Population-averaged Model Research Articles

29: Inpatient Mortality for Sepsis Patients From the Emergency Department Versus Direct Admission: A Nationwide Cross-Sectional Study

Early aggressive resuscitation in patients with sepsis decreases mortality. Evidenced-based guidelines exist for both resuscitation in the emergency department (ED) and for care-environments outside of the ED, typically the intensive care unit. It has not been demonstrated on a national level if one venue for initial resuscitation is superior. We hypothesized that patients with a principal diagnosis of sepsis admitted via the ED would have lower inpatient mortality than patients admitted directly to the hospital. We performed a cross-sectional analysis of 91,828 admissions categorized as either admitted via the ED or directly to the inpatient hospital with a principal diagnosis of sepsis from 351 hospitals in the 2007 Nationwide Inpatient Sample. Admissions were excluded if admitted to a hospital with less than 25 ED or 25 direct sepsis admissions in 2007, or if the patient was transferred into or out of the hospital from/to another hospital. Univariate association of patient and hospital factors with mortality by admission route was evaluated by chi-square test or ANOVA. A population-averaged logistic regression model was used to estimate the effects of age, sex, co-morbid conditions, payer-status, median zip code income, hospital bed-size, teaching-status, hospital-wide sepsis case volume, and route of admission on the likelihood of either early (two-day post-admission) or overall inpatient mortality. The analysis compared mortality after 65,903 ED sepsis admissions and 25,925 sepsis admissions admitted directly to the hospital. Overall sepsis mortality for the sample was 18.0%: 17.8% for patients admitted via the ED and 18.7% for those admitted directly to the hospital (p<0.05). Patients admitted via the ED were older (69.5 versus 68.7, p<0.001) and had more co-morbid conditions coded (3.5 versus 3.1, p<0.001). Direct-to-hospital admissions had a greater proportion with a cancer diagnosis (13.6% versus 10.8%, p<0.001). Alcohol abuse, chronic heart failure, chronic pulmonary disease, coagulopathy, fluid and electrolyte disorder, renal failure, and liver failure were coded more frequently among patients admitted through the ED (p<0.001). ED admissions were more likely to be covered by Medicaid or be without insurance (11.8% versus 10.0%, p<0.001). Hospital length of stay was similar by admission route (direct admissions mean of 9.2 days versus 9.1 for ED admissions, p=0.17). ED admissions were more likely to be to large bed-size or teaching hospitals (p<0.001). The risk-adjusted odds of inpatient death was 0.89 (95% CI 0.85-0.92) for ED admissions as compared to direct-to-hospital admissions. A similar result was found for the odds of early death with the ED admission route equally as protective (OR=0.90 95% CI 0.85-0.96). After adjustment for co-morbid conditions and other significant patient and hospital factors, mortality outcomes for patients admitted to the hospital with a principal diagnosis of sepsis differed between directly admitted patients and patients admitted through the ED. Being admitted via the ED was associated with an 11% lower odds of inpatient mortality in this large, heterogeneous sample. This evidence supports the valuable role that the ED may provide in the early aggressive resuscitation of patients with sepsis.

Regression modelling of correlated data in ecology: subject‐specific and population averaged response patterns

Summary 1. Statistical methods that assume independence among observations result in optimistic estimates of uncertainty when applied to correlated data, which are ubiquitous in applied ecological research. Mixed effects models offer a potential solution and rely on the assumption that latent or unobserved characteristics of individuals (i.e. random effects) induce correlation among repeated measurements. However, careful consideration must be given to the interpretation of parameters when using a nonlinear link function (e.g. logit). Mixed model regression parameters reflect the change in the expected response within an individual associated with a change in that individual’s covariates [i.e. a subject‐specific (SS) interpretation], which may not address a relevant scientific question. In particular, a SS interpretation is not natural for covariates that do not vary within individuals (e.g. gender). 2. An alternative approach combines the solution to an unbiased estimating equation with robust measures of uncertainty to make inferences regarding predictor–outcome relationships. Regression parameters describe changes in the average response among groups of individuals differing in their covariates [i.e. a population‐averaged (PA) interpretation]. 3. We compare these two approaches [mixed models and generalized estimating equations (GEE)] with illustrative examples from a 3‐year study of mallard (Anas platyrhynchos) nest structures. We observe that PA and SS responses differ when modelling binary data, with PA parameters behaving like attenuated versions of SS parameters. Differences between SS and PA parameters increase with the size of among‐subject heterogeneity captured by the random effects variance component. Lastly, we illustrate how PA inferences can be derived (post hoc) from fitted generalized and nonlinear‐mixed models. 4. Synthesis and applications. Mixed effects models and GEE offer two viable approaches to modelling correlated data. The preferred method should depend primarily on the research question (i.e. desired parameter interpretation), although operating characteristics of the associated estimation procedures should also be considered. Many applied questions in ecology, wildlife management and conservation biology (including the current illustrative examples) focus on population performance measures (e.g. mean survival or nest success rates) as a function of general landscape features, for which the PA model interpretation, not the more commonly used SS model interpretation may be more natural.

