Douglas J. Taylor

Application of mixed models to assess exposures monitored by construction workers during hot processes

Particulate exposures were assessed among construction workers engaged in hot processes in four jobs (boilermakers, ironworkers, pipefitters and welder-fitters) at nine sites in the U.S. After being trained by occupational hygienists, the workers obtained shift-long personal samples at each site for total particulates (TP). Selected samples were also assayed for manganese (Mn), nickel (Ni), and chromium (Cr). Workers provided information about process- and task-related covariates that were present on the days of monitoring. Data were investigated with mixed-model regression analyses that designated the jobs and covariates as fixed effects and the worker and error terms as random effects. Results indicated that the within-worker variance components, but not the between-worker variance components, could be pooled among jobs. Mean air levels for a given agent varied by roughly six to 100 fold among the jobs, with boilermakers and ironworkers experiencing much higher levels of TP and Mn than pipefitters and welder-fitters. Limited data also suggested that welder-fitters were exposed to greater levels of Ni and Cr than pipefitters. Sufficient sample sizes were available to evaluate the effects of covariates upon exposures to TP and Mn. As expected, processes involving more than 50% hot work led to substantially higher levels of TP and Mn than those involving shorter durations of hot work. Local-exhaust or mechanical ventilation reduced exposure to TP (but not Mn) by as much as 44%, and shielded or manual arc welding increased exposure to Mn (but not TP) by about 80%. Parameters estimated with these mixed models were used to calculate probabilities that workers were exposed at levels above U.S. occupational exposure limits (OELs). Regarding TP and Mn, these calculations suggested that 26-95% of exposures to boilermakers and pipefitters and 2-13% of exposures to pipefitters and welder-fitters exceeded the current Threshold Limit Values. Among welder-fitters, limited data also pointed to probabilities of 2-50% for exceeding particular OELs for Ni and Cr. Using the significance of the estimated random-worker effects as a gauge for the uniformity of exposure within a job, administrative or engineering changes appear appropriate for reducing exposures to boilermakers and ironworkers, while individual personal environments should be investigated for pipefitters and welder-fitters.

Comparative survival of hepatitis A virus, poliovirus and indicator viruses in geographically diverse seawaters

The presence and persistence of enteric viruses in sewage contaminated seawater is an important public health concern for bathing, surfing and shellfishing. In an effort to find suitable indicators of enteric viruses in seawater, we compared the survival of two groups of enteric bacteriophages, F-specific coliphages (FRNA phages) and somatic Salmonella bacteriophages (SS phages), to the survival of two human enteric viruses, hepatitis A virus (HAV) and poliovirus type 1 (PV-1), in coastal seawater from three geographic areas (So. California, Hawaii, and North Carolina) at 20°C. Concentrations of all four viruses decreased over 30 days from their initial titers and there was little difference in the survival of a particular virus among the three seawaters. However, the extent of reduction varied among the four viruses. Survival was greater for the SS phages than for any of the other viruses, with an estimated 4 log 10 reduction time of about 10 weeks. FRNA phages and PV-1 were inactivated rapidly, with 4 log 10 reductions in ~ 1 week. HAV reductions were intermediate between SS phages and FRNA phages, with 4 log 10 reductions in about 4 weeks. The observed differences in virus survival suggest that SS phages are more persistent in seawater than other viruses and hence may be good indicators for enteric viruses in seawater.

Computing Confidence Bounds for Power and Sample Size of the General Linear Univariate Model

The power of a test, the probability of rejecting the null hypothesis in favor of an alternative, may be computed using estimates of one or more distributional parameters. Statisticians frequently fix mean values and calculate power or sample size using a variance estimate from an existing study. Hence computed power becomes a random variable for a fixed sample size. Likewise, the sample size necessary to achieve a fixed power varies randomly. Standard statistical practice requires reporting uncertainty associated with such point estimates. Previous authors studied an asymptotically unbiased method of obtaining confidence intervals for noncentrality and power of the general linear univariate model in this setting. We provide exact confidence intervals for noncentrality, power, and sample size. Such confidence intervals, particularly one-sided intervals, help in planning a future study and in evaluating existing studies.

BIAS IN LINEAR MODEL POWER AND SAMPLE SIZE CALCULATION DUE TO ESTIMATING NONCENTRALITY

Data analysts frequently calculate power and sample size for a planned study using mean and variance estimates from an initial trial. Hence power, or the sample size needed to achieve a fixed power, varies randomly. Such calculations can be very inaccurate in the General Linear Univariate Model (GLUM). Biased noncentrality estimators and censored power calculations create inaccuracy. Censoring occurs if only certain outcomes of an initial trial lead to a power calculation. For example, a confirmatory study may be planned (and a sample size estimated) only following a significant result in the initial trial. Computing accurate point estimates or confidence bounds of GLUM noncentrality, power, or sample size in the presence of censoring involves truncated noncentral F distributions. We recommend confidence bounds, whether or not censoring occurs. A power analysis of data from humans exposed to carbon monoxide demonstrates the substantial impact on sample size that may occur. The results highlight potential biases and should aid study planning and interpretation.

