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PubMed1987

Extended Mantel-Haenszel estimating procedure for multivariate logistic regression models.

A class of estimating functions is proposed for the estimation of multivariate relative risk in stratified case-control studies. It reduces to the well-known Mantel-Haenszel estimator when there is a single binary risk factor. Large-sample properties of the solutions to the proposed estimating equations are established for two distinct situations. Efficiency calculations suggest that the proposed estimators are nearly fully efficient relative to the conditional maximum likelihood estimator for the parameters considered. Application of the proposed method to family data and longitudinal data, where the conditional likelihood approach fails, is discussed. Two examples from case-control studies and one example from a study on familial aggregation are presented.

Analysis of Variance↗

PubMed1995

Case mix of home health patients under capitated and fee-for-service payment.

OBJECTIVE: We compare case mix of Medicare home health patients under HMO and FFS payment. STUDY DESIGN: A pseudo-experimental design was employed to study case mix using three types of Medicare-certified home health agencies (HHAs): HMO-owned agencies, pure FFS agencies that admit few Medicare HMO patients (less than 5 percent of admissions are Medicare HMO patients), and mixed (or contractual) agencies that admit at least 15 Medicare FFS patients and 15 Medicare HMO patients per month. SAMPLES OF PROVIDERS AND PATIENTS: Random samples of Medicare-aged patients (> or = 65 years) were selected at admission between June 1989 and November 1991 from the 38 study HHAs. Sample sizes by agency type were: 308 patients from 9 HMO-owned agencies; 529 patients from 15 pure FFS agencies; and 381 HMO patients and 414 FFS patients from 14 contractual agencies. DATA: Primary longitudinal data were prospectively collected at admission for all patients on health status indicators, demographics, admission source, and home environment. MEASURES: The most important case-mix measures were functional and physiologic indicators of health status, including (instrumental) activities of daily living ([I]ADLs). Selected indicators of demographic variables, prior location, living situation, characteristics of informal caregivers, mental/behavioral factors, and resource needs were also used. PRINCIPAL FINDINGS: (a) The case mix of Medicare FFS patients compared with Medicare HMO patients was more intense in terms of impairments in ADLs, IADLs, and various physiologic conditions. Pressure ulcers as well as neurological and orthopedic impairments requiring rehabilitation care were also more prevalent among FFS patients. (b) Relative to HMO patients admitted to contractual agencies, HMO patients admitted to HMO-owned agencies were moderately more dependent in ADLs and IADLs. However, only 62 percent of HMO patients admitted to HMO-owned agencies, in contrast to 77 percent of HMO patients admitted to contractual agencies, had been hospitalized during the 30 days prior to home health admission. (c) In all, the case mix of patients receiving care from HMO-owned agencies is more heterogeneous than the case mix of HMO patients receiving care from contractual agencies. CONCLUSIONS: The case-mix (and selected utilization) findings indicate that HMOs use home health care differently than does the FFS sector. The greater diversity of case mix for HMO-owned agencies and the narrower or less diverse case mix that characterizes HMO patients receiving home care on a contractual basis point to the likelihood of cost differences among the two types of HMO patients and FFS patients, and raise the question of possible outcome differences.

Activities of Daily Living↗

PubMedDate not supplied

Rural vs. urban demand for medical imaging personnel.

Although there has been some anecdotal evidence regarding the demand for medical imaging personnel in the hospital setting, few statewide studies have documented the demand for such staff or compared data longitudinally. Using data from the North Carolina Council for Allied Health, the study reported in this article documented mean minimum hourly salaries and mean maximum hourly salaries, vacancy rates and time required to fill vacancies for nuclear medicine technologists, radiographers and ultrasonographers in rural and urban hospitals. Results indicated the vacancy rates were highest for ultrasonographers and lowest for radiographers. There were vacancy differences in rural compared to urban settings and for part-time compared to full-time employees.

