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Log Odds and the Interpretation of Logit Models.

ABSTRACT: OBJECTIVE:We discuss how to interpret coefficients from logit models, focusing on the importance of the standard deviation (σ) of the error term to that interpretation. STUDY DESIGN:We show how odds ratios are computed, how they depend on the standard deviation (σ) of the error term, and their sensitivity to different model specifications. We also discuss alternatives to odds ratios. PRINCIPAL FINDINGS:There is no single odds ratio; instead, any estimated odds ratio is conditional on the data and the model specification. Odds ratios should not be compared across different studies using different samples from different populations. Nor should they be compared across models with different sets of explanatory variables. CONCLUSIONS:To communicate information regarding the effect of explanatory variables on binary {0,1} dependent variables, average marginal effects are generally preferable to odds ratios, unless the data are from a case-control study.

SUBMITTER: Norton EC

PROVIDER: S-EPMC5867187 | biostudies-other | 2018 Apr

REPOSITORIES: biostudies-other

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Log Odds and the Interpretation of Logit Models.

Norton Edward C EC Dowd Bryan E BE

Health services research 20170530 2

<h4>Objective</h4>We discuss how to interpret coefficients from logit models, focusing on the importance of the standard deviation (σ) of the error term to that interpretation.<h4>Study design</h4>We show how odds ratios are computed, how they depend on the standard deviation (σ) of the error term, and their sensitivity to different model specifications. We also discuss alternatives to odds ratios.<h4>Principal findings</h4>There is no single odds ratio; instead, any estimated odds ratio is cond ...[more]

PMID: 28560732

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Project description:BACKGROUND:Globally, colorectal cancer (CRC) is the third and second leading cancer in men and women respectively with 600,000 deaths per year. Traditionally, clinicians have relied solely on nodal disease involvement, and measurements such as lymph node ratio (LNR; the ratio of metastatic/positive lymph nodes to total number of lymph nodes examined), when determining patient prognosis in CRC. The log odds of positive lymph nodes (LODDS) is a logistic transformation formula that uses pathologic lymph node data to stratify survival differences among patients within a single stage of disease. This formula allows clinicians to identify whether patients with clinically aggressive tumours fall into higher-risk groups regardless of nodal positivity and can potentially guide adjuvant treatment modalities. The aim of this study was to investigate whether LODDS in colon cancer provides better prognostication compared to LNR. METHODS:A retrospective study of patients on the prospectively maintained Cabrini Monash University Department of Surgery colorectal neoplasia database, incorporating data from hospitals in Melbourne Australia, identified patients entered between January 2010 and March 2016. Association of LODDS and LNR with clinical variables were analysed. Disease-free (DFS) and overall (OS) survival were investigated with Cox regression and Kaplan-Meier survival analyses. RESULTS:There were 862 treatment episodes identified in the database (402 male, 47%). The median patient age was 73 (range 22-100?years). There were 799 colonic cancers and 63 rectosigmoid cancers. The lymph node yield (LNY) was suboptimal (<?12) in 168 patients (19.5%) (p?=?0.05). The 5-year OS for the different LNR groups were 86, 91 and 61% (p?<?0.001) for LNR0 (655 episodes), LNR1 (128 episodes) and LNR2 (78 episodes), respectively. For LODDS, they were 85, 91 and 61% (p?<?0.001) in LODDS0 (569 episodes), LODDS1 (217 episodes) and LODDS2 (75 episodes) groups (p?<?0.001). Overall survival rates were comparable between the LNR and LODDS group and for LNY?<?12 and stage III patients when each were sub-grouped by LODDS and LNR. CONCLUSION:This study has shown for that the prognostic impact of LODDS is comparable to LNR for colon cancer patients. Accordingly, LNR is recommended for prognostication given its ease of calculation.

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Log Odds and the Interpretation of Logit Models.

Publications

Log Odds and the Interpretation of Logit Models.

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