Issues in the analysis of repeated categorical outcomes

A generalized transition model for grouped longitudinal categorical data

Transition models are an important framework that can be used to model longitudinal categorical data. They are particularly useful when the primary interest is in prediction. The available methods for this class of models are suitable for the cases in which responses are recorded individually over time. However, in many areas, it is common for categorical data to be recorded as groups, that is, different categories with a number of individuals in each. As motivation we consider a study in insect movement and another in pig behaviou. The first study was developed to understand the movement patterns of female adults of Diaphorina citri, a pest of citrus plantations. The second study investigated how hogs behaved under the influence of environmental enrichment. In both studies, the number of individuals in different response categories was observed over time. We propose a new framework for considering the time dependence in the linear predictor of a generalized logit transition model using a quantitative response, corresponding to the number of individuals in each category. We use maximum likelihood estimation and present the results of the fitted models under stationarity and non-stationarity assumptions, and use recently proposed tests to assess non-stationarity. We evaluated the performance of the proposed model using simulation studies under different scenarios, and concluded that our modeling framework represents a flexible alternative to analyze grouped longitudinal categorical data.

Assessment of the Non-Technical Skills for Surgeons (NOTSS) framework in the USA

Background

Surgeons' non-technical skills are important for patient safety. The Non-Technical Skills for Surgeons assessment tool was developed in the UK and recently adapted to the US surgical context (NOTSS-US). The aim of this study was to evaluate the reliability and distribution of non-technical skill ratings given by attending (consultant) surgeons who underwent brief online training.

Methods

Attending surgeons across six specialties at a large US academic medical centre underwent a 10-min online training, then rated 60-s standardized videos of simulated operations. Intraclass correlation coefficient (ICC), and mean(s.d.) values for NOTSS-US ratings were determined for each non-technical skill category (score range 1–5, where 1 indicates poor, 3 average and 5 excellent) and for total NOTSS-US score (range 4–20; sum of 4 category scores). Outcomes were adjusted for rater characteristics including sex, specialty and clinical experience.

Results

A total of 8889 ratings were submitted by 81 surgeon raters on 30 simulated intraoperative videos. The mean(s.d.) total NOTSS-US score for all videos was 9·5(4·8) of 20. The within-video ICC for total NOTSS-US score was 0·64 (95 per cent c.i. 0·57 to 0·70). For individual non-technical skill categories, the ICC was highest for social skills (communication/teamwork: 0·63, 95 per cent c.i. 0·56 to 0·71; leadership: 0·64, 0·55 to 0·72) and lowest for cognitive skills (situation awareness: 0·54, 0·45 to 0·62; decision-making: 0·50, 0·41 to 0·59). Women gave higher total NOTSS-US scores than men (adjusted mean difference 0·93, 95 per cent c.i. 0·44 to 1·43; P = 0·001).

Conclusion

After brief online training, the inter-rater reliability of the NOTSS-US assessment tool achieved moderate strength among trained surgeons rating simulated intraoperative videos.

Effect of the Serious Illness Care Program on Health Care Utilization at the End of Life for Patients with Cancer

Objectives: To determine the effect of the Serious Illness Care Program on health care utilization at the end of life in oncology. Design: Analysis of the secondary outcome of health care utilization as part of a cluster-randomized clinical trial that ran from 2012 to 2016. Clinicians in the intervention group received training, coaching, and system supports to have discussions with patients using a Serious Illness Conversation Guide (SICG); clinicians in the control arm followed usual care. Setting/Subject: Patients with advanced cancer who died within two years of enrollment at the Dana-Farber Cancer Institute. Measurement: Health care utilization was abstracted from the electronic medical record using the National Quality Forum (NQF)-endorsed indicators of aggressive cancer care at the end of life and scored from 0 to 6 (one point for each aggressive indicator); t tests and chi-square tests were used to determine differences between intervention and control patients. Results: The charts of 159 patients who died were reviewed. Neither the main outcome of mean number of aggressive indicators (0.9 vs. 0.9, p = 0.84) nor the proportion of patients with any aggressive care (49% intervention [95% CI: 40-57] vs. 54% control [95% CI: 42-67]) differed between patients in the intervention and control groups. Conclusion: In this analysis of a secondary outcome from a randomized clinical trial of the Serious Illness Care Program, intervention and control patients had similar end-of-life health care utilization as measured by the mean number of NQF-endorsed indicators. Future research efforts should focus on studying the strategies by which communication about patients' prognosis, values, and goals leads to personalized care plans.

