Can I apply quasi-Poisson regression on discontinuous data? I'm trying to relate the concentrations of certain air pollutants to the incidence of a disease, but I don't have continuous data on that pollution. I have daily data on cases and deaths from the disease, and meteorological parameters, but pollution measurements were taken every 4 days, and there were days when it was not possible to measure due to a problem with the equipment.
I intend to apply Poisson regression to evaluate the effect of exposure to pollution on a given day with a gap of 0, 4, 8, 12 and 16 days after exposure. If I did the calculation of moving averages in excel, could I apply this data in quasi-Poisson Regression?

You can aggregate the other variables to have the same level of granularity as the pollution measurements. So deaths at t would be measured as total deaths in the past four days (t, t-1, t-2, t-3). I would also include a lag pollution term from t-4 as a covariate to pick up conditions closer to the start of the four-day window. For things like wind, maybe max would be better than an average.
The broken sensor days could be handled with traditional imputation techniques. This may not work if sensors break because pollution is heavy.
If you have time series data, you might consider a regression model for TS (like regression with Newey-West standard errors). The usual/quasi Poisson models both assume that errors are independent across observations, which is inappropriate with observations that are periods.