Diagnostic Imaging↗

PubMed1993

Some conceptual and statistical issues in analysis of longitudinal psychiatric data. Application to the NIMH treatment of Depression Collaborative Research Program dataset.

Longitudinal studies have a prominent role in psychiatric research; however, statistical methods for analyzing these data are rarely commensurate with the effort involved in their acquisition. Frequently the majority of data are discarded and a simple end-point analysis is performed. In other cases, so called repeated-measures analysis of variance procedures are used with little regard to their restrictive and often unrealistic assumptions and the effect of missing data on the statistical properties of their estimates. We explored the unique features of longitudinal psychiatric data from both statistical and conceptual perspectives. We used a family of statistical models termed random regression models that provide a more realistic approach to analysis of longitudinal psychiatric data. Random regression models provide solutions to commonly observed problems of missing data, serial correlation, time-varying covariates, and irregular measurement occasions, and they accommodate systematic person-specific deviations from the average time trend. Properties of these models were compared with traditional approaches at a conceptual level. The approach was then illustrated in a new analysis of the National Institute of Mental Health Treatment of Depression Collaborative Research Program dataset, which investigated two forms of psychotherapy, pharmacotherapy with clinical management, and a placebo with clinical management control. Results indicated that both person-specific effects and serial correlation play major roles in the longitudinal psychiatric response process. Ignoring either of these effects produces misleading estimates of uncertainty that form the basis of statistical tests of hypotheses.

Analysis of Variance↗

PubMed1998

Does practice make perfect? Examining the relationship between hospital surgical volume and outcomes for hip fracture patients in Quebec.

OBJECTIVES: Most tests of the practice-makes-perfect hypothesis have used cross-sectional data, which reveal that patients receiving surgery in high-volume hospitals tend to experience better postsurgery outcomes. This study uses longitudinal data to explicitly examine whether any given hospital's patient outcomes change as its surgery volume varies with time. METHODS: Longitudinal data from all hospitals conducting hip fracture surgery in Quebec between 1990 and 1993 were used to examine the relationship between surgery volume and outcomes. The longitudinal data allowed volume to be measured using the actual number of surgeries performed by the admitting hospital in the 12 months before a patient's surgery. Determinants of postsurgery length of stay were assessed using ordinary least squares regression, and the explanators of inpatient mortality were identified using logistic regression. The regressions included fixed effects (hospital-specific dummy variables) to control for systematic differences in outcomes across hospitals that persist with time. Therefore, the coefficient on hip fracture surgery volume in the regression models captured differences in outcomes that were attributable to changes in surgery volume within hospitals with time. RESULTS: The fixed effects were significant explanators of both postsurgery length of stay and inpatient mortality, indicating that there were significant differences in outcomes across hospitals that persisted with time. In regressions that excluded the fixed effects, the coefficient on surgery volume was significant. In contrast, the coefficient on surgery volume was insignificant when the fixed effects were included. CONCLUSIONS: Longitudinal data revealed that after controlling for differences in hospital outcomes that were fixed with time, hospitals performing more surgeries in one period than in another experienced no significant improvement in outcomes. These results do not support the "practice makes perfect" hypothesis. The volume-outcome relationship for hip fracture patients thus appears to reflect fixed differences in quality between high-volume and low-volume hospitals.

Comorbidity↗

PubMed1990

A comparative study of two statistical models for the analysis of binary data from longitudinal studies.

This study extensively compares two statistical models for the analysis of binary data from longitudinal studies. The first model was proposed by Zeger, Liang, and Self, which was abbreviated as ZLS model and another model was proposed by Origasa. The comparison focuses on both analytical and statistical view-points. The first discusses a type of the models and the second evaluates the effect from model misspecification by stimulation, assuming that the ZLS model is true.

Computer Simulation↗

PubMed2006

Estimation in regression models for longitudinal binary data with outcome-dependent follow-up.

