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1.  An updated prostate cancer staging nomogram (Partin tables) based on cases from 2006 to 2011 
BJU international  2012;111(1):10.1111/j.1464-410X.2012.11324.x.
To update the 2007 Partin tables in a contemporary patient population.
Patients and Methods
The study population consisted of 5,629 consecutive men who underwent RP and staging lymphadenectomy at the Johns Hopkins Hospital between January 1, 2006 and July 30, 2011 and met inclusion criteria.
Polychotomous logistic regression analysis was used to predict the probability of each pathologic stage category: organ-confined disease (OC), extraprostatic extension (EPE), seminal vesicle involvement (SV+), or lymph node involvement (LN+) based on preoperative criteria.
Preoperative variables included biopsy Gleason score (6, 3+4, 4+3, 8, and 9–10), serum PSA (0–2.5, 2.6–4.0, 4.1–6.0, 6.1–10.0, greater than 10.0 ng/mL), and clinical stage (T1c, T2c, and T2b/T2c).
Bootstrap re-sampling with 1000 replications was performed to estimate 95% confidence intervals for predicted probabilities of each pathologic state.
The median PSA was 4.9 ng/mL, 63% had Gleason 6 disease, and 78% of men had T1c disease.
73% of patients had OC disease, 23% had EPE, 3% had SV+ but not LN+, and 1% had LN+ disease. Compared to the previous Partin nomogram, there was no change in the distribution of pathologic state.
The risk of LN+ disease was significantly higher for tumours with biopsy Gleason 9–10 than Gleason 8 (O.R. 3.2, 95% CI 1.3–7.6).
The c-indexes for EPE vs. OC, SV+ vs. OC, and LN+ vs. OC were 0.702, 0.853, and 0.917, respectively.
Men with biopsy Gleason 4+3 and Gleason 8 had similar predicted probabilities for all pathologic stages.
Most men presenting with Gleason 6 disease or Gleason 3+4 disease have <2% risk of harboring LN+ disease and may have lymphadenectomy omitted at RP.
The distribution of pathologic stages did not change at our institution between 2000–2005 and 2006–2011.
The updated Partin nomogram takes into account the updated Gleason scoring system and may be more accurate for contemporary patients diagnosed with prostate cancer.
PMCID: PMC3876476  PMID: 22834909
prostate cancer; prostatectomy; prostage-specific antigen; nomograms; staging
2.  Reporting and Methods in Clinical Prediction Research: A Systematic Review 
PLoS Medicine  2012;9(5):e1001221.
Walter Bouwmeester and colleagues investigated the reporting and methods of prediction studies in 2008, in six high-impact general medical journals, and found that the majority of prediction studies do not follow current methodological recommendations.
We investigated the reporting and methods of prediction studies, focusing on aims, designs, participant selection, outcomes, predictors, statistical power, statistical methods, and predictive performance measures.
Methods and Findings
We used a full hand search to identify all prediction studies published in 2008 in six high impact general medical journals. We developed a comprehensive item list to systematically score conduct and reporting of the studies, based on recent recommendations for prediction research. Two reviewers independently scored the studies. We retrieved 71 papers for full text review: 51 were predictor finding studies, 14 were prediction model development studies, three addressed an external validation of a previously developed model, and three reported on a model's impact on participant outcome. Study design was unclear in 15% of studies, and a prospective cohort was used in most studies (60%). Descriptions of the participants and definitions of predictor and outcome were generally good. Despite many recommendations against doing so, continuous predictors were often dichotomized (32% of studies). The number of events per predictor as a measure of statistical power could not be determined in 67% of the studies; of the remainder, 53% had fewer than the commonly recommended value of ten events per predictor. Methods for a priori selection of candidate predictors were described in most studies (68%). A substantial number of studies relied on a p-value cut-off of p<0.05 to select predictors in the multivariable analyses (29%). Predictive model performance measures, i.e., calibration and discrimination, were reported in 12% and 27% of studies, respectively.
The majority of prediction studies in high impact journals do not follow current methodological recommendations, limiting their reliability and applicability.
Please see later in the article for the Editors' Summary
Editors' Summary
There are often times in our lives when we would like to be able to predict the future. Is the stock market going to go up, for example, or will it rain tomorrow? Being able predict future health is also important, both to patients and to physicians, and there is an increasing body of published clinical “prediction research.” Diagnostic prediction research investigates the ability of variables or test results to predict the presence or absence of a specific diagnosis. So, for example, one recent study compared the ability of two imaging techniques to diagnose pulmonary embolism (a blood clot in the lungs). Prognostic prediction research investigates the ability of various markers to predict future outcomes such as the risk of a heart attack. Both types of prediction research can investigate the predictive properties of patient characteristics, single variables, tests, or markers, or combinations of variables, tests, or markers (multivariable studies). Both types of prediction research can include also studies that build multivariable prediction models to guide patient management (model development), or that test the performance of models (validation), or that quantify the effect of using a prediction model on patient and physician behaviors and outcomes (impact assessment).
Why Was This Study Done?
With the increase in prediction research, there is an increased interest in the methodology of this type of research because poorly done or poorly reported prediction research is likely to have limited reliability and applicability and will, therefore, be of little use in patient management. In this systematic review, the researchers investigate the reporting and methods of prediction studies by examining the aims, design, participant selection, definition and measurement of outcomes and candidate predictors, statistical power and analyses, and performance measures included in multivariable prediction research articles published in 2008 in several general medical journals. In a systematic review, researchers identify all the studies undertaken on a given topic using a predefined set of criteria and systematically analyze the reported methods and results of these studies.
What Did the Researchers Do and Find?
