Temporal changes in the proportion of Salmonella outbreaks associated with 12 food commodity groups in the United States.

Using data from 20 years of Salmonella foodborne outbreaks, this study investigates significant trends in the proportion of outbreaks associated with 12 broad commodity groups. Outbreak counts are demonstrated to have a stronger trend signal than outbreak illness counts. The number of outbreaks with an identified food vehicle increased significantly between 1998 and 2000. This was followed by a 10-year period when the number of outbreaks decreased. The number of outbreaks increased significantly between 2010 and 2014 and then remained unchanged for the remainder of the study period. During the period of 1998 through 2017, the proportion of outbreaks for three commodities groups, consisting of eggs, pork and seeded vegetables, changed significantly. No significant changes were observed in the remaining nine commodity groups. Simple approximations are derived to highlight the effect of dependencies between outbreak proportions and a consumption analysis for meat and poultry is used to enhance the limited interpretability of the changes in these proportions. Given commodity-specific approaches to verifying food safety and promoting pathogen reduction, regulatory agencies benefit from analyses that elucidate illness trends attributable to the products under their jurisdiction. Results from this trend analysis can be used to inform the development and assessment of new pathogen reduction programmes in the United States.

Comparing Characteristics of Sporadic and Outbreak-Associated Foodborne Illnesses, United States, 2004-2011.

Outbreak data have been used to estimate the proportion of illnesses attributable to different foods. Applying outbreak-based attribution estimates to nonoutbreak foodborne illnesses requires an assumption of similar exposure pathways for outbreak and sporadic illnesses. This assumption cannot be tested, but other comparisons can assess its veracity. Our study compares demographic, clinical, temporal, and geographic characteristics of outbreak and sporadic illnesses from Campylobacter, Escherichia coli O157, Listeria, and Salmonella bacteria ascertained by the Foodborne Diseases Active Surveillance Network (FoodNet). Differences among FoodNet sites in outbreak and sporadic illnesses might reflect differences in surveillance practices. For Campylobacter, Listeria, and Escherichia coli O157, outbreak and sporadic illnesses are similar for severity, sex, and age. For Salmonella, outbreak and sporadic illnesses are similar for severity and sex. Nevertheless, the percentage of outbreak illnesses in the youngest age category was lower. Therefore, we do not reject the assumption that outbreak and sporadic illnesses are similar.

Fitting a distribution to censored contamination data using Markov Chain Monte Carlo methods and samples selected with unequal probabilities.

The fitting of statistical distributions to chemical and microbial contamination data is a common application in risk assessment. These distributions are used to make inferences regarding even the most pedestrian of statistics, such as the population mean. The reason for the heavy reliance on a fitted distribution is the presence of left-, right-, and interval-censored observations in the data sets, with censored observations being the result of nondetects in an assay, the use of screening tests, and other practical limitations. Considerable effort has been expended to develop statistical distributions and fitting techniques for a wide variety of applications. Of the various fitting methods, Markov Chain Monte Carlo methods are common. An underlying assumption for many of the proposed Markov Chain Monte Carlo methods is that the data represent independent and identically distributed (iid) observations from an assumed distribution. This condition is satisfied when samples are collected using a simple random sampling design. Unfortunately, samples of food commodities are generally not collected in accordance with a strict probability design. Nevertheless, pseudosystematic sampling efforts (e.g., collection of a sample hourly or weekly) from a single location in the farm-to-table continuum are reasonable approximations of a simple random sample. The assumption that the data represent an iid sample from a single distribution is more difficult to defend if samples are collected at multiple locations in the farm-to-table continuum or risk-based sampling methods are employed to preferentially select samples that are more likely to be contaminated. This paper develops a weighted bootstrap estimation framework that is appropriate for fitting a distribution to microbiological samples that are collected with unequal probabilities of selection. An example based on microbial data, derived by the Most Probable Number technique, demonstrates the method and highlights the magnitude of biases in an estimator that ignores the effects of an unequal probability sample design.

Estimating changes in public health following implementation of hazard analysis and critical control point in the United States broiler slaughter industry.

