Computing Adjusted Risk Ratios and Risk Differences in Stata
TL;DR: In this article, a post-estimation command, adjrr, is proposed to calculate adjusted risk ratios and adjusted risk differences after running a logit or probit model with a binary, a multinomial, or an ordered outcome.
Abstract: In this article, we explain how to calculate adjusted risk ratios and risk differences when reporting results from logit, probit, and related nonlinear models. Building on Stata�s margins command, we create a new postestimation command, adjrr, that calculates adjusted risk ratios and adjusted risk differences after running a logit or probit model with a binary, a multinomial, or an ordered outcome. adjrr reports the point estimates, delta-method standard errors, and 95% confidence intervals and can compute these for specific values of the variable of interest. It automatically adjusts for complex survey design as in the fit model. Data from the Medical Expenditure Panel Survey and the National Health and Nutrition Examination Survey are used to illustrate multiple applications of the command.
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TL;DR: This trial has high generalisability and approximates convalescent plasma use in real life settings with limited laboratory capacity and was not associated with a reduction in progression to severe covid-19 or all cause mortality.
Abstract: Objective To investigate the effectiveness of using convalescent plasma to treat moderate coronavirus disease 2019 (covid-19) in adults in India. Design Open label, parallel arm, phase II, multicentre, randomised controlled trial. Setting 39 public and private hospitals across India. Participants 464 adults (≥18 years) admitted to hospital (screened 22 April to 14 July 2020) with confirmed moderate covid-19 (partial pressure of oxygen in arterial blood/fraction of inspired oxygen (PaO2/FiO2) ratio between 200 mm Hg and 300 mm Hg or a respiratory rate of more than 24/min with oxygen saturation 93% or less on room air): 235 were assigned to convalescent plasma with best standard of care (intervention arm) and 229 to best standard of care only (control arm). Interventions Participants in the intervention arm received two doses of 200 mL convalescent plasma, transfused 24 hours apart. The presence and levels of neutralising antibodies were not measured a priori; stored samples were assayed at the end of the study. Main outcome measure Composite of progression to severe disease (PaO2/FiO2 Results Progression to severe disease or all cause mortality at 28 days after enrolment occurred in 44 (19%) participants in the intervention arm and 41 (18%) in the control arm (risk difference 0.008 (95% confidence interval −0.062 to 0.078); risk ratio 1.04, 95% confidence interval 0.71 to 1.54). Conclusion Convalescent plasma was not associated with a reduction in progression to severe covid-19 or all cause mortality. This trial has high generalisability and approximates convalescent plasma use in real life settings with limited laboratory capacity. A priori measurement of neutralising antibody titres in donors and participants might further clarify the role of convalescent plasma in the management of covid-19. Trial registration Clinical Trial Registry of India CTRI/2020/04/024775.
561 citations
United States Public Health Service1, Centers for Disease Control and Prevention2, Harvard University3, New York University4, University of Colorado Denver5, University of Texas at Dallas6, Nationwide Children's Hospital7, Johns Hopkins University8, Yale University9, Westchester Medical Center10, Rutgers University11, University of Alabama at Birmingham12, Children's Mercy Hospital13, University of Miami14, University of North Carolina at Chapel Hill15, Baylor College of Medicine16, University of Mississippi17, Vanderbilt University18, SUNY Downstate Medical Center19, California State University, Long Beach20, University of Minnesota21, Saint Barnabas Medical Center22, University of Arkansas for Medical Sciences23, Children's Hospital Oakland Research Institute24, Boston Children's Hospital25, University of Washington26, Central Michigan University27, Icahn School of Medicine at Mount Sinai28, University of Iowa29, Indiana University30, Emory University31, Medical University of South Carolina32, University of Pennsylvania33, Northwestern University34
TL;DR: In this article, the authors compared clinical characteristics and outcomes of children and adolescents with MIS-C vs those with severe coronavirus disease 2019 (COVID-19) at 66 US hospitals in 31 states.
