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PubMed2006

Statistical analysis of longitudinal psychiatric data with dropouts.

Longitudinal studies are used in psychiatric research to address outcome changes over time within and between individuals. However, because participants may drop out of a study prematurely, ignoring the nature of dropout often leads to biased inference, and in turn, wrongful conclusions. The purpose of the present paper is: (1) to review several dropout processes, corresponding inferential issues and recent methodological advances; (2) to evaluate the impact of assumptions regarding the dropout processes on inference by simulation studies and an illustrative example using psychiatric data; and (3) to provide a general strategy for practitioners to perform analyses of longitudinal data with dropouts, using software available commercially or in the public domain. The statistical methods used in this paper are maximum likelihood, multiple imputation and semi-parametric regression methods for inference, as well as Little's test and index of sensitivity to nonignorability (ISNI) for assessing statistical dropout mechanisms. We show that accounting for the nature of the dropout process influences results and that sensitivity analysis is useful in assessing the robustness of parameter estimates and related uncertainties. We conclude that recording the causes of dropouts should be an integral part of any statistical analysis with longitudinal psychiatric data, and we recommend performing a sensitivity analysis when the exact nature of the dropout process cannot be discerned.

Antidepressive Agents↗

PubMed1991

Longitudinal Gompertzian analysis of stomach cancer mortality in the U.S., 1962-1987: a thermodynamic analogy of its declining mortality.

Age-adjusted mortality rates for stomach cancer (SC) in the United States from 1962 to 1987 were subjected to longitudinal Gompertzian analysis. Age-adjusted SC mortality rate distributions between age 50 and 85 years were highly Gompertzian for each and every year for both men and women. The environmental 'temperature' or intensity factor declined (improved) 1.55-fold for men and 2.04-fold for women in 1987 as compared to 1962. If the environmental 'pressure' or frequency factor had remained constant, the age at the theoretical common intersect point would have been 56.0 years for men and 80.0 years for women and overall SC mortality would have increased. However, between 1962 and 1987, non-age-standardized annual crude SC mortality rates decreased 46.8% for men and 44.0% for women. The thermodynamic analogy for this apparent discrepancy is that the environmental 'pressure' factor has not remained constant, but rather declined 51.7% for men and 60.9% for women between 1962 and 1987. This suggests that the overall frequency of environmental challenges that contribute to SC mortality has become significantly reduced.

Age Factors↗

PubMed1995

Heterosexual transmission of HIV analysed by generalized estimating equations.

A longitudinal analysis of a partner study is compared with a cross-sectional analysis which identify behavioural and biological risk factors for heterosexual transmission of HIV. Using generalized estimating equations (GEEs) a random effects logistic model is used for the longitudinal analysis. These approaches are illustrated by the Edinburgh heterosexual partner study. The longitudinal analysis finds that 'high-risk' sexual practices, unprotected intercourse for HIV and a low CD4 count in the index case significantly increase the risk of HIV transmission. The cross-sectional analysis, however, only indicates 'high-risk' sexual practices as favourable for HIV transmission.

Adolescent↗

PubMed2003

Segregation and linkage analysis for longitudinal measurements of a quantitative trait.

We present a method for using slopes and intercepts from a linear regression of a quantitative trait as outcomes in segregation and linkage analyses. We apply the method to the analysis of longitudinal systolic blood pressure (SBP) data from the Framingham Heart Study. A first-stage linear model was fit to each subject's SBP measurements to estimate both their slope over time and an intercept, the latter scaled to represent the mean SBP at the average observed age (53.7 years). The subject-specific intercepts and slopes were then analyzed using segregation and linkage analysis. We describe a method for using the standard errors of the first-stage intercepts and slopes as weights in the genetic analyses. For the intercepts, we found significant evidence of a Mendelian gene in segregation analysis and suggestive linkage results (with LOD scores >or= 1.5) for specific markers on chromosomes 1, 3, 5, 9, 10, and 17. For the slopes, however, the data did not support a Mendelian model, and thus no formal linkage analyses were conducted.

Adult Children↗

PubMed1998

A comparison of the random-effects pattern mixture model with last-observation-carried-forward (LOCF) analysis in longitudinal clinical trials with dropouts.

The last-observation-carried-forward imputation method is commonly used for imputting data missing due to dropouts in longitudinal clinical trials. The method assumes that outcome remains constant at the last observed value after dropout, which is unlikely in many clinical trials. Recently, random-effects regression models have become popular for analysis of longitudinal clinical trial data with dropouts. However, inference obtained from random-effects regression models is valid when the missing-at-random dropout process is present. The random-effects pattern-mixture model, on the other hand, provides an approach that is valid under more general missingness mechanisms. In this article we describe the use of random-effects pattern-mixture models under different patterns for dropouts. First, subjects are divided into groups depending on their missing-data patterns, and then model parameters are estimated for each pattern. Finally, overall estimates are obtained by averaging over the missing-data patterns and corresponding standard errors are obtained using the delta method. A typical longitudinal clinical trial data set is used to illustrate and compare the above methods of data analyses in the presence of missing data due to dropouts.

