This is a very frequently-cited reference, but it's old. I'd have a look at "Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression"

http://aje.oxfordjournals.org/content/165/6/710.long

Abstract

The rule of thumb that logistic and Cox models should be used with a minimum of 10 outcome events per predictor variable (EPV), based on two simulation studies, may be too conservative. The authors conducted a large simulation study of other influences on confidence interval coverage, type I error, relative bias, and other model performance measures. They found a range of circumstances in which coverage and bias were within acceptable levels despite less than 10 EPV, as well as other factors that were as influential as or more influential than EPV. They conclude that this rule can be relaxed, in particular for sensitivity analyses undertaken to demonstrate adequate control of confounding.

A further interesting paper : Courvoisier, D.S. et al., 2011. Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure. Journal of Clinical Epidemiology, 64(9), pp.993–1000.

This paper points out that correlations among your predictor variables will push up the required sample size, while the value of the odds ratio will also affect it, so that there is no general rule you can apply!

In response to this, I think that there are two suggestions I can make:

1. Choose predictor variables based on theory, not availability. It is better to use a small set of predictors that test an interesting hypothesis than to have a large number of predictors that were chosen simply because the data were there.

2. Make sure that predictors don’t overlap. If you put education and social class into a prediction model, they measure overlapping constructs. The well-educated tend to have higher social class. Does your hypothesis really state that the two constructs have different effects? Choose one good measure of each construct rather than having multiple overlapping measures.

You can please follow the links below to obtain certain interesting informations:-

1. http://www.surveysystem.com/sscalc.htm

2. https://www.qualtrics.com/blog/determining-sample-size/

You can please download pdfs of the files attached herewith which will provide you with valuable informations.

Thank you for suggestion Ronán Michael Conroy. Is this method of sample size determination dependent to the intended type of analysis? For example, i have several specific objectives and each specific objective requires different analysis. On of the specific objective involve Poisson regression. Is the formula valid if we used it for other analysis apart from logistic regression? 

To calculate the sample size, you should estimate this proportion based on:

1- Expert opinion

2- Results from pilot study

3- Previous literature and records

BW

Negida.A

The always necessary information for a good advice is to know what kind of outcome you have in mind when asking for issues related to analysis (i.e. sample size). According to the information you give, Sandip Chakraborti plus that of Ahmen Negida advices are appropriate, provided you want to explore one single proportion (single  sample) Sandip's is enough. If you intend to carry out an analytical desing , as it would be comparing two cohorts, Ahmed's is suitable. The latter is also useful if you igbnore at all what the proportion of disease is in your community and need a "reference"  proportion to fulfill the data required by the first formulas.

You can use this formula roo

N=z2(p×1-p)/d2

Z=z1-@/2p=proportion

D=difference

Dear Shantha , As the study is retrospective cohort ,you 1stly  should be clear about the variables or suspected factors which may predispose a person to develop dengue than those who are not with these factors . Once these variables are identified , you have to search for the proportions of these variables playing role in making people more prone to develop the dengue i.e. outcome from the literature . For example you have selected four variables , then the reference proportion will be the least of all these 4. you can use WHO software for calculation of sample size for your study . Logistic regression will be used for analysis only . It is not so cumbersome as it is looking presently. Ihope it will solve your problem . 

Dear Shantha, looking at the issued advices  I have to ask you whether you have one series of patients and intend to calculate how many are necessary to detect a certain proportion of a given outcome, or you have two cohorts (cases with  and cases without the target disease and what you want is to learn the amount of cases and controls as to properly assess a given event. Moreover, you might have just one case series and intend to split it in two groups to proceed with statistical analysis. To focus on the best answer to your question is necessary to know which is the material you have in the mentioned terms. Otherwise I am affraid you may get more confused than helped.

Dear Patricio Herrara,

Yes, i agree. Assumed the we intended to find the prognostic factors of severe dengue patients compared to non-severe patients [outcome = severe (1) and not severe (0)]. In this scenario, it is clear that the proportion, p = severe dengue cases / confirmed dengue cases. However, if we intended to find the prognostic factors of dengue cases, then the outcome will be dengue vs non dengue. The question is regarding the proportion. in this scenario, what supposed to be the proportion of dengue, 

a) proportion of dengue = confirmed dengue cases / suspected dengue cases

or 

b) proportion of dengue = confirmed dengue cases/ population.

Since,all population are susceptible to get dengue. But only certain group of cases suspected to have dengue and blood test is performed to confirm the disease.

Are you interested in finding the prognostic factors of severe dengue patients compared to non-severe patients [if so, then outcome severe and not severe - is not correct, rather these are two levels of an independent variable].  If you are intended to find the risk factors of dengue cases [then the outcome will be dengue vs non dengue].

The question regarding the proportion: it varies according to the scenario. Moreover if you are going for option b, i.e.,  proportion of dengue = confirmed dengue cases/ population.

How will you find the population unless it is an community based.

. The researcher is still not clear , what he is intended to determine . In such situation no one can help him out .  As far as I had gathered , the investigator wants to know the factors responsible for causation of dengue i.e. predisposing factors , may be . In such case I had already suggested him , the methods to determine the sample size .

Make use of the proportion of Dengue fever out of all the patients who presented in the health facility within the period under study. That is, your denominator should be 'all the cases presenting in the hospital (including with Dengue fever) within the period of interest.

I think i got it now. Thank you so much for the kind guidance.