Logistic Regression via Excel Spreadsheets: Mechanics, Model Selection, and Relative Predictor Importance

Logistic regression is one of the most fundamental tools in predictive analytics. Graduate business analytics students are often familiarized with implementation of logistic regression using Python, R, SPSS, or other software packages. However, an understanding of the underlying maximum likelihood model and the mechanics of estimation are often lacking. This paper describes two Excel workbooks that can be used to enhance conceptual understanding of logistic regression in several respects: (i) by providing a clear formulation and solution of the maximum likelihood estimation problem; (ii) by showing the process for testing the significance of logistic regression coefficients; (iii) by demonstrating different methods for model selection to avoid overfitting, specifically, all possible subsets ordinary least squares regression and l1-regularized logistic regression (lasso); and (iv) by illustrating the measurement of relative predictor importance using all possible subsets.

Predictors for extubation failure in COVID-19 patients using a machine learning approach

Introduction Determining the optimal timing for extubation can be challenging in the intensive care. In this study, we aim to identify predictors for extubation failure in critically ill patients with COVID-19. Methods We used highly granular data from 3464 adult critically ill COVID patients in the multicenter Dutch Data Warehouse, including demographics, clinical observations, medications, fluid balance, laboratory values, vital signs, and data from life support devices. All intubated patients with at least one extubation attempt were eligible for analysis. Transferred patients, patients admitted for less than 24 h, and patients still admitted at the time of data extraction were excluded. Potential predictors were selected by a team of intensive care physicians. The primary and secondary outcomes were extubation without reintubation or death within the next 7 days and within 48 h, respectively. We trained and validated multiple machine learning algorithms using fivefold nested cross-validation. Predictor importance was estimated using Shapley additive explanations, while cutoff values for the relative probability of failed extubation were estimated through partial dependence plots. Results A total of 883 patients were included in the model derivation. The reintubation rate was 13.4% within 48 h and 18.9% at day 7, with a mortality rate of 0.6% and 1.0% respectively. The grandient-boost model performed best (area under the curve of 0.70) and was used to calculate predictor importance. Ventilatory characteristics and settings were the most important predictors. More specifically, a controlled mode duration longer than 4 days, a last fraction of inspired oxygen higher than 35%, a mean tidal volume per kg ideal body weight above 8 ml/kg in the day before extubation, and a shorter duration in assisted mode (< 2 days) compared to their median values. Additionally, a higher C-reactive protein and leukocyte count, a lower thrombocyte count, a lower Glasgow coma scale and a lower body mass index compared to their medians were associated with extubation failure. Conclusion The most important predictors for extubation failure in critically ill COVID-19 patients include ventilatory settings, inflammatory parameters, neurological status, and body mass index. These predictors should therefore be routinely captured in electronic health records.

Identifying patients at risk for nonroutine discharge after surgery for cervical myelopathy: an analysis from the Quality Outcomes Database

OBJECTIVE Optimizing patient discharge after surgery has been shown to impact patient recovery and hospital/physician workflow and to reduce healthcare costs. In the current study, the authors sought to identify risk factors for nonroutine discharge after surgery for cervical myelopathy by using a national spine registry. METHODS The Quality Outcomes Database cervical module was queried for patients who had undergone surgery for cervical myelopathy between 2016 and 2018. Nonroutine discharge was defined as discharge to postacute care (rehabilitation), nonacute care, or another acute care hospital. A multivariable logistic regression predictive model was created using an array of demographic, clinical, operative, and patient-reported outcome characteristics. RESULTS Of the 1114 patients identified, 11.2% (n = 125) had a nonroutine discharge. On univariate analysis, patients with a nonroutine discharge were more likely to be older (age ≥ 65 years, 70.4% vs 35.8%, p < 0.001), African American (24.8% vs 13.9%, p = 0.007), and on Medicare (75.2% vs 35.1%, p < 0.001). Among the patients younger than 65 years of age, those who had a nonroutine discharge were more likely to be unemployed (70.3% vs 36.9%, p < 0.001). Overall, patients with a nonroutine discharge were more likely to present with a motor deficit (73.6% vs 58.7%, p = 0.001) and more likely to have nonindependent ambulation (50.4% vs 14.0%, p < 0.001) at presentation. On multivariable logistic regression, factors associated with higher odds of a nonroutine discharge included African American race (vs White, OR 2.76, 95% CI 1.38–5.51, p = 0.004), Medicare coverage (vs private insurance, OR 2.14, 95% CI 1.00–4.65, p = 0.04), nonindependent ambulation at presentation (OR 2.17, 95% CI 1.17–4.02, p = 0.01), baseline modified Japanese Orthopaedic Association severe myelopathy score (0–11 vs moderate 12–14, OR 2, 95% CI 1.07–3.73, p = 0.01), and posterior surgical approach (OR 11.6, 95% CI 2.12–48, p = 0.004). Factors associated with lower odds of a nonroutine discharge included fewer operated levels (1 vs 2–3 levels, OR 0.3, 95% CI 0.1–0.96, p = 0.009) and a higher quality of life at baseline (EQ-5D score, OR 0.43, 95% CI 0.25–0.73, p = 0.001). On predictor importance analysis, baseline quality of life (EQ-5D score) was identified as the most important predictor (Wald χ2 = 9.8, p = 0.001) of a nonroutine discharge; however, after grouping variables into distinct categories, socioeconomic and demographic characteristics (age, race, gender, insurance status, employment status) were identified as the most significant drivers of nonroutine discharge (28.4% of total predictor importance). CONCLUSIONS The study results indicate that socioeconomic and demographic characteristics including age, race, gender, insurance, and employment may be the most significant drivers of a nonroutine discharge after surgery for cervical myelopathy.