Clinical Trials as Topic↗

PubMedDate not supplied

Dispersion models and longitudinal data analysis.

Dispersion models provide a flexible class of non-normal distributions with many potential applications in biostatistics, accommodating a wide range of continuous, discrete and mixed data. Starting with Liang and Zeger's generalized estimating equation method, we review some recent applications of dispersion models in longitudinal data analysis, including state space models based on the Tweedie class of exponential dispersion models. In medical applications the latent process of a state space model may often be interpreted as an unobserved potential morbidity process, which is modelled as a function of time varying covariates. By allowing a multivariate response vector of 'symptoms', the model integrates several response variables of mixed types into a single model. For growth curve models, the latent process reflects the 'true' growth.

Air Pollutants↗

PubMed1996

Escalated substance use: a longitudinal grouping analysis from early to middle adolescence.

The authors surveyed a cohort of 1,184 adolescents in the 7th, 8th, and 9th grades. Measures of tobacco, alcohol, and marijuana use and of constructs from 3 theoretical models of substance use were obtained at each point. Clustering analysis for 3-wave substance use data indicated subgroups of nonusers, minimal experimenters, late starters, and escalators. Discriminant function analyses tested whether study variables differentiated the subgroups. One discriminant function accounted for the majority of between-group association; it had loadings for (high) life stress, nonadaptive coping, deviance-prone attitudes, and parental and peer substance use, and (low) parental support, academic competence, and behavioral control. Escalators were high on this function; late starters and experimenters had intermediate values; and nonusers were low on the function. Implications for theories of vulnerability to substance abuse are discussed.

Adolescent↗

PubMed2005

Regression analysis of longitudinal binary data with time-dependent environmental covariates: bias and efficiency.

Generalized estimating equations (Liang and Zeger, 1986) is a widely used, moment-based procedure to estimate marginal regression parameters. However, a subtle and often overlooked point is that valid inference requires the mean for the response at time t to be expressed properly as a function of the complete past, present, and future values of any time-varying covariate. For example, with environmental exposures it may be necessary to express the response as a function of multiple lagged values of the covariate series. Despite the fact that multiple lagged covariates may be predictive of outcomes, researchers often focus interest on parameters in a 'cross-sectional' model, where the response is expressed as a function of a single lag in the covariate series. Cross-sectional models yield parameters with simple interpretations and avoid issues of collinearity associated with multiple lagged values of a covariate. Pepe and Anderson (1994), showed that parameter estimates for time-varying covariates may be biased unless the mean, given all past, present, and future covariate values, is equal to the cross-sectional mean or unless independence estimating equations are used. Although working independence avoids potential bias, many authors have shown that a poor choice for the response correlation model can lead to highly inefficient parameter estimates. The purpose of this paper is to study the bias-efficiency trade-off associated with working correlation choices for application with binary response data. We investigate data characteristics or design features (e.g. cluster size, overall response association, functional form of the response association, covariate distribution, and others) that influence the small and large sample characteristics of parameter estimates obtained from several different weighting schemes or equivalently 'working' covariance models. We find that the impact of covariance model choice depends highly on the specific structure of the data features, and that key aspects should be examined before choosing a weighting scheme.

Air Pollutants↗

PubMed1994

Analysis of longitudinal data in craniofacial research: some strategies.

Although it is generally acknowledged that longitudinal data provide the most information on growth and development and other time-dependent phenomena, such data are often analyzed by conventional (cross-sectional) statistical methods. This widespread practice ignores the distinctive characteristics (e.g., covariance structure) of longitudinal data and may yield misleading results. The purpose of this article is to present some strategies and make available computer programs for the appropriate analysis of longitudinal data. User-friendly PC programs for the estimation of average growth curves, computation of tracking indices, prediction of future values, diagnosis, classification, clustering, estimation of missing values, and testing hypotheses concerning individual and group differences are presented. Benefits of these methods over the usual techniques are illustrated with the example of maxillary growth in the rhesus monkey.

Animals↗

PubMed1992

Longitudinal Gompertzian analysis of emphysema mortality in the US, 1962-1987: the differing basis for evolving mortality patterns in men and women.

