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Partly conditional survival models for longitudinal data.

It is common in longitudinal studies to collect information on the time until a key clinical event, such as death, and to measure markers of patient health at multiple follow-up times. One approach to the joint analysis of survival and repeated measures data adopts a time-varying covariate regression model for the event time hazard. Using this standard approach, the instantaneous risk of death at time t is specified as a possibly semi-parametric function of covariate information that has accrued through time t. In this manuscript, we decouple the time scale for modeling the hazard from the time scale for accrual of available longitudinal covariate information. Specifically, we propose a class of models that condition on the covariate information through time s and then specifies the conditional hazard for times t, where t > s. Our approach parallels the "partly conditional" models proposed by Pepe and Couper (1997, Journal of the American Statistical Association 92, 991-998) for pure repeated measures applications. Estimation is based on the use of estimating equations applied to clusters of data formed through the creation of derived survival times that measure the time from measurement of covariates to the end of follow-up. Patient follow-up may be terminated either by the occurrence of the event or by censoring. The proposed methods allow a flexible characterization of the association between a longitudinal covariate process and a survival time, and facilitate the direct prediction of survival probabilities in the time-varying covariate setting.

Acquired Immunodeficiency Syndrome↗

Use of ultrasound longitudinal data in the diagnosis of abnormal fetal growth.

Normal ranges for biparietal diameter (BPD), head circumference (HC), abdominal circumference (AC), and femur length (FL) were established from longitudinal data of singleton pregnancies of Arabian mothers. The data were used to develop a normogram of fetal "growth rate" for each parameter. It is suggested that a normogram of "fetal growth" is of less variance than absolute measurements and could be more useful in the early identification of growth abnormalities than absolute fetal measurements.

Female↗

A stochastic model of malaria transition rates from longitudinal data: considering the risk of "lost to follow-up".

A model, using stochastic processes, is developed to estimate some epidemiological parameters of malaria in a homogeneous population from longitudinal data. Assessments of transition probabilities from one state of health to the other are made taking "lost to follow-up" as a competing risk. The model is based on the assumptions that individuals are transferred at constant rate between states, and only one transition is possible between two consecutive surveys. It shows a good fit to the observed data; the model is simple to understand and can easily be used if computer facilities are not available.

Epidemiologic Methods↗

Specific language impairment as a maturational lag: evidence from longitudinal data on language and motor development.

Longitudinal language-test data on 87 language-impaired children assessed at the ages of four, 4 1/2 and 5 1/2 years were converted to age-equivalent scores to compare the rates of development of children who recover from early language delay with those who have more persisting problems. On most measures, over the 18-month period all the children progressed by about 18 months. Thus although children with good and poor outcomes were distinguished in terms of initial level of performance, they did not differ in rate of progress. Speed on a peg-moving task was closely related to language performance. Children who had a good outcome after early language delay had significantly impaired scores at four years, but subsequently were indistinguishable from a control group. Quantitative but not qualitative differences in peg-moving performance were found for children with good and poor outcomes. No association was found between presumptive aetiological factors and language or pegboard performance. These findings are interpreted in terms of a theory which attributes specific language impairment to a maturational lag in neurological development.

Child, Preschool↗

Perceived smoking norms, socioenvironmental factors, personal attitudes and adolescent smoking in China: a mediation analysis with longitudinal data.

PURPOSE: To gather information on inter-relationships among risk factors affecting adolescent smoking for tobacco control in China, the world's largest tobacco producer and consumer. METHOD: Longitudinal data were collected six months apart in 2003 from 813 students in grades 7, 8, 10, and 11 from two schools in Beijing, China. Linear regression was used to assess both the direct effect from predictor variables (smoking among influential others, pro-tobacco media, and attitudes toward smoking) on cigarette use and the indirect effect mediated through the perceived smoking norms (percentage of smokers among peers). RESULTS: Among the 803 subjects (mean age of 15.5 years, SD = 1.7; 52.1% female), 18.3% of males and 1.7% of females smoked in the past 30 days. Smoking among influential others (best friends, father, mother, male teachers, female teachers, and adults in general) and perceived positive psychological and social rewards from smoking at baseline were associated with number of cigarettes smoked at follow-up, whereas exposure to pro-tobacco media was not significantly associated with smoking. The mediated effect was greater for adult smoking (70% to 90%) than for best friend smoking (11% to 16%). CONCLUSION: Smoking among influential others and attitudes toward smoking influence adolescent smoking both directly and indirectly. The finding of the indirect effect mediated through perceived smoking norms expands our knowledge on smoking etiology. Effective adolescent smoking intervention programs in China need to include a component targeting adult smoking to reduce perceived smoking norms.