A common approach to reducing microbial contamination has been the implementation of a Hazard Analysis and Critical Control Point (HACCP) program to prevent or reduce contamination during production. One example is the Pathogen Reduction HACCP program implemented by the U.S. Department of Agriculture's Food Safety and Inspection Service (FSIS). This program consisted of a staged implementation between 1996 and 2000 to reduce microbial contamination on meat and poultry products. Of the commodities regulated by FSIS, one of the largest observed reductions was for Salmonella contamination on broiler chicken carcasses. Nevertheless, how this reduction might have influenced the total number of salmonellosis cases in the United States has not been assessed. This study incorporates information from public health surveillance and surveys of the poultry slaughter industry into a model that estimates the number of broiler-related salmonellosis cases through time. The model estimates that-following the 56% reduction in the proportion of contaminated broiler carcasses observed between 1995 and 2000-approximately 190,000 fewer annual salmonellosis cases (attributed to broilers) occurred in 2000 compared with 1995. The uncertainty bounds for this estimate range from approximately 37,000 to 500,000 illnesses. Estimated illnesses prevented, due to the more modest reduction in contamination of 13% between 2000 and 2007, were not statistically significant. An analysis relating the necessary magnitude of change in contamination required for detection via human surveillance also is provided.

Assessing the effectiveness of performance standards for Salmonella contamination of chicken parts.

The United States Department of Agriculture's Food Safety and Inspection Service implemented Salmonella performance standards for establishments producing chicken parts in 2016. The standards were chosen based on the assumption that a 30 % reduction in the occurrence of Salmonella-contaminated chicken parts samples (i.e., legs, breasts or wings) would result following implementation of the performance standard program. The derivation of the performance standards was based on data collected prior to the implementation of the standards and in the intervening years, so overall changes in the Salmonella contamination of this product can be assessed. This study presents a historical review of changes in Salmonella contamination on chicken parts as these changes relate to the performance standard. The analysis demonstrates that the reduction in Salmonella contaminated chicken parts samples was more than 75 %, so the FSIS risk assessment significantly underestimated the actual reduction in Salmonella contamination. An analysis of chicken parts samples collected at retail demonstrates reductions of a similar magnitude. Changes in the characteristics of Salmonella contamination that are potentially relevant to the occurrence or severity of human illness, such as seasonal changes in contamination, the composition of serotypes and changes in antimicrobial resistance, are also assessed. Small but significant seasonal increases in contamination were observed, with the peaks occurring in late winter rather than the more traditional late summer peak. Rapid changes in both the five most common serotypes and antimicrobial resistance patterns were also observed.

A quantitative risk metric to support individual sanitary measure reviews in international trade.

In order for the United States Department of Agriculture's (USDA) Food Safety and Inspection Service (FSIS) to make an equivalence determination for a foreign meat, poultry or egg products inspection procedure that differs from FSIS inspection procedures (an Individual Sanitary Measure or ISM), a country must demonstrate objectively that its food safety inspection system provides the same level of public health protection as the FSIS inspection system. To evaluate microbiological testing data that such countries may submit to this end, we present a possible risk metric to inform FSIS's assessment of whether products produced under an alternative inspection system in another country pose no greater consumer risk of foodborne illness than products produced under FSIS inspection. This metric requires evaluation of prevalence estimates of pathogen occurrence in products for the foreign country and the U.S. and determining what constitutes an unacceptable deviance of another country's prevalence from the U.S. prevalence, i.e., the margin of equivalence. We define the margin of equivalence as a multiple of the standard error of the U.S. prevalence estimate. Minimizing the margin of equivalence ensures the maximum public health protection for U.S. consumers, but an optimum choice must also avoid undue burden for quantitative data from alternative inspection systems in the foreign country. Across a wide range of U.S. prevalence levels and sample sizes, we determine margin of equivalence values that provide high confidence in conclusions as to whether or not the country's product poses no greater risk of foodborne illness from microbiological pathogens. These margins of equivalence can be used to inform FSIS's equivalence determination for an ISM request from a foreign country. Illustrative examples are used to support this definition of margin of equivalence. This approach is consistent with the World Trade Organization's concept of risk equivalence and is transparent and practical to apply in situations when FSIS makes an equivalence determination for an ISM requested by a foreign country.

Methodology for determining the appropriateness of a linear dose-response function.