Age-specific mortality rates for emphysema in the United States from 1962 through 1987 were subjected to longitudinal Gompertzian analysis, a method that can be used to identify and distinguish aggregate genetic, environmental, and competitive influences upon mortality. Annual crude emphysema mortality rates (per 100,000) among men increased from 11.77 in 1962 to 20.94 in 1968, and then fell to 7.74 in 1987. The basis for this rise and fall is shown to be the corresponding changes in environmental influences upon emphysema mortality in men. Between 1962 and 1987, the annual crude emphysema mortality rates among women increased from 1.71 to 4.25. The basis for the increase of emphysema mortality in women, on the other hand, is shown to be an enhancement of the competitiveness of emphysema as a cause of mortality in women, and not the result of worsening environmental influences. The capability to distinguish between environmental and competitive influences upon evolving human mortality patterns could have a significant impact upon public health policy.

Adult↗

PubMed1996

Intent-to-treat analysis for longitudinal studies with drop-outs.

We consider intent-to-treat (IT) analysis of clinical trials involving longitudinal data subject to drop-out. Common methods, such as Last Observation Carried Forward imputation or incomplete-data methods based on models that assume random dropout, have serious drawbacks in the IT setting. We propose a method that involves multiple imputation of the missing values following drop-out based on an "as treated" model, using actual dose after drop-out if this is known, or imputed doses that incorporate a variety of plausible alternative assumptions if unknown. The multiply-imputed data sets are then analyzed using IT methods, were subjects are classified by randomization group rather than by the dose actually received. Results from the multiply-imputed data sets are combined using the methods of Rubin (1987, Multiple Imputation for Nonresponse in Surveys). A novel feature of the proposed method is that the models for imputation differ from the model used for the analysis of the filled-in data. The method is applied to data on a clinical trial for Tacrine in the treatment of Alzheimer's disease.

Alzheimer Disease↗

PubMed1991

Longitudinal Gompertzian analysis of breast cancer mortality in the U.S., 1962-1987: demonstration of a disorder displaying complex deterministic mortality dynamics.

Age-adjusted mortality rates for breast cancer (BC) in the United States from 1962 to 1987 were subjected to longitudinal Gompertzian analysis. Age-adjusted BC mortality rate distributions for women display two distinct Gompertzian slopes. Between age 15 and 40 years, age-adjusted BC mortality rate distributions intercepted at age 33.5 years and mortality rate (per 100,000) 5.83. Between age 50 and 85 years, age-adjusted BC mortality rate distributions intercepted at age 60.4 years and mortality rate 77.0. These two distinct Gompertzian regions correspond to the clinical and biological classification of BC into pre- and post-menopausal varieties. The observation that postmenopausal BC increases in environments conducive to survival and that premenopausal BC increases in environments that are less favorable becomes understandable when BC mortality dynamics are viewed from a competitive and deterministic perspective.

Adolescent↗

PubMed1990

Longitudinal Gompertzian analysis of stroke mortality in the U.S., 1951-1986: declining stroke mortality is the natural consequence of competitive deterministic mortality dynamics.

Age-adjusted mortality rates for stroke in the United States from 1951 to 1986 were subjected to longitudinal Gompertzian analysis. Age-adjusted stroke mortality rate distributions were determined by a variable environmental factor and a constant Gompertz slope. Compared to 1951 values, the environmental factor in 1986 had declined (improved) 49.8% for men and 59.1% for women. This was associated with a 51.9% and 31.4% decrease in the annual crude mortality rate from stroke for men and women respectively. However, the Gompertz slope remained remarkably constant from 1951 to 1986; 0.050152 for men and 0.048341 for women. The constant Gompertz slope for age-adjusted mortality rate distributions for stroke is in sharp contrast to the increasing Gompertz slope which occurs with an improving environment in 'degenerative' diseases and aging in general. These findings suggest that the recent dramatic decline in overall stroke mortality is the natural consequence of competitive deterministic mortality dynamics. As the overall environment becomes more conducive to human survival, Gompertzian diseases with converging mortality rate distributions must increase as causes of human mortality at the expense of diseases with constant Gompertz slopes.

Adult↗

PubMed1992

Longitudinal Gompertzian analysis of cervical cancer mortality in the US, 1962-1987: a method of quantitatively demonstrating changing environmental influences upon deterministic mortality dynamics.

Age-specific mortality rates for cervical cancer (CC) in the United States from 1962 through 1987 were subjected to longitudinal Gompertzian analysis. Age-specific CC mortality rate distributions for women display two distinct Gompertzian slopes, one between age 20 and 35 years and the other between age 40 and 85 years. These two distinct Gompertzian regions suggest that CC may be clinically and biologically classified into pre- and postmenopausal varieties, similar to breast cancer. Between 1962 and 1987, the annual crude CC mortality rate declined 60.0%. The basis for the decline of CC mortality is shown to be that aggregate environmental (etiopathogenic) influences upon premenopausal CC age-specific mortality rate distributions decreased 57.8%, and upon postmenopausal CC, decreased 28.0%.