In many observational studies, individuals are measured repeatedly over time, although not necessarily at a set of pre-specified occasions. Instead, individuals may be measured at irregular intervals, with those having a history of poorer health outcomes being measured with somewhat greater frequency and regularity. In this paper, we consider likelihood-based estimation of the regression parameters in marginal models for longitudinal binary data when the follow-up times are not fixed by design, but can depend on previous outcomes. In particular, we consider assumptions regarding the follow-up time process that result in the likelihood function separating into two components: one for the follow-up time process, the other for the outcome measurement process. The practical implication of this separation is that the follow-up time process can be ignored when making likelihood-based inferences about the marginal regression model parameters. That is, maximum likelihood (ML) estimation of the regression parameters relating the probability of success at a given time to covariates does not require that a model for the distribution of follow-up times be specified. However, to obtain consistent parameter estimates, the multinomial distribution for the vector of repeated binary outcomes must be correctly specified. In general, ML estimation requires specification of all higher-order moments and the likelihood for a marginal model can be intractable except in cases where the number of repeated measurements is relatively small. To circumvent these difficulties, we propose a pseudolikelihood for estimation of the marginal model parameters. The pseudolikelihood uses a linear approximation for the conditional distribution of the response at any occasion, given the history of previous responses. The appeal of this approximation is that the conditional distributions are functions of the first two moments of the binary responses only. When the follow-up times depend only on the previous outcome, the pseudolikelihood requires correct specification of the conditional distribution of the current outcome given the outcome at the previous occasion only. Results from a simulation study and a study of asymptotic bias are presented. Finally, we illustrate the main results using data from a longitudinal observational study that explored the cardiotoxic effects of doxorubicin chemotherapy for the treatment of acute lymphoblastic leukemia in children.

Adolescent↗

PubMed2005

Summarizing data through a piecewise linear growth curve model.

Most of the research in clinical trials is based on longitudinal designs, which involve repeated measurements of a variable of interest. Such designs are very powerful, both statistically and scientifically. Recent advances in statistical theory and software development incorporate the covariance structures such as unstructured, compound symmetry, auto-regressive and random effects, etc., for analysing longitudinal data. Hathaway et al. propose a technique for summarizing longitudinal data using linear growth curve model and establish that the number of summary statistics is fixed as four irrespective of the length of study. In this paper, we develop a procedure for analysing the longitudinal data through a piecewise linear growth curve model on the lines of Hathaway et al. Under different covariance structures, the linear model is fitted for Leprosy data and the residual sum of squares computed. Goodness of fit has also been considered for various models. In order to prove that the proposed method is robust and better than the others in terms of goodness of fit, simulation studies are carried out and the results presented.

Biometry↗

PubMed1979

Analysis of longitudinal twin data. Basic model and applications to physical growth measures.

A formal model is presented for the analysis of longitudinal twin data, based on the underlying analysis-of-variance model for repeated measures. The model is developed in terms of the expected values for the variance components representing twin concordance, and the derivation is provided for computing within-pair (intraclass) correlations, and for estimating the percent of variance explained by each component. The procedures are illustrated with physical growth data extending from birth to six years, and concordance estimates are obtained for average size and for the pattern of spurts and lags in growth. A test of significance is also described for comparing monozygotic twins with dizygotic twins. The procedures are particularly useful for assessing chronogenetic influences on development, especially whether the episodes of acceleration and lag occur in parallel for genetically matched twins. The model may be employed with psychological data also.

Analysis of Variance↗

PubMedDate not supplied

What can go wrong when you assume that correlated data are independent: an illustration from the evaluation of a childhood health intervention in Brazil.

The key analytical challenge presented by longitudinal data is that observations from one individual tend to be correlated. Although longitudinal data commonly occur in medicine and public health, the issue of correlation is sometimes ignored or avoided in the analysis. If longitudinal data are modelled using regression techniques that ignore correlation, biased estimates of regression parameter variances can occur. This bias can lead to invalid inferences regarding measures of effect such as odds ratios (OR) or risk ratios (RR). Using the example of a childhood health intervention in Brazil, we illustrate how ignoring correlation leads to incorrect conclusions about the effectiveness of the intervention.

