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Fitting a Weibull Curve to a Kaplan-Meier Survival Curve

A D3 animation of how least squares regression Webiull fitting works on a Kaplan-Meier survival curve.

<!DOCTYPE html>
<meta charset="utf-8">
  <head>
   	<link href='https://fonts.googleapis.com/css?family=Play' rel='stylesheet' type='text/css'>
<style>

body {
	margin:auto;
	font-family: 'Play', sans-serif;
	font-size:100%;
}

text {
    font-family: 'Play', sans-serif;
}

</style>

var WeibullPlot = function(opts) {
    var margin = opts.margin || {top: 20, right: 20, bottom: 70, left: 60};
    var height = opts.height || 410;
    var width = opts.width || 880;

var dur = opts.duration || 3000;
    var del = opts.delay || 250;
    var ease = opts.ease || d3.easeLinear;

var s = {};

//Prep Data 
    var data = {};

data.gridLines = {
        x: [1].concat(d3.range(3,49,3)),
        y: d3.range(.01,1,.01)
    };
    
    data.gridLabels = {
        x: [3, 12, 24, 36],
        y: [.01, .05, .10, .25, .50, .75, .99]
    };

data.points = [];
    data.points.push({x:1,y:0.0296});
    data.points.push({x:2,y:0.0496});
    data.points.push({x:3,y:0.089});
    data.points.push({x:4,y:0.099});
    data.points.push({x:5,y:0.1199});
    data.points.push({x:6,y:0.1599});
    data.points.push({x:7,y:0.18}); 
    data.points.push({x:8,y:0.1899}); 
    data.points.push({x:9,y:0.215});
    data.points.push({x:10,y:0.225});
    data.points.push({x:11,y:0.2375});
    data.points.push({x:12,y:0.265});

data.regCoeffs = lsReg(
        data.points.map(function(d) { return xWeib(d.x)}),
        data.points.map(function(d) { return yWeib(d.y)}) 
    );

data.regLine = data.gridLines.x.map(function(d) {
        return {
            x: xWeib(d),
            y: xWeib(d)*data.regCoeffs[0] + data.regCoeffs[1]
        }
    });

// Set Scales
    var scale = {};
    scale.x = d3.scaleLinear()
        .range([0,width])
        .domain(d3.extent(data.gridLines.x));
    
    scale.y = d3.scaleLinear()
        .range([height,0])
        .domain(d3.extent(data.gridLines.y));

// Draw

s.svg = d3.select("#" + opts.elementId)
        .append("svg")
        .attr("height", height + margin.top + margin.bottom)
        .attr("width", width + margin.left + margin.right)
        .style("-webkit-user-select","none")
        .style("cursor","default");

s.chart = s.svg.append("g")
        .attr("transform","translate(" + margin.left + "," + margin.top + ")");

// Draw Grid
    s.gridLines = {};
    s.gridLabels = {};
    s.gridLines.y = s.chart.selectAll(".yLines")
        .data(data.gridLines.y)
        .enter()
        .append("line")
        .attr("x1",0)
        .attr("x2",width)
        .attr("y1", function(d) { return scale.y(d)})
        .attr("y2", function(d) { return scale.y(d)})
        .style("stroke-opacity", function(d) {  return (data.gridLabels.y.indexOf(+d3.format(".2")(d))<0)?.20:.55; })
        .style("stroke","black");
    
    s.gridLabels.y = s.chart.selectAll(".yLabels")
        .data(data.gridLabels.y)
        .enter()
        .append("text")
        .attr("x",0)
        .attr("y", function(d) { return scale.y(d)})
        .attr("text-anchor","end")
        .attr("dx",-2)
        .style("font-size",".8em")
        .text(function(d) { return d3.format('.2p')(d) });

s.gridLines.x = s.chart.selectAll(".xLines")
        .data(data.gridLines.x)
        .enter()
        .append("line")
        .attr("x1",function(d) { return scale.x(d)})
        .attr("x2",function(d) { return scale.x(d)})
        .attr("y1", 0)
        .attr("y2", height)
        .style("stroke-opacity", function(d) {  return (data.gridLabels.x.concat([1,48]).indexOf(d)<0)?.20:.55; })
        .style("stroke","black");
    
	s.gridLabels.x = s.chart.selectAll(".xLabels")
		.data(data.gridLabels.x)
		.enter()
		.append("text")
		.attr("y",height)
		.attr("x", function(d) { return scale.x(d)})
		.attr("text-anchor","start")
		.attr("dy",16)
		.style("font-size",".8em")
        .text(function(d) { return d + ' months'});
    
