Understanding the Effect of Categorization of a Continuous Predictor with Application to Neuro Oncology

Many Neuro-Oncology studies commonly assess the association between a prognostic factor (predictor) and disease or outcome, such as the association between age and glioma. Predictors can be continuous (e.g., age) or categorical (e.g., race/ethnicity). Effects of categorical predictors are frequently easier to visualize and interpret than effects of continuous variables. This makes it an attractive, and seemingly justifiable, option to subdivide the continuous predictors into categories (e.g., age< 50 years vs. age ≥50 years). However, this approach results in loss of information (and power) compared to the continuous version. This review outlines the use cases for continuous and categorized predictors and provides tips and pitfalls for interpretation of these approaches.

The Effect of Delay Duration on Delay Discounting across Adulthood

Literature has been mixed about the relationship between age and delay discounting, or the willingness to wait for delayed rewards. We posit that some of this heterogeneity may be attributable to inconsistent delay durations across studies. Here we investigate how delay duration influences discounting across adulthood by systematically varying the duration of the delay between the smaller, sooner and the larger, later option. 288 healthy participants (Age range: 25-84 years) completed an online delay-discounting task that probed 12 different time delays across 3 discount rates. Discounting was analyzed in two statistical models that treated delay duration as either a categorical or a continuous predictor. Longer delays were generally associated with decreased discounting. However, this was dependent on both age of the participant and delay duration. Both models revealed that, at short to moderate time delays, older adults discounted less than younger adults. However, at very long delays (10 years), older adults discounted more than younger adults. The future time horizons of the participants significantly did not significantly impacted discounting. Results suggest older adults may discount more than younger adults only for extremely long delays (i.e: ~10 years). If this result is replicable, future research could investigate why this reversal in discounting exists and where the inflection point lies.

Association between body mass index and mortality in hospitalised patients with community-acquired pneumonia

The obesity paradox postulates that increased body mass index (BMI) is protective in certain patient populations. We aimed to investigate the association of BMI and different weight classes with outcomes in hospitalised patients with community-acquired pneumonia (CAP).This cohort study is a secondary data analysis of the University of Louisville Pneumonia Study database, a prospective study of hospitalised adult patients with CAP from June of 2014 to May of 2016 in Louisville, KY. BMI as a predictor was assessed both as a continuous and categorical variable. Patients were categorised as weight classes based on WHO definitions: BMI<18.5 (underweight), BMI of 18.5 to <25 (normal weight), BMI of 25.0 to <30 (overweight), BMI of 30 to <35 (obesity class I), BMI of 35 to <40 (obesity class II), and BMI≥40 (obesity class III). Study outcomes, including time to clinical stability, length of stay, clinical failure, and mortality, were assessed in hospital, at 30-days, at 6-months, and at 1-year. Clinical failure was defined as the need for noninvasive ventilation, invasive ventilation, or vasopressors within 1 week of admission. Patient characteristics and crude outcomes were stratified by BMI categories, and generalised additive binomial regression models were performed to analyse the impact of BMI as a continuous variable on study outcomes adjusting for possible confounding variables.7449 patients were included in the study. Median time to clinical stability was 2 days for every BMI group. There was no association between BMI as a continuous predictor and length of stay <5 days (χ2=1.83, EDF=2.74, p=0.608). Clinical failure was highest in the class III obesity group, and higher BMI as a continuous predictor was associated with higher odds of clinical failure. BMI as a continuous predictor was significantly associated with 30-day (χ2=39.97, EDF=3.07, p<0.001), 6-month (χ2=89.42, EDF=3.44, p<0.001) and 1-year (χ2=83.97, EDF=2.89, p<0.001) mortalities. BMI ≤24.14 was a risk factor whereas BMI ≥26.97 was protective for mortality at 1-year. The incremental benefit of increasing BMI plateaued at 35.We found a protective benefit of obesity on mortality in CAP patients. However, we uniquely demonstrate that the association between BMI and mortality is not linear, and no incremental benefit of increasing BMI levels is observed in those with obesity classes II and III.

Do not group quantitative variables

This chapter explores the problems caused by categorizing quantitative variables (here termed continuous variables). Optimum decisions are made by applying a utility function to a predicted value. At the decision point, one can solve for the personalized cutpoint for predicted risk that optimizes the decision. Dichotomization on independent variables is completely at odds with making optimal decisions. To make an optimal decision, the cutpoint for a predictor would necessarily be a function of the continuous values of all the other predictors. Moreover, categorization assumes that the relationship between the predictor and the response is flat within intervals; this assumption is far less reasonable than a linearity assumption in most cases. Categorization of continuous variables using percentiles is particularly hazardous. To make a continuous predictor be more accurately modelled when categorization is used, multiple intervals are required.

