The median hazard ratio: a useful measure of variance and general contextual effects in multilevel survival analysis

Multilevel data occurs frequently in many research areas like health services research and epidemiology. A suitable way to analyze such data is through the use of multilevel regression models (MLRM). MLRM incorporate cluster‐specific random effects which allow one to partition the total individual variance into between‐cluster variation and between‐individual variation. Statistically, MLRM account for the dependency of the data within clusters and provide correct estimates of uncertainty around regression coefficients. Substantively, the magnitude of the effect of clustering provides a measure of the General Contextual Effect (GCE). When outcomes are binary, the GCE can also be quantified by measures of heterogeneity like the Median Odds Ratio (MOR) calculated from a multilevel logistic regression model. Time‐to‐event outcomes within a multilevel structure occur commonly in epidemiological and medical research. However, the Median Hazard Ratio (MHR) that corresponds to the MOR in multilevel (i.e., ‘frailty’) Cox proportional hazards regression is rarely used. Analogously to the MOR, the MHR is the median relative change in the hazard of the occurrence of the outcome when comparing identical subjects from two randomly selected different clusters that are ordered by risk. We illustrate the application and interpretation of the MHR in a case study analyzing the hazard of mortality in patients hospitalized for acute myocardial infarction at hospitals in Ontario, Canada. We provide R code for computing the MHR. The MHR is a useful and intuitive measure for expressing cluster heterogeneity in the outcome and, thereby, estimating general contextual effects in multilevel survival analysis. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

Active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio

This paper considers methods for testing for superiority or non-inferiority in active-control trials with binary data, when the relative treatment effect is expressed as an odds ratio. Three asymptotic tests for the log-odds ratio based on the unconditional binary likelihood are presented, namely the likelihood ratio, Wald and score tests. All three tests can be implemented straightforwardly in standard statistical software packages, as can the corresponding confidence intervals. Simulations indicate that the three alternatives are similar in terms of the Type I error, with values close to the nominal level. However, when the non-inferiority margin becomes large, the score test slightly exceeds the nominal level. In general, the highest power is obtained from the score test, although all three tests are similar and the observed differences in power are not of practical importance.     

Interval estimation of generalized odds ratio in data with repeated measurements

When the underlying responses are on an ordinal scale, the generalized odds ratio (GOR), defined as the ratio of the proportions of concordant and discordant pairs, is a useful index to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable. We discuss interval estimation of the GOR for ordinal data with repeated measurements. On the basis of the Dirichlet-multinomial model, we develop three asymptotic interval estimators of the GOR using Wald's test statistic, a logarithmic transformation, and a method analogous to Fieller's theorem, respectively. To evaluate and compare the finite-sample performance of these estimators, we apply Monte Carlo simulation. We find that when the number of subjects per group is not large, the coverage probability of interval estimator using Wald's test statistic is likely to be less than the desired confidence level. By contrast, the coverage probability of the other two estimators are approximately equal to or larger than the desired confidence level. When the number of subjects per group is small and the intraclass correlation between repeated measurements within subjects is large, we note that applying the interval estimator derived from a method analogous to Fieller's theorem can lose efficiency. We also note that the interval estimator using the logarithmic transformation is generally preferable to the other two estimators with respect to both the coverage probability and the average length. Finally, on the basis of a few preliminary simulations, we do find some robustness for all the estimators developed here. We include an example comparing the inflammation grade after lung transplant between surgeries to illustrate the use of the proposed interval estimators.     

Analysis of survival data by the proportional odds model

A model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time. A non-parametric estimate is given for the survivor function. The theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time. The model is fitted to data using maximum likelihood estimation, and an example of its use in the analysis of a lung cancer trial is given.     

Test non-inferiority (and equivalence) based on the odds ratio under a simple crossover trial

For testing the non-inferiority (or equivalence) of a generic drug to a standard drug, the odds ratio (OR) of patient response rates has been recommended to measure the relative treatment efficacy. On the basis of a random effects logistic regression model, we develop asymptotic test procedures for testing non-inferiority and equivalence with respect to the OR of patient response rates under a simple crossover design. We further derive exact test procedures, which are especially useful for the situations in which the number of patients in a crossover trial is small. We address sample size calculation for testing non-inferiority and equivalence based on the asymptotic test procedures proposed here. We also discuss estimation of the OR of patient response rates for both the treatment and period effects. Finally, we include two examples, one comparing two solution aerosols in treating asthma, and the other one studying two inhalation devices for asthmatics, to illustrate the use of the proposed test procedures and estimators.     