The researchers identified all the multivariable prediction studies meeting their predefined criteria that were published in 2008 in six high impact general medical journals by browsing through all the issues of the journals (a hand search). They then scored the methods and reporting of each study using a comprehensive item list based on recent recommendations for the conduct of prediction research (for example, the reporting recommendations for tumor marker prognostic studies—the REMARK guidelines). Of 71 retrieved studies, 51 were predictor finding studies, 14 were prediction model development studies, three externally validated an existing model, and three reported on a model's impact on participant outcome. Study design, participant selection, definitions of outcomes and predictors, and predictor selection were generally well reported, but other methodological and reporting aspects of the studies were suboptimal. For example, despite many recommendations, continuous predictors were often dichotomized. That is, rather than using the measured value of a variable in a prediction model (for example, blood pressure in a cardiovascular disease prediction model), measurements were frequently assigned to two broad categories. Similarly, many of the studies failed to adequately estimate the sample size needed to minimize bias in predictor effects, and few of the model development papers quantified and validated the proposed model's predictive performance.
What Do These Findings Mean?
These findings indicate that, in 2008, most of the prediction research published in high impact general medical journals failed to follow current guidelines for the conduct and reporting of clinical prediction studies. Because the studies examined here were published in high impact medical journals, they are likely to be representative of the higher quality studies published in 2008. However, reporting standards may have improved since 2008, and the conduct of prediction research may actually be better than this analysis suggests because the length restrictions that are often applied to journal articles may account for some of reporting omissions. Nevertheless, despite some encouraging findings, the researchers conclude that the poor reporting and poor methods they found in many published prediction studies is a cause for concern and is likely to limit the reliability and applicability of this type of clinical research.
Additional Information
Please access these websites via the online version of this summary at
The EQUATOR Network is an international initiative that seeks to improve the reliability and value of medical research literature by promoting transparent and accurate reporting of research studies; its website includes information on a wide range of reporting guidelines including the REMARK recommendations (in English and Spanish)
A video of a presentation by Doug Altman, one of the researchers of this study, on improving the reporting standards of the medical evidence base, is available
The Cochrane Prognosis Methods Group provides additional information on the methodology of prognostic research
PMCID: PMC3358324  PMID: 22629234
3.  Predictors of the number of under-five malnourished children in Bangladesh: application of the generalized poisson regression model 
BMC Public Health  2013;13:11.
Malnutrition is one of the principal causes of child mortality in developing countries including Bangladesh. According to our knowledge, most of the available studies, that addressed the issue of malnutrition among under-five children, considered the categorical (dichotomous/polychotomous) outcome variables and applied logistic regression (binary/multinomial) to find their predictors. In this study malnutrition variable (i.e. outcome) is defined as the number of under-five malnourished children in a family, which is a non-negative count variable. The purposes of the study are (i) to demonstrate the applicability of the generalized Poisson regression (GPR) model as an alternative of other statistical methods and (ii) to find some predictors of this outcome variable.
The data is extracted from the Bangladesh Demographic and Health Survey (BDHS) 2007. Briefly, this survey employs a nationally representative sample which is based on a two-stage stratified sample of households. A total of 4,460 under-five children is analysed using various statistical techniques namely Chi-square test and GPR model.
The GPR model (as compared to the standard Poisson regression and negative Binomial regression) is found to be justified to study the above-mentioned outcome variable because of its under-dispersion (variance < mean) property. Our study also identify several significant predictors of the outcome variable namely mother’s education, father’s education, wealth index, sanitation status, source of drinking water, and total number of children ever born to a woman.
Consistencies of our findings in light of many other studies suggest that the GPR model is an ideal alternative of other statistical models to analyse the number of under-five malnourished children in a family. Strategies based on significant predictors may improve the nutritional status of children in Bangladesh.
PMCID: PMC3599578  PMID: 23297699
Malnutrition; Under-five children; Predictors; Generalized Poisson regression model; Bangladesh
4.  Haplotype-Based Regression Analysis and Inference of Case–Control Studies with Unphased Genotypes and Measurement Errors in Environmental Exposures 
Biometrics  2007;64(3):673-684.
Summary. It is widely believed that risks of many complex diseases are determined by genetic susceptibilities, environmental exposures, and their interaction. Chatterjee and Carroll (2005, Biometrika 92, 399–418) developed an efficient retrospective maximum-likelihood method for analysis of case–control studies that exploits an assumption of gene–environment independence and leaves the distribution of the environmental covariates to be completely nonparametric. Spinka, Carroll, and Chatterjee (2005, Genetic Epidemiology 29, 108–127) extended this approach to studies where certain types of genetic information, such as haplotype phases, may be missing on some subjects. We further extend this approach to situations when some of the environmental exposures are measured with error. Using a polychotomous logistic regression model, we allow disease status to have K + 1 levels. We propose use of a pseudolikelihood and a related EM algorithm for parameter estimation. We prove consistency and derive the resulting asymptotic covariance matrix of parameter estimates when the variance of the measurement error is known and when it is estimated using replications. Inferences with measurement error corrections are complicated by the fact that the Wald test often behaves poorly in the presence of large amounts of measurement error. The likelihood-ratio (LR) techniques are known to be a good alternative. However, the LR tests are not technically correct in this setting because the likelihood function is based on an incorrect model, i.e., a prospective model in a retrospective sampling scheme. We corrected standard asymptotic results to account for the fact that the LR test is based on a likelihood-type function. The performance of the proposed method is illustrated using simulation studies emphasizing the case when genetic information is in the form of haplotypes and missing data arises from haplotype-phase ambiguity. An application of our method is illustrated using a population-based case–control study of the association between calcium intake and the risk of colorectal adenoma.
PMCID: PMC2672569  PMID: 18047538
EM algorithm; Errors in variables; Gene-environment independence; Gene-environment interactions; Likelihood-ratio tests in misspecified models; Inferences in measurement error models; Profile likelihood; Semiparametric methods
5.  Asthma exacerbation and proximity of residence to major roads: a population-based matched case-control study among the pediatric Medicaid population in Detroit, Michigan 
Environmental Health  2011;10:34.