Response of Multiple Recurrent TaT1 Bladder Cancer to Intravesical Apaziquone (EO9): Comparative Analysis of Tumor Recurrence Rates

Previous studies have demonstrated that intravesical administration of apaziquone (EOquin) has ablative activity against superficial bladder cancer marker lesions with 8 out of 12 complete responses recorded. We present a comparison between the rates of tumor recurrence before and after treatment with apaziquone. The rate of tumor recurrence after treatment with apaziquone was compared with each patient's historical record of recurrences obtained from a retrospective analysis of the patients' case notes. The time to each recurrence event before apaziquone treatment and the time to the first recurrence after apaziquone treatment were recorded, and the data were analyzed using a population-averaged linear regression model using Stata Release, version 9.2, software. Of the eight complete responses obtained in the Phase I study, tumor recurrence occurred in 4 patients and the remaining 4 patients remained disease free after a median follow-up of 31 months. The time to the first recurrence after apaziquone treatment was significantly longer (P <0.001) compared with the historical pattern and recurrence interval before apaziquone. Before apaziquone instillation, the mean +/- SE recurrence rate and tumor rate per year was 1.5 +/- 0.2 and 4.8 +/- 1.2, respectively, and these decreased to 0.6 +/- 0.25 and 1.5 +/- 0.8, respectively, after apaziquone treatment (P <0.05). The results of this study indicate that early recurrences after treatment with apaziquone are infrequent and the interval to recurrence is significantly greater compared with the historical recurrence times for these patients. Larger prospective randomised trials are warranted to confirm these results.

Modeling longitudinal count data with dropouts

This paper explores the utility of different approaches for modeling longitudinal count data with dropouts arising from a clinical study for the treatment of actinic keratosis lesions on the face and balding scalp. A feature of these data is that as the disease for subjects on the active arm improves their data show larger dispersion compared with those on the vehicle, exhibiting an over-dispersion relative to the Poisson distribution. After fitting the marginal (or population averaged) model using the generalized estimating equation (GEE), we note that inferences from such a model might be biased as dropouts are treatment related. Then, we consider using a weighted GEE (WGEE) where each subject's contribution to the analysis is weighted inversely by the subject's probability of dropout. Based on the model findings, we argue that the WGEE might not address the concerns about the impact of dropouts on the efficacy findings when dropouts are treatment related. As an alternative, we consider likelihood-based inference where random effects are added to the model to allow for heterogeneity across subjects. Finally, we consider a transition model where, unlike the previous approaches that model the log-link function of the mean response, we model the subject's actual lesion counts. This model is an extension of the Poisson autoregressive model of order 1, where the autoregressive parameter is taken to be a function of treatment as well as other covariates to induce different dispersions and correlations for the two treatment arms. We conclude with a discussion about model selection.

Application of Penalized Splines in Analyzing Neuronal Data

Neuron experiments produce high-dimensional data structures. Therefore, application of smoothing techniques in the analysis of neuronal data from electrophysiological experiments has received considerable attention of late. We investigate the use of penalized splines in the analysis of neuronal data. This is first illustrated when interested in the temporal trend of a single neuron. An approach to investigate the maximal firing rate, based on the penalizedspline model is proposed. Determination of the time of maximal firing rate is based on non-linear optimization of the objective function with the corresponding confidence intervals constructed based on the first-order derivative function. To distinguish between the curves from different experimental conditions in a moment-by-moment sense, bias adjusted simulation-based simultaneous confidence bands leading to global inference in the time domain are constructed. The bands are an extension of the approach proposed by Ruppert et al. (2003). These methods are in a second step extended towards the analysis of a population of neurons via a marginal or population-averaged model.