Age Factors↗

PubMed2000

Ante-dependence modeling in a longitudinal study of periodontal disease: the effect of age, gender, and smoking status.

BACKGROUND: It is generally accepted that periodontal disease progresses by a series of bursts that are interspersed by periods of stability or even gain of attachment. In order to analyze longitudinal data on a patient's disease experience, it is necessary to use models which accommodate serial dependence. Ante-dependence between the results of a series of periodontal examinations over time can be modeled using a Markov chain. This model describes temporal changes in patients' levels of disease in terms of transition probabilities, which allow for both regression and progression of the disease. The aim of the present study was to demonstrate the use of a Markov chain model to analyze data from a longitudinal study investigating the progression of periodontal disease in an adult population. METHODS: The study population consisted of 504 volunteers; however, only 456 were included in the analysis because the remaining 48 subjects did not give consecutive data. Subjects were examined at baseline, 6 months, and 1, 2, and 3 years. Probing depths (PD) were recorded using an automated probe. Disease was defined as four or more sites with PD > or = 4 mm. Markov chain modeling was used to determine the effect of age, gender, and smoking on the natural progression and regression (healing) of periodontal disease. RESULTS: Smoking and increasing age had no effect on the progression of disease in this population, but did have a significant effect (P values < or = 0.05) in reducing the regression of disease; i.e., their effect on disease appears to be inhibition of the natural healing process. Gender had no significant effects. CONCLUSIONS: These results demonstrate how ante-dependence modeling of longitudinal data can reveal effects that may not be immediately apparent from the data, with smoking and increasing age being seen to inhibit the healing process rather than promote disease progression.

Adolescent↗

PubMed2004

Sensitivity analysis of longitudinal binary data with non-monotone missing values.

This paper highlights the consequences of incomplete observations in the analysis of longitudinal binary data, in particular non-monotone missing data patterns. Sensitivity analysis is advocated and a method is proposed based on a log-linear model. A sensitivity parameter that represents the relationship between the response mechanism and the missing data mechanism is introduced. It is shown that although this parameter is identifiable, its estimation is highly questionable. A far better approach is to consider a range of plausible values and to estimate the parameters of interest conditionally upon each value of the sensitivity parameter. This allows us to assess the sensitivity of study's conclusion to assumptions regarding the missing data mechanism. The method is applied to a randomized clinical trial comparing the efficacy of two treatment regimens in patients with persistent asthma.

Adrenal Cortex Hormones↗

PubMed1991

Sources of variation in longitudinal assessment of maximal aerobic power in teenage boys and girls: the Amsterdam Growth and Health Study.

Maximal oxygen uptake (VO2 max), generally accepted as a valid method for measuring state and change of aerobic fitness, was repeatedly measured in 93 males and 107 females 5 times over a period of 8 years. A direct measurement was made using a treadmill running test with constant speed (8 km/hr) and increasing slope. Oxygen uptake was analyzed continuously by an open-circuit technique. The reproducibility of VO2 max estimated from interperiod correlations resulted in high test-retest correlations of approximately 0.9 in both males and females. Inspection of the longitudinal data from the multiple-longitudinal design with four measurements in three cohorts did not reveal confounding effects, such as time of measurement effects, cohort effects, and drop-out effects. A comparison of the longitudinal data evaluated over four years with data from a comparable control group that was measured once during the four-year period also failed to show any testing effects. In 40% of the males and 50% of the females no leveling-off in VO2 max could be demonstrated; that is, there was an increase of more than 150 ml in the last stage of running. A comparison of subjects who showed leveling-off with those who showed no leveling-off supports the idea that in the age range 12-23 years leveling-off is not a prerequisite for reaching a true VO2 max. Repeated measurement of VO2 max, using a maximal running test on a treadmill appears to be a reliable method to describe the individual development of aerobic fitness in males and females in the age range 12-23 years.