The relationship between asthma and traffic-related pollutants has received considerable attention. The use of individual-level exposure measures, such as residence location or proximity to emission sources, may avoid ecological biases.
This study focused on the pediatric Medicaid population in Detroit, MI, a high-risk population for asthma-related events. A population-based matched case-control analysis was used to investigate associations between acute asthma outcomes and proximity of residence to major roads, including freeways. Asthma cases were identified as all children who made at least one asthma claim, including inpatient and emergency department visits, during the three-year study period, 2004-06. Individually matched controls were randomly selected from the rest of the Medicaid population on the basis of non-respiratory related illness. We used conditional logistic regression with distance as both categorical and continuous variables, and examined non-linear relationships with distance using polynomial splines. The conditional logistic regression models were then extended by considering multiple asthma states (based on the frequency of acute asthma outcomes) using polychotomous conditional logistic regression.
Asthma events were associated with proximity to primary roads with an odds ratio of 0.97 (95% CI: 0.94, 0.99) for a 1 km increase in distance using conditional logistic regression, implying that asthma events are less likely as the distance between the residence and a primary road increases. Similar relationships and effect sizes were found using polychotomous conditional logistic regression. Another plausible exposure metric, a reduced form response surface model that represents atmospheric dispersion of pollutants from roads, was not associated under that exposure model.
There is moderately strong evidence of elevated risk of asthma close to major roads based on the results obtained in this population-based matched case-control study.
PMCID: PMC3224543  PMID: 21513554
6.  Considering health insurance: how do dialysis initiates with Medicaid coverage differ from persons without Medicaid coverage? 
Background. Type of health insurance is an important mediator of medical outcomes in the United States. Medicaid, a jointly sponsored Federal/State programme, is designed to serve medically needy individuals. How these patients differ from non-Medicaid-enrolled incident dialysis patients and how these differences have changed over time have not been systematically examined.
Methods. Using data from the United States Renal Data System, we identified individuals initiating dialysis from 1995 to 2004 and categorized their health insurance status. Longitudinal trends in demographic, risk behaviour, functional, comorbidity, laboratory and dialysis modality factors, as reported on the Medical Evidence Form (CMS-2728), were examined in all insurance groups. Polychotomous logistic regression was used to estimate adjusted generalized ratios (AGRs) for these factors by insurance status, with Medicaid as the referent insurance group.
Results. Overall, males constitute a growing percentage of both Medicaid and non-Medicaid patients, but in contrast to other insurance groups, Medicaid has a higher proportion of females. Non-Caucasians also constitute a higher proportion of Medicaid patients than non-Medicaid patients. Body mass index increased in all groups over time, and all groups witnessed a significant decrease in initiation on peritoneal dialysis. Polychotomous regression showed generally lower AGRs for minorities, risk behaviours and functional status, and higher AGRs for males, employment and self-care dialysis, for non-Medicaid insurance relative to Medicaid.
Conclusions. While many broad parallel trends are evident in both Medicaid and non-Medicaid incident dialysis patients, many important differences between these groups exist. These findings could have important implications for policy planners, providers and payers.
PMCID: PMC2910325  PMID: 19736241
demographics; dialysis; end-stage renal disease; insurance; Medicaid
7.  Pretreatment SUVmax predicts progression-free survival in early-stage non-small cell lung cancer treated with stereotactic body radiation therapy 
This retrospective study aims to assess the usefulness of SUVmax from FDG-PET imaging as a prognosticator for primary biopsy-proven stage I NSCLC treated with SBRT.
This study includes 95 patients of median age 77 years, with primary, biopsy-confirmed peripheral stage IA/IB NSCLC. All patients were treated with 60Gy in 3 fractions with a median treatment time of six days. Local, regional, and distant failures were evaluated independently according to the terms of RTOG1021. Local, regional, and distant control, overall- and progression-free survival were estimated by the Kaplan-Meier method. Cox proportional hazards regression was performed to determine whether SUVmax, age, KPS, gender, tumor size/T stage, or smoking history influenced outcomes. SUVmax was evaluated as both a continuous and as a dichotomous variable using a cutoff of <5 and ≥5.
Median follow-up for the cohort was 16 months. Median OS and PFS were 25.3 and 40.3 months, respectively. SUV with a cutoff value of 5 predicted for OS and PFS (p = .024 for each) but did not achieve significance for LC (p = .256). On Cox univariate regression analysis, SUV as a dichotomous variable predicted for both OS and PFS (p = .027 and p = .030, respectively). Defined as a continuous variable, SUVmax continued to predict for OS and PFS (p = .032 and p = .003), but also predicted LC (p = .045) and trended toward significance for DC (p = .059).
SUVmax did not predict for OS as a dichotomous or continuous variable. It did, however, predict for PFS as a continuous variable (p = .008), neared significance for local control (p = .057) and trended towards, significance for distant control (p = .092).
SUVmax appears to be a statistically and clinically significant independent prognostic marker for progression-free survival in patients with stage I NSCLC treated with SBRT. Prospective studies to more accurately define the role of tumor FDG uptake in the prognosis of NSCLC are warranted.
PMCID: PMC3922961  PMID: 24479954
8.  Polytomous diagnosis of ovarian tumors as benign, borderline, primary invasive or metastatic: development and validation of standard and kernel-based risk prediction models 
Hitherto, risk prediction models for preoperative ultrasound-based diagnosis of ovarian tumors were dichotomous (benign versus malignant). We develop and validate polytomous models (models that predict more than two events) to diagnose ovarian tumors as benign, borderline, primary invasive or metastatic invasive. The main focus is on how different types of models perform and compare.