Abstract: Importance Refinement of criteria for multisystem inflammatory syndrome in children (MIS-C) may inform efforts to improve health outcomes. Objective To compare clinical characteristics and outcomes of children and adolescents with MIS-C vs those with severe coronavirus disease 2019 (COVID-19). Setting, Design, and Participants Case series of 1116 patients aged younger than 21 years hospitalized between March 15 and October 31, 2020, at 66 US hospitals in 31 states. Final date of follow-up was January 5, 2021. Patients with MIS-C had fever, inflammation, multisystem involvement, and positive severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reverse transcriptase–polymerase chain reaction (RT-PCR) or antibody test results or recent exposure with no alternate diagnosis. Patients with COVID-19 had positive RT-PCR test results and severe organ system involvement. Exposure SARS-CoV-2. Main Outcomes and Measures Presenting symptoms, organ system complications, laboratory biomarkers, interventions, and clinical outcomes. Multivariable regression was used to compute adjusted risk ratios (aRRs) of factors associated with MIS-C vs COVID-19. Results Of 1116 patients (median age, 9.7 years; 45% female), 539 (48%) were diagnosed with MIS-C and 577 (52%) with COVID-19. Compared with patients with COVID-19, patients with MIS-C were more likely to be 6 to 12 years old (40.8% vs 19.4%; absolute risk difference [RD], 21.4% [95% CI, 16.1%-26.7%]; aRR, 1.51 [95% CI, 1.33-1.72] vs 0-5 years) and non-Hispanic Black (32.3% vs 21.5%; RD, 10.8% [95% CI, 5.6%-16.0%]; aRR, 1.43 [95% CI, 1.17-1.76] vs White). Compared with patients with COVID-19, patients with MIS-C were more likely to have cardiorespiratory involvement (56.0% vs 8.8%; RD, 47.2% [95% CI, 42.4%-52.0%]; aRR, 2.99 [95% CI, 2.55-3.50] vs respiratory involvement), cardiovascular without respiratory involvement (10.6% vs 2.9%; RD, 7.7% [95% CI, 4.7%-10.6%]; aRR, 2.49 [95% CI, 2.05-3.02] vs respiratory involvement), and mucocutaneous without cardiorespiratory involvement (7.1% vs 2.3%; RD, 4.8% [95% CI, 2.3%-7.3%]; aRR, 2.29 [95% CI, 1.84-2.85] vs respiratory involvement). Patients with MIS-C had higher neutrophil to lymphocyte ratio (median, 6.4 vs 2.7,P Conclusions and Relevance This case series of patients with MIS-C and with COVID-19 identified patterns of clinical presentation and organ system involvement. These patterns may help differentiate between MIS-C and COVID-19.
493 citations
TL;DR: The transfusion of up to 500 ml of convalescent plasma with unknown levels of neutralizing antibodies in 84 patients with confirmed EVD was not associated with a significant improvement in survival, and no serious adverse reactions associated with the use of convalscent plasma were observed.
Abstract: BackgroundIn the wake of the recent outbreak of Ebola virus disease (EVD) in several African countries, the World Health Organization prioritized the evaluation of treatment with convalescent plasma derived from patients who have recovered from the disease. We evaluated the safety and efficacy of convalescent plasma for the treatment of EVD in Guinea. MethodsIn this nonrandomized, comparative study, 99 patients of various ages (including pregnant women) with confirmed EVD received two consecutive transfusions of 200 to 250 ml of ABO-compatible convalescent plasma, with each unit of plasma obtained from a separate convalescent donor. The transfusions were initiated on the day of diagnosis or up to 2 days later. The level of neutralizing antibodies against Ebola virus in the plasma was unknown at the time of administration. The control group was 418 patients who had been treated at the same center during the previous 5 months. The primary outcome was the risk of death during the period from 3 to 16 days aft...
440 citations
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...Age 5–15 yr 8 (10) 1/8 (12) 53 (13) 10/53 (19)...
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...≥30 cycles 13 (15) 3/13 (23) 49 (12) 6/49 (12)...
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TL;DR: Among patients with severe traumatic brain injury, early prophylactic hypothermia compared with normothermic management did not improve neurologic outcomes at 6 months, and these findings do not support the use of early proPHylactic Hypothermia for patients withsevere traumatic brain injuries.