Two-Year Outcomes of Children on Non-Nucleoside Reverse Transcriptase Inhibitor and Protease Inhibitor Regimens in a South African Pediatric Antiretroviral Program

Few data exist on the efficacy of the limited regimens for children with HIV, which are available in sub-Saharan Africa. Retrospective cohort study to evaluate the clinical and laboratory outcomes of 391 children who received protease inhibitor (PI) or non-nucleoside reverse transcription inhibitor (nNRTI)-containing highly active antiretroviral regimens (HAART) from a Cape Town clinic. Endpoints included CD4% and count, viral loads, weight-for-age Z score (WAZ), survival, drug changes, and loss to follow-up over 24 months. A generalized estimating equation population-averaged model was used to identify associations with virological suppression, and a log-rank test explored associations with survival. Overall, this cohort achieved a sustained doubling of median CD4% from baseline, steady increase of median WAZ, and survival of 91%, despite only 49% virologic suppression at 24 months. However, when analyzed according to regimen, PI-containing regimens had better virologic suppression at all time points. There were no differences in immunologic and growth endpoints between regimens or in survival. In a multivariate model predicting virologic suppression at any duration up to 24 months and adjusting for baseline CD4%, regimen, age, baseline WAZ, duration of HAART, and year of HAART initiation, nNRTI-based regimens (odds ratio [OR]: 0.38; 95% confidence interval [CI]: 0.19-0.77) and length of time on HAART were inversely associated with virologic suppression. Age (OR: 1.23 per year; 95% CI: 1.09-1.39) was positively associated with virologic suppression. The benefits of HAART are substantial in this setting, although PI regimens achieved greater virologic suppression than nNRTIs. Further exploration of regimens and dosing of antiretrovirals for children in these settings is needed.

TOPICAL COCONUT OIL APPLICATION REDUCES TRANSEPIDERMAL WATER LOSS IN PRETERM VERY LOW BIRTH WEIGHT NEONATES: A RANDOMIZED CLINICAL TRIAL

INTRODUCTION: Topical emollients have been shown to reduce transepidermal water loss (TEWL). Such an effect of coconut oil (often used in traditional massage of infants in India) has not been studied. OBJECTIVE: Our goal was to determine the efficacy of topical coconut-oil application in reducing TEWL in preterm very low birth weight (VLBW) neonates. METHODS: Seventy-four preterm VLBW infants were randomly assigned at 12 hours of age to either 4 mL of topical coconut-oil application every 12 hours for 7 days (n = 37) or no oil application (n = 37). TEWL was measured at 12 hours of age and thereafter every 12 hours for 7 days in both groups by using a Vapometer (Delfin Technologies, Kuopio, Finland), a portable closed-chamber evaporimeter. The ambient and skin-surface relative humidity and temperature were recorded simultaneously. RESULTS: Birth weight (1213 ± 214 vs 1164 ± 208 g), gestation (32 ± 2 vs 31 ± 2 weeks), and other baseline variables were comparable between the 2 groups. TEWL was significantly lower in the infants in the coconut-oil group at each point of measurement. Although TEWL declined for those in both groups during the first week of life, proportional reduction in TEWL in the infants in the coconut-oil group was much greater compared with controls. Significantly lower TEWL in the infants in the coconut-oil group persisted after adjusting for differences in baseline variables by using a generalized estimating equation population-averaged model (an advanced form of regression analysis) (mean difference: 6.8 g/m2 per hour all during first week of life [95% confidence interval: 3.5–10.2]; P = .000). CONCLUSIONS: Coconut-oil application in preterm VLBW neonates reduced TEWL by as much as 46%. Such an impact is expected to be of clinical importance, because it could reduce initial weight loss, promote better growth, and reduce fluid requirements.

Analytic Investigation Into Effect of Population Heterogeneity on Parameter Ratio Estimates

A homogeneous tumor control probability (TCP) model has previously been used to estimate the alpha/beta ratio for prostate cancer from clinical dose-response data. For the ratio to be meaningful, it must be assumed that parameter ratios are not sensitive to the type of tumor control model used. We investigated the validity of this assumption by deriving analytic relationships between the alpha/beta estimates from a homogeneous TCP model, ignoring interpatient heterogeneity, and those of the corresponding heterogeneous (population-averaged) model that incorporated heterogeneity. The homogeneous and heterogeneous TCP models can both be written in terms of the geometric parameters D(50) and gamma(50). We show that the functional forms of these models are similar. This similarity was used to develop an expression relating the homogeneous and heterogeneous estimates for the alpha/beta ratio. The expression was verified numerically by generating pseudo-data from a TCP curve with known parameters and then using the homogeneous and heterogeneous TCP models to estimate the alpha/beta ratio for the pseudo-data. When the dominant form of interpatient heterogeneity is that of radiosensitivity, the homogeneous and heterogeneous alpha/beta estimates differ. This indicates that the presence of this heterogeneity affects the value of the alpha/beta ratio derived from analysis of TCP curves. The alpha/beta ratio estimated from clinical dose-response data is model dependent--a heterogeneous TCP model that accounts for heterogeneity in radiosensitivity will produce a greater alpha/beta estimate than that resulting from a homogeneous TCP model.