Covariates-dependent confidence intervals for the difference or ratio of two median survival times

In this paper, we are concerned with the estimation of the discrepancy between two treatments when right-censored survival data are accompanied with covariates. Conditional confidence intervals given the available covariates are constructed for the difference between or ratio of two median survival times under the unstratified and stratified Cox proportional hazards models, respectively. The proposed confidence intervals provide the information about the difference in survivorship for patients with common covariates but in different treatments. The results of a simulation study investigation of the coverage probability and expected length of the confidence intervals suggest the one designed for the stratified Cox model when data fit reasonably with the model. When the stratified Cox model is not feasible, however, the one designed for the unstratified Cox model is recommended. The use of the confidence intervals is finally illustrated with a HIV+ data set.     

项目地区获取孕产期保健知识对孕产妇死亡率影响的研究

目的:分析孕产妇及其家属获取孕产期保健知识对孕产妇死亡率的影响,探讨提高该地区的孕产期保健知识的有效措施。方法:采用1∶1配对病例对照研究方法,选择孕产妇死亡率较高、人均收入较低、多民族聚居的贵州省内22个项目县中所有在2004年死亡的农村孕产妇与非死亡的孕产妇,应用多因素Logistic回归分析了解获取孕产期保健知识的内容和途径对孕产妇死亡率的影响。结果:被调查地区孕产妇了解孕产期保健知识的比例低于45%。其中,对照组获取孕产期保健知识多于病例组,两组获取知识的内容和途径存在明显差异,病例组获取知识的主要途径是自己的经验和亲朋传说。结论:该地区孕产妇对孕产期保健知识的获取不足,存在信息来源、获取信息的能力、理解信息的程度、宣传方式方法的差异,这些差异影响了孕产妇死亡率。     

Improving communication between hospitals and care homes: the development of a daily living plan for older people

The present study describes a practice development project that produced a user-led daily living plan (DLP), which was developed in partnership with older people, and staff from health and social care settings. The DLP was designed to facilitate communication of the daily living preferences of older people, ensuring that continuity of care and support could be maintained and that their future care can be planned on an individualised basis when they move from hospital to a care home. In the process of developing and implementing the DLP, more effective person-centred communication between hospitals and care homes was achieved, and some of the hospital staff's ideas about care homes changed.     

The analysis of efficiency among a small number of organisations: how inferences can be improved by exploiting patient-level data

Those responsible for monitoring and managing the performance of health-care organisations face the common problem that the relationship between observed performance and effort is difficult to establish. A solution is to compare the performance of multiple organisations, but this requires a sufficient number of comparators. Faced with a small sample, it may be possible to exploit other information sources. Multilevel regression models are applied to analyse the performance of six Danish vascular departments in 2004 using a patient-level data set. We find that treatment costs are higher for smokers, older patients, patients with cerebrovascular and pulmonal diseases and for those subject to acute hospitalisation and with longer lengths of stay. Costs are lower for patients who are having follow-up surgery and for patients who receive some form of home care, suggesting that there may be some substitution of care input between vascular departments and other care providers. We estimate the relative efficiency of each department. The construction of confidence intervals allows the six departments to be sorted into two groups containing the least and most efficient departments. Conclusions about relative efficiency are robust to model specification, choice of estimator and hold at the 95% confidence level.     

2型糖尿病患者白蛋白尿与肾动态显像GFR的关系及影响因素

目的探讨2型糖尿病（type2diabetesmellitus,T2DM）患者尿白蛋8／肌酐比值（urinaryalbumincreatinineratio,UACR）与。肾动态显像法肾小球滤过率（glomerularfiltrationrate,GFR）的关系,分析糖尿病患者UACR与GFR的影响因素。方法收集167例病情稳定的T2DM患者资料,根据尿UACR进行分组,比较各组GFR及肾功能减低的发生率。并对UAER与GFR进行相关及回归分析。结果分组分析显示UACR各组间GFR差异有统计学意义（均有P〈0．05）;3组间肾功能减低的发生率差异有统计学意义（均有P〈0．05）,直线相关分析显示T2DM患者UACR与GFR呈明显负相关（r=一0．41,P〈0．001）;但在UACR正常的患者中仍有11．9％患者出现肾功能减低。糖尿病患者UACR与GFR均与病程、血压、血糖控制及血清肌酐有关（UACR与上述各因素呈正相关,GFR与上述各因素呈负相关）;男性更易出现UACR升高、GFR下降;此外GFR还与体质指数（bodymassindex,BMI）及年龄呈负相关。多因素逐步回归分析显示影响UACR的主要因素是：舒张压、糖化血红蛋白、血清肌酐,影响GFR的主要因素是：血清肌酐、年龄、平均血压、糖化血红蛋白。结论T2DM患者UACR与GFR有共同的危险因素亦有不同的影响因素,UACR仍然是T2DM肾病筛查的重要指标,但单独检测UACR可能会遗漏部分肾功能减低患者,因此结合GFR的测定能更好地反映患者肾受损的状态。     