Adolescent↗

Structural equation modeling with longitudinal data: strategies for examining group differences and reciprocal relationships.

This article describes the use of structural equation modeling with latent variables to examine group differences and test competing models about cause-effect relationships in passive longitudinal designs. This approach is compared with several other statistical methods including analysis of cross-lagged panel correlations, regression analysis, and path analysis. The mechanics and advantages of structural equation modeling are illustrated using an example based on a 3-wave longitudinal study of adolescents' alcohol use. Within this example, the generalizability of the measurement model and structural model are assessed across gender and time, and competing models about the causes and consequences of adolescents' alcohol use are tested. The article concludes with a discussion of some of the strengths and limitations of using structural equation modeling with longitudinal data.

Adolescent↗

The analysis of longitudinal data using mixed model L-splines.

L-splines are a large family of smoothing splines defined in terms of a linear differential operator. This article develops L-splines within the context of linear mixed models and uses the resulting mixed model L-spline to analyze longitudinal data from a grassland experiment. In the spirit of time-series analysis, a periodic mixed model L-spline is developed, which partitions data into a smooth periodic component plus smooth long-term trend.

Biomass↗

Analysis of interval-censored longitudinal data with application to onco-haematology.

The analysis of repeated measurements on a biomarker, either alone or jointly with the analysis of time to the event of interest, is an area of active research. Nevertheless, we are not yet able to deal in complete generality with these complex data, which frequently consist of error-prone, sparse and intermittent values. In many cancer studies, they arise in the framework of clinical trials and thus their relationship with prognosis is a primary focus. In such a setting, the Cox model is regarded as the standard technique for analysis. The aim of this work is to illustrate an alternative approach to the analysis of studies in which the biomarker values are complicated by interval censoring and an event occurs when the biomarker itself passes a certain threshold. We propose a linear mixed model with a Gaussian stochastic process that allows for interval-censored data and can be used both to track the biomarker trajectory and to estimate the probability of event occurrence. It is developed within the classic approach to longitudinal data analysis that was previously adapted for left-censored data, only. We apply this method to a study on the minimal residual disease (MRD) in childhood leukaemia. MRD is an interval-censored measurement of residual leukaemic cells that was scheduled at 9 time-points during treatment. The aim is to investigate the relationship between MRD and the disease process. Relapse, the event of interest, may conveniently be represented as MRD over a pre-defined threshold. Our focus is on modelling the probability of relapse conditional on MRD observed prior to it. Results show that the approach is promising as it allows proper description of the data, while maintaining flexibility of modelling, feasibility of computations and interpretability of results.

Biomarkers↗

Measurement and explanation of socioeconomic inequality in health with longitudinal data.

This paper presents a method to compare indices of inequality in health that are based on short-run and long-run measures of health and income. For pure health inequality (as measured by the Gini coefficient) and income-related health inequality (as measured by the concentration index), we show how measures derived from longitudinal data can be related to cross section Gini and concentration indices that have been typically reported in the literature to date, along with measures of health mobility inspired by the literature on income mobility. We also show how these measures of mobility can be usefully decomposed into the contributions of different factors. We apply these methods to investigate the degree of income-related mobility in the GHQ measure of psychological well-being in the first nine waves of the British Household Panel Survey (BHPS). This reveals that dynamics increase the absolute value of the concentration index of GHQ on income by 15%, or 1.7% per year on average, for men, and 5%, or 0.6% per year, for women.

Cross-Sectional Studies↗

A model-based approach to estimate the AIDS-free time distribution in homosexual men using longitudinal data.

A model-based approach is developed to estimate the distribution of time from seroconversion to diagnosis with acquired immunodeficiency syndrome (AIDS) as a function of selected time-dependent covariates. The approach is applied to longitudinal data collected over 4 years of follow-up from 450 men seropositive for the human immunodeficiency virus (90 AIDS cases) and 62 seroconverters (nine AIDS cases) participating in the Chicago part of the Multicenter AIDS Cohort Study. Because of the periodic nature of monitoring, the seroconversion time is interval-censored for seroconverters and left-censored for seroprevalent cohort members; the end-point is right-censored for 413 individuals. Since serological monitoring is not continuous but only at regularly scheduled visit times, a model for the discrete hazard rate (DHR) is proposed that is a generalized linear model that relates the DHR to the covariate history through the complementary log-log link. Classification trees are used for preliminary screening of covariates to identify predictors of AIDS that should be incorporated into the DHR model. The missing seroconversion times for all men are imputed 100 times to obtain 100 completed datasets from which the parameters of the DHR are then estimated using the maximum-likelihood method. The final DHR model includes the following infection progression (marker) variables: CD4%, hemoglobin, p24 antigen, and CD4% x p24 antigen interaction. Using this DHR model, the discrete survival distribution of AIDS-free time is estimated for the given population. The jackknife procedure is used to assess the precision of the estimated survival distribution.