    // Draw Legend 
    (function() {
        var km = s.chart.append("g")
            .attr("transform","translate(" + width*(2/7) + "," + (height + 30) + ")");
        
        km.append("rect")
            .attr("height",30)
            .attr("width", width/7)
            .style("fill","#d11141" )
            .attr("rx",4)
            .style("stroke","gray");

km.append("text")
            .style("text-anchor","middle")
            .attr("dy","1.25em")
            .attr("dx", +km.select("rect").attr("width")/2)
            .text("Kaplan-Meier")
            .style("fill","white");

var wf = s.chart.append("g")
            .attr("transform","translate(" + width*(4/7) + "," + (height + 30) + ")");

wf.append("rect")
            .attr("height",30)
            .attr("width", width/7)
            .style("fill","#00aedb" )
            .attr("rx",4)
            .style("stroke","gray");

wf.append("text")
            .style("text-anchor","middle")
            .attr("dy","1.25em")
            .attr("dx", +wf.select("rect").attr("width")/2)
            .text("Weibull")
            .style("fill","white");
    })();

drawKM();

// Draw KM Line
    function drawKM() {

// Transform Spacing
    function weibullSpace() {
        scale.x.domain([xWeib(1),xWeib(48)]);
        scale.y.domain([yWeib(.01),yWeib(.99)]);

var line = d3.line()
            .x(function(d) { return scale.x(xWeib(d.x))})
            .y(function(d) { return scale.y(yWeib(d.y))})
            .curve(d3.curveStepAfter);
        
        s.gridLines.y.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("y1", function(d) { return scale.y(yWeib(d))})
            .attr("y2", function(d) { return scale.y(yWeib(d))});

s.gridLines.x.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("x1", function(d) { return scale.x(xWeib(d))})
            .attr("x2", function(d) { return scale.x(xWeib(d))});

s.gridLabels.y.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("y", function(d) { return scale.y(yWeib(d));});

s.gridLabels.x.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("x", function(d) { return scale.x(xWeib(d));});

s.kmLine.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("d", line)
            .on("end", drawRegLine);
    }

// Draw straight regression Line
    function drawRegLine() {

var line = d3.line()
            .x(function(d) { return scale.x(d.x)})
            .y(function(d) { return scale.y(d.y)})
            .curve(d3.curveBasis)

s.regLine = s.chart.selectAll(".regLine")
            .data([data.regLine])
            .enter()
            .append("path")
            .attr("d", line)
            .style("stroke","#00aedb")
            .style("stroke-width",1.5)
            .style("fill","none")
            .each(function(d) {
                var tl = this.getTotalLength();
                var l = d3.select(this)
                l.attr("stroke-dasharray", tl + " " + tl)
                    .attr("stroke-dashoffset", tl)
                    .transition()
                    .duration(dur)
                    .delay(del)
                    .attr("stroke-dashoffset", 0)
                    .on("end", function() { 
                         l.attr("stroke-dasharray","0 0");
                         normalSpace();
                    })
            })   
    }

// Transform Spacing
    function normalSpace() {
        scale.x.domain(d3.extent(data.gridLines.x));
        scale.y.domain(d3.extent(data.gridLines.y));

var line = d3.line()
            .x(function(d) { return scale.x(d.x)})
            .y(function(d) { return scale.y(d.y)})
            .curve(d3.curveStepAfter);

var regLine = d3.line()		
            .x(function(d) { return scale.x(xUnweib(d.x))})
            .y(function(d) { return scale.y(yUnweib(d.y))})
            .curve(d3.curveBasis);
        
        s.gridLines.y.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("y1", function(d) { return scale.y(d)})
            .attr("y2", function(d) { return scale.y(d)});

s.gridLines.x.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("x1", function(d) { return scale.x(d)})
            .attr("x2", function(d) { return scale.x(d)});

s.gridLabels.y.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("y", function(d) { return scale.y(d);});

s.gridLabels.x.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("x", function(d) { return scale.x(d);});

s.kmLine.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("d", line);

s.regLine.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .attr("d", regLine)
            .on("end", reset)

}

// Reset the chart and start again
    function reset() {
    
        s.kmLine.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .style("opacity",0)
            .transition()
            .duration(dur)
            .ease(ease)
            .remove();

s.regLine.transition()
            .duration(dur)
            .ease(ease)
            .delay(del)
            .style("opacity",0)
            .transition()
            .duration(dur)
            .ease(ease)
            .remove()
            .on("end", drawKM)
    }

function xWeib(x) {
        return Math.log(x);
    }

function yWeib(y) {
        return Math.log(Math.log(1/(1 - y)));
    }

function xUnweib(x) {
        return  Math.pow(Math.E,x);
    }

function yUnweib(y) {
        return  1 -1/Math.pow(Math.E,Math.pow(Math.E,y));
    }

function lsReg(X,Y) {
        var meanX = d3.mean(X),
            meanY = d3.mean(Y);

var ssXX = d3.sum(X.map(function(d) { return Math.pow(d - meanX, 2); })),
            ssYY = d3.sum(Y.map(function(d) { return Math.pow(d - meanY, 2); }));

var ssXY = d3.sum(X.map(function(d, i) { return (d - meanX) * (Y[i] - meanY);}))

var slope = ssXY / ssXX;
        var intercept = meanY - (meanX * slope);

return [slope, intercept];
    }

}

</script>
<div id="chart"></div>
<script>
    WeibullPlot({elementId:"chart"});
</script>

https://d3js.org/d3.v4.min.js