A mortality study of cobalt production workers: An extension of the follow-up

The follow-up of a cohort of workers employed in an electrochemical plant producing cobalt and sodium, previously studied from 1950–1980, has been extended from 1981–1988. The standardized mortality ratio (SMR) for all causes of death was 0.85 (95% confidence interval [CI] + 0.76–0.95, 309 observed) for the whole cohort, and 0.95 (95% CI + 0.83–1.08, 247 observed) for the subcohort of workers born in France. With regard to lung cancer mortality among cobalt production workers, which is the main objective of the study, the SMRs were, respectively, 0.85 (95% CI + 0.18–2.50, 3 observed) and 1.16 (95% CI + 0.24–3.40, 3 observed). Neither did any excess of mortality from diseases of the circulatory and of the respiratory systems appear among cobalt production workers. Maintenance workers, however, exhibited high SMRs for lung cancer, reaching statistical significance for duration of exposure and time since first exposure ≥ 30 years. This study does not support the hypothesis of a relationship between lung cancer and cobaltexposure. © 1993 Wiley-Liss. Inc.     

Multilevel modelling for measuring interaction of effects between multiple categorical variables: An illustrative application using risk factors for preeclampsia

Background

Measuring multiple and higher-order interaction effects between multiple categorical variables proves challenging.

Objectives

To illustrate a multilevel modelling approach to studying complex interactions.

Methods

We apply a two-level random-intercept linear regression to a binary outcome for individuals (level-1) nested within strata (level-2) defined by all observed combinations of multiple categorical exposure variables. As a pedagogic application, we analyse 36 strata defined by five risk factors of preeclampsia (parity, previous preeclampsia, chronic hypertension, multiple pregnancies, body mass index category) among 652,603 women in the Swedish Medical Birth Registry between 2002 and 2010.

Results

The absolute risk of preeclampsia was 4% but was predicted to vary from 1% to 44% across strata. The stratum discriminatory accuracy was 30% according to the variance partition coefficient (VPC) and 0.73 according to the area under the receiver operating characteristic curve (AUC). While the risk heterogeneity across strata was primarily due to the main effects of the categories defining the strata, 5% of the variation was attributable to their two- and higher-way interaction effects. One stratum presented a positive interaction, and two strata presented negative interaction.

Conclusions

Multilevel modelling is an innovative tool for identifying and analysing higher-order interaction effects. Further work is needed to explore how this approach can best be applied to making causal inferences.     

Circumstances of Pregnancy: Low Income Women in Georgia Describe the Difference between Planned and Unplanned Pregnancies

Introduction and Background: The United States has a higher rate of unintended pregnancies than many other developed countries despite the availability of effective contraception. Using Azjen's Theory of Planned Behavior and Luker's Theory of Contraceptive Risk Taking this qualitative study explores the reasons for the high rate of unintended pregnancy among low income women in Georgia. Methods: Six focus groups (N=39) were conducted at county health department clinics. Women were recruited at the clinics to participate in a discussion of Pregnancy and Motherhood. All English or Spanish speaking women between the ages of 18 and 49 were eligible for participation. Results: Three dimensions of pregnancy planning emerged-the decision to have a child, taking specific behaviors to increase the likelihood of conception, and making plans to care for a child. Planned pregnancies may occur when a couple or a woman decides that they are ready to have a child, but also occur in less stable situations that pose risks for the family and the child. Unplanned pregnancies may be welcomed or be unwanted depending on the circumstances. Women perceive advantages and disadvantages to planned and unplanned pregnancies. Discussion: There are major differences between the definition and values of planned and unplanned pregnancies promoted by public health practitioners and those of the women in our study. This suggests the need for research on the circumstances in which pregnancies occur, as well as targeted interventions and policies that help women and men define and achieve the circumstances in which they would like to bear and rear children.     