Comparison of subject-specific and population averaged models for count data from cluster-unit intervention trials

Maximum likelihood estimation techniques for subject-specific (SS) generalized linear mixed models and generalized estimating equations for marginal or population-averaged (PA) models are often used for the analysis of cluster-unit intervention trials. Although both classes of procedures account for the presence of within-cluster correlations, the interpretations of fixed effects including intervention effect parameters differ in SS and PA models. Furthermore, closed-form mathematical expressions relating SS and PA parameters from the two respective approaches are generally lacking. This paper investigates the special case of correlated Poisson responses where, for a log-linear model with normal random effects, exact relationships are available. Equivalent PA model representations of two SS models commonly used in the analysis of nested cross-sectional cluster trials with count data are derived. The mathematical results are illustrated with count data from a large non-randomized cluster trial to reduce underage drinking. Knowledge of relationships among parameters in the respective mean and covariance models is essential to understanding empirical comparisons of the two approaches.

A Conformational Dynamics Study of α-l-Rhap-(1→2)[α-l-Rhap-(1→3)]-α-l-Rhap-OMe in Solution by NMR Experiments and Molecular Simulations

The conformational preference of alpha-l-Rhap-(1-->2)[alpha-l-Rhap-(1-->3)]-alpha-l-Rhap-OMe in solution has been studied by NMR spectroscopy using one-dimensional (1)H,(1)H T-ROESY experiments and measurement of trans-glycosidic (3)J(C,H) coupling constants. Molecular dynamics (MD) simulations with a CHARMM22 type of force field modified for carbohydrates were performed with water as the explicit solvent. The homonuclear cross-relaxation rates, interpreted as effective proton-proton distances, were compared to those obtained from simulation. Via a Karplus torsional relationship, (3)J(C,H) values were calculated from simulation and compared to experimental data. Good agreement was observed between experimental data and the MD simulation, except for one inter-residue T-ROE between protons in the terminal sugar residues. The results show that the trisaccharide exhibits substantial conformational flexibility, in particular along the psi glycosidic torsion angles. Notably, for these torsions, a high degree of correlation (77%) was observed in the MD simulation revealing either psi(2)(+) psi(3)(+) or psi(2)(-)psi(3)(-) states. The simulations also showed that non-exoanomeric conformations were present at the phi torsion angles, but to a limited extent, with the phi(3) state populated to a larger extent than the phi(2) state. Further NMR analysis of the trisaccharide by translational diffusion measurements and (13)C T(1) relaxation experiments quantified global reorientation using an anisotropic model together with interpretation of the internal dynamics via the "model-free" approach. Fitting of the dynamically averaged states to experimental data showed that the psi(2)(+)psi(3)(+) state is present to approximately 49%, psi(2)(-) psi(3)(-) to approximately 39%, and phi(3) (non-exo) to approximately 12%. Finally, using a dynamic and population-averaged model, (1)H,(1)H T-ROE buildup curves were calculated using a full relaxation matrix approach and were found to be in excellent agreement with experimental data, in particular for the above inter-residue proton-proton interaction between the terminal residues.

Pseudomonas aeruginosa,Staphylococcus aureus, and Fluoroquinolone Use

Few long-term multicenter investigations have evaluated the relationships between aggregate antimicrobial drug use in hospitals and bacterial resistance. We measured fluoroquinolone use from 1999 through 2003 in a network of US hospitals. The percentages of fluoroquinolone-resistant Pseudomonas aeruginosa and methicillin-resistant Staphylococcus aureus (MRSA) were obtained from yearly antibiograms at each hospital. Univariate linear regression showed significant associations between a hospital's volume of fluoroquinolone use and percent resistance in most individual study years (1999-2001 for P. aeruginosa, 1999-2002 for S. aureus). When the method of generalized estimating equations was used, a population-averaged longitudinal model incorporating total fluoroquinolone use and the previous year's resistance (to account for autocorrelation) did not show a significant effect of fluoroquinolone use on percent resistance for most drug-organism combinations, except for the relationship between levofloxacin use and percent MRSA. The ecologic relationship between fluoroquinolone use and resistance is complex and requires further study.