Prospective Evaluation of a Multifaceted Intervention to Improve Outcomes in Intensive Care: The Promoting Respect and Ongoing Safety Through Patient Engagement Communication and Technology Study

OBJECTIVES

Studies comprehensively assessing interventions to improve team communication and to engage patients and care partners in ICUs are lacking. This study examines the effectiveness of a patient-centered care and engagement program in the medical ICU.

DESIGN

Prospective intervention study.

SETTING

Medical ICUs at large tertiary care center.

PATIENTS

Two thousand one hundred five patient admissions (1,030 before and 1,075 during the intervention) from July 2013 to May 2014 and July 2014 to May 2015.

INTERVENTIONS

Structured patient-centered care and engagement training program and web-based technology including ICU safety checklist, tools to develop shared care plan, and messaging platform. Patient and care partner access to online portal to view health information, participate in the care plan, and communicate with providers.

MEASUREMENTS AND MAIN RESULTS

Primary outcome was aggregate adverse event rate. Secondary outcomes included patient and care partner satisfaction, care plan concordance, and resource utilization. We included 2,105 patient admissions, (1,030 baseline and 1,075 during intervention periods). The aggregate rate of adverse events fell 29%, from 59.0 per 1,000 patient days (95% CI, 51.8-67.2) to 41.9 per 1,000 patient days (95% CI, 36.3-48.3; p < 0.001), during the intervention period. Satisfaction improved markedly from an overall hospital rating of 71.8 (95% CI, 61.1-82.6) to 93.3 (95% CI, 88.2-98.4; p < 0.001) for patients and from 84.3 (95% CI, 81.3-87.3) to 90.0 (95% CI, 88.1-91.9; p < 0.001) for care partners. No change in care plan concordance or resource utilization.

CONCLUSIONS

Implementation of a structured team communication and patient engagement program in the ICU was associated with a reduction in adverse events and improved patient and care partner satisfaction.

Testing Equality in Ordinal Data with Repeated Measurements: A Model-Free Approach

In randomized clinical trials, we often encounter ordinal categorical responses with repeated measurements. We propose a model-free approach with using the generalized odds ratio (GOR) to measure the relative treatment effect. We develop procedures for testing equality of treatment effects and derive interval estimators for the GOR. We further develop a simple procedure for testing the treatment-by-period interaction. To illustrate the use of test procedures and interval estimators developed here, we consider two real-life data sets, one studying the gender effect on pain scores on an ordinal scale after hip joint resurfacing surgeries, and the other investigating the effect of an active hypnotic drug in insomnia patients on ordinal categories of time to falling asleep.

Visualising and modelling changes in categorical variables in longitudinal studies

BACKGROUND

Graphical techniques can provide visually compelling insights into complex data patterns. In this paper we present a type of lasagne plot showing changes in categorical variables for participants measured at regular intervals over time and propose statistical models to estimate distributions of marginal and transitional probabilities.

METHODS

The plot uses stacked bars to show the distribution of categorical variables at each time interval, with different colours to depict different categories and changes in colours showing trajectories of participants over time. The models are based on nominal logistic regression which is appropriate for both ordinal and nominal categorical variables. To illustrate the plots and models we analyse data on smoking status, body mass index (BMI) and physical activity level from a longitudinal study on women's health. To estimate marginal distributions we fit survey wave as an explanatory variable whereas for transitional distributions we fit status of participants (e.g. smoking status) at previous surveys.

RESULTS

For the illustrative data the marginal models showed BMI increasing, physical activity decreasing and smoking decreasing linearly over time at the population level. The plots and transition models showed smoking status to be highly predictable for individuals whereas BMI was only moderately predictable and physical activity was virtually unpredictable. Most of the predictive power was obtained from participant status at the previous survey. Predicted probabilities from the models mostly agreed with observed probabilities indicating adequate goodness-of-fit.

CONCLUSIONS

The proposed form of lasagne plot provides a simple visual aid to show transitions in categorical variables over time in longitudinal studies. The suggested models complement the plot and allow formal testing and estimation of marginal and transitional distributions. These simple tools can provide valuable insights into categorical data on individuals measured at regular intervals over time.

Annual rescreening for alcohol misuse: diminishing returns for some patient subgroups

BACKGROUND

Routine alcohol screening is widely recommended, and Medicare now reimburses for annual alcohol screening. Although up to 18% of patients will screen positive for alcohol misuse, the value of annual rescreening for patients who repeatedly screen negative is unknown.

OBJECTIVE

To evaluate the probability of converting to a positive alcohol screen at annual rescreening among VA outpatients who previously screened negative 2-4 times.

RESEARCH DESIGN

Retrospective cohort study.