Adult↗

PubMed1990

Longitudinal Gompertzian analysis of amyotrophic lateral sclerosis mortality in the U.S., 1977-1986: evidence for an inherently susceptible population subset.

Age-adjusted mortality rates for amyotrophic lateral sclerosis (ALS) for men and women in the United States from 1977 to 1986 were determined and subjected to longitudinal Gompertzian analysis. The exponential decline in the rate of increase of age-adjusted ALS mortality rates after age 55 years is most consistent with the existence of an inherently susceptible population subset that is decreasing faster than the general population. In the U.S. between 1977 and 1986, annual age-adjusted ALS mortality rate distributions were determined by a common fixed intersect point (for men, the death rate at age 46.38 years was 0.91/100,000; for women, the death rate at age 45.85 years was 0.46/100,000); and an environmental factor that varied erratically during the decade by a factor of 7.21 for men and 11.64 for women. On the average, the U.S. environment during this period was 4.33 times more conducive to mortality from ALS in men than in women. Overall ALS mortality between 1977 and 1986 increased 46% and 49% for men and women, respectively. The common fixed intersect point in mortality rate distributions suggests that these increases were real and not merely the result of improved diagnosis and/or better reporting. The overall increase in ALS mortality most likely results from an effective increase in the susceptible population subset due to increasing life expectancy, rather than to environmental factors. That is, as life expectancy increases, more of the susceptible population subset live long enough to express the disease.

Adult↗

PubMed1998

Analysis of longitudinal data. Beyond MANOVA.

BACKGROUND: Longitudinal data arise frequently in psychiatric investigations, and are most often analysed by multivariate analysis of variance (MANOVA) procedures. However, as routinely applied, the method is not satisfactory, particularly when the data are affected by subjects dropping-out of the study. More suitable methods are now available. METHOD: Problems with the MANOVA approach are discussed and the advantages of alternative procedures stressed. RESULTS: Using MANOVA on complete cases to analyse unbalanced longitudinal data can be seriously misleading. More recently developed methods are far more suitable, but only if the missing values are non-informative. CONCLUSIONS: Routine use of MANOVA for the analysis of longitudinal data, particularly when there is a substantial proportion of drop-outs, is ill advised. Statisticians have considerably enriched the available methodologies during the past decade, and psychiatric researchers dealing with such data should be aware of the advantages of the newer methods.

Analysis of Variance↗

PubMed1997

Time-to-event analysis of longitudinal follow-up of a survey: choice of the time-scale.

Following individuals sampled in a large-scale health survey for the development of diseases and/or death offers the opportunity to assess the prognostic significance of various risk factors. The proportional hazards regression model, which allows for the control of covariates, is frequently used for the analysis of such data. The authors discuss the appropriate time-scale for such regression models, and they recommend that age rather than time since the baseline survey (time-on-study) be used. Additionally, with age as the time-scale, control for calendar-period and/or birth cohort effects can be achieved by stratifying the model on birth cohort. Because, as discussed by the authors, many published analyses have used regression models with time-on-study as the time-scale, it is important to assess the magnitude of the error incurred from this type of incorrect modeling. The authors provide simple conditions for when incorrect use of time-on-study as the time-scale will nevertheless yield approximately unbiased proportional hazards regression coefficients. Examples are given using data from the first National Health and Nutrition Examination Survey (NHANES I) Epidemiologic Followup Study. Additional issues concerning the analysis of longitudinal follow-up of survey data are briefly discussed.

Adult↗

PubMed1991

Analysis of longitudinal data with unmeasured confounders.

Confounding in longitudinal or clustered data creates special problems and opportunities because the relationship between the confounder and covariate of interest may differ across and within individuals or clusters. A well-known example of such confounding in longitudinal data is the presence of cohort and period effects in models of aging in epidemiologic research. We first formulate a data-generating model with confounding and derive the distribution of the response variable unconditional on the confounder. We then examine the properties of the regression coefficient for some analytic approaches when the confounder is omitted from the fitted model. The expected value of the regression coefficient differs in across- and within-individual regression. In the multivariate case, within- and between-individual information is combined and weighted according to the assumed covariance structure. We assume compound symmetry in the fitted covariance matrix and derive the variance, bias, and mean squared error of the slope estimate as a function of the fitted within-individual correlation. We find that even in this simplest multivariate case, the trade-off between bias and variance depends on a large number of parameters. It is generally preferable to fit correlations somewhat above the true correlation to minimize the effect of between-individual confounders or cohort effects. Period effects can lead to situations where it is advantageous to fit correlations that are below the true correlation. The results highlight the trade-offs inherent in the choice of method for analysis of longitudinal data, and show that an appropriate choice can be made only after determining whether within- or between-individual confounding is the major concern.

Analysis of Variance↗