Microbial food safety risk assessment models can often at times be simplified by eliminating the need to integrate a complex dose-response relationship across a distribution of exposure doses. This is possible if exposure pathways lead to pathogens at exposure that consistently have a small probability of causing illness. In this situation, the probability of illness will follow an approximately linear function of dose. Consequently, the predicted probability of illness per serving across all exposures is linear with respect to the expected value of dose. The majority of dose-response functions are approximately linear when the dose is low. Nevertheless, what constitutes "low" is dependent on the parameters of the dose-response function for a particular pathogen. In this study, a method is proposed to determine an upper bound of the exposure distribution for which the use of a linear dose-response function is acceptable. If this upper bound is substantially larger than the expected value of exposure doses, then a linear approximation for probability of illness is reasonable. If conditions are appropriate for using the linear dose-response approximation, for example, the expected value for exposure doses is two to three logs(10) smaller than the upper bound of the linear portion of the dose-response function, then predicting the risk-reducing effectiveness of a proposed policy is trivial. Simple examples illustrate how this approximation can be used to inform policy decisions and improve an analyst's understanding of risk.

Framework for microbial food-safety risk assessments amenable to Bayesian modeling.

Regulatory agencies often perform microbial risk assessments to evaluate the change in the number of human illnesses as the result of a new policy that reduces the level of contamination in the food supply. These agencies generally have regulatory authority over the production and retail sectors of the farm-to-table continuum. Any predicted change in contamination that results from new policy that regulates production practices occurs many steps prior to consumption of the product. This study proposes a framework for conducting microbial food-safety risk assessments; this framework can be used to quantitatively assess the annual effects of national regulatory policies. Advantages of the framework are that estimates of human illnesses are consistent with national disease surveillance data (which are usually summarized on an annual basis) and some of the modeling steps that occur between production and consumption can be collapsed or eliminated. The framework leads to probabilistic models that include uncertainty and variability in critical input parameters; these models can be solved using a number of different Bayesian methods. The Bayesian synthesis method performs well for this application and generates posterior distributions of parameters that are relevant to assessing the effect of implementing a new policy. An example, based on Campylobacter and chicken, estimates the annual number of illnesses avoided by a hypothetical policy; this output could be used to assess the economic benefits of a new policy. Empirical validation of the policy effect is also examined by estimating the annual change in the numbers of illnesses observed via disease surveillance systems.

Comparative history of Campylobacter contamination on chicken meat and campylobacteriosis cases in the United States: 1994-2018.

In many countries campylobacteriosis ranks as one of the most frequently reported foodborne illnesses and poultry is the commodity that is most often associated with these illnesses. Nevertheless, efforts to reduce the occurrence of pathogen contamination on poultry are often more focused on Salmonella. While some control measures are pathogen specific, such as pre-harvest vaccination for Salmonella, improvements in sanitary dressing and interventions applied during the slaughter process can be effective against all forms of microbial contamination. To investigate the potential effectiveness of these non-specific pathogen reduction strategies in the United States, it is helpful to assess if, and by how much, Campylobacter contamination of chicken meat has changed across time. This study assesses change considering data collected in both slaughter and retail establishments and comparing observed trends in contamination with trends in human surveillance data. The results support the assertion that substantial reductions in Campylobacter contamination of chicken meat in the late 1990s and early 2000s contributed to a reduction in the human case rate of campylobacteriosis. Further reductions in chicken meat contamination between 2013 and 2018 are more difficult to associate with trends in human illnesses, with one contributing factor being the inclusion of culture independent diagnostic test results in the official case counts during that time. Other contributing factors are discussed.

Determining relationships between the seasonal occurrence of Escherichia coli O157:H7 in live cattle, ground beef, and humans.

The prevalence and concentration of many foodborne pathogens exhibit seasonal patterns at different stages of the farm-to-table continuum. Escherichia coli O157:H7 is one such pathogen. While numerous studies have described the seasonal trend of E. coli O157:H7 in live cattle, ground beef, and human cases, it is difficult to relate the results from these different studies and determine the interrelationships that drive the seasonal pattern of beef-related human illnesses. This study uses a common modeling approach, which facilitates the comparisons across data sets, to relate prevalence in live cattle to raw ground beef and human illness. The results support an intuitive model where a seasonal rise of E. coli O157:H7 in cattle drives increased ground beef prevalence and a corresponding rise in the human case rate. We also demonstrate the use of these models to assess the public health impact of consumer behaviors. We present an example that suggests that the probability of illness, associated with summertime cooking and handling practices, is not substantially higher than the baseline probability associated with more conventional cooking and handling practices during the remainder of the year.