SUBJECTS

A total of 179,035 VA outpatients (10,588 women) who previously screened negative on 2 and up to 4 consecutive annual alcohol screens and were rescreened the next year.

MEASURES

AUDIT-C alcohol screening scores (range, 0-12) were obtained from electronic medical record data. The probability of converting to a positive screen (scores: men ≥4; women, ≥3) at rescreening after 2-4 prior negative screens was evaluated overall and across subgroups based on age, sex, and prior negative screen scores (scores: men, 0-3; women, 0-2).

RESULTS

The overall probability of converting to a positive subsequent screen decreased modestly from 3.5% to 1.9% as the number of prior consecutive negative screens increased from 2 to 4, yet varied widely across subgroups based on age, sex, and prior negative screen scores (0.6%-38.7%).

CONCLUSIONS

The likelihood of converting to a positive screen at annual rescreening is strongly influenced by age, sex, and scaled screening scores on prior negative alcohol screens. Algorithms for the frequency of repeat alcohol screening for patients who repeatedly screen negative should be based on these factors. These results may have implications for other routine behavioral health screenings.

Probability and predictors of patients converting from negative to positive screens for alcohol misuse

BACKGROUND

Medicare reimburses providers for annual alcohol screening. However, the benefit of rescreening patients a year after a negative screen for alcohol misuse is unknown. We hypothesized that some subgroups of patients who screen negative would have a very low probability of converting to a positive subsequent screen (e.g., <0.1%), calling into question the value of annual alcohol screening for some patient subgroups.

METHODS

This retrospective cohort study estimated the probability of converting to a positive screen for alcohol misuse a year after a negative screen among outpatients from 30 Veterans Health Administration (VA) medical centers. Alcohol Use Disorders Identification Test-Consumption (AUDIT-C) alcohol screening scores (range 0 to 12 points) from 2004 to 2008 were obtained from electronic health record data. Eligible patients screened negative on their initial screen (AUDIT-C scores 0 to 3 for men; 0 to 2 for women). The main outcome was a positive subsequent screen (AUDIT-C scores ≥4 men; ≥3 women).

RESULTS

Among 21,081 women and 323,913 men who screened negative on an initial screen, 5.4% and 6.0%, respectively, screened positive a year later. The adjusted probability of converting to a positive subsequent screen varied from 2.1 to 38.9% depending on age, gender, and initial negative screen score. Women, older patients, and those with initial AUDIT-C scores of 0 were least likely to a convert to a positive subsequent screen, while younger men with AUDIT-C scores of 3 were most likely to a convert to a positive subsequent screen.

CONCLUSIONS

The probability of a positive subsequent screen varied depending on age, gender, and initial negative screen score but exceeded 2% in all patient subgroups. Annual rescreening appears reasonable for all VA patients who had a negative screen the year prior.

A binning method for analyzing mixed longitudinal data measured at distinct time points

For longitudinal data where the response and time-dependent predictors within each individual are measured at distinct time points, traditional longitudinal models such as generalized linear mixed effects models or marginal models cannot be directly applied. Instead, some preprocessing such as smoothing is required to temporally align the response and predictors. We propose a binning method, which results in equally spaced bins of time. After incorporating binning, traditional models can be applied. The proposed binning approach was applied on a longitudinal hemodialysis study to look for possible contemporaneous and lagged effects between occurrences of a health event (i.e. infection) and levels of a protein marker of inflammation (i.e. C-reactive protein). Both Poisson mixed effects models and zero-inflated Poisson (ZIP) mixed effects models were applied to the subsequent data, and some important biological findings about contemporaneous and lagged associations were uncovered. In addition, a simulation study was conducted to investigate various properties of the binning approach.

A review of multivariate longitudinal data analysis

Repeated observation of multiple outcomes is common in biomedical and public health research. Such experiments result in multivariate longitudinal data, which are unique in the sense that they allow the researcher to study the joint evolution of these outcomes over time. Special methods are required to analyse such data because repeated observations on any given response are likely to be correlated over time while multiple responses measured at a given time point will also be correlated. We review three approaches for analysing such data in the light of the associated theory, applications and software. The first method consists of the application of univariate longitudinal tools to a single summary outcome. The second method aims at estimating regression coefficients without explicitly modelling the underlying covariance structure of the data. The third method combines all the outcomes into a single joint multivariate model. We also introduce a multivariate longitudinal dataset and use it to illustrate some of the techniques discussed in the article.

