Local central limit theorems, the high-order correlations of rejective sampling and logistic likelihood asymptotics

Let I_1,...,I_n be independent but not necessarily identically distributed Bernoulli random variables, and let X_n=\sum_{j=1}^nI_j. For \nu in a bounded region, a local central limit theorem expansion of P(X_n=EX_n+\nu) is developed to any given degree. By conditioning, this expansion provides information on the high-order correlation structure of dependent, weighted sampling schemes of a population E (a special case of which is simple random sampling), where a set d\subset E is sampled with probability proportional to \prod_{A\in d}x_A, where x_A are positive weights associated with individuals A\in E. These results are used to determine the asymptotic information, and demonstrate the consistency and asymptotic normality of the conditional and unconditional logistic likelihood estimator for unmatched case-control study designs in which sets of controls of the same size are sampled with equal probability.Comment: Published at http://dx.doi.org/10.1214/009053604000000706 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Are Nested Case-Control Studies Biased?

It has been recently asserted that the nested case-control study design, in which case-control sets are sampled from cohort risk sets, can introduce bias (“study design bias”) when there are lagged exposures. The bases for this claim include a theoretic and an “empirical evaluation” argument. Both of these arguments are examined and found to be incorrect. Appropriate methods to explore the performance of nested case-control study designs, analysis methods, and compute power and sample size from an existing cohort are described. This empirical evaluation approach relies on simulating case-control outcomes from risk sets in the cohort from which the case-control study is to be performed. Because it is based on the underlying cohort structure, the empirical evaluation can provide an assessment that is tailored to the specific characteristics of the study under consideration. The methods are illustrated using samples from the Colorado Plateau uranium miners cohort

Background stratified Poisson regression analysis of cohort data

Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as ‘nuisance’ variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this ‘conditional’ regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models

Lagging Exposure Information in Cumulative Exposure-Response Analyses

Lagging exposure information is often undertaken to allow for a latency period in cumulative exposure-disease analyses. The authors first consider bias and confidence interval coverage when using the standard approaches of fitting models under several lag assumptions and selecting the lag that maximizes either the effect estimate or model goodness of fit. Next, they consider bias that occurs when the assumption that the latency period is a fixed constant does not hold. Expressions were derived for bias due to misspecification of lag assumptions, and simulations were conducted. Finally, the authors describe a method for joint estimation of parameters describing an exposure-response association and the latency distribution. Analyses of associations between cumulative asbestos exposure and lung cancer mortality among textile workers illustrate this approach. Selecting the lag that maximizes the effect estimate may lead to bias away from the null; selecting the lag that maximizes model goodness of fit may lead to confidence intervals that are too narrow. These problems tend to increase as the within-person exposure variation diminishes. Lagging exposure assignment by a constant will lead to bias toward the null if the distribution of latency periods is not a fixed constant. Direct estimation of latency periods can minimize bias and improve confidence interval coverage

TNF-Receptor Inhibitor Therapy for the Treatment of Children with Idiopathic Pneumonia Syndrome. A Joint Pediatric Blood and Marrow Transplant Consortium and Children's Oncology Group Study (ASCT0521)

AbstractIdiopathic pneumonia syndrome (IPS) is an acute, noninfectious lung disorder associated with high morbidity and mortality after hematopoietic cell transplantation. Previous studies have suggested a role for TNFα in the pathogenesis of IPS. We report a multicenter phase II trial investigating a soluble TNF-binding protein, etanercept (Enbrel, Amgen, Thousand Oaks, CA), for the treatment of pediatric patients with IPS. Eligible patients were < 18 years old, within 120 days after transplantation, and with radiographic evidence of a diffuse pneumonitis. All patients underwent a pretherapy broncho-alveolor lavage (BAL) to establish the diagnosis of IPS. Systemic corticosteroids (2.0 mg/kg/day) plus etanercept (.4 mg/kg twice weekly × 8 doses) were administered. Response was defined as survival and discontinuation of supplemental oxygen support by day 28 of study. Thirty-nine patients (median age, 11 years; range, 1 to 17) were enrolled, with 11 of 39 patients nonevaluable because of identification of pathogens from their pretherapy BAL. In the remaining 28 patients, the median fraction of inspired oxygen at study entry was 45%, with 17 of 28 requiring mechanical ventilation. Complete responses were seen in 20 (71%) patients, with a median time to response of 10 days (range, 1 to 24). Response rates were higher for patients not requiring mechanical ventilation at study entry (100% versus 53%, P = .01). Overall survival at 28 days and 1 year after therapy were 89% (95% confidence interval [CI], 70% to 96%) and 63% (95% CI, 42% to 79%), respectively. Plasma levels of proinflammatory cytokines were significantly increased at onset of therapy, subsequently decreasing in responding patients. The addition of etanercept to high-dose corticosteroids was associated with high response rates and survival in children with IPS

A population-based study of tumor gene expression and risk of breast cancer death among lymph node-negative patients

INTRODUCTION: The Oncotype DX assay was recently reported to predict risk for distant recurrence among a clinical trial population of tamoxifen-treated patients with lymph node-negative, estrogen receptor (ER)-positive breast cancer. To confirm and extend these findings, we evaluated the performance of this 21-gene assay among node-negative patients from a community hospital setting. METHODS: A case-control study was conducted among 4,964 Kaiser Permanente patients diagnosed with node-negative invasive breast cancer from 1985 to 1994 and not treated with adjuvant chemotherapy. Cases (n = 220) were patients who died from breast cancer. Controls (n = 570) were breast cancer patients who were individually matched to cases with respect to age, race, adjuvant tamoxifen, medical facility and diagnosis year, and were alive at the date of death of their matched case. Using an RT-PCR assay, archived tumor tissues were analyzed for expression levels of 16 cancer-related and five reference genes, and a summary risk score (the Recurrence Score) was calculated for each patient. Conditional logistic regression methods were used to estimate the association between risk of breast cancer death and Recurrence Score. RESULTS: After adjusting for tumor size and grade, the Recurrence Score was associated with risk of breast cancer death in ER-positive, tamoxifen-treated and -untreated patients (P = 0.003 and P = 0.03, respectively). At 10 years, the risks for breast cancer death in ER-positive, tamoxifen-treated patients were 2.8% (95% confidence interval [CI] 1.7–3.9%), 10.7% (95% CI 6.3–14.9%), and 15.5% (95% CI 7.6–22.8%) for those in the low, intermediate and high risk Recurrence Score groups, respectively. They were 6.2% (95% CI 4.5–7.9%), 17.8% (95% CI 11.8–23.3%), and 19.9% (95% CI 14.2–25.2%) for ER-positive patients not treated with tamoxifen. In both the tamoxifen-treated and -untreated groups, approximately 50% of patients had low risk Recurrence Score values. CONCLUSION: In this large, population-based study of lymph node-negative patients not treated with chemotherapy, the Recurrence Score was strongly associated with risk of breast cancer death among ER-positive, tamoxifen-treated and -untreated patients