High Porcine Parvovirus Antibodies in Sow Herds: Prevalence and Associated Factors

Porcine parvovirus (PPV) is widespread among swine. Our objective was to determine the prevalence of loosely housed sow herds in Finland with at least one animal with high (infection level) PPV antibodies and to gather basic knowledge about vaccination practices. In addition, selected factors associated with high antibody levels found in sows were examined. Altogether, 247 animals were sampled in 21 randomly chosen loosely housed sow herds. Samples were analysed with the haemagglutination inhibition (HI) test. PPV proved to be common; in 17 farms (81%) at least one animal had a high titre (>1 : 512), and 44% of all animals sampled had a high titre. The vaccination programmes had many shortcomings. In the generalised estimation equations (GEE) population-averaged model developed, the factors found to have a significant (p < or = 0.05) effect on HI titres were herd size, parity of two or greater and storage of the vaccine vial after use. Non-returning rate, re-breeding interval and litter size did not differ between herds with no high HI titres (n = 4) and those with at least one high HI titre (n = 17).

Study of clinical course of organ dysfunction in intensive care.

Multiple organ dysfunction is a common cause of death in intensive care units. We describe the daily course of multiple organ dysfunction measured by the Sequential Organ Failure Assessment score in a population-based cohort of critically ill patients. Prospective cohort study. Adult multisystem intensive care units in the Calgary Health Region. A total of 1,436 patients admitted from May 1, 2000 to April 30, 2001. Temporal change in Sequential Organ Failure Assessment score. None; observational study. The mean age was 58 yrs (range, 14-100). The mean +/- sd intensive care unit admission Acute Physiology and Chronic Health Evaluation II score was 25 +/- 9. The median intensive care unit length of stay was 4 days (interquartile range, 2-8), and the median hospital length of stay was 15 days (interquartile range, 7-32). A total of 20.5% of patients were infected at admission, and 26.0% were immediately postoperative. Intensive care unit mortality was 27.0%, and hospital mortality was 35.1%. The daily Sequential Organ Failure Assessment score was significantly higher in nonsurvivors than survivors. A population-averaged model determined a mean rate of change of Sequential Organ Failure Assessment score to be -0.29 per day (95% confidence interval, -0.32 to -0.25) for survivors and -0.03 per day (95% confidence interval, -0.08 to 0.03) for nonsurvivors (overall regression, p <.0001). Patients with infection had higher admission Sequential Organ Failure Assessment scores compared with patients without infection (difference, 1.8; p <.001), but a similar rate of daily change. Multiple organ dysfunction, does not follow a course of progressive and sequential failure. Evidence of differential daily change should further inform the use of organ failure scores as surrogate outcomes in clinical trials.

Comparison of methods for analyzing longitudinal binary outcomes: cognitive status as an example

Longitudinal data generate correlated observations. Ignoring correlation can lead to incorrect estimation of standard errors, resulting in incorrect inferences of parameters. In the example used here, standard logistic regression, a population-averaged (PA) model fit using generalized estimating equations (GEE), and random-intercept models are used to model binary outcomes at baseline, three and six years later. The outcomes indicate cognitive impairment versus no cognitive impairment in a sample of community dwelling elders. The models include both time-invariant (age, gender) and time-varying (time, interactions with time) covariates. The absolute estimates from random-intercept models are larger than those of both standard logistic and GEE models. Compared to the model fit using GEE that accounts for time dependency, standard logistic regression models overestimate standard errors of time-varying covariates (such as time, and time by problems with activities of daily living), and underestimate the standard errors of time-invariant covariates (such as age and gender). The standard errors from the random-intercept model are larger than those from logistic regression and GEE models. The choice of models, GEE or random-intercept, depends on the research question and the nature of the covariates. Population-averaged methods are appropriate when between-subjects effects are of interest, and random-effects are useful when subject-specific effects are important.