Quantitative assessment of exposure-response relationships for the efficacy and tolerability of varenicline for smoking cessation

Population exposure-response analyses involving approximately 2,000 cigarette smokers provided an integrated understanding of dose, exposure, patient characteristics, and response relating to the efficacy and tolerability of varenicline for smoking cessation. Full models with a linear function of area under the concentration-time curve at steady state AUC(0-24)(ss) and covariate effects on the baseline probability of response were constructed. Logistic regression results consistently showed that the end-of-treatment abstinence rate increased with increasing varenicline exposure, from 38% at 0.5 mg b.i.d. to 56% at 1 mg b.i.d. (vs. 22% for placebo). Baseline smoking status and age were predictive of smoking cessation, whereas race and gender showed little or no influence. Nausea was the most common adverse event, with an incidence that was gender-related and that increased with varenicline exposure; at a dosage of 1 mg b.i.d. the predicted probability of nausea relative to placebo was 24 vs. 7% in male subjects and 40 vs. 14% in female subjects. The incidence of nausea also showed a decreasing trend with time.

Latent trajectory modelling of multivariate binary data

Latent trajectory analysis is a form of latent class analysis, where the manifest variables are longitudinal measurements of a single outcome. The latent classes may correspond to either constant increasing or decreasing levels of the outcome over time and describe different severity or course of a disease. Extension to multiple outcomes at each time point allows more accurate determination of classes, with classes based on combination of the outcomes, however requiring models which account for both correlation between outcomes and periods. Three models are described for multiple binary outcomes, observed at each time point: a latent class model where all outcomes are considered independent at all time points, a model incorporating random effects for subject only and one incorporating random effects for subject and period. The methods are applied to data on asthma and allergy symptoms in infants, with symptoms recorded at four time points, and it is shown that the incorporation of subject and period heterogeneity results in lower estimates of the number of latent classes.

Dynamic modelling in a study of surgical error management

We demonstrate the use of dynamic longitudinal models to investigate error management in cardiac surgery. Case study data were collected from a multicentre study of the neonatal arterial switch operation (ASO). Information on two types of negative events, or 'errors', observed during surgery, major and minor events, was extracted from case studies. Each event was judged to be recovered from (compensated) or not (uncompensated). The aim of the study was to model compensation given the occurrence of past events within a case. Two models were developed, one for the probability of compensating for a major event and a second model for the probability of compensating for a minor event. Analyses based on dynamic logistic regression models suggest that the total number of preceding minor events, irrespective of compensation status, is negatively related with the ability to compensate for major events. The alternative use of random effects models is investigated for comparison purposes.

Design and methods of the Chronic Kidney Disease in Children (CKiD) prospective cohort study

An estimated 650,000 Americans will have ESRD by 2010. Young adults with kidney failure often develop progressive chronic kidney disease (CKD) in childhood and adolescence. The Chronic Kidney Disease in Children (CKiD) prospective cohort study of 540 children aged 1 to 16 yr and have estimated GFR between 30 and 75 ml/min per 1.73 m2 was established to identify novel risk factors for CKD progression; the impact of kidney function decline on growth, cognition, and behavior; and the evolution of cardiovascular disease risk factors. Annually, a physical examination documenting height, weight, Tanner stage, and standardized BP is conducted, and cognitive function, quality of life, nutritional, and behavioral questionnaires are completed by the parent or the child. Samples of serum, plasma, urine, hair, and fingernail clippings are stored in biosamples and genetics repositories. GFR is measured annually for 2 yr, then every other year using iohexol, HPLC creatinine, and cystatin C. Using age, gender, and serial measurements of Tanner stage, height, and creatinine, compared with iohexol GFR, a formula to estimate GFR that will improve on traditional pediatric GFR estimating equations when applied longitudinally is expected to be developed. Every other year, echocardiography and ambulatory BP monitoring will assess risk for cardiovascular disease. The primary outcome is the rate of decline of GFR. The CKiD study will be the largest North American multicenter study of pediatric CKD.

Continuous Time Markov Models for Binary Longitudinal Data

Longitudinal data usually consist of a number of short time series. A group of subjects or groups of subjects are followed over time and observations are often taken at unequally spaced time points, and may be at different times for different subjects. When the errors and random effects are Gaussian, the likelihood of these unbalanced linear mixed models can be directly calculated, and nonlinear optimization used to obtain maximum likelihood estimates of the fixed regression coefficients and parameters in the variance components. For binary longitudinal data, a two state, non-homogeneous continuous time Markov process approach is used to model serial correlation within subjects. Formulating the model as a continuous time Markov process allows the observations to be equally or unequally spaced. Fixed and time varying covariates can be included in the model, and the continuous time model allows the estimation of the odds ratio for an exposure variable based on the steady state distribution. Exact likelihoods can be calculated. The initial probability distribution on the first observation on each subject is estimated using logistic regression that can involve covariates, and this estimation is embedded in the overall estimation. These models are applied to an intervention study designed to reduce children's sun exposure.

