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A probit- log- skew-normal mixture model for repeated measures data with excess zeros, with application to a cohort study of paediatric respiratory symptoms.

Mahmud S, Lou WW, Johnston NW - BMC Med Res Methodol (2010)

Bottom Line: The severity of the symptoms was also greater for the week a child was viral positive.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Community Health Sciences, The Aga Khan University, Stadium Road, PO Box 3500, Karachi 74800 Pakistan. sadia.mahmud@aku.edu

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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Probability of being LRT symptom free versus the week of the year.
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Figure 2: Probability of being LRT symptom free versus the week of the year.

Mentions: The final fit of the mixture model (1) to DAVIS data is reported in Table 1. The covariates significantly associated with the probability of having no LRT symptoms were asthmatic/non-asthmatic status, week of follow-up and viral infection status (probit component). The highly significant positive estimate of ╬▓virus indicates that for the week a child was viral positive, the probability of being LRT symptom free was much less than that for the week the child was viral negative (p-value < 0.0001, beta = 2.459). The variable week was modeled as quadratic in the linear predictor of the regression model of the probit component. Moreover, there was a significant interaction between the asthmatic/non-asthmatic status and (the linear term of) week of follow-up (Wald p-value = 0.0150). We also examined the interaction of asthmatic/non-asthmatic status with the quadratic term in week (that is asthmatic*week*week) but that was insignificant based on the Wald, likelihood, AIC and BIC criteria. The probability of being LRT symptom free was lower in the beginning of the year, increased from January to August, and after that decreased until December (Figure 2). The association between the probability of being symptom free and the asthmatic/non-asthmatic status can be clearly seen from Figure 2; the probability of being symptom free is smaller for asthmatics relative to non-asthmatics throughout the year, the difference being more pronounced in the beginning of the year.


A probit- log- skew-normal mixture model for repeated measures data with excess zeros, with application to a cohort study of paediatric respiratory symptoms.

Mahmud S, Lou WW, Johnston NW - BMC Med Res Methodol (2010)

Probability of being LRT symptom free versus the week of the year.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2902491&req=5

Figure 2: Probability of being LRT symptom free versus the week of the year.
Mentions: The final fit of the mixture model (1) to DAVIS data is reported in Table 1. The covariates significantly associated with the probability of having no LRT symptoms were asthmatic/non-asthmatic status, week of follow-up and viral infection status (probit component). The highly significant positive estimate of ╬▓virus indicates that for the week a child was viral positive, the probability of being LRT symptom free was much less than that for the week the child was viral negative (p-value < 0.0001, beta = 2.459). The variable week was modeled as quadratic in the linear predictor of the regression model of the probit component. Moreover, there was a significant interaction between the asthmatic/non-asthmatic status and (the linear term of) week of follow-up (Wald p-value = 0.0150). We also examined the interaction of asthmatic/non-asthmatic status with the quadratic term in week (that is asthmatic*week*week) but that was insignificant based on the Wald, likelihood, AIC and BIC criteria. The probability of being LRT symptom free was lower in the beginning of the year, increased from January to August, and after that decreased until December (Figure 2). The association between the probability of being symptom free and the asthmatic/non-asthmatic status can be clearly seen from Figure 2; the probability of being symptom free is smaller for asthmatics relative to non-asthmatics throughout the year, the difference being more pronounced in the beginning of the year.

Bottom Line: The severity of the symptoms was also greater for the week a child was viral positive.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Community Health Sciences, The Aga Khan University, Stadium Road, PO Box 3500, Karachi 74800 Pakistan. sadia.mahmud@aku.edu

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.

Show MeSH
Related in: MedlinePlus