SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the proposed estimators in two simple situations is considered. The approach is closely related to quasi-likelih ood. Some key ironh: Estimating equation; Generalized linear model; Longitudinal data; Quasi-likelihood; Repeated measures.

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Longitudinal data analysis using generalized linear models

Background An improvement in overall survival among patients with metastatic melanoma has been an elusive goal. In this phase 3 study, ipilimumab — which blocks cytotoxic T-lymphocyte–associated antigen 4 to potentiate an antitumor T-cell response — administered with or without a glycoprotein 100 (gp100) peptide vaccine was compared with gp100 alone in patients with previously treated metastatic melanoma. Methods A total of 676 HLA-A*0201–positive patients with unresectable stage III or IV melanoma, whose disease had progressed while they were receiving therapy for metastatic disease, were randomly assigned, in a 3:1:1 ratio, to receive ipilimumab plus gp100 (403 patients), ipilimumab alone (137), or gp100 alone (136). Ipilimumab, at a dose of 3 mg per kilogram of body weight, was administered with or without gp100 every 3 weeks for up to four treatments (induction). Eligible patients could receive reinduction therapy. The primary end point was overall survival. Results The median overall survival was 10.0 months among patients receiving ipilimumab plus gp100, as compared with 6.4 months among patients receiving gp100 alone (hazard ratio for death, 0.68; P<0.001). The median overall survival with ipilimumab alone was 10.1 months (hazard ratio for death in the comparison with gp100 alone, 0.66; P = 0.003). No difference in overall survival was detected between the ipilimumab groups (hazard ratio with ipilimumab plus gp100, 1.04; P = 0.76). Grade 3 or 4 immune-related adverse events occurred in 10 to 15% of patients treated with ipilimumab and in 3% treated with gp100 alone. There were 14 deaths related to the study drugs (2.1%), and 7 were associated with immune-related adverse events. Conclusions Ipilimumab, with or without a gp100 peptide vaccine, as compared with gp100 alone, improved overall survival in patients with previously treated metastatic melanoma. Adverse events can be severe, long-lasting, or both, but most are reversible with appropriate treatment. (Funded by Medarex and Bristol-Myers Squibb; ClinicalTrials.gov number, NCT00094653.)

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Improved Survival with Ipilimumab in Patients with Metastatic Melanoma.

With explanatory covariates, the standard analysis for competing risks data involves modeling the cause-specific hazard functions via a proportional hazards assumption Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type In recent years many clinicians have begun using the cumulative incidence function, the marginal failure probabilities for a particular cause, which is intuitively appealing and more easily explained to the nonstatistician The cumulative incidence is especially relevant in cost-effectiveness analyses in which the survival probabilities are needed to determine treatment utility Previously, authors have considered methods for combining estimates of the cause-specific hazard functions under the proportional hazards formulation However, these methods do not allow the analyst to directly assess the effect of a covariate on the marginal probability function In this article we pro

http://www.clinicalpredictionmodels.org/lib/exe/fetch.php?id=additional%3Achapter04&cache=cache&media=additional:fine_and_gray_competing_risk_1999.pdf

A Proportional Hazards Model for the Subdistribution of a Competing Risk

Longitudinal data sets are comprised of repeated observations of an outcome and a set of covariates for each of many subjects. One objective of statistical analysis is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlation among the repeated observations for a given subject. This paper proposes a unifying approach to such analysis for a variety of discrete and continuous outcomes. A class of generalized estimating equations (GEEs) for the regression parameters is proposed. The equations are extensions of those used in quasi-likelihood (Wedderburn, 1974, Biometrika 61, 439-447) methods. The GEEs have solutions which are consistent and asymptotically Gaussian even when the time dependence is misspecified as we often expect. A consistent variance estimate is presented. We illustrate the use of the GEE approach with longitudinal data from a study of the effect of mothers' stress on children's morbidity.

Longitudinal data analysis for discrete and continuous outcomes.

Background: The finding of a decrease in contralateral breast cancer incidence following tamoxifen administration for adjuvant therapy led to the concept that the drug might play a role in breast cancer prevention. To test this hypothesis, the National Surgical Adjuvant Breast and Bowel Project initiated the Breast Cancer Prevention Trial (P-1) in 1992. Methods: Women (N = 13 388) at increased risk for breast cancer because they 1) were 60 years of age or older, 2) were 35‐59 years of age with a 5-year predicted risk for breast cancer of at least 1.66%, or 3) had a history of lobular carcinoma in situ were randomly assigned to receive placebo (n = 6707) or 20 mg/day tamoxifen (n = 6681) for 5 years. Gail’s algorithm, based on a multivariate logistic regression model using combinations of risk factors, was used to estimate the probability (risk) of occurrence of breast cancer over time. Results: Tamoxifen reduced the risk of invasive breast cancer by 49% (two-sided P<.00001), with cumulative incidence through 69 months of follow-up of 43.4 versus 22.0 per 1000 women in the placebo and tamoxifen groups, respectively. The decreased risk occurred in women aged 49 years or younger (44%), 50‐59 years (51%), and 60 years or older (55%); risk was also reduced in women with a history of lobular carcinoma in situ (56%) or atypical hyperplasia (86%) and in those with any category of predicted 5-year risk. Tamoxifen reduced the risk of noninvasive breast cancer by 50% (two-sided P<.002). Tamoxifen reduced the occurrence of estrogen receptor-positive tumors by 69%, but no difference in the occurrence of estrogen receptor-negative tumors was seen. Tamoxifen administration did not alter the average annual rate of ischemic heart disease; however, a reduction in hip, radius (Colles’), and spine fractures was observed. The rate of endometrial cancer was increased in the tamoxifen group (risk ratio = 2.53; 95% confidence interval = 1.35‐4.97); this increased risk occurred predominantly in women aged 50 years or older. All endometrial cancers in the tamoxifen group were stage I (localized disease); no endometrial cancer deaths have occurred in this group. No liver cancers or increase in colon, rectal, ovarian, or other tumors was observed in the tamoxifen group. The rates of stroke, pulmonary embolism, and deep-vein thrombosis were elevated in the tamoxifen group; these events occurred more frequently in women aged 50 years or older. Conclusions: Tamoxifen decreases the incidence of invasive and noninvasive breast cancer. Despite side effects resulting from administration of tamoxifen, its use as a breast cancer preventive agent is appropriate in many women at increased risk for the disease. [J Natl Cancer Inst 1998;90:1371‐88]