Changes in Salmonella Contamination in Meat and Poultry Since the Introduction of the Pathogen Reduction and Hazard Analysis and Critical Control Point Rule.

ABSTRACT: In 1996, the Food Safety and Inspection Service (FSIS) published its pathogen reduction and hazard analysis and critical control point (PR-HACCP) rule. The intention of this program was to reduce microbial contamination on meat, poultry, and egg products. The program was implemented in stages between January 1998 and January 2000, with sampling for Escherichia coli O157:H7 and/or Salmonella in large production establishments beginning in 1998. As the PR-HACCP program begins its third decade, it is reasonable to question whether there have been reductions in the frequency of pathogen-contaminated meat and poultry products reaching consumers. This study summarizes the results for over 650,000 samples collected by FSIS between 2000 and 2018 in slaughter and processing establishments across the United States and compares these results to the roughly 100,000 retail samples collected by the U.S. Food and Drug Administration between 2002 and 2017. The data demonstrate that there has been an overall reduction in the occurrence of Salmonella on meat and poultry products, but the direction and magnitude of change has not been consistent over time or across commodities. Although the available data do not support the identification of causal factors for the observed changes, a historical review of the timing of various factors and policy decisions generates potential hypotheses for the observed changes.

Risk assessment to estimate the probability of a chicken flock infected with H5N1 highly pathogenic avian influenza virus reaching slaughter undetected.

Highly pathogenic avian influenza (HPAI) H5N1 is an infectious disease of fowl that can cause rapid and pervasive mortality resulting in complete flock loss. It has also been shown to cause death in humans. Although H5N1 HPAI virus (HPAIV) has not been identified in the United States, there are concerns about whether an infected flock could remain undetected long enough to pose a risk to consumers. This paper considers exposure from an Asian lineage H5N1 HPAIV-infected chicken flock given that no other flocks have been identified as H5N1 HPAIV positive (the index flock). A state-transition model is used to evaluate the probability of an infected flock remaining undetected until slaughter. This model describes three possible states within the flock: susceptible, infected, and dead, and the transition probabilities that predict movements between the possible states. Assuming a 20,000-bird house with 1 bird initially infected, the probability that an H5N1 HPAIV-infected flock would be detected before slaughter is approximately 94%. This is because H5N1 HPAIV spreads rapidly through a flock, and bird mortality quickly reaches high levels. It is assumed that approximately 2% or greater bird mortality due to H5N1 HPAIV would result in on-farm identification of the flock as infected. The only infected flock likely to reach slaughter undetected is one that was infected within approximately 3.5 days of shipment. In this situation, there is not enough time for high mortality to present. These results suggest that the probability of an infected undetected flock going to slaughter is low, yet such an event could occur if a flock is infected at the most opportune time.

Estimating herd prevalence of bovine brucellosis in 46 USA states using slaughter surveillance.

Making valid inferences about herd prevalence from data collected at slaughter is difficult because the observed sample is dependent on the number of animals sampled from each herd, which varies with herd size and culling practices, and the probability of a positive test result, which depends on variable within-herd prevalence levels as well as test sensitivity and specificity. In this study, brucellosis herd prevalence among beef cow-calf operations is estimated from slaughter surveillance data using a method that combines process modeling with Bayesian inference. Inferences are made for two populations; the first population comprises cow-calf beef herds in a typical U.S. state. The second population represents all beef herds in a collection of 46 low-risk states. The Bayesian Monte Carlo method used in this study links process model inputs to observed surveillance results via Bayes Theorem. The surveillance evidence across multiple years is accumulated at a discounted rate based on the probability of introducing new infection into an area. The process model's inputs include herd size, culling rate per herd, within-herd prevalence, serologic test performance, and the probability of successfully investigating positive results. The surveillance results comprise the number of cows and bulls tested at slaughter and the number of affected herds detected each year. The results find at least 95% confidence that brucellosis herd prevalence among beef cow-calf herds is less than 0.014% (3 per 21,500 herds) and 0.00081% (5 per 6,15,770) after 5 years of slaughter surveillance (with no detections of affected herds) in a typical U.S. state and across 46 low-risk U.S. states, respectively. These results were based on conservative modeling assumptions, but sensitivity analysis suggests only slight changes in the results from changing the assumed process model input values. The most influential analytic input was the probability of introducing new infection into a putatively brucellosis-free state or group of states.