The analysis of asthma control under a Markov assumption with use of covariates

In studies of disease states and their relation to evolution, data on the state are usually obtained at in frequent time points during follow-up. Moreover in many applications, there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution. We developed a continuous-time Markov model with use of time-dependent covariates and a Markov model with piecewise constant intensities to model asthma evolution. Methods to estimate the effect of covariates on transition intensities, to test the assumption of time homogeneity and to assess goodness-of-fit are proposed. We apply these methods to asthma control. We consider a three-state model and we discuss in detail the analysis of asthma control evolution.

Use of a Markov transition model to analyse longitudinal low-back pain data

In a randomized clinical trial to assess the effectiveness of different strategies for treating low-back pain in a managed-care setting, 681 adult patients presenting with low-back pain were randomized to four treatment groups: medical care with and without physical therapy; and chiropractic care with and without physical modalities. Follow-up information was obtained by questionnaires at two and six weeks, six, 12 and 18 months and by a telephone interview at four weeks. One outcome measurement at each follow-up is the patient's self-report on the perception of low-back pain improvement from the previous survey, recorded as 'A lot better,' 'A little better,' 'About the same' and 'Worse.' Since the patient's perception of improvement may be influenced by past experience, the outcome is analysed using a transition (first-order Markov) model. Although one could collapse categories to the point that logistic regression analysis with repeated measurements could be used, here we allow for multiple categories by relating transition probabilities to covariates and previous outcomes through a polytomous logistic regression model with Markov structure. This approach allows us to assess not only the effects of treatment assignment and baseline characteristics but also the effects of past outcomes in analysing longitudinal categorical data.

Statistical methods for repeated qualitative assessments on scales

Assessments of auditory communication are commonly performed with questionnaires or multi-item instruments. The item responses generate ordered categorical data. The aim of the work reported here was to present a statistical approach that takes account of the non-metric properties of data from rating scales for description of multi-item assessments and for evaluation of change in a study concerning the function of and satisfaction with hearing aids. A small data set from an ongoing study at the Ahlsén Research Institute, Orebro University Hospital was used in the worked examples. The use of individual and median group profiles provided an interpretable description of the data. By means of the ranking approach, which ties the ranks to the pairs of data, the systematic group change in hearing function was evaluated separately from the additional individual changes. The use and misuse of parametric statistical methods on ordered categorical data are also discussed.

Vitamin a supplementation of vitamin a deficient measles patients lowers the risk of measles-related pneumonia in zambian children

This is an a posteriori analysis of previously published data to assess whether improving vitamin A (VA) status resolves measles-related pneumonia (MP). Nonhospitalized acute measles patients (2 d of rash onset) had their VA status determined based on the molar ratio of retinol-binding protein to transthyretin (RBP/TTR). Using a cutoff value of </=0.36, indicative of marginal VA deficiency, 82 children were diagnosed as marginally VA deficient and 114 were diagnosed as VA sufficient. At baseline, marginally VA-deficient patients had significantly lower serum retinol and higher serum C-reactive protein concentrations than VA-sufficient children. At the 2-wk follow-up visit, serum retinol and the RBP/TTR ratio were significantly greater in marginally VA-deficient measles patients receiving VA supplements than in those receiving placebo; whereas in VA-sufficient measles patients, retinol increased in those receiving VA supplements or placebo. Concomitantly the odds ratio of unresolved pneumonia in marginally VA-deficient measles patients receiving VA supplements compared with those receiving placebo was 0.20 (95% confidence interval, 0.05-0.71). In conclusion, VA supplements during measles infection improved VA status of VA-deficient children and helped resolve MP, demonstrating the importance of determining VA status when assessing the efficacy of VA supplements.

Complete imputation of missing repeated categorical data: one-sample applications

Longitudinal studies with repeated measures are often subject to non-response. Methods currently employed to alleviate the difficulties caused by missing data are typically unsatisfactory, especially when the cause of the missingness is related to the outcomes. We present an approach for incomplete categorical data in the repeated measures setting that allows missing data to depend on other observed outcomes for a study subject. The proposed methodology also allows a broader examination of study findings through interpretation of results in the framework of the set of all possible test statistics that might have been observed had no data been missing. The proposed approach consists of the following general steps. First, we generate all possible sets of missing values and form a set of possible complete data sets. We then weight each data set according to clearly defined assumptions and apply an appropriate statistical test procedure to each data set, combining the results to give an overall indication of significance. We make use of the EM algorithm and a Bayesian prior in this approach. While not restricted to the one-sample case, the proposed methodology is illustrated for one-sample data and compared to the common complete-case and available-case analysis methods.