Abstract: Importance After severe traumatic brain injury, induction of prophylactic hypothermia has been suggested to be neuroprotective and improve long-term neurologic outcomes. Objective To determine the effectiveness of early prophylactic hypothermia compared with normothermic management of patients after severe traumatic brain injury. Design, Setting, and Participants The Prophylactic Hypothermia Trial to Lessen Traumatic Brain Injury–Randomized Clinical Trial (POLAR-RCT) was a multicenter randomized trial in 6 countries that recruited 511 patients both out-of-hospital and in emergency departments after severe traumatic brain injury. The first patient was enrolled on December 5, 2010, and the last on November 10, 2017. The final date of follow-up was May 15, 2018. Interventions There were 266 patients randomized to the prophylactic hypothermia group and 245 to normothermic management. Prophylactic hypothermia targeted the early induction of hypothermia (33°C-35°C) for at least 72 hours and up to 7 days if intracranial pressures were elevated, followed by gradual rewarming. Normothermia targeted 37°C, using surface-cooling wraps when required. Temperature was managed in both groups for 7 days. All other care was at the discretion of the treating physician. Main Outcomes and Measures The primary outcome was favorable neurologic outcomes or independent living (Glasgow Outcome Scale–Extended score, 5-8 [scale range, 1-8]) obtained by blinded assessors 6 months after injury. Results Among 511 patients who were randomized, 500 provided ongoing consent (mean age, 34.5 years [SD, 13.4]; 402 men [80.2%]) and 466 completed the primary outcome evaluation. Hypothermia was initiated rapidly after injury (median, 1.8 hours [IQR, 1.0-2.7 hours]) and rewarming occurred slowly (median, 22.5 hours [IQR, 16-27 hours]). Favorable outcomes (Glasgow Outcome Scale–Extended score, 5-8) at 6 months occurred in 117 patients (48.8%) in the hypothermia group and 111 (49.1%) in the normothermia group (risk difference, 0.4% [95% CI, –9.4% to 8.7%]; relative risk with hypothermia, 0.99 [95% CI, 0.82-1.19]; P = .94). In the hypothermia and normothermia groups, the rates of pneumonia were 55.0% vs 51.3%, respectively, and rates of increased intracranial bleeding were 18.1% vs 15.4%, respectively. Conclusions and Relevance Among patients with severe traumatic brain injury, early prophylactic hypothermia compared with normothermia did not improve neurologic outcomes at 6 months. These findings do not support the use of early prophylactic hypothermia for patients with severe traumatic brain injury. Trial Registration clinicaltrials.gov Identifier:NCT00987688; Anzctr.org.au Identifier:ACTRN12609000764235
188 citations
TL;DR: Methods for group comparisons using predicted probabilities and marginal effects on probabilities are developed for regression models for binary outcomes and how this interpretive framework can be used with a broad class of regression models and can be extended to any number of groups is considered.
Abstract: Methods for group comparisons using predicted probabilities and marginal effects on probabilities are developed for regression models for binary outcomes. Unlike approaches based on the comparison ...
187 citations
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...For example, the relative risk ratio (RRR), also called the adjusted risk ratio, is often used in medicine and epidemiology (Bender and Kuss 2010; Greenland 1987; Norton et al. 2013)....
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References
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TL;DR: There is no longer any good justification for fitting logistic regression models and estimating odds ratios when the odds ratio is not a good approximation of the risk or prevalence ratio.
Abstract: We would like to make the readership aware that risk or prevalence ratios and differences, when they are the parameter of interest, can be directly calculated by using SAS software (SAS Institute, Inc., Cary, North Carolina). There is no longer any good justification for fitting logistic regression models and estimating odds ratios when the odds ratio is not a good approximation of the risk or prevalence ratio. Instead, SAS PROC GENMOD’s log-binomial regression (1) capability can be used for estimation and inference about the parameter of interest. Here is an example of the code required to analyze the breast cancer survival data discussed by Greenland (2):
1,652 citations
TL;DR: The present article describes how most of these methods for estimating risk ratios from adjusted odds ratios when the outcome is common can be subsumed under a general formulation that also encompasses traditional standardization methods and methods for projecting the impact of partially successful interventions.
