Gourab,

You can generalize your results if and only if you can collect a probability representative sample, which means randomly selecting the 1,000 from the 20,000 as well as ensuring that the sample "looks like" the population in terms of distribution (gender, age, income, etc). This means having 1000 physicians randomly selected from all hospitals in that country as well as ensuring the other characteristics of the sample look like those of the population.

e.g.; if the population has a mean age of 40 years and is made up of 69% males, your sample needs to have similar numbers.

Good luck!

I agree with Anderson. If you can enroll matched population, then it will become a representative sample of the whole country. 

Gourd,

Selecting a segment of population that truly represents the whole set is not a trivial issue. This is why it is generally best to have as large a group as feasible, covering the obvious and plausible relevant variables, such as geographical regions within a nation, gender, age etc.

   The general problem is how representative is your data to the population as a whole. It doesn't matter if you have a sample size of 4 or 40,000 -- if you can prove that your sample size is representative. Failing such proof, we intuitively know that there is a better chance that the sample size of 40,000 is representative of the entire population than is the sample size of 4. But there is no absolute guarantee that this is the case, it is simply more likely.

   Usually, the more convenient the sampling the less likely it is to give you the answer that you seek. So you choose 10 hospitals, but how representative are these 10 relative to all the hospitals? Are there hospitals that are outliers? So one hospital happens to be in the poorest neighborhood with the highest crime rate and five gangs are fighting for control. The other hospital is in a neighborhood where all the rich people live. Is there any difference between these two in terms of doctor outcomes as it relates to your study?

  The easy approach would be to survey 300 doctors at one hospital and be done. This is not likely to be representative of all doctors. At the other extreme would be to use a random number generator to select a value from 1 to 200. Go to each hospital and count the doctors as they arrive for work on that shift, and use the random number to find the doctor that will be asked to take the survey. The ending sample size is the same as before, but it is much harder to think of how it would be biased. The obvious way to bias the latter approach would be to arrive at the hospital at 8:00 every time. However, as long as you sample all shifts (possibly at random), you can overcome this issue. You should consider carefully random versus planned. So one possible random result is that I always sample first shift. If I would discard this outcome then I have a biased-random randomization. In contrast a planned sampling would be 50 doctors from each shift. As Tausif said, getting a representative sample is not a trivial issue.

Surely the country has a general registry of doctors, or a medical society. I would be most likely to trust a random sample from all the doctors rather than struggling with an attempt at attaining a randomization within some sort of stratification (hospitals etc.).

Even so, if this is a yes-no sample, a sample of  just 1000 might be a little small assuming you wish to estimate within a few percent, or even have a confidence interval which is not ridiculously wide.  I hope your method of getting the sample size takes the minimum reasonable difference (how close you seek to approach the truth) into account. Since this is not a quality control issue and the population is not exactly little, you can  work more easily with a normal approximation (and a finite population correction if you sample more than 5% of N). That is, when your population is large enough the effect of non-replacement becomes negligible, and  the CLT is sufficient at smaller sample sizes than yours anyway . 

In answering Tausif (who favors quota sampling and larger samples) states

"... how representative is your data to the population as a whole. It doesn't matter if you have a sample size of 4 or 40,000 -- if you can prove that your sample size is representative. Failing such proof, we intuitively know that there is a better chance that the sample size of 40,000 is representative of the entire population than is the sample size of 4. But there is no absolute guarantee that this is the case, it is simply more likely."

One never can prove that a sampling actually done is true random sampling.

There are only plausibility checks to detect deviations as are contained in the references that Chalamalla has mentioned.

Furthermore, random sampling (or random assignment) can lead to a highly biased sample - only the risk of getting a biased sample is small and calculable. (For the extreme case of a sample of 4, these calculations would lead to the result that this risk is too high so that no one would use such small samples)

To minimize the variance of estimates from the sample, it is best to slice the population into homogenous layers and then sample randomly within the layers.

As smoking habits have changed over the years, age and gender of the doctors should form two layers (you might think of other influence variables but it would be difficult to get the data on them).

Then, I would look for a registry of doctors as Lewis has suggested. Make sure that this registry covers all doctors (including all ages and status as intramural or outside hospitals etc.)