The effect of insurance coverage changes on drug utilization in HIV disease

BACKGROUND

Insurance coverage facilitates access to life-saving medications for many patients with HIV disease. Thus, the effects of insurance coverage changes, such as the gain or loss of coverage, may be important in explaining patient access and adherence to the medications used in the treatment of HIV disease.

OBJECTIVES

The study's objective was to examine whether changes in health insurance coverage affect rates of prescription drug use by patients with HIV disease.

METHODS

Data were ascertained from adults participating in a series of up to six interviews as part of the AIDS Costs and Services Utilization Survey (ACSUS). ACSUS was an 18-month panel survey of patients in care for HIV/AIDS at 26 sites located in 10 U.S. cities. Poisson regression analyses with generalized estimating equations were conducted to determine the effects of demographic and socioeconomic variables on the acquisition rate of antiretrovirals, antipneumocystics, and antidepressants. The analytic sample consisted of 1566 respondents who provided 6518 interviews.

RESULTS

Although changes in insurance coverage were common, complete loss of insurance was reported in only 1.5% of the interviews whereas gaining insurance was reported in 3.3% of interviews. Having no coverage was associated with significantly lower rates of antiretroviral (rate ratio [RR], 0.73), antipneumocystic (RR, 0.58) and antidepressant use (RR, 0.31). Gaining insurance coverage was associated with lower antiretroviral (RR, 0.75) and antipneumocystic (RR, 0.70) use whereas losing insurance was associated with lower antiretroviral use (RR, 0.58). In multivariate analyses, these associations remained.

CONCLUSIONS

Changes in health insurance coverage are associated with lower rates of drug use for some medications used by patients with HIV disease.

Analysis of binary outcomes in longitudinal studies using weighted estimating equations and discrete-time survival methods: prevalence and incidence of smoking in an adolescent cohort

Longitudinal studies are increasingly popular in epidemiology. In this tutorial we provide a detailed review of methods used by us in the analysis of a longitudinal (multiwave or panel) study of adolescent health, focusing on smoking behaviour. This example is explored in detail with the principal aim of providing an introduction to the analysis of longitudinal binary data, at a level suited to statisticians familiar with logistic regression and survival analysis but not necessarily experienced in longitudinal analysis or estimating equation methods. We describe recent advances in statistical methodology that can play a practical role in applications and are available with standard software. Our approach emphasizes the importance of stating clear research questions, and for binary outcomes we suggest these are best organized around the key epidemiological concepts of prevalence and incidence. For prevalence questions, we show how unbiased estimating equations and information-sandwich variance estimates may be used to produce a valid and robust analysis, as long as sample size is reasonably large. We also show how the estimating equation approach readily extends to accommodate adjustments for missing data and complex survey design. A detailed discussion of gender-related differences over time in our smoking outcome is used to emphasize the need for great care in separating longitudinal from cross-sectional information. We show how incidence questions may be addressed using a discrete-time version of the proportional hazards regression model. This approach has the advantages of providing estimates of relative risks, being feasible with standard software, and also allowing robust information-sandwich variance estimates.

A randomized design for repeated binary outcomes used to evaluate continued effectiveness of a breast cancer control intervention strategy

The literature has not discussed in detail design and evaluation strategies for the assessment of continued effectiveness of intervention strategies. In this article we present an approach to evaluating continued effectiveness with two repeated binary outcomes that are related to the use of preventive services. We present a two-stage design with independent randomization procedures for each of two successive controlled trials and discuss the implications of the randomization plan for the statistical evaluation. Intervention effectiveness for each year is determined by an adjusted odds ratio that compares the odds of procedure use for those who received the intervention to those who did not. Changes in the two adjusted odds ratios between successive years are assessed within the context of a regressive logistic model. We demonstrate these methods by applying them to the Metropolitan Detroit Project to Reduce Avoidable Mortality from Breast Cancer. In this project, computer-generated physician mammography reminders placed prominently in medical records were used to promote mammography referrals among women visiting primary care clinics during a 2-year intervention period. An assessment of the change in intervention effectiveness as well as an adjusted estimate of the overall intervention effectiveness for the 2 years were obtained from a multivariate regressive logistic model. The advantage of this approach was its potential for reducing bias and producing a balanced comparison between intervention groups during the second year of intervention. This issue was important because previous work indicated that having had a mammogram had a significant impact on subsequent mammography use. An important component in the implementation of this design was an information management system that facilitated doing two randomization procedures efficiently. As information and computer technology advance, and as more sophisticated information systems are used for data management, designs such as these become reasonable alternatives to consider.