Analysis of resulting data from estrogen receptor reporter gene assays

Screening methods for detecting single chemicals and chemical mixtures that have endocrine effects are of increasing importance. One such assay used by many laboratories to screen for potential estrogenicity is the estrogen receptor (ER) transcriptional activation assay, also known as an ER “reporter gene assay.” When applied in screening situations or to mechanistic studies, the assay appears to be quite reliable in giving a qualitative indication of a compound’s potential to activate ER-regulated target genes. Reporter gene assays also are advantageous for more complex applications, such as the analysis of chemical mixtures, but such applications present some challenges for statistical analysis. In particular, the need to transiently transfect cells with DNA constructs each time a reporter gene experiment is run may be a major factor contributing to a significant amount of interexperiment variability in strictly reproducing concentration-effect curves. This article reports on the use of nonlinear mixed models to account for the different sources of variability in analyzing such data. A population-averaged model is selected for use in the analysis of mixtures of chemicals. The models are illustrated with data from an ER reporter gene assay used to analyze tertiary mixtures of chemicals expected to exhibit additivity or synergy based on prior scientific reports. The models yielded the expected conclusions, and thus, validated the statistical approach.

Analysis of toxicology data with covariates specific to each observation

The standard approach for analysis of teratology studiesis to use a population-averaged model with primary interest on evaluating dose-response effects. For example, generalized estimating equations (GEEs) have become popular for analysis of both developmental toxicity and reproducti vestudies (Ryan 1992). Such an approach is typically appropriate since the covariate of interest—exposure level—is constant for each litter of animals. Recently, however, there has been growing interest in evaluating effects of covariates that can vary between individuals within a cluster. This article explores several opportunities generated by teratology studies with individual-level covariates both in terms of modeling approaches and in decomposition of litter effects into genetic and environmental components.

Accommodating negative intracluster correlation with a mixed effects logistic model for bivariate binary data

We extend the random intercept logistic model to accommodate negative intracluster correlations for bivariate binary response data. This approach assumes a single random effect per cluster but entails separate affine transformations of this random effect for the two responses of the pair. We show this approach works for two data sets and a simulation whereas other mixed effects approaches fail. The two data sets are from a crossover trial and a developmental toxicity study of the effects of chemical exposure on malformation risk among rat pups. Comparisons are made with the conditional likelihood approach and with generalized estimating equations estimation of the population-averaged logit model. Simulations show the conditional likelihood approach does not perform well for moderate to strong negative correlations as a positive intracluster correlation is assumed. The proposed mixed effects approach appears to be slightly more conservative than the population-averaged approach with respect to coverage of confidence intervals. Nonetheless, the statistical literature suggests that mixed effects models provide information in addition to that provided by population-averaged models under scientific contexts such as crossover trials. Extensions to trivariate and higher-dimensional responses also are addressed. However, such extensions require certain constraints on the correlation structure.

Subject-Specific and Population-Averaged Continuation Ratio Logit Models for Multiple Discrete Time Survival Profiles

SUMMARY Subject-specific and population-averaged continuation ratio logit models are presented for multivariate discrete time survival data. The models characterize data from a psychological experiment by using a quadratic polynomial relationship across time that depends on a time-independent condition. A multivariate normal random effects distribution is imposed on intercept, linear and quadratic terms in the subject-specific model, which is fitted by using a combination of Gibbs sampling and buffered stochastic substitution. Variance components that tend towards 0 are addressed in this context. In addition, generalized estimating equations estimates of the parameters in the population-averaged model are compared with analogous estimates for the mixed effects model.

Linear Regression Analysis for Highly Stratified Failure Time Data

Abstract In this article we consider cases where data consist of many small and independent groups of correlated failure time observations. For each failure time, which may be censored, some important covariates are also recorded. Our goal is to examine the covariate effects on the individual failure time observations. We assume that the logarithm of each failure time is linearly related to its covariates. We then take a population-averaged model approach to obtain inference procedures for the regression parameters without specifying the joint distribution of the observations within the group. The new proposals do not need complicated and unstable nonparametric estimates for the hazard function of the error term. Their properties are extensively examined for practical sample sizes. Comparisons among various procedures are also performed. All the methods studied in this article are illustrated with examples.

Linear Regression Analysis for Highly Stratified Failure Time Data

Abstract In this article we consider cases where data consist of many small and independent groups of correlated failure time observations. For each failure time, which may be censored, some important covariates are also recorded. Our goal is to examine the covariate effects on the individual failure time observations. We assume that the logarithm of each failure time is linearly related to its covariates. We then take a population-averaged model approach to obtain inference procedures for the regression parameters without specifying the joint distribution of the observations within the group. The new proposals do not need complicated and unstable nonparametric estimates for the hazard function of the error term. Their properties are extensively examined for practical sample sizes. Comparisons among various procedures are also performed. All the methods studied in this article are illustrated with examples.