Evaluating the effectiveness of pasteurization for reducing human illnesses from Salmonella spp. in egg products: results of a quantitative risk assessment.

As part of the process for developing risk-based performance standards for egg product processing, the United States Department of Agriculture (USDA) Food Safety and Inspection Service (FSIS) undertook a quantitative microbial risk assessment for Salmonella spp. in pasteurized egg products. The assessment was designed to assist risk managers in evaluating egg handling and pasteurization performance standards for reducing the likelihood of Salmonella in pasteurized egg products and the subsequent risk to human health. The following seven pasteurized liquid egg product formulations were included in the risk assessment model, with the value in parentheses indicating the estimated annual number of human illnesses from Salmonella from each: egg white (2636), whole egg (1763), egg yolk (708), whole egg with 10% salt (407), whole egg with 10% sugar (0), egg yolk with 10% salt (11), and egg yolk with 10% sugar (0). Increased levels of pasteurization were predicted to be highly effective mitigations for reducing the number of illnesses. For example, if all egg white products were pasteurized for a 6-log(10) reduction of Salmonella, the estimated annual number of illnesses from these products would be reduced from 2636 to 270. The risk assessment identified several data gaps and research needs, including a quantitative study of cross-contamination during egg product processing and characterization of egg storage times and temperatures (i) on farms and in homes, (ii) for eggs produced off-line, and (iii) for egg products at retail. Pasteurized egg products are a relatively safe food; however, findings from this study suggest increased pasteurization can make them safer.

Updating a 2-class attributes sampling plan to account for changes in laboratory methods.

Advances in microbiological testing methods have led to faster and less expensive assays. Given these advances, it is logical to employ these assays for use in the sampling plan of an existing microbiological criterion. A change in the performance characteristics of the assay can affect the intended effect of the microbiological criterion. This study describes a method for updating a 2-class attributes sampling plan to account for the different test sensitivity and specificity of a new assay and provides an example based on the replacement of a culture-based assay with a real-time polymerase chain reaction assay.

Adoption of Neutralizing Buffered Peptone Water Coincides with Changes in Apparent Prevalence of Salmonella and Campylobacter of Broiler Rinse Samples.

Buffered peptone water is the rinsate commonly used for chicken rinse sampling. A new formulation of buffered peptone water was developed to address concerns about the transfer of antimicrobials, used during poultry slaughter and processing, into the rinsate. This new formulation contains additives to neutralize the antimicrobials, and this neutralizing buffered peptone water replaced the original formulation for all chicken carcass and chicken part sampling programs run by the Food Safety and Inspection Service beginning in July 2016. Our goal was to determine whether the change in rinsate resulted in significant differences in the observed proportion of positive chicken rinse samples for both Salmonella and Campylobacter. This assessment compared sampling results for the 12-month periods before and after implementation. The proportion of carcass samples that tested positive for Salmonella increased from approximately 0.02 to almost 0.06. Concurrently, the proportion of chicken part samples that tested for Campylobacter decreased from 0.15 to 0.04. There were no significant differences associated with neutralizing buffered peptone water for the other two product-pathogen pairs. Further analysis of the effect of the new rinsate on corporations that operate multiple establishments demonstrated that changes in the percent positive rates differed across the corporations, with some corporations being unaffected, while others saw all of the establishments operated by the corporation move from passing to failing the performance standard and vice versa. The results validated earlier concerns that antimicrobial contamination of rinse samples was causing false-negative Salmonella testing results for chicken carcasses. The results also indicate that additional development work may still be required before the rinsate is sufficiently robust for its use in Campylobacter testing.

Monte Carlo approaches for determining power and sample size in low-prevalence applications.

The prevalence of disease in many populations is often low. For example, the prevalence of tuberculosis, brucellosis, and bovine spongiform encephalopathy range from 1 per 100,000 to less than 1 per 1,000,000 in many countries. When an outbreak occurs, epidemiological investigations often require comparing the prevalence in an exposed population with that of an unexposed population. To determine if the level of disease in the two populations is significantly different, the epidemiologist must consider the test to be used, desired power of the test, and determine the appropriate sample size for both the exposed and unexposed populations. Commonly available software packages provide estimates of the required sample sizes for this application. This study shows that these estimated sample sizes can exceed the necessary number of samples by more than 35% when the prevalence is low. We provide a Monte Carlo-based solution and show that in low-prevalence applications this approach can lead to reductions in the total samples size of more than 10,000 samples.