A multi-center dataset containing 1066 women was used for model development and internal validation, whilst another multi-center dataset of 1938 women was used for temporal and external validation. Models were based on standard logistic regression and on penalized kernel-based algorithms (least squares support vector machines and kernel logistic regression). We used true polytomous models as well as combinations of dichotomous models based on the 'pairwise coupling' technique to produce polytomous risk estimates. Careful variable selection was performed, based largely on cross-validated c-index estimates. Model performance was assessed with the dichotomous c-index (i.e. the area under the ROC curve) and a polytomous extension, and with calibration graphs.
For all models, between 9 and 11 predictors were selected. Internal validation was successful with polytomous c-indexes between 0.64 and 0.69. For the best model dichotomous c-indexes were between 0.73 (primary invasive vs metastatic) and 0.96 (borderline vs metastatic). On temporal and external validation, overall discrimination performance was good with polytomous c-indexes between 0.57 and 0.64. However, discrimination between primary and metastatic invasive tumors decreased to near random levels. Standard logistic regression performed well in comparison with advanced algorithms, and combining dichotomous models performed well in comparison with true polytomous models. The best model was a combination of dichotomous logistic regression models. This model is available online.
We have developed models that successfully discriminate between benign, borderline, and invasive ovarian tumors. Methodologically, the combination of dichotomous models was an interesting approach to tackle the polytomous problem. Standard logistic regression models were not outperformed by regularized kernel-based alternatives, a finding to which the careful variable selection procedure will have contributed. The random discrimination between primary and metastatic invasive tumors on temporal/external validation demonstrated once more the necessity of validation studies.
PMCID: PMC2988009  PMID: 20961457
9.  Determinants of dental user groups among an elderly, low-income population. 
Health Services Research  1996;30(6):809-825.
OBJECTIVE: We test whether or not there are differences for selected variables among five dental user groups and one nondental group within an elderly, low-income population. DATA SOURCE: We used ten years of Medicare Part B claims data from the Cincinnati Health Department for all clinic users 62 years of age and older who participated in the Municipal Health Services Program. STUDY DESIGN: A polychotomous logistic regression model determined the ability to differentiate between the groups for each of the selected variables, controlling for race. Next, a polychotomous stepwise logistic regression was used in finding a multivariate model for determining dental user group membership. Logistic regression was used to ascertain which variables were discriminators between any two types of dental users. PRINCIPAL FINDINGS: Mean number of medical visits, mean number of prescriptions filled, and race are determinants of group membership, with the nondental group having more medical visits and more likely to be white. Although year of birth cohort is statistically significant in determining dental user types, the direction of effect is not constant across the comparisons. However, the relative risk for being in the two complete denture groups, compared to both compliant subgroups, increases with each older cohort. CONCLUSIONS: Higher levels of medical use may "crowd out" dental use, even when it is without user cost, either because the medical problems are treated as a higher priority, or because dealing with medical needs leaves too little perceived time or energy to seek dental care. Even in a low-income population seeking dental care, there appears to be a birth cohort effect with a decline in the younger elderly who require two complete dentures.
PMCID: PMC1070094  PMID: 8591931
10.  Can early closure and restenosis after endoluminal stenting be predicted from clinical, procedural, and angiographic variables at the time of intervention? 
British Heart Journal  1995;74(6):592-597.
OBJECTIVES--To develop a statistical model to assess the risk of early closure and restenosis on the basis of the information available at the time of stent implantation. DESIGN--An exploratory forward, stepwise multivariate logistic regression for each adverse event and multivariate polychotomous analysis for both events. SETTING--Tertiary referral centre for interventional treatment of coronary artery disease. PATIENTS--243 consecutive, successful stenting procedures between 1986 and 1993 with the Wallstent, the Palmaz-Schatz and Wiktor stents with analysis of clinical, procedural, and angiographic variables. MEAN OUTCOME MEASURES--Early closure was defined as angiographically documented stent thrombosis within the first 3 weeks after implantation and restenosis according to the 50% reference diameter reduction criterion. RESULTS--Overall early closure and restenosis rates were 14.4% (35/243) and 19.2% (40/208, for a 97% repeat angiography rate). The statistical model predicted a worse outcome for male patients, with less restenosis in female patients. The only risk factor in female patients was the presence of collaterals to the target lesion. For male patients the following risk factors for closure and restenosis were retained: multiple stent implantation during the same session, the presence of collaterals to the target lesion, stenting of the left anterior descending artery or of the left circumflex artery, and bailout stenting. Only bailout stenting implied a decreased restenosis risk. CONCLUSIONS--Clinical, procedural and angiographic variables increase the risk for early closure and restenosis after endoluminal stenting. The prediction models described above need to be validated prospectively.
PMCID: PMC484111  PMID: 8541161
11.  Comparing paired biomarkers in predicting quantitative health outcome subject to random censoring 
Statistical methods in medical research  2012;10.1177/0962280212460434.
This paper uses a non-parametric test, based on consistently estimated discrimination accuracy defined as concordance probability between quantitative predictor and outcome, to compare paired biomarkers in predicting a health outcome, possibly subject to random censoring. Comparing with the Wilcoxon test for paired predictors based on Harrell’s C-index, we found that the proposed test is better in presence of random censoring, although the two unbiased tests are equivalent for outcome either uncensored or censored by a constant. A simulation study also demonstrates that the bias in estimated difference in concordance probability, due to ignoring random censoring, results in overestimated power, especially when random censoring is heavy. The method was applied in two studies, where the biomarkers measured from the same study subjects are correlated. The first study on 299 school children in Bangladesh found the associations that higher blood arsenic and manganese were related to lower intellectual test scores, while the differences between the biomarkers in predicting the intellectual test scores were not statistically significant. The second study on 418 patients with primary biliary cirrhosis found that the baseline serum bilirubin had greater discrimination accuracy than the baseline serum albumin in predicting survival time.
