That looks OK.

The "trick" is to keep track of persons and time.

Working with:

The proportion of the population that dies each day is:

So the number of deaths in the 5 million population is:

There are about 365 days in a year (leap years have 366) so the number of deaths in a year is:

which is what you get.

A few things to consider ...

You have to bear in mind that your estimate of CMR may not be very accurate. This is often the case with mortality estimates made from surveys.

Since we are dealing with estimates we should account for uncertainty. An easy way of doing this is to do the calculation for the lower 95% confidence limit, the point estimate, and the upper 95% confidence limit for CMR.

Populations change over time. We have a start population (5 million). If population is growing at 2.41% per year (that's the 2017 estimate for 2017 for Rwanda) then after a year that 5 million becomes:

You can use the mid-point:

Using this gives:

Assuming (your data will likely be different) the 95% CI for the CMR is [0.09,0.25] we have:

To be able to "safely say" I think you should (if possible) check your CMR, use 95% CIs to account for imprecision in the CMR estimate, and correct the population for growth. When reporting results you should use words like "estimated" and "predicted" and present the estimate with a 95% confidence interval. With what I have above I'd say something like " an estimated 29,552 (95% CI = 16,623 - 46,175) deaths predicted to occur over the year".

I hope this is of some use.

Mark I was a bit worry because in my case my expected death per year looks really large. I was wondering if I did something wrong and got confused with the per day vs per year usage. Thank you very much for taking the time to respond to my question . I very much appreciate the detailed answers and explanation on how I can incorporate the CIs in my interpretation.

It gets a bit confusing as person-times vary. Often we have "per 1000 per day" or "per 100,000 per year" or even or "per 1000 live births" (with time unspecified). With emergencies we have "per 10,000 per day". I find that keeping track of the persons and the times and checking all conversions and calculations helps.

You numbers are large because you have a large population (5 million) and a long period (365 days). I find it useful to familiarise myself with magnitudes so I can spot when something is way off. Try, for example, going to WolframAlpha and specifying "mortality Burundi". This give 115,050 deaths per year on a 10.9 million population. This is much larger then your 29,200. If we standardise to 5 million it is:

Your number does not seem so very large.

I hope this helps.

Thanks a lot for the explanation and for elaborating more on it. Thanks a lot.

Hello Mark I have a related question I am sure if I should open a new thread for it. The question is this, if in a small-scale survey say done in two different area of State A say urban and rural area and the under-5 mortality estimate obtained for the two areas are:

0.35[0.30 - 0.41] per 1000 live births and 0.17[0.11 - 0.20] per 1000 live births.

Can one make a general statement about the under-5 mortality of State A in the absence of the sample size by averaging the under-5 mortality (0.35+0.17)/2 = 0.26[0.21 - 31] per 1000 live birth in State A ?

I know that some operation seems okay mathematically but I am not sure if it makes sense in this content?

We need to assume that the mortality rate for the rural area is from a sample that is representative of the rural population and the mortality rate for the urban area is representative of the urban population. In that case we can combine the two estimates.

A simple average (as you have above) is not appropriate unless the two populations are of equal size. What is needed is a weighted average:

where:

Assuming:

We get:

The pooled rate is closer to the rural rate because, in this example, most people live in the rural area (urbanisation is at c. 18%).

We should always present a confident interval (or similar) when we make an estimate. This is not so easy. We need to pool variances. Survey samples are complex and the variance is influenced by the proportion, the sample size, and the survey design effect. We can get over this by calculating the standard error (SE) from survey results from each survey:

With the example results we have:

The pooled SE is:

where:

With the example results we have:

The pooled estimate is:

Notes ...

(a) When you do these sorts of calculation you should do them to the full precision throughout and only round at the end. I did not do this above so there will be some accumulated rounding error in the final result above.

(b) This is an approximate method based on estimates that were probably made using approximate methods. The 95% CI is only "nominal" and is unlikely to have 95% coverage. Theses sorts of methods are usually good enough.

(c) The original results are very different from each other (i.e. 0.35 vs. 0.17 with 95$ CIs that do not overlap). When this is the case then you should present the results separately as well as the pooled results.

(d) Check my arithmetic.

I hope this is of some use.

Mark thanks once more for your insightful response. In my case I don't have information about the population I am going to assign them equal weight and lists that as the limitation.

I would not do this. I would try to find statistics on urbanisation for the country you are working in and use that. This will likely be better tha assuming 50% urbanisation. If you have to make a guess then it is best to make an informed guess.

You can find useful data from UN DESA / Population Division. The "Data in Excel Files" section is useful.

Thanks for your response.

I am looking for a good book that covers fundamentals of the calculation of crude mortality and everything or most things that one needs to know about crude mortality estimates. Useful recommendation will be highly appreciated.