Random Forest Model to Assess Predictor Importance and Nowcast Severe Storms using High-Resolution Radar–GOES Satellite–Lightning Observations

Few studies have assessed combined satellite, lightning, and radar databases to diagnose severe storm potential. The research goal here is to evaluate next-generation, 60-second update frequency geostationary satellite and lightning information with ground-based radar to isolate which variables, when used in concert, provide skillful discriminatory information for identifying severe (hail ≥2.5 cm in diameter, winds ≥25 m s–1, tornadoes) versus non-severe storms. The focus of this study is predicting severe thunderstorm and tornado warnings. A total of 2,004 storms in 2014–2015 were objectively tracked with 49 potential predictor fields related to May, daytime Great Plains convective storms. All storms occurred when 1-min Geostationary Operational Environmental Satellite (GOES)–14 “super rapid scan” data were available. The study used three importance methods to assess predictor importance related to severe warnings, and random forests to provide a model and skill evaluation measuring the ability to predict severe storms. Three predictor importance methods show that GOES mesoscale atmospheric motion vector derived cloud-top divergence and above anvil cirrus plume presence provide the most satellite-based discriminatory power for diagnosing severe warnings. Other important fields include Earth Networks Total Lightning flash density, GOES estimated cloud-top vorticity, and overshooting-top presence. Severe warning predictions are significantly improved at the 95% confidence level when a few important satellite and lightning fields are combined with radar fields, versus when only radar data are used in the random forests model. This study provides a basis for including satellite and lightning fields within machine-learning models to help forecast severe weather.

Analysis of Unmet Healthcare Needs in Ireland: A Data Mining Approach

This study explores data form the Survey of Income and Living Condition (SILC), related to factors contributing to unmet healthcare needs in Ireland. We analysed predisposing, enabling and needs factors by building predictive models and measured the predictor importance by sensitivity analysis. Results show that critical factors for meeting the healthcare needs include financial status, degree of urbanization, indicators of social exclusion and deprivations, and self-perceived general health condition. Identifying and quantifying those factors form raw data may facilitate decision making in the domain.

Predictor Analysis in Group Decision Making

Priority vectors in the Analytic Hierarchy Process (AHP) are commonly estimated as constant values calculated by the pairwise comparison ratios elicited from an expert. For multiple experts, or panel data, or other data with varied characteristics of measurements, the priority vectors can be built as functions of the auxiliary predictors. For example, in multi-person decision making, the priorities can be obtained in regression modeling by the demographic and socio-economic properties. Then the priorities can be predicted for individual respondents, profiled by each predictor, forecasted in time, studied by the predictor importance, and estimated by the characteristic of significance, fit and quality well-known in regression modeling. Numerical results show that the suggested approaches reveal useful features of priority behavior, that can noticeably extend the AHP abilities and applications for numerous multiple-criteria decision making problems. The considered methods are useful for segmentation of the respondents and finding optimum managerial solutions specific for each segment. It can help to decision makers to focus on the respondents’ individual features and to increase customer satisfaction, their retention and loyalty to the promoted brands or products.