PMCID: PMC4390496  PMID: 23070589
C-index; Concordance probability; Discrimination accuracy; Paired predictors; Random censoring
12.  Optimum binary cut-off threshold of a diagnostic test: comparison of different methods using Monte Carlo technique 
Using Monte Carlo simulations, we compare different methods (maximizing Youden index, maximizing mutual information, and logistic regression) for their ability to determine optimum binary cut-off thresholds for a ratio-scaled diagnostic test variable. Special attention is given to the stability and precision of the results in dependence on the distributional characteristics as well as the pre-test probabilities of the diagnostic categories in the test population.
Fictitious data sets of a ratio-scaled diagnostic test with different distributional characteristics are generated for 50, 100 and 200 fictitious “individuals” with systematic variation of pre-test probabilities of two diagnostic categories. For each data set, optimum binary cut-off limits are determined employing different methods. Based on these optimum cut-off thresholds, sensitivities and specificities are calculated for the respective data sets. Mean values and SD of these variables are computed for 1000 repetitions each.
Optimizations of cut-off limits using Youden index and logistic regression-derived likelihood ratio functions with correct adaption for pre-test probabilities both yield reasonably stable results, being nearly independent from pre-test probabilities actually used. Maximizing mutual information yields cut-off levels decreasing with increasing pre-test probability of disease. The most precise results (in terms of the smallest SD) are usually seen for the likelihood ratio method. With this parametric method, however, cut-off values show a significant positive bias and, hence, specificities are usually slightly higher, and sensitivities are consequently slightly lower than with the two non-parametric methods.
In terms of stability and bias, Youden index is best suited for determining optimal cut-off limits of a diagnostic variable. The results of Youden method and likelihood ratio method are surprisingly insensitive against distributional differences as well as pre-test probabilities of the two diagnostic categories. As an additional bonus of the parametric procedure, transfer of the likelihood ratio functions, obtained from logistic regression analysis, to other diagnostic scenarios with different pre-test probabilities is straightforward.
Electronic supplementary material
The online version of this article (doi:10.1186/s12911-014-0099-1) contains supplementary material, which is available to authorized users.
PMCID: PMC4253606  PMID: 25421000
13.  Pharmacogenomics Bias - Systematic distortion of study results by genetic heterogeneity 
Decision analyses of drug treatments in chronic diseases require modeling the progression of disease and treatment response beyond the time horizon of clinical or epidemiological studies. In many such models, progression and drug effect have been applied uniformly to all patients; heterogeneity in progression, including pharmacogenomic effects, has been ignored.
We sought to systematically evaluate the existence, direction and relative magnitude of a pharmacogenomics bias (PGX-Bias) resulting from failure to adjust for genetic heterogeneity in both treatment response (HT) and heterogeneity in progression of disease (HP) in decision-analytic studies based on clinical study data.
We performed a systematic literature search in electronic databases for studies regarding the effect of genetic heterogeneity on the validity of study results. Included studies have been summarized in evidence tables.
In the case of lacking evidence from published studies we sought to perform our own simulation considering both HT and HP. We constructed two simple Markov models with three basic health states (early-stage disease, late-stage disease, dead), one adjusting and the other not adjusting for genetic heterogeneity. Adjustment was done by creating different disease states for presence (G+) and absence (G-) of a dichotomous genetic factor. We compared the life expectancy gains attributable to treatment resulting from both models and defined pharmacogenomics bias as percent deviation of treatment-related life expectancy gains in the unadjusted model from those in the adjusted model. We calculated the bias as a function of underlying model parameters to create generic results.
We then applied our model to lipid-lowering therapy with pravastatin in patients with coronary atherosclerosis, incorporating the influence of two TaqIB polymorphism variants (B1 and B2) on progression and drug efficacy as reported in the DNA substudy of the REGRESS trial.
We found four studies that systematically evaluated heterogeneity bias. All of them indicated that there is a potential of heterogeneity bias. However, none of these studies explicitly investigated the effect of genetic heterogeneity. Therefore, we performed our own simulation study.
Our generic simulation showed that a purely HT-related bias is negative (conservative) and a purely HP-related bias is positive (liberal). For many typical scenarios, the absolute bias is smaller than 10%. In case of joint HP and HT, the overall bias is likely triggered by the HP component and reaches positive values >100% if fractions of „fast progressors" and „strong treatment responders" are low.
In the clinical example with pravastatin therapy, the unadjusted model overestimated the true life-years gained (LYG) by 5.5% (1.07 LYG vs. 0.99 LYG for 56-year-old men).
We have been able to predict the pharmacogenomics bias jointly caused by heterogeneity in progression of disease and heterogeneity in treatment response as a function of characteristics of patients, chronic disease, and treatment. In the case of joint presence of both types of heterogeneity, models ignoring this heterogeneity may generate results that overestimate the treatment benefit.
PMCID: PMC3011301  PMID: 21289909
14.  Prognostic survival model for people diagnosed with invasive cutaneous melanoma 
BMC Cancer  2015;15:27.
The ability of medical practitioners to communicate risk estimates effectively to patients diagnosed with melanoma relies on accurate information about prognostic factors and their impact on survival. This study reports the development of one of the few melanoma prognostic models, called the Melanoma Severity Index (MSI), based on population-based cancer registry data.
Data from the Queensland Cancer Registry for people (20–89 years) diagnosed with a single invasive melanoma between 1995 and 2008 (n = 28,654; 1,700 melanoma deaths). Additional clinical information about metastasis, ulceration and positive lymph nodes was manually extracted from pathology forms. Flexible parametric survival models were combined with multivariable fractional polynomial for selecting variables and transformations of continuous variables. Multiple imputation was used for missing covariate values.