Ordinal invariant measures for individual and group changes in ordered categorical data

Subjective judgements of complex variables are commonly recorded as ordered categorical data. The rank-invariant properties of such data are well known, and there are various statistical approaches to the analysis and modelling of ordinal data. This paper focuses on the non-additive property of ordered categorical data in the analysis of change. A rank-invariant non-parametric method of analysis is presented that is valid regardless of the number of response categories. The unique feature of this method is the augmented ranking approach that is related to the joint distribution of paired observations. This approach makes it possible to measure separately the individual order-preserved categorical changes, which are attributable to the group change, and the individual categorical changes that are not consistent with the pattern of group change. The method is applied to analysis of change in a three-point scale and in a visual analogue scale of continuous ordinal responses.

A community-wide promotion of asthma self-management in New Zealand

Asthma affects approximately 9% of young adults in New Zealand, with evidence of an increase in prevalence over recent years. Morbidity and mortality from this condition have caused widespread concern. In response to identified deficiencies in asthma management, initiatives to promote self-management using an asthma action plan were promoted throughout the Canterbury region in 1991 as part of a regional pilot study. A resource kit was prepared and self-management principles were promoted to general practitioners in discussion workshops. A community-wide promotion of the action plan was followed by a process and outcome evaluation. The plan and associated resources were well received by doctors and patients. Seventy-seven percent of doctors responding to a questionnaire had used the plan, and of these, 94% indicated that they would continue to use the plan in the future. Patients who obtained a completed plan experienced a greater reduction in nocturnal waking with asthma and improved self-management skills.

The analysis of binary and categorical data from crossover trials

A review is presented of methods for the analysis of discrete data from crossover trials. The definition and interpretation of the model for the data is used as a central theme. Distinctions are drawn between different types of model, particularly marginal and subject specific. It is seen how much recent methodology for analysing correlated categorical data can be applied successfully to the crossover setting. The current accessibility of each method is considered and the different approaches are illustrated and compared using two examples.

Modelling transitional and joint marginal distributions in repeated categorical data

When a repeated measures endpoint classifies people into several categories, marginal and transitional models provide two distinct approaches for data analysis. Marginal models estimate the probabilities of being in different categories over time. Transitional models estimate the probability of changing between any two given states during follow-up visits. This paper develops transitional and marginal models and applies them to a clinical trial of treatments of opiate addiction. The primary outcome was the presence or absence of opiates in a thrice weekly urine test, administered for 17 weeks. Subjects frequently miss visits, however, and in effect respond in one of three ways to a visit: missing, opiates present or opiates absent. Thus we have three possible states. Our transitional model conditions on the current state and models the transition from state k to one of the other (0, ..., K-1) states using a mutinomial logit model. This model generalizes previous work of Muenz and Rubinstein. Significant covariates in this model are predictive of state changes. Our marginal model views the state at each time point, rather than the transitions, as the primary response. Here we model the probability of being in state k with a multinomial logit model. Correlation within individuals over visits can be handled by applying the approach of Zeger and Liang or the bootstrap. Significant covariates in this model can include more 'global' summaries of a person such as extent of previous opiate use. Both marginal and transitional models are needed to provide a complete description of an individual's behaviour over time since global summaries might not affect transitions. Of particular substantive interest is how the opiate treatments affect both the marginal and transition probabilities.

A comparison of likelihood-based and marginal estimating equation methods for analysing repeated ordered categorical responses with missing data: application to an intervention trial of vitamin prophylaxis for oesophageal dysplasia

The purpose of this research was to develop appropriate methods for analysing repeated ordinal categorical data that arose in an intervention trial to prevent oesophageal cancer. The measured response was the degree of oesophageal dysplasia at 2.5 and 6 years after randomization. An important feature was that some response measurements were missing, and the missingness was not 'completely at random' (MCAR). We show that standard likelihood-based methods and standard methods based on marginal estimating equations yield biased results, and we propose adaptations to both these approaches that yield valid inference under the weaker 'missing at random' (MAR) assumption. On the basis of efficiency calculations, simulation studies of finite sample properties, ease of computation, and flexibility for testing and exploring a range of treatment models, we recommend the adapted likelihood-based approach for problems of this type, in which there are abundant data for estimating parameters.