Simultaneous Assessment of Occupational Exposures from Multiple Worker Groups

The methods developed by Rappaport et al. [Ann. Occup. Hyg. 39 (1995) 469] and Lyles et al. [J. Agri. Bio. Environ. Stat. 2 (1997a) 64; Ann. Occup. Hyg. 41 (1997b) 63]) for assessing workplace exposures on a group-by-group basis are extended to allow for the simultaneous assessment of data from multiple worker groups within the same industry. These extended methods allow models to be fit simultaneously to data on all groups in a study, even when some of the groups might not contribute adequate information to be modeled separately. We assume that the exposures are log-normally distributed, and that they can be adequately modeled by a mixed effects regression model with parameters for exposure levels and for between- and within-worker variance components. Simultaneously analyzing data from multiple groups is only advantageous when at least one of these variance components can be assumed to be homogeneous across the groups. Here, we advocate testing an assumption of homogeneous within-worker variance components, sigma(2)(w,h), using a likelihood ratio test to choose between a full model (distinct sigma(2)(w,h) for each group) and a reduced model (common sigma(2)(w) across groups). We then develop a procedure, which is conditional on the results of the likelihood ratio test, for testing whether or not each group of workers is overexposed to the contaminant of interest. This modeling and testing procedure was applied to 39 different data sets, each containing data for multiple groups, from a wide variety of industries. For these data, the testing procedure generally resulted in the same conclusion regarding overexposure under both models, even in those data sets where the within-worker variance components appeared to be quite heterogeneous. We also conducted a small simulation study to estimate the significance level of the proposed testing procedure, and found that the significance levels tended to be adequately close to the specified nominal level when a likelihood ratio test with significance level of at least 0.01 was used as a preliminary test. Additionally, we make specific recommendations for designing studies and suggest a method for determining whether engineering and administrative controls or individual-level interventions would be of most benefit to an overexposed group of workers.

Analytic, Computational, and Approximate Forms for Ratios of Noncentral and Central Gaussian Quadratic Forms

Many useful statistics equal the ratio of a possibly noncentral chi-square to a quadratic form in Gaussian variables with all positive weights. Expressing the density and distribution function as positively weighted sums of corresponding F functions has many advantages. The mixture forms have analytic value when embedded within a more complex problem. The mixture forms also have computational value. The expansions work well with quadratic forms having few components and small degrees of freedom. A more general algorithm from earlier literature can take longer or fail to converge in the same setting. Many approximations have been suggested for the problem. A positively weighted noncentral quadratic form can always have two moments matched to a noncentral chi-square. For a single quadratic form, the noncentral form performs neither uniformly more or less accurately than older approximations. The approach also gives a noncentral F approximation for any ratio of a positively weighted noncentral form to a positively weighted central quadratic form. The method provides better accuracy for noncentral ratios than approximations based on a single chi-square. The accuracy suffices for many practical applications, such as power analysis, even with few degrees of freedom. Naturally the approximation proves much faster and simpler to compute than any exact method. Embedding the approximation in analytic expressions provides simple forms which correctly guarantee only positive values have nonzero probabilities, and also automatically reduce to partially or fully exact results when either quadratic form has only one term.

NONINFERIORITY TESTING IN CROSSOVER TRIALS WITH CORRELATED BINARY OUTCOMES AND SMALL EVENT PROPORTIONS WITH APPLICATIONS TO THE ANALYSIS OF CONDOM FAILURE DATA

Regulatory agencies may require demonstrating a new therapy or device as noninferior to an existing method. For example, a new condom type must demonstrate noninferiority to existing latex condoms before consideration as an equivalent method of pregnancy prevention. Studies designed to assess condom effectiveness typically measure experimental and standard condom failure in a crossover trial, resulting in unbalanced correlated binary outcomes with low event proportions. We used simulations to evaluate the test size of a simple population average approach to noninferiority testing with the small event proportions, intracluster correlations, and sample sizes frequently found in condom studies. Results emphasize the importance of considering test accuracy when designing any study.

Estimating and Comparing Correct-Use Failure Probabilities in Clinical Studies of Condom Functionality

In a clinical study comparing the failure probabilities of two condom types, the sample of all reported acts of intercourse in which a study condom was used by a randomized participant is typically defined to be the primary analysis sample. However, it may also be desirable to make comparisons among only those acts in which the participants correctly followed all condom use instructions before, during, and after the act of intercourse (i.e., the “correct-use” subset). The timing associated with the definition of correct use creates a dilemma in that an act cannot be classified as a “correct-use act” until after the completion of both intercourse and withdrawal; if a condom fails (e.g., breaks or slips completely off of the penis) during intercourse then the couple has no chance at correct use during withdrawal. As a result of the implicitly conditional nature of this problem, it is not a simple matter to specify a correct-use subset of the primary analysis sample. With this in mind, we develop estimators for the correct-use failure probabilities, the corresponding standard errors, and test statistics for comparing the correct-use failure probabilities between condom groups. We demonstrate the utility of the proposed methods by applying them to data from a clinical study of condom contraceptive effectiveness, and we use simulated data to investigate the finite sample properties of the proposed methods. The simulation results indicate that one of our proposed estimators is at least approximately unbiased, even in small samples. Furthermore, one-sided noninferiority tests performed using this estimator tend to have sizes that are only marginally larger than the nominal test size in moderate to large samples.

Comparison of clinical findings between intensity-windowed versus CLAHE presentations of chest CT images

We are investigating how radiologistss readings of standard intensity windowed (IW) chest computed tomography (CT) films compare with readings of the same images processed with contrast limited adaptive histogram equalization (CLAHE). Previously reported studies where CLAHE has been tested have involved detection of computer generated targets in medical images. Our study is designed to evaluate CLAHE when applied to clinical material and to compare the diagnostic information perceived by the radiologists from CLAHE processed images to that from the conventional IW images. Our initial experiment with two radiologists did not yield conclusive results, due in part, to inadequate observer training prior to the experiment. The initial experimental protocol was redesigned to include more in-depth training. Three new radiologist observers were recruited for the follow-up study. Results from the initial study are reviewed and the follow-up study is presented. In the new study we find that while CLAHE and IW are not statistically significantly different overall, there are specific clinical findings where the radiologists were less comfortable reading CLAHE presentations. Advantages and disadvantages of using CLAHE as a replacement or as an adjunct to IW are discussed.