The MSI contained the variables thickness (transformed, explained 40.6% of variation in survival), body site (additional 1.9% in variation), metastasis (1.8%), positive nodes (0.7%), ulceration (1.3%), age (1.1%). Royston and Sauerbrei’s D statistic (measure of discrimination) was 1.50 (95% CI = 1.44, 1.56) and the corresponding RD2 (measure of explained variation) was 0.47 (0.45, 0.49), demonstrating strong explanatory performance. The Harrell-C statistic was 0.88 (0.88, 0.89). Lacking an external validation dataset, we applied internal-external cross validation to demonstrate the consistency of the prognostic information across geographically-defined subsets of the cohort.
The MSI provides good ability to predict survival for melanoma patients. Beyond the immediate clinical use, the MSI may have important public health and research applications for evaluations of public health interventions aimed at reducing deaths from melanoma.
PMCID: PMC4328047  PMID: 25637143
Melanoma; Survival; Prognostic model; Thickness; Population-based; Risk
15.  Correlates of D-dimer in older persons 
Background and aims
D-dimer is a marker of active fibrinolysis. Understanding how age-related factors affect D-dimer levels may help the interpretation of high D-dimer levels in older individuals.
776 Baltimore Longitudinal Study on Aging (BLSA) participants (mean age 68.4±13.9 yrs) were divided into three groups according to baseline D-dimer levels >200 ng/mL; 100–200 ng/mL and <100 ng/mL.
D-dimer level increased with age (p<0.0001). Using polychotomous logistic regression models, we found that age, cholesterol, triglycerides, creatinine, erythrocyte sedimentation rate, hemoglobin and body mass index were independently associated with D-dimer level.
Rising levels of D-dimer with age can be explained in part by the high prevalence of pro-inflammatory conditions and increasing burden of lipid abnormalities, anemia and obesity. These factors compromise the specificity of D-dimer levels as a diagnostic aid to thrombosis in older individuals.
PMCID: PMC2863304  PMID: 20305364
D-dimer; inflammation; obesity
16.  Retrospective analysis of demographic and clinical factors associated with etiology of febrile respiratory illness among US military basic trainees 
BMC Infectious Diseases  2014;14:576.
Basic trainees in the US military have historically been vulnerable to respiratory infections. Adenovirus and influenza are the most common etiological agents responsible for febrile respiratory illness (FRI) among trainees and present with similar clinical signs and symptoms. Identifying demographic and clinical factors associated with the primary viral pathogens causing FRI epidemics among trainees will help improve differential diagnosis and allow for appropriate distribution of antiviral medications. The objective of this study was to determine what demographic and clinical factors are associated with influenza and adenovirus among military trainees.
Specimens were systematically collected from military trainees meeting FRI case definition (fever ≥38.0°C with either cough or sore throat; or provider-diagnosed pneumonia) at eight basic training centers in the USA. PCR and/or cell culture testing for respiratory pathogens were performed on specimens. Interviewer-administered questionnaires collected information on patient demographic and clinical factors. Polychotomous logistic regression was employed to assess the association between these factors and FRI outcome categories: laboratory-confirmed adenovirus, influenza, or other FRI. Sensitivity, specificity, positive and negative predictive value were calculated for individual predictors and clinical combinations of predictors.
Among 21,570 FRI cases sampled between 2004 and 2009, 63.6% were laboratory-confirmed adenovirus cases and 6.6% were laboratory-confirmed influenza cases. Subjects were predominantly young men (86.8% men; mean age 20.8 ± 3.8 years) from Fort Jackson (18.8%), Great Lakes (17.1%), Fort Leonard Wood (16.3%), Marine Corps Recruit Depot (MCRD) San Diego (19.0%), Fort Benning (13.3%), Lackland (7.5%), MCRD Parris Island (8.7%), and Cape May (3.2%). The best multivariate predictors of adenovirus were the combination of sore throat (odds ratio [OR], 2.94; 95% confidence interval [CI], 2.66–3.25), cough (OR, 2.33; 95% CI, 2.11–2.57), and fever (OR, 2.07; 95% CI, 1.90–2.26) with a PPV of 77% (p ≤ .05). A combination of cough, fever, training week 0–2 and acute onset were most predictive of influenza (PPV =38%; p ≤ .05).
Specific demographic and clinical factors were associated with laboratory-confirmed influenza and adenovirus among military trainees. Findings from this study can guide clinicians in the diagnosis and treatment of military trainees presenting with FRI.
PMCID: PMC4264259  PMID: 25475044
Adenovirus; Influenza; Military trainees; Military medicine; Diagnosis
17.  Influence of Patient Characteristics on Success of Ambulatory Blood Pressure Monitoring 
Pharmacotherapy  2008;28(11):1341-1347.
Study Objective
To examine the influence of specific patient characteristics on the success of ambulatory blood pressure monitoring (ABPM).
Retrospective analysis.
University-affiliated family care center.
Five hundred thirty patients (mean age 52.7 yrs, range 14–90 yrs) who were undergoing ABPM between January 1, 2001, and July 1, 2007.
Measurement and Main Results
Specific patient characteristics were identified through an electronic medical record review and then examined for association with ABPM session success rate. These patient characteristics included age, sex, weight, height, body mass index (BMI), occupation, clinic blood pressure, travel distance to clinic, and presence of diabetes mellitus or renal disease. The percentage of valid readings obtained during an ABPM session was analyzed continuously (0–100%), whereas overall session success was analyzed dichotomously (0–79% or 80–100%). Univariate and multivariate regression analyses were performed to examine the influence of patient characteristics on the percentage of valid readings and the overall likelihood of achieving a successful session. In the 530 patients, the average percentage of valid readings was 90%, and a successful ABPM session (≥ 80% valid readings) was obtained in 84.7% (449 patients). A diagnosis of diabetes was found to negatively predict ABPM session success (continuous variable analysis, p=0.019; dichotomous variable analysis, odds ratio [OR] 0.45, 95% confidence interval [CI] 0.23–0.87, p=0.019), as did renal disease (continuous variable analysis, p=0.006; dichotomous variable analysis, OR 0.39, 95% CI 0.17–0.90, p=0.027) and increasing BMI (continuous variable analysis, p<0.001; dichotomous variable analysis, OR 0.78, 95% CI 0.65–0.93, p=0.005). Renal disease and BMI remained significant predictors in adjusted analyses.