Adolescent↗

PubMed2005

Non-parametric paired two-sample tests for censored survival data incorporating longitudinal covariate information.

In this manuscript, we present non-parametric two-sample tests for paired censored survival data incorporating longitudinal covariate information. These tests take advantage of information collected at baseline and post-baseline to provide efficiency gains when censoring is uninformative. Additionally, these methods adjust for potential bias from informative censoring that is captured by the baseline and longitudinal covariates. Finite sample properties are investigated with simulation, and we illustrate methodology with an example from the Early Treatment Diabetic Retinopathy Study.

Computer Simulation↗

PubMed2002

Performance of weighted estimating equations for longitudinal binary data with drop-outs missing at random.

The generalized estimating equations (GEE) approach is commonly used to model incomplete longitudinal binary data. When drop-outs are missing at random through dependence on observed responses (MAR), GEE may give biased parameter estimates in the model for the marginal means. A weighted estimating equations approach gives consistent estimation under MAR when the drop-out mechanism is correctly specified. In this approach, observations or person-visits are weighted inversely proportional to their probability of being observed. Using a simulation study, we compare the performance of unweighted and weighted GEE in models for time-specific means of a repeated binary response with MAR drop-outs. Weighted GEE resulted in smaller finite sample bias than GEE. However, when the drop-out model was misspecified, weighted GEE sometimes performed worse than GEE. Weighted GEE with observation-level weights gave more efficient estimates than a weighted GEE procedure with cluster-level weights.

Computer Simulation↗

PubMed2005

Reliability in multi-site structural MRI studies: effects of gradient non-linearity correction on phantom and human data.

Longitudinal and multi-site clinical studies create the imperative to characterize and correct technological sources of variance that limit image reproducibility in high-resolution structural MRI studies, thus facilitating precise, quantitative, platform-independent, multi-site evaluation. In this work, we investigated the effects that imaging gradient non-linearity have on reproducibility of multi-site human MRI. We applied an image distortion correction method based on spherical harmonics description of the gradients and verified the accuracy of the method using phantom data. The correction method was then applied to the brain image data from a group of subjects scanned twice at multiple sites having different 1.5 T platforms. Within-site and across-site variability of the image data was assessed by evaluating voxel-based image intensity reproducibility. The image intensity reproducibility of the human brain data was significantly improved with distortion correction, suggesting that this method may offer improved reproducibility in morphometry studies. We provide the source code for the gradient distortion algorithm together with the phantom data.

Calibration↗

PubMedDate not supplied

Review of guidelines and literature for handling missing data in longitudinal clinical trials with a case study.

Missing data in clinical trials are inevitable. We highlight the ICH guidelines and CPMP points to consider on missing data. Specifically, we outline how we should consider missing data issues when designing, planning and conducting studies to minimize missing data impact. We also go beyond the coverage of the above two documents, provide a more detailed review of the basic concepts of missing data and frequently used terminologies, and examples of the typical missing data mechanism, and discuss technical details and literature for several frequently used statistical methods and associated software. Finally, we provide a case study where the principles outlined in this paper are applied to one clinical program at protocol design, data analysis plan and other stages of a clinical trial.

Clinical Trials as Topic↗

PubMed2004

Regression models for unbalanced longitudinal ordinal data: computer software and a simulation study.

A computer program GGOREX in the form of a SAS macro is developed for the analysis of longitudinal ordinal data. It is extended from GEECAT and GEEGOR developed by Williamson, Lipsitz and Kim in their paper in 1999. An illustrative example with some preliminary data from a study conducted by the National Institute of Child Health and Human Development and the University of Alabama at Birmingham is given. Another set of computer programs is developed to make it possible to conduct a simulation study to validate the GGOREX procedure in a finite sample. A simple computer program in FORTRAN using the IMSL software library is developed to solve for the probability distribution of the longitudinal ordinal responses according to the correlation specification.

Computer Simulation↗