Abstract: Some recent articles have discussed biased methods for estimating risk ratios from adjusted odds ratios when the outcome is common, and the problem of setting confidence limits for risk ratios. These articles have overlooked the extensive literature on valid estimation of risks, risk ratios, and risk differences from logistic and other models, including methods that remain valid when the outcome is common, and methods for risk and rate estimation from case-control studies. The present article describes how most of these methods can be subsumed under a general formulation that also encompasses traditional standardization methods and methods for projecting the impact of partially successful interventions. Approximate variance formulas for the resulting estimates allow interval estimation; these intervals can be closely approximated by rapid simulation procedures that require only standard software functions.
671 citations
"Computing Adjusted Risk Ratios and ..." refers background in this paper
...The search for the best way to estimate risk ratios has shown that these statistics can be estimated in a number of ways from different kinds of models (e.g., Flanders and Rhodes 1987; Greenland and Holland 1991; Greenland 2004)....
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TL;DR: The concept of the odds ratio is now wellestablished in epidemiology, largely because it serves as a link between results obtained from follow-up studies and those obtainable from case-control studies.
Abstract: The concept of the odds ratio is now wellestablished in epidemiology, largely because it serves as a link between results obtainable from follow-up studies and those obtainable from case-control studies (1-7). Odds ratios also naturally arise when considering small sample analysis of 2 X 2 tables and in logistic and log-linear modeling (2-4, 8). This ubiquity, along with certain technical considerations, has led some authors to treat the odds ratio as perhaps a "universal" measure of epidemiologic effect, in that they would estimate odds ratios in follow-up studies as well as case-control studies (6, 9); others have expressed reservations about the utility of the odds ratio as something other than an estimate of an incidence ratio (10, 11).
467 citations
"Computing Adjusted Risk Ratios and ..." refers background in this paper
...For these reasons and other reasons, many people have called for researchers to report risk ratios instead of odds ratios (e.g., Greenland 1987; Spiegelman and Hertzmark 2005; Cummings 2009)....
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TL;DR: When a study outcome is rare in all strata used for an analysis, the odds ratio estimate of causal effects will approximate the risk ratio; therefore, odds ratios from most case-control studies can be interpreted as risk ratios.
Abstract: When a study outcome is rare in all strata used for an analysis, the odds ratio estimate of causal effects will approximate the risk ratio; therefore, odds ratios from most case-control studies can be interpreted as risk ratios. However, if a study outcome is common, the odds ratio will be further from 1 than the risk ratio. There is debate regarding the merits of risk ratios compared with odds ratios for the analysis of trials and cohort and cross-sectional studies with common outcomes. Odds ratios are conveniently symmetrical with regard to the outcome definition; the odds ratio for outcome Y is the inverse of the odds ratio for the outcome not Y. Risk ratios lack this symmetry, so it may be necessary to present 1 risk ratio for outcome Y and another for outcome not Y. Risk ratios, but not odds ratios, have a mathematical property called collapsibility; this means that the size of the risk ratio will not change if adjustment is made for a variable that is not a confounder. Because of collapsibility, the risk ratio, assuming no confounding, has a useful interpretation as the ratio change in average risk due to exposure among the exposed. Because odds ratios are not collapsible, they usually lack any interpretation either as the change in average odds or the average change in odds (the average odds ratio).
357 citations
"Computing Adjusted Risk Ratios and ..." refers background in this paper
...For these reasons and other reasons, many people have called for researchers to report risk ratios instead of odds ratios (e.g., Greenland 1987; Spiegelman and Hertzmark 2005; Cummings 2009)....
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...For alternatives, see Cummings (2009, 2011) and Localio and colleagues (2007)....
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TL;DR: Regression risk analysis should be the new standard for presenting findings from multiple regression analysis of dichotomous outcomes for cross-sectional, cohort, and population-based case-control studies, particularly when outcomes are common or effect size is large.
Abstract: Objective
To develop and validate a general method (called regression risk analysis) to estimate adjusted risk measures from logistic and other nonlinear multiple regression models. We show how to estimate standard errors for these estimates. These measures could supplant various approximations (e.g., adjusted odds ratio [AOR]) that may diverge, especially when outcomes are common.
274 citations