For most patients, ABPM was successful; however, elevated BMI and renal disease were associated with less complete ABPM session results. Adaptation and individualization of the ABPM process may be necessary to improve results in these patients.
PMCID: PMC4084605  PMID: 18956994
ambulatory blood pressure monitoring; ABPM; kidney diseases; diabetes mellitus; body mass index; BMI
18.  Regression Calibration for Dichotomized Mismeasured Predictors* 
Epidemiologic research focuses on estimating exposure-disease associations. In some applications the exposure may be dichotomized, for instance when threshold levels of the exposure are of primary public health interest (e.g., consuming 5 or more fruits and vegetables per day may reduce cancer risk). Errors in exposure variables are known to yield biased regression coefficients in exposure-disease models. Methods for bias-correction with continuous mismeasured exposures have been extensively discussed, and are often based on validation substudies, where the “true” and imprecise exposures are observed on a small subsample. In this paper, we focus on biases associated with dichotomization of a mismeasured continuous exposure. The amount of bias, in relation to measurement error in the imprecise continuous predictor, and choice of dichotomization cut point are discussed. Measurement error correction via regression calibration is developed for this scenario, and compared to naïly using the dichotomized mismeasured predictor in linear exposure-disease models. Properties of the measurement error correction method (i.e., bias, mean-squared error) are assessed via simulations.
PMCID: PMC2743435  PMID: 20046953
19.  Regression Calibration for Dichotomized Mismeasured Predictors* 
Epidemiologic research focuses on estimating exposure-disease associations. In some applications the exposure may be dichotomized, for instance when threshold levels of the exposure are of primary public health interest (e.g., consuming 5 or more fruits and vegetables per day may reduce cancer risk). Errors in exposure variables are known to yield biased regression coefficients in exposure-disease models. Methods for bias-correction with continuous mismeasured exposures have been extensively discussed, and are often based on validation substudies, where the “true” and imprecise exposures are observed on a small subsample. In this paper, we focus on biases associated with dichotomization of a mismeasured continuous exposure. The amount of bias, in relation to measurement error in the imprecise continuous predictor, and choice of dichotomization cut point are discussed. Measurement error correction via regression calibration is developed for this scenario, and compared to naïvely using the dichotomized mismeasured predictor in linear exposure-disease models. Properties of the measurement error correction method (i.e., bias, mean-squared error) are assessed via simulations.
PMCID: PMC2743435  PMID: 20046953
measurement error correction; dichotomizing covariates; regression calibration
20.  Youden Index and Optimal Cut-Point Estimated from Observations Affected by a Lower Limit of Detection 
The receiver operating characteristic (ROC) curve is used to evaluate a biomarker’s ability for classifying disease status. The Youden Index (J), the maximum potential effectiveness of a biomarker, is a common summary measure of the ROC curve. In biomarker development, levels may be unquantifiable below a limit of detection (LOD) and missing from the overall dataset. Disregarding these observations may negatively bias the ROC curve and thus J. Several correction methods have been suggested for mean estimation and testing; however, little has been written about the ROC curve or its summary measures. We adapt non-parametric (empirical) and semi-parametric (ROC-GLM [generalized linear model]) methods and propose parametric methods (maximum likelihood (ML)) to estimate J and the optimal cut-point (c*) for a biomarker affected by a LOD. We develop unbiased estimators of J and c* via ML for normally and gamma distributed biomarkers. Alpha level confidence intervals are proposed using delta and bootstrap methods for the ML, semi-parametric, and non-parametric approaches respectively. Simulation studies are conducted over a range of distributional scenarios and sample sizes evaluating estimators’ bias, root-mean square error, and coverage probability; the average bias was less than one percent for ML and GLM methods across scenarios and decreases with increased sample size. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods. We address the limitations and usefulness of each method in order to give researchers guidance in constructing appropriate estimates of biomarkers’ true discriminating capabilities.
PMCID: PMC2515362  PMID: 18435502
Youden Index; ROC curve; Sensitivity and Specificity; Optimal Cut-Point
21.  Predicting seven day and three month functional outcomes after an ED visit for acute non-traumatic low back pain 
Recent work has shown that two-thirds of patients report functional disability one week after an ED visit for non-traumatic musculoskeletal low back pain (LBP). Nearly half of these patients report functional disability three months later. Identifying high-risk predictors of functional disability at each of these two time points will allow emergency clinicians to provide individual patients with an evidence-based understanding of their risk of protracted symptomatology.
To determine whether five high-risk features previously identified in various primary care settings predict poor functional outcomes among ED patients. The hypothesized predictors are: low back pain related functional disability at baseline, radicular signs, depression, a work-related injury, or a history of chronic or recurrent LBP prior to the index episode.
We conducted a prospective observational cohort study of ED patients with a chief complaint of non-traumatic LBP, which the ED attending physician classified as musculoskeletal. We interviewed patients in the ED prior to discharge and performed a baseline assessment of functional disability using the 24 item Roland-Morris questionnaire. We also tri-chotomized the patient’s baseline history of LBP into chronic (defined as 30 straight days with continuous LBP or a history of acute exacerbations more frequently than once per week); episodic (acute exacerbations more frequently than once per year but less frequently than once per week); or rarely/never (less frequently than once per year or no prior history of LBP). We performed telephone follow-up one week and three months after ED discharge using a scripted closed-question data collection instrument. The primary outcome was any functional limitation attributable to LBP at one week and three months, defined as a score greater than zero on the Roland-Morris questionnaire. We used logistic regression, adjusted for age, sex, and educational level, to assess the independent association between functional disability and each of the five hypothesized predictors listed above.