Acquired Immunodeficiency Syndrome↗

Effect of prednisone and hydroxychloroquine on coronary artery disease risk factors in systemic lupus erythematosus: a longitudinal data analysis.

PURPOSE: To determine the effect of prednisone dose and hydroxychloroquine dose on the coronary artery disease risk factors serum cholesterol level, mean arterial blood pressure, and weight in patients with systemic lupus erythematosus. PATIENTS AND METHODS: A longitudinal cohort study of 264 patients with systemic lupus erythematosus was conducted. For all patients in the cohort, serum cholesterol, mean arterial pressure, weight, prednisone dose, hydroxychloroquine dose, and other potential confounding variables were recorded at each visit. Regression analysis appropriate for longitudinal data was used to assess the effect of prednisone on serum cholesterol and mean arterial pressure. To assess the effect of prednisone on weight, patients' weights were compared 90 days before and after a 10-mg or 20-mg increase in prednisone. RESULTS: A total of 3,027 patient visits were analyzed. In the regression model for serum cholesterol, a change in prednisone dose of 10 mg was associated with a change in cholesterol of 7.5 +/- 1.46 (SE) mg% after adjustment for the other significant variables in the model, including sex, race, hydroxychloroquine dose, and proteinuria. In the regression model for hydroxychloroquine, the 200-mg and the 400-mg dose were both associated with lower serum cholesterol (8.9 +/- 3.44 SE mg%). In the regression model for mean arterial blood pressure, a 10-mg change in prednisone dose led to a change in mean arterial blood pressure of 1.1 mm Hg after adjustment for age, weight, and antihypertensive drug use. A 10-mg increase in prednisone dose was associated with a mean weight change of 5.50 +/- 1.23 (SE) lb. CONCLUSIONS: Changes in prednisone dose led to definable changes in risk factors for coronary artery disease, even after adjustment for other variables known to affect these risk factors. According to longitudinal regression analysis, hydroxychloroquine therapy was associated with lower serum cholesterol.

Adult↗

Testing for omitted variables and non-linearity in regression models for longitudinal data.

When fitting regression models to investigate the relationship between an outcome variable and independent variables of primary interest, there is often concern whether omitted variables or assuming a different functional relationship could have changed the conclusion or interpretation of the results. In longitudinal studies of aging, the concern with omitted variables is well known in the context of cohort and period effects, which refer to unmeasured variables systematically related to the individual's year of birth and secular trends in outcome, respectively. We present and compare three approaches to detecting omitted confounders and non-linearity in the random effects model for longitudinal data (Laird and Ware, 1982) with random slope and intercept across individuals. The first approach compares simple unweighted within and between regression coefficients, the second is the Hausman specification test for regression models, and the third approach involves testing directly the significance of functions of individual specific covariate means means i, in the random effects regression model. This last approach is motivated by the models that arise when cohort or period effects are ignored. We compare the three approaches, and illustrate their application.

Analysis of Variance↗

Binary partitioning for continuous longitudinal data: categorizing a prognostic variable.

We investigate a binary partitioning algorithm in the case of a continuous repeated measures outcome. The procedure is based on the use of the likelihood ratio statistic to evaluate the performance of individual splits. The procedure partitions a set of longitudinal data into two mutually exclusive groups based on an optimal split of a continuous prognostic variable. A permutation test is used to assess the level of significance associated with the optimal split, and a bootstrap confidence interval is obtained for the optimal split.

Adolescent↗

Transitions to mobility difficulty associated with lower extremity osteoarthritis in high functioning older women: longitudinal data from the Women's Health and Aging Study II.

