PU525 Unit 8 Dental Visit Logistic Regression Example

Covered, Low-Income, Older, Smoking or Rural: A Regression Analysis Modeling Whether Adults Aged 18 to 64 in a Composite State Saw a Dentist in the Past Year, Translating Each Odds Ratio Into a Statement an Oral Health Program Could Use

[Student Name]

Purdue University Global

PU525: Biostatistics for Public Health

Unit 8 Regression Analysis

[Instructor Name]

[Date]

The survey and every estimate are composite and bracketed for the writer's own data; the methods and research cited are real.

The Survey and the Question

The state's annual adult health survey asks: "Within the past year, have you visited a dentist or dental clinic for any reason?" Of [3,200] adults aged 18 to 64, [62] percent said yes, weighted to the state population.

Variable Table

Outcome: dental visit in the past year, yes or no. Dental coverage: yes, compared with no coverage (reference). Low income, under twice the federal poverty line: yes, compared with higher income (reference). Age: in ten-year units, continuous. Current smoking: yes, compared with no (reference). Rural residence: yes, compared with urban (reference).

Why These Five Predictors

The predictors were chosen before fitting the model, based on the state's oral health plan and prior research, not by testing many variables and keeping the significant ones. Coverage and income reflect cost; age reflects changing dental needs; smoking reflects a high-risk group the program wants to reach; and rural residence reflects access. Choosing predictors in advance protects the results from being shaped by chance associations in this particular sample. Other plausible factors, such as education and race or ethnicity, were left for a second model so that the first answers the program's specific questions clearly.

Checking the Model

Before interpreting the output, the analysis checked for strong correlations between predictors, which could make individual odds ratios unstable. Coverage and income were moderately related, as expected, but not so strongly that their separate effects could not be estimated. Age was entered as a continuous term after a plot showed the proportion with a visit rising roughly steadily across age groups. Missing values affected [4] percent of respondents, mostly for income, and those respondents were excluded; a sensitivity analysis including them with an unknown-income category gave nearly identical results.

Model Output

Odds ratios with 95 percent confidence intervals, from a logistic model accounting for the survey's weights and design: Dental coverage: [2.41] ([2.04] to [2.85]), P below [0.001]. Low income: [0.58] ([0.49] to [0.68]), P below [0.001]. Age, per ten years: [1.08] ([1.02] to [1.15]), P [0.01]. Current smoking: [0.66] ([0.55] to [0.80]), P below [0.001]. Rural residence: [0.81] ([0.68] to [0.97]), P [0.02].

Interpretation, Predictor by Predictor

Coverage: among adults alike in income, age, smoking and residence, those with dental coverage had about [2.4] times the odds of a visit as those without. This is the largest association in the model and is consistent with research identifying cost as the main barrier to dental care (Vujicic et al., 2016). Low income: holding coverage and the rest constant, lower-income adults had about [42] percent lower odds of a visit. Coverage does not remove the effect of income, perhaps because of copayments, time off work or distance. Age: each additional decade was associated with about [8] percent higher odds. Smoking: smokers had about a third lower odds, which matters because they have higher risk of gum disease. Rural residence: rural adults had about a fifth lower odds, consistent with fewer dentists outside cities. Coverage roughly doubles the odds of a visit, but low-income adults with coverage still go less often than higher-income adults with coverage.

Odds Are Not Risks When the Outcome Is Common

With [62] percent of adults reporting a visit, odds ratios exaggerate how much the probability of a visit changes. For an uninsured adult with a [55] percent predicted probability, an odds ratio of [2.41] corresponds to a predicted probability of about [75] percent with coverage, an increase of about [20] percentage points, not a doubling. Methods exist to convert odds ratios to approximate relative risks for common outcomes, but reporting predicted probabilities is often clearest (Zhang & Yu, 1998).

Model Fit

The model's ability to distinguish adults with and without a visit, summarized by a c-statistic of [0.68], is moderate: the five predictors explain part of the variation, not all of it. A goodness-of-fit test did not suggest poor calibration (Hosmer et al., 2013).

Statements for the Oral Health Program

Expanding dental coverage is likely to increase visits more than any other factor modeled. Coverage alone will not close the income gap; programs should address costs beyond coverage and offer evening and weekend hours. Tobacco cessation and dental programs share a population and could refer to each other. Rural access needs attention through mobile clinics or teledentistry triage.

Limits

The survey is cross-sectional, so associations are not proof of cause; people who value dental care may also seek coverage. Self-reported visits may be overstated. Unmeasured factors, such as dental anxiety, are not in the model.

Common Errors to Avoid

Treating an odds ratio as if it described change in probability for an outcome most people have. Interpreting a coefficient without naming the reference group. Ignoring survey weights.

References

Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied logistic regression (3rd ed.). Wiley.

Vujicic, M., Buchmueller, T., & Klein, R. (2016). Dental care presents the highest level of financial barriers, compared to other types of health care services. Health Affairs, 35(12), 2176-2182. https://doi.org/10.1377/hlthaff.2016.0800

Zhang, J., & Yu, K. F. (1998). What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA, 280(19), 1690-1691. https://doi.org/10.1001/jama.280.19.1690