We approached 894 patients for participation and included 556. We obtained follow-up on 97% and 92% of our sample at one week and three months, respectively. Two of the five hypothesized variables predicted functional disability at both time points: Higher baseline Roland-Morris score (OR 4.3 95%CI 2.6, 6.9) and chronic LBP (OR 2.3 95%CI 1.1, 4.8) were associated with seven-day functional disability. These same two variables predicted functional disability three months after ED discharge--higher baseline Roland-Morris score (OR 2.3 95%CI 1.4, 3.9) and chronic LBP (OR 2.8 95%CI 1.5, 5.2). The remaining three hypothesized predictors (depression, radicular signs, and on-the-job injury) did not predict functional outcome at either time point.
ED patients with worse baseline functional impairment and a history of chronic low back pain are two to four times most likely to suffer poor short and longer term outcomes.
PMCID: PMC3434270  PMID: 22633712
22.  Linear theory for filtering nonlinear multiscale systems with model error 
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline.
PMCID: PMC4032560  PMID: 25002829
filtering multi-scale systems; covariance inflation; stochastic parameterization; uncertainty quantification; model error; parameter estimation
23.  Multi-Way Multi-Group Segregation and Diversity Indices 
PLoS ONE  2010;5(6):e10912.
How can we compute a segregation or diversity index from a three-way or multi-way contingency table, where each variable can take on an arbitrary finite number of values and where the index takes values between zero and one? Previous methods only exist for two-way contingency tables or dichotomous variables. A prototypical three-way case is the segregation index of a set of industries or departments given multiple explanatory variables of both sex and race. This can be further extended to other variables, such as disability, number of years of education, and former military service.
Methodology/Principal Findings
We extend existing segregation indices based on Euclidean distance (square of coefficient of variation) and Boltzmann/Shannon/Theil index from two-way to multi-way contingency tables by including multiple summations. We provide several biological applications, such as indices for age polyethism and linkage disequilibrium. We also provide a new heuristic conceptualization of entropy-based indices. Higher order association measures are often independent of lower order ones, hence an overall segregation or diversity index should be the arithmetic mean of the normalized association measures at all orders. These methods are applicable when individuals self-identify as multiple races or even multiple sexes and when individuals work part-time in multiple industries.
The policy implications of this work are enormous, allowing people to rigorously test whether employment or biological diversity has changed.
PMCID: PMC2879365  PMID: 20532222
24.  The intermediate endpoint effect in logistic and probit regression 
An intermediate endpoint is hypothesized to be in the middle of the causal sequence relating an independent variable to a dependent variable. The intermediate variable is also called a surrogate or mediating variable and the corresponding effect is called the mediated, surrogate endpoint, or intermediate endpoint effect. Clinical studies are often designed to change an intermediate or surrogate endpoint and through this intermediate change influence the ultimate endpoint. In many intermediate endpoint clinical studies the dependent variable is binary, and logistic or probit regression is used.
The purpose of this study is to describe a limitation of a widely used approach to assessing intermediate endpoint effects and to propose an alternative method, based on products of coefficients, that yields more accurate results.
The intermediate endpoint model for a binary outcome is described for a true binary outcome and for a dichotomization of a latent continuous outcome. Plots of true values and a simulation study are used to evaluate the different methods.
Distorted estimates of the intermediate endpoint effect and incorrect conclusions can result from the application of widely used methods to assess the intermediate endpoint effect. The same problem occurs for the proportion of an effect explained by an intermediate endpoint, which has been suggested as a useful measure for identifying intermediate endpoints. A solution to this problem is given based on the relationship between latent variable modeling and logistic or probit regression.
More complicated intermediate variable models are not addressed in the study, although the methods described in the article can be extended to these more complicated models.
Researchers are encouraged to use an intermediate endpoint method based on the product of regression coefficients. A common method based on difference in coefficient methods can lead to distorted conclusions regarding the intermediate effect.
PMCID: PMC2857773  PMID: 17942466
25.  Surgical site infection in abdominal trauma patients: risk prediction and performance of the NNIS and SENIC indexes 
Canadian Journal of Surgery  2011;54(1):17-24.
The National Nosocomial Infections Surveillance (NNIS) and Efficacy of Nosocomial Infection Control (SENIC) indexes are designed to develop control strategies and to reduce morbidity and mortality rates resulting from infections in surgical patients. We sought to assess the application of these indexes in patients under-going surgery for abdominal trauma and to develop an alternative model to predict surgical site infections (SSIs).
We conducted a prospective cohort study between November 2000 and March 2002. The main outcome measure was SSIs. We evaluated the variables included in the NNIS and SENIC indexes and some preoperative, intraoperative and postoperative variables that could be risk factors related to the development of SSIs. We performed multivariate analyses using a forward logistic regression method. Finally, we assessed infection risk prediction, comparing the estimated probabilities with actual occurrence using the areas under the receiver operating characteristic (ROC) curves.
Overall, 614 patients underwent an exploratory laparotomy. Of these, 85 (13.8%) experienced deep incisional and organ/intra-abdominal SSIs. The independent variables associated with this complication were an Abdominal Trauma Index score greater than 24, abdominal contamination and admission to the intensive care unit. We proposed a model for predicting deep incisional and organ/intra-abdominal SSIs using these variables (alternative model). The areas under the ROC curves were compared using the estimated probabilities for this alternative model and for the NNIS and SENIC scores. The analysis revealed a greater area under the ROC curve for the alternative model. The NNIS and SENIC scores did not perform as well as the alternative model in patients with abdominal trauma.
The NNIS and SENIC indexes were inferior to the proposed alternative model for predicting SSIs in patients undergoing surgery for abdominal trauma.
PMCID: PMC3038362  PMID: 21251428

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