Siblings’ neonatal mortality risks and birth spacing in Bangladesh

This paper studies the familial association of neonatal mortality in Matlab, Bangladesh and its relationship to birth-spacing effects on mortality. Findings show that familial association is strongest for siblings of adjacent birth orders. Moreover, birth-spacing effects on neonatal mortality are stronger when the preceding child has survived the neonatal period than when it has died. Transitional (Markov), random-effects, and marginal models for correlated data are introduced, and are contrasted in interpretation and technique. Familial association of neonatal mortality can be approximated well by a first-order Markov model using generalized estimating equations (GEE) to allow for higher-order correlation.

Comparison of methods for the analysis of longitudinal interval count data

Longitudinal studies are often concerned with estimating the recurrence rate of a non-fatal event. In many cases, only the total number of events occurring during successive time intervals is known. We compared a mixed Poisson-gamma regression method proposed by Thall and a quasi-likelihood method proposed by Zeger and Liang for the analysis of such data, in the case where the mean was correctly specified, using simulation techniques with large samples. Both methods produced similar standard errors in most situations, except in the case of time-dependent covariates with non-Poisson-gamma data where they were seriously underestimated by the Thall method. A simple method for discriminating between the variance forms of the two methods is described. The findings are applied to the analyses of clinical trials of non-melanoma skin cancer and familial polyposis. This study extends the findings of Breslow concerning variance misspecification in overdispersed Poisson and quasi-likelihood models to the longitudinal setting.

Evaluating the effects of tubal sterilization on menstrual function: selected issues in data analysis

We examined selected issues in data analysis in the Collaborative Review of Sterilization (CREST). CREST is a multicentre, prospective, observational study of women undergoing tubal sterilization. We analysed menstrual function after sterilization in over 5000 women who were enrolled in the period 1978-1983 and followed for 5 years with yearly follow-up interviews. To take into account the dependency among repeated responses from the same individuals, we used the generalized estimating equations (GEE) approach to longitudinal data analysis. Marginal modelling resulted in a statistically significant increase in the odds of menstrual dysfunction at 5 years after tubal sterilization. Transitional modelling produced rates of menstrual dysfunction given a woman's menstrual function at baseline, after adjusting for other baseline characteristics such as method of contraception before sterilization. To examine the direction of the bias that could result from non-random missing data, we refitted our models using imputed values. The models with imputed values showed the same trends as the original models.

Statistical methods for longitudinal and clustered designs with binary responses

Dependent binary response data arise frequently in practice due to repeated measurements in longitudinal studies or to subsampling primary sampling units as in fields such as teratology and ophthalmology. Several classes of approaches have recently been proposed to analyse such repeated binary outcome data. The different classes of approaches measure different effects of covariates on binary responses and address different statistical questions. This article compares the different classes of approaches in terms of parameter interpretation and magnitude, standard errors of model parameters and Wald tests for covariate effects. The results help to clarify the substantive questions which data analysts can address with each approach, as well as why the covariate effects measured by different approaches may be different. Finally, I will provide guidelines to the advantages and disadvantages of alternative approaches for analysing dependent binary responses. Simulations and example data illustrate these findings.

An overview of methods for the analysis of longitudinal data

This paper reviews statistical methods for the analysis of discrete and continuous longitudinal data. The relative merits of longitudinal and cross-sectional studies are discussed. Three approaches, marginal, transition and random effects models, are presented with emphasis on the distinct interpretations of their coefficients in the discrete data case. We review generalized estimating equations for inferences about marginal models. The ideas are illustrated with analyses of a 2 x 2 crossover trial with binary responses and a randomized longitudinal study with a count outcome.

An annotated bibliography of methods for analysing correlated categorical data

This paper provides an annotated bibliography of over 100 articles concerning methods for analysing correlated categorical response data. Most of the papers listed here concern categorical regression models and estimation, with particular emphasis on binary responses. The papers are classified by several characteristics which group them according to common themes. The bibliography serves as a reference of methods for analysts of correlated categorical data, as well as for persons interested in methodologic work in this active area of statistical research.

Alternative approaches to the analysis of binary and categorical repeated measurements

The purpose of this paper is to describe, illustrate, and compare a number of different approaches to the analysis of repeated binary and categorical data. These approaches include empirical generalized least squares and generalized estimating equations, as well as traditional log-linear modeling methods. It is shown that the interpretation of the parameters in the various models depends critically on the type of model fitted. In particular, we contrast the population-averaged and subject-specific models. Two example data sets are used to illustrate the approaches, and throughout we concentrate on methods that can be easily implemented.