OBJECTIVE: To assess the impact of lower extremity osteoarthritis (OA) on transitions to mobility difficulty, and to assess the influence of pain, excess weight, and quadriceps strength on these transitions. METHODS: We analyzed longitudinal data acquired from 199 participants in the Women's Health and Aging Study II (ages 70-79 years) who initially reported no lower extremity limitation (e.g., difficulty walking one-quarter mile) or difficulty in activities of daily living (ADL; e.g., transferring). Prevalent lower extremity OA was determined from validated algorithms encompassing multiple data sources. Markov transition models were created to analyze the first transition from no difficulty at baseline to lower extremity limitations, ADL difficulty, or both 18, 36, and 72 months later. RESULTS: Compared with women without OA (n = 140), a higher proportion of women with lower extremity OA (n = 59) initially reported pain on most days and more severe pain while walking (P < 0.05). Women with OA were also heavier, with a higher proportion being obese or overweight (P < 0.001). Lower extremity OA, higher body mass index, and lower knee extensor strength independently increased the risk of transition to combined lower extremity and ADL difficulty first over 72 months. CONCLUSION: Lower extremity OA increased the likelihood of developing difficulty in both lower extremity tasks and ADL over 72 months in a cohort of initially high functioning older women. Two modifiable factors, higher relative weight and lower knee extensor strength, substantially impacted these transitions, and therefore warrant increased attention in the management of lower extremity OA.

Activities of Daily Living↗

Determinants of quality of life changes among long-term cardiac transplant survivors: results from longitudinal data.

BACKGROUND: Cross-sectional analyses have identified significant associations between quality of life (QOL), and comorbidities and adverse effects in cardiac transplant recipients. However, little is known about factors that influence changes in QOL over time. This study examines both cross-sectional and longitudinal data from long-term survivors to identify factors that affect differences in QOL among recipients and individual changes in QOL during a 1-year period. METHODS: Self-selected enrollees completed questionnaires, including QOL scales, at 3-month intervals. Repeated measures multiple regression analysis was used to examine the association between the QOL scales and comorbidities, adverse effects, and compliance measures, controlling for other factors. RESULTS: We included 569 participants in the analysis, with a mean time since transplantation of 8.6 years. Cross-sectional results showed that the number of comorbidities, treatment non-compliance, and several adverse effects were associated with low QOL. In longitudinal results, waiting to take medications and taking less medication because of lifestyle restrictions were associated with decreases in QOL over time. Hair loss, changes in face shape, and decreased sexual interest or ability also had the largest adverse effects on changes in QOL. CONCLUSIONS: These findings provide new opportunities for interventions to address factors related to decreases in QOL. Clinicians should actively solicit information about compliance with medication regimens. In addition, information about the adverse effects of medications should be considered when making therapeutic decisions.

Adult↗

Stature and body weight growth during adolescence based on longitudinal data of Japanese children born during World War II.

Longitudinal survey data of stature and body weight from age 7 to 17 were obtained for 100 boys and 100 girls during World War II. The growth rates and the average annual increments were compared with those of children born after the war. Growth attained at age 7 as a percentage of that at age 17 is larger in children of the control group, presumably as a result of an improved environment affecting the growth increment. The age at maximum velocity is six months to one year earlier for the current group of children. Although the maximum velocities for both items and sexes are nearly the same in the groups compared, the total increments are larger in the current group of children. Age, distance, and maximum velocity at adolescent growth spurt were obtained for each child. The mean values were compared according to growth patterns and growth attained at age 7. The "increasing type" growth group has the highest velocity at the greatest distance and the oldest age for stature. Children who were taller or heavier at age 7 have velocity peaks with greater distances.

Adolescent↗

A new nonparametric technique for constructing percentiles and normal ranges for growth curves determined from longitudinal data.

A new nonparametric method is proposed for the construction of percentile curves and normal ranges which can be used to classify an individual's growth, velocity, and acceleration of growth dynamically over a time interval selected for its biological importance. Although the procedure requires longitudinal data, it is not necessary that all subjects be measured at identical times. Unlike classic static methods it does not provide percentile curves that are typical of no one. The median curve is the actual curve of the most "central" individual. The method is applicable to growth curves of any form with a general computer program already available for many forms. The technique is demonstrated for growth in weight curves smoothed by high degree polynomials.

Adolescent↗

Polynomials with asymptotes for longitudinal data.

I use Laguerre polynomials to model growth curves or time--response curves known to approach an asymptote as time approaches infinity. An example is with measurements on a variable or variables from subjects recovering from surgery. These variables can often vary in a non-monotonic fashion for which a functional form of the curve is unknown. Using a longitudinal data mixed model, one can include in the model random subject effects, within-subject serial correlation and fixed or time varying covariates. I present two examples that involve groups of subjects recovering from surgery.

Anterior Cruciate Ligament↗