Impact of surgeon and hospital factors on surgical decision-making for grade 1 degenerative lumbar spondylolisthesis: a Quality Outcomes Database analysis

OBJECTIVESurgical treatment for degenerative spondylolisthesis has been proven to be clinically challenging and cost-effective. However, there is a range of thresholds that surgeons utilize for incorporating fusion in addition to decompressive laminectomy in these cases. This study investigates these surgeon- and site-specific factors by using the Quality Outcomes Database (QOD).METHODSThe QOD was queried for all cases that had undergone surgery for grade 1 spondylolisthesis from database inception to February 2019. In addition to patient-specific covariates, surgeon-specific covariates included age, sex, race, years in practice (0–10, 11–20, 21–30, > 30 years), and fellowship training. Site-specific variables included hospital location (rural, suburban, urban), teaching versus nonteaching status, and hospital type (government, nonfederal; private, nonprofit; private, investor owned). Multivariable regression and predictor importance analyses were performed to identify predictors of the treatment performed (decompression alone vs decompression and fusion). The model was clustered by site to account for site-specific heterogeneity in treatment selection.RESULTSA total of 12,322 cases were included with 1988 (16.1%) that had undergone decompression alone. On multivariable regression analysis clustered by site, adjusting for patient-level clinical covariates, no surgeon-specific factors were found to be significantly associated with the odds of selecting decompression alone as the surgery performed. However, sites located in suburban areas (OR 2.32, 95% CI 1.09–4.84, p = 0.03) were more likely to perform decompression alone (reference = urban). Sites located in rural areas had higher odds of performing decompression alone than hospitals located in urban areas, although the results were not statistically significant (OR 1.33, 95% CI 0.59–2.61, p = 0.49). Nonteaching status was independently associated with lower odds of performing decompression alone (OR 0.40, 95% CI 0.19–0.97, p = 0.04). Predictor importance analysis revealed that the most important determinants of treatment selection were dominant symptom (Wald χ2 = 34.7, accounting for 13.6% of total χ2) and concurrent diagnosis of disc herniation (Wald χ2 = 31.7, accounting for 12.4% of total χ2). Hospital teaching status was also found to be relatively important (Wald χ2 = 4.2, accounting for 1.6% of total χ2) but less important than other patient-level predictors.CONCLUSIONSNonteaching centers were more likely to perform decompressive laminectomy with supplemental fusion for spondylolisthesis. Suburban hospitals were more likely to perform decompression only. Surgeon characteristics were not found to influence treatment selection after adjustment for clinical covariates. Further large database registry experience from surgeons at high-volume academic centers at which surgically and medically complex patients are treated may provide additional insight into factors associated with treatment preference for degenerative spondylolisthesis.

Personalized Key Drivers for Individual Responses in Regression Modeling

Identification of personalized key drivers is useful to managers in finding a special set of tools for each customer for a better contingency to a higher satisfaction and loyalty and for diminishing risk and uncertainty of decision making. Finding the most attractive attributes of a product for a buyer, or the main helpful features of a medicine for a patient, can be considered via identifying the key drivers in regression modeling. The problem of predictor importance is usually considered on the aggregate level for a set of all respondents. This article shows how to identify a specific set of key drivers for each individual respondent. Two techniques are proposed: the orthonormal matrices used for the relative importance by Gibson and R. Johnson, and the cooperative game theory by Shapley value of predictors in regression. Numerical estimations show that a specific set of key drivers can be found for each respondent or customer, that can be valuable for managerial decisions in marketing research and other areas of practical statistical modeling.

Predictor Importance in Future and Concurrent Predictions of Oral Reading Fluency

Background: Reading fluency is an important aspect of reading, yet little is known about what contributes to individual differences in reading fluency. The present study employs the use of dominance analysis to examine predictor importance in the prediction of 1st and 3rd grade oral reading fluency (ORF) from 1st grade reading related measures.Methods: Data from 312 children were collected in 1st grade on Sight Word Efficiency (SWE), Phonemic Decoding Efficiency (PDE), word identification (WID), word attack (WA), elision, sound matching, rapid letter naming (RLN), listening comprehension (LC), oral vocabulary, Dynamic Assessment CVCE score, Dynamic Assessment CVC score and ORF as well as ORF in 3rd grade. The relative importance of these measures in the prediction of concurrent and future ORF was examined using dominance analysis.Results: Results revealed SWE to be the most important predictor in the prediction of 1st grade ORF, achieving complete dominance over all other variables examined here. However, in the prediction of 3rd grade ORF, WID was the most important predictor, achieving some type of dominance over all other variables including conditional dominance over SWE. Conclusion: Word reading provided the most to the prediction of ORF with timed favored in the 1st grade model and untimed favored in the 3rd grade model. Implications for screening are discussed.