the non-zero values of individuals in treatment and control groups. Methods for calculation of statistical power are also presented. When computing the sample sizes, caution is needed as some irregularities occur, namely that the location parameter is sometimes underestimated due to the mixture distribution and left censoring. In such cases, the aforementioned methods fail. We calculated the required sample size for a recent randomized chemoprevention trial estimating the effect of oltipraz on reducing aflatoxin. A Monte Carlo simulation study was also conducted to investigate the performance of the proposed methods. The simulation results illustrate that the proposed methods provide adequate sample size estimates. However, when the aforementioned irregularity occurs, our methods are restricted and further research is needed.