Estimating the association between blood pressure variability and cardiovascular disease: An application using the ARIC Study

The association between visit-to-visit systolic blood pressure variability and cardiovascular events has recently received a lot of attention in the cardiovascular literature. But, blood pressure variability is usually estimated on a person-by-person basis and is therefore subject to considerable measurement error. We demonstrate that hazard ratios estimated using this approach are subject to bias due to regression dilution, and we propose alternative methods to reduce this bias: a two-stage method and a joint model. For the two-stage method, in stage one, repeated measurements are modelled using a mixed effects model with a random component on the residual standard deviation (SD). The mixed effects model is used to estimate the blood pressure SD for each individual, which, in stage two, is used as a covariate in a time-to-event model. For the joint model, the mixed effects submodel and time-to-event submodel are fitted simultaneously using shared random effects. We illustrate the methods using data from the Atherosclerosis Risk in Communities study.     

Exploring the cost-effectiveness of advance care planning (by taking a family carer perspective): Findings of an economic modelling study

Advance care planning is considered an important part of high-quality end-of-life care. Its cost-effectiveness is currently unknown. In this study, we explore the cost-effectiveness of a strategy, in which advance care planning is offered systematically to older people at the end-of-life compared with standard care. We conducted decision-analytic modelling. The perspective was health and social care and the time horizon was 1 year. Outcomes included were quality-adjusted life years as they referred to the surviving carers. Data sources included published studies, national statistics and expert views. Average total cost in the advance care planning versus standard care group was £3,739 versus £3,069. The quality-adjusted life year gain to carers was 0.03 for the intervention in comparison with the standard care group. Based on carer's health-related quality-of-life, the average cost per quality-adjusted life year was £18,965. The probability that the intervention was cost-effective was 55% (70%) at a cost per quality-adjusted life year threshold of £20,000 (£30,000). Conducting cost-effectiveness analysis for advance care planning is challenging due to uncertainties in practice and research, such as a lack of agreement on how advance care planning should be provided and by whom (which influences its costs), and about relevant beneficiary groups (which influences its outcomes). However, even when assuming relatively high costs for the delivery of advance care planning and only one beneficiary group, namely, family carers, our analysis showed that advance care planning was probably cost-effective.     

Measuring Hospital Care from the Patients' Perspective: An Overview of the CAHPS® Hospital Survey Development Process

Objective. To describe the developmental process for the CAHPS^® Hospital Survey.
Study Design. A pilot was conducted in three states with 19,720 hospital discharges.
Methods of Analysis. A rigorous, multi-step process was used to develop the CAHPS Hospital Survey. It included a public call for measures, multiple Federal Register notices soliciting public input, a review of the relevant literature, meetings with hospitals, consumers and survey vendors, cognitive interviews with consumer, a large-scale pilot test in three states and consumer testing and numerous small-scale field tests.
Findings. The current version of the CAHPS Hospital Survey has survey items in seven domains, two overall ratings of the hospital and five items used for adjusting for the mix of patients across hospitals and for analytical purposes.
Conclusions. The CAHPS Hospital Survey is a core set of questions that can be administered as a stand-alone questionnaire or combined with a broader set of hospital specific items.     

Modeling efficiency at the process level: an examination of the care planning process in nursing homes

Objective. To examine the efficiency of the care planning process in nursing homes.
Methods: We collected detailed primary data about the care planning process for a stratified random sample of 107 nursing homes from Kansas and Missouri. We used these data to calculate the average direct cost per care plan and used data on selected deficiencies from the Online Survey Certification and Reporting System to measure the quality of care planning. We then analyzed the efficiency of the assessment process using corrected ordinary least squares (COLS) and data envelopment analysis (DEA).
Results: Both approaches suggested that there was considerable inefficiency in the care planning process. The average COLS score was 0.43; the average DEA score was 0.48. The correlation between the two sets of scores was quite high, and there was no indication that lower costs resulted in lower quality. For-profit facilities were significantly more efficient than not-for-profit facilities.
Conclusions. Multiple studies of nursing homes have found evidence of inefficiency, but virtually all have had measurement problems that raise questions about the results. This analysis, which focuses on a process with much simpler measurement issues, finds evidence of inefficiency that is largely consistent with earlier studies. Making nursing homes more efficient merits closer attention as a strategy for improving care. Increasing efficiency by adopting well-designed, reliable processes can simultaneously reduce costs and improve quality.