Covariate measurement error adjustment for matched case-control studies.

We propose a conditional scores procedure for obtaining bias-corrected estimates of log odds ratios from matched case-control data in which one or more covariates are subject to measurement error. The approach involves conditioning on sufficient statistics for the unobservable true covariates that are treated as fixed unknown parameters. For the case of Gaussian nondifferential measurement error, we derive a set of unbiased score equations that can then be solved to estimate the log odds ratio parameters of interest. The procedure successfully removes the bias in naive estimates, and standard error estimates are obtained by resampling methods. We present an example of the procedure applied to data from a matched case-control study of prostate cancer and serum hormone levels, and we compare its performance to that of regression calibration procedures.

Permutation tests for joinpoint regression with applications to cancer rates.

The identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data. We apply a joinpoint regression model to describe such continuous changes and use the grid-search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors. We find the number of significant joinpoints by performing several permutation tests, each of which has a correct significance level asymptotically. Each p-value is found using Monte Carlo methods, and the overall asymptotic significance level is maintained through a Bonferroni correction. These tests are extended to the situation with non-constant variance to handle rates with Poisson variation and possibly autocorrelated errors. The performance of these tests are studied via simulations and the tests are applied to U.S. prostate cancer incidence and mortality rates.

Conditional logistic regression with sandwich estimators: application to a meta-analysis.

Motivated by a meta-analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis, we explore the use of sandwich estimators of variance with conditional logistic regression. Classical conditional logistic regression assumes that the parameters are fixed effects across all clusters, while the sandwich estimator gives appropriate inferences for either fixed effects or random effects. However, inference using the standard Wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters. Since our example violates this condition, we introduce two modifications to the standard Wald test. First, we reduce the bias of the empirical variance estimator (the middle of the sandwich) by using standardized residuals. Second, we approximately account for the variance of these estimators by using the t-distribution instead of the normal distribution, where the degrees of freedom are estimated using Satterthwaite's approximation. Through simulations, we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random. We achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters.

Effect of different types and amounts of fat on the development of mammary tumors in rodents: a review.

We performed a meta-analysis on data extracted from 97 reports of experiments, involving a total of 12,803 mice or rats, studying the effect on mammary tumor incidence of different types of dietary fatty acids. Fatty acids were categorized into saturated, monounsaturated, n-6 polyunsaturated, and n-3 polyunsaturated. We modeled the relation between tumor incidence and percentage of total calories from these fatty acids using conditional logistic regression and allowing for varying effects between experiments, and for each fatty acid we estimated the effect of substituting the fatty acid calories for nonfat calories. Our results show that n-6 polyunsaturated fatty acids (PUFAs) have a strong tumor-enhancing effect and that saturated fats have a weaker tumor-enhancing effect. The n-3 PUFAs have a small protective effect that is not statistically significant. There is no significant effect of monounsaturated fats. n-6 PUFAs have a stronger tumor-enhancing effect at levels under 4% of total calories, but an effect is still present at intake levels greater than 4% of calories. In addition, when the intake of n-6 PUFAs is at least 4% of calories, the n-6 PUFA effect remains stronger than the saturated fat effect.

Statistical analysis of animal cancer chemoprevention experiments.

We explore the use of a statistical model proposed by Kokoska (1987, Biometrics 43, 525-534) for the analysis of animal cancer chemoprevention experiments. We show, using an example, that the results derived from the method can be sensitive to the parametric forms of the distributions that are assumed, particularly to the distribution of the number of tumors per animal. We propose goodness-of-fit tests to aid in the choice of the distributions.