Researchers analyzed data on 4406 individuals, aged 66 and over, who are covered

Question

Researchers analyzed data on 4406 individuals, aged 66 and over, who are covered by Medicare, a public insurance program. The objective is to model the demand for medical cares (captured by the number of physician office visits) by the covariates available for the patients. Here, we adopt the number of physician office visits "ofp" as the dependent variable and use the health status variables "hosp" (number of hospital stays), "numchron" (number of chronic conditions) as well as the socio-economic variables "gender" (0: female, 1: male), "school"(number of years of education) and "privins" (private insurance indicator) as explanatory variables. (a) Fitting a Poisson regress on model we have the following R output, What does the estimated coefficient of gender "-0.116485" mean? Interpret it in the context of the research question. Signif. Codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1' ' 1 (Dispersion parameter for poisson family taken to be 1) Null deviance: 26943 on 4405 degrees of freedom Residual deviance: 23527 on 4400 degrees of freedom (b) Can you make a hypothesis test manually for the effect of "hosp" on "ofp" after controlling for over-dispersion in the above model? (Write the null and alternative hypotheses, the test statistic, and give a range of your value. You can use normal distribution instead of t distribution whenever you want. The 95%, 99% and 99.9% percentiles of N (0, 1) are 1.64, 2.33 and 3.09 respectively.) (c) Adding the interaction between "hosp" and "gender", and also using a quasi-Poisson model, we have the following R output. Calculate the effects of "hosp" on "ofp" using this new model, separately for male and female individuals.

Explanation / Answer

a) The gender coefficient interpretation:

In case of Male gender the no. of physicians visit is 0.89 (e^-0.1165) times (less than) that of the female case.

b) Test for significance of 'hosp' variable:

H0: 'hosp' variable is insignificant i.e. coefficient of 'hosp' =0

Ha: 'hosp' variable is significant i.e. coefficient of 'hosp' not equal 0

since p-value for the coeffeicient <0.01 so, we reject H0 at 99%, 95%, 90% confidence level.

Thus, yes  'hosp' variable is significant.

c) For male:

Unit increase in no. of hospital stays increases the no. of physicians visits by 1.227 (=EXP(0.166+0.0389)) times.

For female:

Unit increase in no. of hospital stays increases the no. of physicians visits by 1.18 (=EXP(0.166+0)) times.

d) The interaction term is reflecting the extra weight to male candidates for no. of physicians visits. It is clear from the answer in section c. The difference (in multiplicative term) is arising out of the coefficient of that interaction term which is e^0.0389.

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