A probit- log- skew-normal mixture model for repeated measures data with excess zeros, with application to a cohort study of paediatric respiratory symptoms
Bibliographic record
Abstract
BACKGROUND: A zero-inflated continuous outcome is characterized by occurrence of "excess" zeros that more than a single distribution can explain, with the positive observations forming a skewed distribution. Mixture models are employed for regression analysis of zero-inflated data. Moreover, for repeated measures zero-inflated data the clustering structure should also be modeled for an adequate analysis. METHODS: Diary of Asthma and Viral Infections Study (DAVIS) was a one year (2004) cohort study conducted at McMaster University to monitor viral infection and respiratory symptoms in children aged 5-11 years with and without asthma. Respiratory symptoms were recorded daily using either an Internet or paper-based diary. Changes in symptoms were assessed by study staff and led to collection of nasal fluid specimens for virological testing. The study objectives included investigating the response of respiratory symptoms to respiratory viral infection in children with and without asthma over a one year period. Due to sparse data daily respiratory symptom scores were aggregated into weekly average scores. More than 70% of the weekly average scores were zero, with the positive scores forming a skewed distribution. We propose a random effects probit/log-skew-normal mixture model to analyze the DAVIS data. The model parameters were estimated using a maximum marginal likelihood approach. A simulation study was conducted to assess the performance of the proposed mixture model if the underlying distribution of the positive response is different from log-skew normal. RESULTS: Viral infection status was highly significant in both probit and log-skew normal model components respectively. The probability of being symptom free was much lower for the week a child was viral positive relative to the week she/he was viral negative. The severity of the symptoms was also greater for the week a child was viral positive. The probability of being symptom free was smaller for asthmatics relative to non-asthmatics throughout the year, whereas there was no difference in the severity of the symptoms between the two groups. CONCLUSIONS: A positive association was observed between viral infection status and both the probability of experiencing any respiratory symptoms, and their severity during the year. For DAVIS data the random effects probit -log skew normal model fits significantly better than the random effects probit -log normal model, endorsing our parametric choice for the model. The simulation study indicates that our proposed model seems to be robust to misspecification of the distribution of the positive skewed response.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.047 | 0.060 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".