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Tamoxifen for Prevention of Breast Cancer: Report of the National Surgical Adjuvant Breast and Bowel Project P-1 Study

Comprehensive gene expression patterns generated from cDNA microarrays were correlated with detailed clinico-pathological characteristics and clinical outcome in an unselected group of 99 node-negative and node-positive breast cancer patients. Gene expression patterns were found to be strongly associated with estrogen receptor (ER) status and moderately associated with grade, but not associated with menopausal status, nodal status, or tumor size. Hierarchical cluster analysis segregated the tumors into two main groups based on their ER status, which correlated well with basal and luminal characteristics. Cox proportional hazards regression analysis identified 16 genes that were significantly associated with relapse-free survival at a stringent significance level of 0.001 to account for multiple comparisons. Of 231 genes previously reported by others [van't Veer, L. J., et al. (2002) Nature 415, 530-536] as being associated with survival, 93 probe elements overlapped with the set of 7,650 probe elements represented on the arrays used in this study. Hierarchical cluster analysis based on the set of 93 probe elements segregated our population into two distinct subgroups with different relapse-free survival (P < 0.03). The number of these 93 probe elements showing significant univariate association with relapse-free survival (P < 0.05) in the present study was 14, representing 11 unique genes. Genes involved in cell cycle, DNA replication, and chromosomal stability were consistently elevated in the various poor prognostic groups. In addition, glutathione S-transferase M3 emerged as an important survival marker in both studies. When taken together with other array studies, our results highlight the consistent biological and clinical associations with gene expression profiles.

https://www.pnas.org/content/pnas/100/18/10393.full.pdf

Breast cancer classification and prognosis based on gene expression profiles from a population-based study

Basic Survey Methodology. Statistical Analysis with Survey Data. Sample Weights and Imputation. Additional Issues in Variance Estimation. Cross--Sectional Analyses. Analysis of Longitudinal Surveys. Analyses Using Multiple Surveys. Population--Based Case--Control Studies. Appendices. References. Indexes.

Analysis of Health Surveys

PURPOSETo define more uniform criteria for risk-based treatment assignment for children with acute lymphoblastic leukemia (ALL), the Cancer Therapy Evaluation Program (CTEP) of the National Cancer Institute (NCI) sponsored a workshop in September 1993. Participants included representatives from the Childrens Cancer Group (CCG), Pediatric Oncology Group (POG), Dana-Farber Cancer Institute (DFCI), St Jude Children's Research Hospital (SJCRH), and the CTEP.METHODSWorkshop participants presented and reviewed data from ALL clinical trials, using weighted averages to combine outcome data from different groups.RESULTSFor patients with B-precursor (ie, non-T, non-B) ALL, the standard-risk category (4-year event-free survival [EFS] rate, approximately 80%) will include patients 1 to 9 years of age with a WBC count at diagnosis less than 50,000/microL. The remaining patients will be classified as having high-risk ALL (4-year EFS rate, approximately 65%). For patients with T-cell ALL, different treatment strategies ...

Uniform approach to risk classification and treatment assignment for children with acute lymphoblastic leukemia.

In the analysis of covariance, the display of adjusted treatment means allows one to compare mean (treatment) group outcomes controlling for different covariate distributions in the groups. Predictive margins are a generalization of adjusted treatment means to nonlinear models. The predictive margin for group r represents the average predicted response if everyone in the sample had been in group r. This paper discusses the use of predictive margins with complex survey data, where an important consideration is the choice of covariate distribution used to standardize the predictive margin. It is suggested that the textbook formula for the standard error of an adjusted treatment mean from the analysis of covariance may be inappropriate for applications involving survey data. Applications are given using data from the 1992 National Health Interview Survey (NHIS) and the Epidemiologic Followup Study to the first National Health and Nutrition Examination Survey (NHANES I).

Edward L. Korn

Papers

Breast cancer classification and prognosis based on gene expression profiles from a population-based study

Analysis of Health Surveys

Uniform approach to risk classification and treatment assignment for children with acute lymphoblastic leukemia.

Predictive margins with survey data.

Analysis of Health Surveys: Korn/Analysis