Does size matter? Lesion size as an indicator of number of cores needed to detect clinically significant prostate cancer.

283 Background: MRI/US fusion guided prostate biopsy (FBx) has been shown to detect clinically significant prostate cancer (csCaP) at higher rates and with fewer cores than standard prostate biopsy. Size plays an important role in assigning a suspicion level (PI-RADS) to lesions identified on MRI. However, tumor characteristics may pose challenges to accurately characterizing the lesion despite the size. This study sought to determine if there are size cutoffs at which a lesion may be accurately characterized as clinically significant cancer with a single biopsy core. Methods: A retrospective analysis of a prospectively maintained database of all patients undergoing FBx at an academic referral center between May 2014 and January 2018 was conducted. At least two FBx cores were taken from each lesion identified on mpMRI. GEE-based univariate logistic regression model with exchangeable correlation was used determine if size was a significant predictor of positive and negative agreement. Predictability of size as a significant continuous predictor was quantified by AUC. Size thresholds at which multiple cores per lesion are needed to avoid missing > 2% of csCaP were calculated, allowing for a 25% discordance rate. Results: An analysis of a total of 1141 FBx of 2200 lesions was performed during the study time interval. Size was a significant predictor of both positive (OR = 2.43, 1.83-3.23, p < 0.01) and negative (OR = 0.58, 0.44-0.76, p < 0.01) agreement of csCaP. AUC% for positive and negative agreement was 65.8 and 57.6, respectively. Size thresholds of 0.65 and 1.70 cm limited CS cancers missed by skipping a second targeted biopsy core to 2% while allowing for a 25% discordance. Conclusions: These data indicate that clinically significant prostate cancer in lesions less than 0.65 cm and greater than 1.70 cm may be characterized with a single targeted biopsy core, sparing 33.5% of lesions (21% patients) a double core targeted biopsy.

When Passion Appears, Exercise Addiction Disappears

There are approximately 1,000 published articles on exercise addiction, which is characterized by exaggerated training yielding adverse effects. In contrast, there are less than 20 identified cases of exercise addiction in the literature. Recently, it was reported that there is an association between exercise addiction and passion. To test the impact of the latter on exercise addiction, we reanalyzed the combined data from two recent studies. High- and low-exercise volume groups differed in exercise addiction even after controlling for age and sex ( p < .001). However, after adding obsessive and harmonious passion as continuous predictor variables, the statistical significance vanished, whereas both predictors emerged as significant ( p < .001). Further, when controlled for the effect of passion, the correlation between exercise addiction and weekly exercise volume turned out to be negative. Therefore, a conceptual confound between the presumed risk of exercise addiction and passion could render the results of several hundreds of published works questionable. The current findings send an important message to scholars in the field: Studying exercise addiction without controlling for passion may yield false results.

One and done?: Utility of PSA density as a predictor of number of cores needed to detect clinically significant prostate cancer.

104 Background: MRI/US fusion guided prostate biopsy (FBx) has been shown to detect clinically significant prostate cancer (csCaP) at higher rates and with fewer cores than standard prostate biopsy. However, the number of targeted cores needed to accurately characterize lesions identified on multiparametric MRI (mpMRI) is unknown. This study sought to determine factors that predict the number of cores needed to accurately characterize lesions during FBx of patients on active surveillance. Methods: A retrospective analysis of a prospectively maintained database of all patients undergoing FBx at an academic referral center between May 2014 and January 2018 was conducted. At least two FBx cores were taken from each lesion identified on mpMRI. Patient and lesion specific factors were analyzed to determine factors that predict the necessity to obtain additional cores to detect csCaP. GEE-based univariate logistic regression model with exchangeable correlation was used to estimate the effects of clinical characteristics including race, BMI, PSA, PSA density (PSAD), lesion location, and PI-RADS score on the proportion of positive and negative agreement. Predictability of a significant continuous predictor was quantified by AUC. The most significant patient-level predictor (PSAD) was further analyzed to determine thresholds at which multiple cores per lesion are needed to avoid missing csCaP. Results: An analysis of a total of 1141 FBx were performed during the study time interval. PSA (OR=1.57, 1.20-2.05, p<0.01) and PSAD (OR=1.43, 1.11-1.85, p<0.01) significantly predicted positive agreement of csCaP. AUC for positive and negative agreement was 57.4 and 61.0 for PSA and 56.4 and 72.3 for PSAD, respectively. Using these thresholds, only 56% lesions would need double core targeted biopsy. In other words, up to 44% of lesions would be accurately characterized with a single biopsy core of the targeted lesion. Conclusions: These data indicate that in patients with a PSAD less than 0.11 ng/ml2 or greater than 0.26 ng/ml2, lesions may be acceptably characterized with a single targeted biopsy core.