Estimating correlation of prevalence at two locations in the farm-to-table continuum using qualitative test data.

The presence or absence of contaminants in food samples changes as a commodity moves along the farm-to-table continuum. Interest lies in the degree to which the prevalence (i.e., infected animals or contaminated sample units) at one location in the continuum, as measured by the proportion of test-positive samples, is correlated with the prevalence at a location later in the continuum. If prevalence of a contaminant at one location in the continuum is strongly correlated with the prevalence of the contaminant later in the continuum, then the effect of changes in contamination on overall food safety can be better understood. Pearson's correlation coefficient is one of the simplest metrics of association between two measurements of prevalence but it is biased when data consisting of presence/absence testing results are used to directly estimate the correlation. This study demonstrates the potential magnitude of this bias and explores the utility of three methods for unbiased estimation of the degree of correlation in prevalence. An example, based on testing broiler chicken carcasses for Salmonella at re-hang and post-chill, is used to demonstrate the methods.

Indirect fluorescent antibody testing of cerebrospinal fluid for diagnosis of equine protozoal myeloencephalitis.

OBJECTIVE: To assess the use of CSF testing with an indirect fluorescent antibody test (IFAT) for diagnosis of equine protozoal myeloencephalitis (EPM) caused by Sarcocystis neurona. SAMPLE POPULATION: Test results of 428 serum and 355 CSF samples from 182 naturally exposed, experimentally infected, or vaccinated horses. PROCEDURE: EPM was diagnosed on the basis of histologic examination of the CNS. Probability distributions were fitted to serum IFAT results in the EPM+ and EPM-horses, and correlation between serum and CSF results was modeled. Pairs of serum-CSF titers were generated by simulation, and titer-specific likelihood ratios and post-test probabilities of EPM at various pretest probability values were estimated. Post-test probabilities were compared for use of a serum-CSF test combination, a serum test only, and a CSF test only. RESULTS: Post-test probabilities of EPM increased as IFAT serum and CSF titers increased. Post-test probability differences for use of a serum-CSF combination and a serum test only were < or = 19% in 95% of simulations. The largest increases occurred when serum titers were from 40 to 160 and pre-test probabilities were from 5% to 60%. In all simulations, the difference between pre- and post-test probabilities was greater for a CSF test only, compared with a serum test only. CONCLUSIONS AND CLINICAL RELEVANCE: CSF testing after a serum test has limited usefulness in the diagnosis of EPM. A CSF test alone might be used when CSF is required for other procedures. Ruling out other causes of neurologic disease reduces the necessity of additional EPM testing.

When Are Qualitative Testing Results Sufficient To Predict a Reduction in Illnesses in a Microbiological Food Safety Risk Assessment?

Process models that include the myriad pathways that pathogen-contaminated food may traverse before consumption and the dose-response function to relate exposure to likelihood of illness may represent a "gold standard" for quantitative microbial risk assessment. Nevertheless, simplifications that rely on measuring the change in contamination occurrence of a raw food at the end of production may provide reasonable approximations of the effects measured by a process model. In this study, we parameterized three process models representing different product-pathogen pairs (i.e., chicken-Salmonella, chicken-Campylobacter, and beef-E. coli O157:H7) to compare with predictions based on qualitative testing of the raw product before consideration of mixing, partitioning, growth, attenuation, or dose-response processes. The results reveal that reductions in prevalence generated from qualitative testing of raw finished product usually underestimate the reduction in likelihood of illness for a population of consumers. Qualitative microbial testing results depend on the test's limit of detection. The negative bias is greater for limits of detection that are closer to the center of the contamination distribution and becomes less as the limit of detection is moved further into the right tail of the distribution. Nevertheless, a positive bias can result when the limit of detection refers to very high contamination levels. Changes in these high levels translate to larger consumed doses for which the slope of the dose-response function is smaller compared with the larger slope associated with smaller doses. Consequently, in these cases, a proportional reduction in prevalence of contamination results in a less than proportional reduction in probability of illness. The magnitudes of the biases are generally less for nonscalar (versus scalar) adjustments to the distribution.